NUREG/CR-2146, Volume 3 - RAMPAC

..... ~.• y.;~.." ..~':,.'..... ".....~NUREG/CR-2146,Vol. 3HEDL-TME 83-18fl'• 1 f ..\ {. , , ~.,: DYNAMIC ANALYSIS TO ESTABLISH NORMAL~~o.~~ SHOCK AND'VIBRATION OF RADIOACTIVEMATERIAL SHIPPING PACKAGESFINAL SUMMARY REPORT';'""~, .'-;.--~iiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiii__Hanf.ord Engineering Development Laboratory'.'. ·t ... · ,S.R. Relds .. ~""Prepnd for the u.s. Nudeii' RBgI8tory Commission

NOTICEThis report was prepared as an account of work sponsored by an agency / the United StatesGovernment. Neither the United States Government nor any agency ther~f, o~ any of their~a' /Jab.,.employees, makes any warranty, expressed or implied, or assumes any I ". I lty of responsibilityfor any third party's use, or the results of such use, of any inform ,~~ apparatus,product or process disclosed in this report, or represents that its use by such thl 'Y wouldnot infringe privately owned rights,Availability of Reference Materials Cited in NRC PublicationsMost documents cited in NRC publications will be available from one of the following sources:1. The NRC Public Document Room, 1717 H Street, N.W.Washington, DC 205552. The N RC/GPO Sales Program, U.S. Nuclear Regulatory Commission,Washington, DC 20555J. The National Technical Information Service, Springfield, VA 22161Although the listing that" follows represents "the majority of documents cited in NRC publications,it is not intended to be exhaustive.Referenced documents available for inspection and copying for a fee from the NRC Public DocumentRoom include NRC correspondence and ir;ternat NRC memoranda; NRC Office of Inspectionand Enforcement bulletins, circulars, informatjon notices, inspection and investigation notices;Licensee Event Reports; vendor reports and correspondence; Commission papers; and applicant andlicensee documents and correspondence.The following documents in the NUREG series are available for purchase from the N RC/GPO SalesProgram: formal NRC staff and contractor reports, NRC·sponsored conference proceedingS; andNRC booklets and brochures. Also available are Regulatory Guides, NRC regulations in the Code ofFederal Regulations. and Nuclear Regulatory Commission Issuances.Documents available from the National Technical Information Service include NUREG seriesreports and technical reports prepared by other federal agencies and reports prepared by ,the AtomicEnergy Commission, forerunner agency to the Nuclear Regulatory Commission.Documents available from public and special technical libraries include all open literature items,such as books, journal and periodical articles, and transactions. Federal Register notices, federal andstate legislation, and congressional reports can usually be obtained from these libraries.Documents such as theses. dissertations. foreign reports and translations, and non-N RC conferenceproceedings are available for purchase from the organization sponsoring the publication cited.Single copies of NRC draft reports are available free upon written request to the Division of TechnicalInformation and Document Control, U.S. Nuclear Regulatory Commission, Washington, DC20555,'"'."Copies of industry codes and standards used in a substantive manner in the NRC ref1ulatory processare maintained at the NRC Library, 7920 Norfolk Avenue, Bethesda, Maryland, and are availablethere for reference use by the public. Codes and standards are usually copyrighted and may bepurchased from the originating organization or, if they are American National Standards, from theAr:Derican National Standards Institute, 1430 Broadway, New York, NY 10018.~':'i.':~-;;:- ~.' • .;i; ~"'"GPO PrInted copy price:J ./h '. ~~.~~.. \__$_7_0_5_0__

NUREG/CR-2146, Vol. 3HEDL-TME 83-18RTDYNAMIC ANALYSIS TO ESTABLISH NORMALSHOCK AND VIBRATION OF RADIOACTIVEMATERIAL SHIPPING PACKAGESFINAL SUMMARY REPORTII'\Hanford Engineering Development LaboratoryOperated by WestinlPJuse Hlllford CompanyP.O. Box 1970 Richland. WA 99352A Subsidirt of Westi90use 8ectric CorporationS. R. FieldsManuscript completed: June 1983Date published: October 1983Prepared 'II' Division of Ell"'" TechnologyOffice of NucIeIr Regulatory R••BlrchU.S. NucIeBr Regulatory CommiaionWIIhiIgtan, D.C. 20666NRC An No. B2283

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NUREG/CR-2146,HEDL-TMEVol. 383-18DYNAMIC ANALYSIS TO ESTABLISHNORMAL SHOCK AND VIBRATIONOF RAD WACT! VEMATERIAL SHIPPING PACKAGESFINAL SUMMARY REPORTS. R. Fields,'jr.ABSTRACTA model to simulate the dynamic behavior of shippingpackages (casks) and their rail car transporters duringnormal transport conditions was developed. This model,CARDS (Cask-Rail Car Dynamic Simulator), was used tosimulate-the-cask-rail car systems used in Tests 3, 10,11, 13, 16 and 18 of the series of rail car couplingtests conducted at the Savannah River Laboratories in1978. On the basis of good agreement between calculatedand measured results for these tests, it was concludedthat the model has been validated as an acceptable toolfor the simulation of similar systems.A companion model, CARRS (Cask-Rail Car Response SpectrumGenerator), consisting of single-degree~f-freedomrepresentationsof the equations of motion in CARDS, wasdeveloped to generate frequency response spectra.A parametric and sensitivity analysis' was conducted thatidentified the most influential of a selected set ofparameters and the response variables that are the mostsensitive to changes in the parameters.iii

ACKNOWLEDGMENTSI wuuld like to acknowledge the specialized technical support provided byS. J. Mech prior to, during, and after the coupling tests conducted at theSavannah River Laboratory in July and August of 1978. His leadership andhard work in the data acquisition and reduction task were instrumental inthe successful completion of this study. He wrote the section on TEST DATACOLLECTION AND REDUCTION in eight of the fifteen quarterly progress reportspublished during the course of the study. Section 2.0, TEST DATA COLLECTIONAND REDUCTION, of this report is an edited version of his contributions.His work was supplemented by excellent contributions from M. S. Nutter andC. Bromley (Boeing Computer Services Richland, Inc.), and H. A. Carlson(Hanford Engineering Development Laboratory). The FFT (Fast Fourier!ransform) program algorithim was written by G. Ray under his-direction.I would also like to thank H. A. Carlson and P. D. Charles (HanfordEngineering Development Laboratory), who were responsible for most of thecomputer-generated plots presented in this report.iv

CONTENTSAbstractAcknowledgmentsFiguresTab lesiiiivviixixSUMMARYINTRODUCTIONTECHNICAL APPROACH AND RESULTS371.0 MODEL DEVELOPMENT 71.1 CASK-RAIL CAR DYNAMIC SIMULATOR (CARDS) 71.1.1 Rail Car Coupler and Draft GearSubsystem Submodel161.1.2 Suspension Subsystem Submodel 371.1.3 Pitching Moment Caused by theOffset of the Coupler and theCenter of Gravity of the Rail Car391.1.4 Cask-Rail Car Bending Submodel 401.1.5 Modeling the Anvil Train 421.2 CASK-RAIL CAR RESPONSE SPECTRUM GENERATOR (CARRS) 442.0 TEST DATA COLLECTION AND REDUCTION 673.0 COLLECT PARAMETER DATA 774.0 MOuEL VALIDATION 794.1 THEIL1S INEQUALITY COEFFICIENTS 794.2 FAST FOURIER TRANSFORMS 834.3 VISUAL COMPARISO~ OF RESPONSE VARIABLES 834.4 FREQUENCY RESPONSE SPECTRA4.5 MODEL VALIDATION AND RESULTS8384v

CONTENTS(Cont1d)Page4.5. 1 Comparison of Measured and CalculatedResults for Test 34.5.2 Comparison of Measured and CalculatedResults for Tests 10 and 114.5.3 Comparison of Measured and CalculatedResults for Tests 13, 16 and 185.0 PARAMETRIC AND SENSITIVITY ANALYSISCONCLUSIONS AND RECOMMENDATIONSREFERENCESAPPENDIX IAPPENDI X IINOMENCLATURE OF TERMSFIGURESAPPENDIX III TABLESAPPENDIX IVAPPENlJIX VAPPENDIX VILISTING OF CARDS MODELLISTING OF CARRS MODELLISTING OF FFT PROGRAM8587891111131-111-1II 1-1IV-lV-lVI-l97 .rvi

FIGURESFigure123456II 78\ 9101112131415Spent Fuel Shipping Cask-Rail Car System ModeledSpring-Mass Model of Cask-Rail Car SystemOne Possible Orientation of Cask-Rail Car SystemAfter ImpactComparison of Orientation of Cask-Rail Car SystemAfter Impact with Initial StateRail Car-Coupler Subsystem ModelCoupler Force vs Time During Impact of Two HopperCars Loaded with Grayel (Spring Constant of "Solid"Draft Gears = 5 x 100 lbs(force)/inch)Coupler Force vs Time During Impact of Two HopperCars Loaded with Gravel (Spring Constant of "Solid"Draft Gears = 1 x 106 lbs(force)/inch)Coupler Force vs Time During Impact of Two HopperCars Loaded with Grave 1 ("S0 1idII Draft Gear Spri ngConstant a Function of Draft Gear Travel, XT)Ratio of "Solid" Draft Gear Spring Constant to aBase ValueCoupler Force vs Time During Impact of Two HopperCars Loaded with GravelRelative Displacement of Two Gravel-Filled HopperCars vs Time During ImpactRelative Velocity of Two Gravel-Filled Hopper Carsvs Time During ImpactRelative Acceleration of Two Gravel-Filled HopperCars vs Time During ImpactCalculated Coupler Force vs Calculated RelativeDisplacement of Two Gravel-Filled Hopper Cars DuringImpactRelative Velocity of Two Gravel-Filled Hopper Carsvs Time During ImpactPageII-3II-3II-411-4II-5II-5II-6II-6II-7II-7II-8II-8II-9I 1-9II-10vii

FIGURES(Cont'd)Figure16 Coupler Force vs Time During Impact of Two GravelFilled Hopper Cars17 Relative Displacement of Two Gravel-Filled HopperCars vs Time During Impact18 Relative Velocity of Two Gravel-Filled Hopper Carsvs Time During Impact19 Relative Acceleration of Two Gravel-Filled HopperCars vs Time During Impact20 Calculated Coupler Force vs Calculated RelativeDisplacement of Two Gravel-Filled Hopper Cars DuringImpact21 Measured Coupler Force vs Measured Relative Displacementof Two Gravel-Filled Hopper Cars DuringImpact22 Arrangement of Springs and Dampers SimulatingRail Car Coupler and Suspension Subsystems~3 Effect of Coupler Offset on Rail Car Rotation24 Deflection Diagrams for Rail Car Beam withRestraints to Define Force-Reaction System11-10I 1-1111-1111-12II-12II-13II-1311-14II -14I.\I25 Spring-Mass Submodel Representing Bending of RailCar26 Deflection Diagrams for Rail Car Beam to DetermineDeflections and Influence Coefficients27 Dynamic Model of Cask-Rail Car System with BendingSubmodel28 Cask-Rail Car and Anvil Train29 Cask-Rail Car and Anvil Train30 Coupler Force Between Cars in the Cask-Rail Car andAnvil Train System31 Horizontal Displacement of Centers of Gravity ofCars in the Cask-Rail Car and Anvil Train System11-15II -15II -16II-16II-17I1-1711-18,- {ivii i

FIGURES(Cont'd)Figure32 Morphological Space Representation of Cask-RailCar Coupling Tests33 Horizontal Acceleration of the Cask-Rail CarDuring Impact with Four Hopper Cars Loaded withBallast. (Test 3 - Instrument 12: Filtered at100 Hz) (Case 1: Measured Coupler Force)34 Shock/Vibration Data Flow for Data ReductionModel Verification35a35b35c36a36b37a37bAcceleration Wave Shape and Corresponding FrequencySpectrum Obtained by Fast Fourier Transform(Horizontal Center Acceleration)Acceleration Wave Shape and Corresponding FrequencySpectrum Obtained by Fast Fourier Transform(Vertical, Stuck End Acceleration)Acceleration Wave Shape and Corresponding FrequencySpectrum Obtained by Fast Fourier Transform(Vertical, Far End Acceleration)Filtering of Acceleration Data Employing InverseFFT (Power Spectra and Time Domain Image)Filtering of Acceleration Data Employing InverseFFT (Time Domain Images)Hanning Window Effect on Power Spectra WhenApplied to Time Domain Data (Horizontal, CenterAcceleration with Hanning Window)Hanning Window Effect on Power Spectra When Appliedto Time Domain Data (Vertical, Struck End Accelerationwith Hanning Window)38 Tiedown Configuration and Instrument Location forCask-Rail Car-Tiedown Tests (Tiedown ConfigurationII All)39 Tiedown Configuration and Instrument Location forCask-Rail Car-Tiedown Tests (Tiedown ConfigurationIIIIB )Page11-1811-19II -19I 1-20II-2011-21II -21I 1-2211-22II-23I 1-23II-24ix

FIGURES(Cont'd)FigurePage40 Tiedown Configuration and Instrument Location forCask-Rail Car-Tiedown Tests (Tiedown Configuration"C") 11-2441 Tiedown Configuration and Instrument Location forCask-Rail Car-Tiedown Tests (Tiedown Configuration"0") 11-2542 Horizontal or Longitudinal Acceleration of Car atCar/Cask Interface vs Time (Instrument No. 12 Unfiltered) 11-2543 Horizontal Displacement of the Car at the StruckEnd vs Time (Instrument No.4 - Unfiltered) 11-2644 Horizontal Acceleration Response of Cask/CarInterface vs Frequency (Instrument No. 12 Unfiltered) 11-2645 Transfer Function Magnitude vs Frequency (VerticalEnergy Transfer from Instrument No. 22 to InstrumentNo. 11) 11-2746 Transfer Function Magnitude vs Frequency (VerticalEnergy Transfer from Instrument No. 11 to InstrumentNo.9) 11-2747 Transfer Function Magnitude vs Frequency (HorizontalEnergy Transfer from Instrument No. 12 toInstrument No. 10) 11-2848 Transfer Function Magnitude vs Frequency (HorizontalEnergy Transfer from Instrument No. 10 toInstrument No.8) 11-2849 Comparison of Calculated and Measured CouplerForces Using Theil's Inequality Coefficient asFigure of Merita11-2950 Comparison of Calculated and Measured RelativeDisplacements of Rail Car Centers of Gravity in theTime Domain Using Theil IS Inequality Coefficient asa Figure of Merit 11-2951 Comparison of Calculated and Measured RelativeVelocities in the Time Domain Using Theil'sInequality Coefficient as a Figure of Merit 11-30x

FIGURES(Cont'd)Figure52 Comparison of Calculated and Measured RelativeAccelerations in the Time Domain using Theil'sInequality Coefficient as a Figure of Merit53 Simultaneous Comparison of Calculated and MeasuredResponse Variables in the Time Domain Using Theil'sMultiple Inequality Coefficient as an Overall Figureof Merit54 Coupler Force vs Time During Impact of Cask-RailCar with Four Hopper Cars Loaded with Ballast(Test 3 - Instrument 3) (Case 1: Measured CouplerForce)I55 Horizontal Force of Interaction Between Cask andRail Car vs Time During Impact with Four HopperCars Loaded with Ballast (Test 3 - Instrument 27)(Case 1: Measured Coupler Force)56 Horizontal Acceleration of the Cask-Rail Car DuringImpact with Four Hopper Cars Loaded with Ballast(Test 3 - Instrument 12: Filtered at 100 Hz)(Case 1: Measured Coupler Force)57 Horizontal Acceleration of the Cask During Impactwith Four Hopper Cars Loaded with Ballast (Test 3 Instrument 8: Filtered at 100 Hz) (Case 1:Measured Coupler Force)58 Vertical Acceleration of the Cask at the Far EndDuring Impact with Four Hopper Cars Loaded withBallast (Test 3 ~ Instrument 11: Filtered at50 Hz) (Case 1: Measured Coupler Force)59 Vertical Acceleration of the Cask at the StruckEnd During Impact with Four Hopper Cars Loadedwith Ballast (Test 3 - Instrument 9: Filteredat 50 Hz) (Case 1: Measured Coupler Force)60 Vertical Displacements of the Cask During Impactwith Four Hopper Cars Loaded with Ballast (Test 3)(Case 1: Measured Coupler Force)61 Vertical Tiedown Forces During Impact with FourHopper Cars Loaded with Ballast (Test 3)(Case 1: Measured Coupler Force)Page11-3011-3111-3111-3211-3211-3311-3311-3411-3411-35xi

FIGURES(Cont'd)Figure62636465666768697071Coupler Force vs Time During Impact of Cask-RailCar with Four Hopper Cars Loaded with Ballast(Test 3 - Instrument 3) (Case 2: CalculatedCoupler Force)Horizontal Force of Interaction Between Cask andRail Car vs Time During Impact with Four HopperCars Loaded with Ballast (Test 3 - Instrument 27)(Case 2: Calculated Coupler Force)Horizontal Acceleration of the Cask-Rail CarDuring Impact with Four Hopper Cars Loaded withBallast (Test 3 - Instrument 12: Filtered at100 Hz) (Case 2: Calculated Coupler Force)Horizontal Acceleration of the Cask During Impactwith Four Hopper Cars Loaded with Ballast (Test 3 Instrument 8: Filtered at 100 Hz) (Case 2:Calculated Coupler Force)Vertical Acceleration of the Cask at the Far EndDuring Impact with Four Hopper Cars Loaded withBallast (Test 3 - Instrument 11: Filtered at50 Hz) (Case 2: Cal£ulated Coupler Force)Vertical Acceleration of the Cask at the StruckEnd During Impact with Four Hopper Cars Loadedwith Ballast (Test 3 - Instrument 9: Filtered at50 Hz) (Case 2: Calculated Coupler Force)Vertical Displacements of the Cask During Impactwith Four Hopper Cars Loaded with Ballast (Test 3)(Case 2: Calculated Coupler Force)Vertical Tiedown Forces During Impact with FourHopper Cars Loaded with Ballast (Test 3)(Case 2: Calculated Coupler Force)Coupler Force vs Time During Impact of Cask-RailCar with Four Hopper Cars Loaded with Ballast(Test 10 - Instrument 3)Horizontal Force of Interaction Between Cask andRail Car vs Time During Impact with Four HopperCars Loaded with Ballast (Test 10 - Instruments27 and 28)Page11-3511-3611-3611-3711-3711-3811-3811-3911-3911-40xii

FIGURES(Cont'd)Figure72737475767778798081828384Horizontal Acceleration of the Cask-Rail Car DuringImpact with Four Hopper Cars Loaded with Ballast(Test 10 - Instrument 12: Filtered at 100 Hz)Horizontal Acceleration of the Cask During Impactwith Four Hopper Cars Loaded with Ballast (Test 10 Instrument 8: Filtered at 100 Hz)Vertical Acceleration of the Cask at the Far EndDuring Impact with Four Hopper Cars Loaded with~allast (Test 10 - Instrument 11: Filtered at50 Hz)Stiffness Coefficient of Horizontal Component ofTieaowns vs Relative Displacement Between Cask andRail Car (Tests 10 and 11)Coupler Force vs Time During Impact of Cask-RailCar with Four Hopper Cars Loaded with Ballast(Test 11 - Instrument 3)Horizontal Force of Interaction Between Cask andRail Car vs Time During Impact with Four HopperCars Loaded with Ballast (Test 11 - Instruments 27and 28)Horizontal Acceleration of the Cask-Rail Car DuringImpact with.Four Hopper Cars Loaded with Ballast(Test 11 - Instrument 12: Filtered at 100 Hz)Horizontal Acceleration of the Cask During Impactwith Four Hopper Cars Loaded with Ballast (Test11 - Instrument 8: Filtered at 100 Hz)Vertical Acceleration of the Cask at the Far EndDuring Impact with Four Hopper Cars Loaded withBallast (Test 11 - Instrument 11: Fi ltered at50 Hz)Cask-Rail Car Configuration Used in Tests 3 and 18Cask-Ra i 1 Car Configuration Used in Tests 10 and 11Cask-Rail Car Configuration Used in Test 13Cask-Rai 1 Car Configuration Used in Test 16Page11-4011-4111-4111-4211-4211-4311-43I 1-4411-4411-4511-4511-4611-46xiii

FIGURES(Cont'd)Figure8586878889909192939495Coupler Force vs Time During Impact of Cask-RailCar with Four Hopper Cars Loaded with Ballast(Test 16 - Instrument 3)Horizontal Force of Interaction Between Cask andRail Car vs Time During Impact with Four HopperCars Loaded with Ballast (Test 16 - Instruments 27and 28)Horizontal Acceleration of the Cask-Rail Car DuringImpact with Four Hopper Cars Loaded with Ballast(Test 16 - Instrument 7: Filtered at 100 Hz)Horizontal Acceleration of the Cask During Impactwith Four Hopper Cars Loaded with Ballast (Test16 - Instrument 8: Filtered at 100 Hz)Vertical Acceleration of the Cask at the Far EndDuring Impact with Four Hopper Cars Loaded withBallast (Test 16 - Instrument 11: Filteredat 50 Hz)Vertical Acceleration of the Cask at the Struck EndDuring Impact with Four Hopper Cars Loaded withBallast (Test 16 - Instrument 9: Filtered at 50 Hz)Horizontal Tiedown Force vs Relative DisplacementBetween Cask and Rail Car (Test 16)Stiffness Coefficient of Horizontal Component ofTiedowns vs Relative Displacement Between Cask andRail Car (Test 16)Coupler Force vs Time During Impact of Cask-RailCar with Four Hopper Cars Loaded with Ballast(Test 13 - Instrument 3)Horizontal Force of Interaction Between Cask andRail Car vs Time During Impact with Four HopperCars Loaded with Ballast (Test 13 - Instruments 27and 28)Horizontal Acceleration of the Cask-Rail Car DuringImpact with Four Hopper Cars Loaded with Ballast(Test 13 - Instrument 7: Filtered at 50 Hz)Page11-4711-4711-4811-4811-4911-49II-50II-50II-51II-51II-52xiv

FIGURES(Cont'd)Figure96979899100101102103104105106Horizontal Acceleration of the Cask During Impactwith Four Hopper Cars Loaded with Ballast (Test13 - Instrument 8: Filtered at 100 Hz) II-52Vertical Acceleration of the Cask at the Far EndDuring Impact with Four Hopper Cars Loaded withballast (Test 13 - Instrument 11: Filtered at 50 Hz) II-53Vertical Acceleration of the Cask at the Struck EndDuring Impact with Four Hopper Cars Loaded withBallast (Test 13 - Instrument 9: Filtered at 50 Hz) II-53Coupler Force vs Time During Impact of Cask-RailCar with Four Hopper Cars Loaded with Ballast(Test 18 - Instrument 3)Horizontal Force of Interaction Between Cask andRail Car vs Time During Impact with Four HopperCars Loaded with Ballast (Test 18 - Instruments 27and 28)II-54II-54Horizontal Acceleration of the Cask-Rail Car DuringImpact with Four Hopper Cars Loaded with Ballast(Test 18 - Instrument 12: Filtered at 50 Hz) II-55Horizontal Acceleration of the Cask During Impactwith Four Hopper Cars Loaded with Ballast (Test18 - Instrument 8: Filtered at 100 Hz) II-55Vertical Acceleration of the Cask at the Far EndOuring Impact with Four Hopper Cars Loaded withBallast (Test 18 - Instrument 11: Filtered at 50 Hz) II-56Vertical Acceleration of the Cask at the Struck EndDuring Impact with Four Hopper Cars Loaded withBallast (Test 18 - Instrument 9: Filtered at 50 Hz) II-56Horizontal Acceleration of the Support for anEquivalent Single-Degree-of-Freedom Sys~em(Preliminary Cases 2, 3 and 4)Vertical Acceleration of the Support for anEquivalent Single-Degree-of-Freedom System(Preliminary Cases 2, 3 and 4)II-57II-57xv

FIGURES(Cont'd)Figure1071081091 10111112113114115116117118Rotational Acceleration of the Support for anEquivalent Single-Degree-of-Freedom System(Preliminary Cases 2, 3 and 4)Response Spectrum: Maximum Absolute RelativeHorizontal Acceleration vs Frequency (PreliminaryCases 1 through 5)Response Spectrum: Maximum Absolute RelativeVertical Acceleration vs Frequency (PreliminaryCases 1 through 5)Response Spectrum: Maximum Absolute RelativeRotational Acceleration vs Frequency (PreliminaryCases 1 through 5)Horizontal Acceleration of the Support for anEquivalent Single-Oegree-of-Freedom System(Requested Base Case and Cases 7 and 8)Vertical Acceleration of the Support for anEquivalent Single-Oegree-of-Freedom System. (Requested Base Case and Cases 7 and 8)Rotational Acceleration of the Support for anEquivalent Single-Oegree-of-Freedom System(Requested Base Case and Cases 7 and 8)Force on the Horizontal Component of the Tiedownat the Struck End (Requested Base Case and Cases7 and 8)Force on the Horizontal Component of the Tiedownat the Far End (Requested Base Case and Cases 7and 8)Force on the Vertical Component of the Tiedown atthe Struck End (Requested Base Case and Cases7" and 8)Force on the Vertical Component of the Tiedown atthe Far End (Requested Base Case and Cases 7 and 8)~Maximum Absolute Relative HoriResponse Spectrum:zontal Acceleration vs Frequency (Requested BaseCase and Cases ] and 8)PageII-58II-58II-59II-59II-6011-6011-6111-61II-6211-62II-6311-63xvi

FIGURES(Cont'd)119 Response Spectrum: Maximum Absolute Relative VerticalAcceleration vs Frequency (Requested BaseCase and Cases 7 and 8)120 Response Spectrum: Maximum Absolute RelativeRotational Acceleration vs Frequency (RequestedBase Case and Cases 7 ana 8)121 Response Spectrum: Maximum Absolute Relative HorizontalAccelerations vs Frequency (Base Case, + 50%~ase Case, and Cases 1, 2, C, D, and 3 through-21)122 Response Spectrum: Maximum Absolute Relative VerticalAccelerations vs Frequency (Base Case, + 50%base Case, and Cases 1, 2, C, D, and 3 through 21)123 Response Spectrum: Maximum Absolute RelativeRotational Accelerations vs Frequency (Base Case,+ 50% Base Case, and Cases 1, 2, C, D, and 3through 21)124 Ranking of Parameters by Absolute Percent Differenceof Absolute Peak Horizontal Support Accelerationfrom Base Case Value125 Ranking of Parameters by Absolute Percent Differenceof Absolute Peak Vertical Support Accelerationfrom Base Case Value126 Ranking of Parameters by Absolute Percent Differenceof Absolute Peak Rotational Support Accelerationfrom Base Case Value127 Ranking pf Parameters by Absolute Percent Differenceof Maximum Absolute Relative HorizontalAcceleration from Base Case Value128 Ranking of Parameters by Absolute Percent Differenceof Maximum Absolute Relative Vertical Accelerationfrom Base Case Value129 Ranking of Parameters by Absolute Percent Differenceof Maximum Absolute Relative RotationalAcceleration from Base Case ValueI 1-6411-6411-65I 1-6511-6611-6611-6711-6711-6811-6811-69xvii

FIGURES(Cont'd)Figure130 Ranking of Parameters by Absolute Percent Differenceof Maximum Absolute Horizontal Tiedown Force(Struck End) from Base Case Value131 Ranking of Parameters by Absolute Percent Differenceof Maximum Absolute Horizontal Tiedown Force(Far End) from Base Case Value132 Ranking of Parameters by Absolute Percent Differenceof Maximum Absolute Vertical Tiedown Force(Struck End) from Base Case Value133 Ranking of Parameters by Absolute Percent Differenceof Maximum Absolute Vertical Tiedown Force(Far End) from Base Case Value134 Sensitivity of Absolute Peak Support Accelerationsto Changes in the Stiffness Coefficients of theVertical Components of the Tiedowns (Requested BaseCase and Cases 7 and 8)135 Sensitivity of Maximax Absolute Relative Accelerationsto Changes in the Stiffness Coefficients ofthe Vertical Components of the Tiedowns (Base Caseand Cases 7 and 8)136 Sensitivity of Absolute Tiedown Forces to Changesin the Stiffness Coefficients of the Vertical Componentsof the Tiedowns (Requested Base Case andCases 7 and 8)Page11-6911-7011-70I 1-7111-7111-7211-72xviii

TABLESTab lePageParameters Used in the CARDT Model for Simulationof Impact Between Two Hopper Cars Loaded withGrave 1I II-32 Summary of Configurations and Conditions of CompletedCask-Rail Car-Tiedown Tests3 Force Terms from the CARDS Test 3 Simulation RunMeasured at the Time (0.116 second) When theVertical Acceleration of the Rail Car (Support)Is a MaximumI II-3I II-44 Force Terms from the CARDS Test 3 Simulation RunMeasured at the Time (0.057 second) When theHorizontal Acceleration of the Rail Car (Support)Is a Maximum 111-45 Input Data and Results from the CARDS Test 3Simulation Run. Results Measured at the Time(0.116 second) When the Vertical Accelerationof the Rail Car (Support) Is a MaximumI II-56 Input Data and Results from the CARDS Test 3Simulation Run. Results Measured at the Time(0.057 second) When the Horizontal Accelerationof the Rail Car (Support) Is a Maximum I II - 57 Instrument Configuration for Cask-Raildown TestsCar-Tie111-68 Measured and Reduced Parameter Values from RailCar Humping Tests (Test No.1: 40-Ton Cask, 70Ton Seaboard Coastline Rail Car, Impact Velocity8.3 mph) I II-79 Theil's Inequality Coefficients for Response VariablesDetermined Using Calculated and MeasuredCoupler Force 111-810 Definitions of Cases Used for Generation ofPreliminary Response Spectra 111-811 Conditions Imposed on Cases Requested forParametric and Sensitivity Analysis and Generationof Response Spectra II 1-9xix

TABLESTable1213141516171819Definitions of IIPure ll Parameters and Their CasesDefinitions of IIComposite ll Parameters and TheirCasesParameter Values Used in Cases Requested forParametric/Sensitivity AnalysisParametric and Sensitivity Analysis - Sensitivityof Response Variables to Parameter ChangesParametric and Sensitivity Analysis - Ranking ofParameters by Absolute Percent Difference ofResponse Variables from Base Case ValuesParametric and Sensitivity Analysis - Sensitivityof Response Variables in Terms of Percent Differencefrom Base Case ValuesParametric and Sensitivity Analysis - Ranking ofIIPure ll Parameters by Influence Coefficient andSens iti vityParametric and Sensitivity Analysis - Ranking ofParameters by Parameter Ratio-Based InfluenceCoefficient and SensitivityPageIII-10III-10III-llII 1-13111-18I II-23II 1-251II-27xx

DYNAMIC ANALY~IS TO ESTA~LISH NORMAL SHOCK AND VIBRATIONOF RADIOACTIVE MATERIAL SHIPPING PACKAGESFINAL SUMMARY REPORTSUMMARYA computer moael CARDS (Cask-Rail Car Qynamic Simulator) was developed forthe U.~. Nuclear Regulatory Commission to provlde input data for a broadrange of radioactive material package-tiedown structural assessments.CARDS simulates the dynamic behavior of shipping packages and their rail cartransporters during nor~al transport conditions. The model was used toidentify parameters that significantly affect the normal shock and vibrationenvironments that, in turn, provide the basis for determining the forcestransmitted to the packages. The determination of these forces is necessaryfor the package-tiedown structural assessments. The objective was to determinethe extent to which the shocks and vibrations experienced by the shippingpackages during normal transport are influenced by, or are sensitiveto, various structural parameters of the transport system (i.e., package,package supports, vehicle characteristics, etc.).It was assumed that the greatest shock suffered by the cask-rail car in itsnormal (not accident) transport environment will be that experienced duringcoupling operations in a IIhumping ll or classification yard. An earlier studyuy the Sanaia Laboratories showed that 99.8% of all train coupling operationsoccurred at speedS of 11.05 mph or less. Eighteen tests were conaucteaat the Savannah River Laboratory in 1978 during which couplingvelocities as high as 11.2 mph were recorded. The CARDS model was used tos imu 1ate six of these tests. On t~e bas LL~~~EULood _aJl!_~~~~~..Q!>!.a_!.~~C!between the ca1cu 1atea ana experirnenta 1 resu lts, it was cone 1uded that CARDSis an acceptable tool f£.l: s~bs~~e~tsTmUTatlOn_~f cas~:rail_car-~stem-Q.ehavi

A companion model CARRS (Cask-Rail Car Response Spectrum Generator), a modelto generate frequency response-spectra using calculated results from CARDS,was also developed. The equations of motion of the cask-rail car 'systemwere transformed into equivalent single-degree-of-freedom (l-DOF) representationof the relative vertical, horizontal and rotational motions betweenthe cask and its rall car platform or support. These equations of motionwere then used to construct CARRS. The right-hand sides of each of theseequivalent l-DOF equations of motion represent the time-varying accelerationsof a platform (rail car) supporting l-DOF devices defined by theleft-hand sides of the respective equations of motion. The definition ofCARRS was also written in the ACSL language.Frequency response spectra were generated by the spectrum generator, CARRS,using the time-varying support accelerations obtained from the simulator,CARDS. Response spectra for a base-case cask-rail car system are presentedin Figures 118 through 123.A parametric and sensitivity analysis was conducted to identify those parametersthat significantly affect the normal shock and vibration environmentand the response of the cask-rail car system. The response of the systemwas defined by the absolute values of the maximum support accelerations, themaxim~"1 relative accelerations between the cask and its support, and the verticaland horizontal tiedown forces. The sensitivities of these responsevariables to changes in various parameters were determined (see Table 18).For all the response variables except the vertical accelerations, the mostinfluential parameter is the vertical distance Zp (see Appendix I, NOMENCLATURE OF TERMS). The parameter that has the most influence on the verticalaccelerations is lOCR, the horizontal distance between the centers-ofgravityof the cask and rail car. The parameter that contributes most to thesensitivities (total changes) of the horizontal accelerations is Wp, thepackage or cask weight. The vertical accelerations are the most sensitive tolOCR; and the rotational accelerations are the most sensitive to {k },the set of stiffness coefficients of the vertlcal components of theYtiedowns.The tiedown forces DUS1MAX, DUS4MAX, DUS2MAx,and DUS3MAX are the most sensitiveto the parameters Wp, {k x }, Zp and Zp, respectively. The ranges ofparameters used to arrive at the sensitivlties were specified at the outsetin the definition of the cases requested by Nuclear Regulatory Commissionpersonnel. More meaningful values of the sensitivities are obtained ifthese ranges represent the uncertainties in the parameters.2

INTRODUCTIONThe objective of this study was to determine the extent to which the shocksand vibrations experienced by radioactive material shipping packages duringnormal transport conditions are influenced by, or are sensitive to, variousstructural parameters of the transport system (i.e., package, package supportsand vehicle). The purpose of this effort was to identify those parametersthat significantly affect the normal shock and vibration environmentsso as to provide the basis for determining the forces transmitted to radioactivematerial packages. Determination of these forces will provide theinput data necessary for a broad range of package-tiedown structuralassessments.A computer model CARDS (Cask-~ail Car Qynamic ~imulator) was developed toprovide the data for these assessments. A companion model CARRS (Cask RailCar Response Spectrum Generator) was also developed to generate frequencyresponse spectra using results from CARDS. These two models were used toidentify parameters that significantly affect the shock and vibrationenvironments and, in turn, the forces transmitted to the packages.It was assumed that the greatest shock suffered by the cask-rail car in itsnormal (not accident) transport environment will be that experienced duringcoupling operations in a "humping" or classification yard. An earlier studyby the Sandia Laboratories showed that 99.8% of all train coupling operationsvccurred at speeds of 11.05 mph or less. Eighteen tests were conducted atthe Savannah River Laboratory in 1978 during which coupling velocities ashigh as 11.2 mph were recorded. The validity of the CARDS model as anacceptable tool for the simulation of cask-rail car systems was establishedby comparison of calculated results with results obtained from six of thesetests.The CARDS and CARRS models were used together to generate frequency responsespectra, to determine the sensitivity of selected response variables tochanges in parameters, and to rank the parameters according to their influenceand their contribution to the sensitivity of the response variables.This report interprets, supplements, consolidates, and summarizes informationpreviously published in the following quarterly progress reports:1.,December 31, 1977), Hanford1978.2. S. R. Fields and S. J. Mech, Dynamic Analysis to Establish Normal Shockand Vibration of Radioactive Material Shipping Packages, NUREG/CR-0161,(HEDL-TME 78-41), Quarterly Progress Report (January 1 - March 31,1978), Hanford Engineering Development Laboratory, July 1978.1 -3

3. ~. R. Fields and S. J. Mech, Dynamic Analysis to Establish Normal Shockand Vibration of Raaioactive Material Shippin Packa es, NUREG/CR-0448,HEDL-TME 78-74 , Quarterly Progress Report Aprl - June 30, 1978),Hanford Engineering Development Laboratory, December 1978.4.~. s. k. Fielas and S. J. Mech, Dynamic Analysis to Establish Normal Shockand Vibration of Raaioactive Material Shippin Pack a es, NUREG/CR-0766,~riEDL- lYlE 79-3 , Quarterly Progress Report ctober - December 31,1978), Hanford Engineering Development Laboratory, June 1979.b. s. R. Fielas and S. J. Mech, Dynamic Analysis to Establish Normal Shockana Vibration of Radioactive Material Shippin Packa es, NUREG/CR-0880,HEUL-T~~ 79-29 , Quarterly Progress Report January - March 31,1979), Hanford Engineering Development Laboratory, July 1979./. ~. R. Fields and S. J. Mech, Dynamic Analysis to Establish Normal Shockand Vibration and Radioactive Material Shippin Packa es, NUREG/CR-1066,(HEUL- T/VIE 79-43 , Quarterly Progress Report Apri 1 1 - June 30, 1979),Hanfora Engirleering Development Laboratory, October 1979.8. ~. R. Fields and S. J. Mech, Dynamic Analysis to Establish Normal Shockand Vibration of Radioactive Material Shippin Packa es, NUREG/CR-1265,HEDL-TME 79-7 ,Quarter y Progress Report Ju y - September 30, 1979),Hanford Engineering Development Laboratory, March 1980.9. S. R. Fields and S. J. Mech, Dynamic Analysis to Establish Normal Shockand Vibration of Radioactive Material Shipping Packages, NUREG/CR-1484,(HEDL-TME 80-24), Quarterly Progress Report (October 1 - December 31, 1979),Hanford Engineering Development Laboratory, August 1980.10. S. R. Fielas, Dynamic Analysis to Establish Normal Shock and Vibrationur Radioactive Material Shipping Packages, NUREG/CR-1685, Volume 1,(~~UL-TME 80-51), Quarterly Progress Report (January 1 - March 31,1980), Hanford Engineering Development Laboratory, January 1981.11. ~. R. Fields, Dynamic Analysis to Establish Normal Shock and Vibrationof Raoioactive Material Shippin Packa es, NUREG/CR-1685, Volume 2,HE L- E 80- 2 , Quarter y Progress eport (April 1 - June 30, 1980),Hanford Engineering Development Laboratory, April 1981.12. S. R. Fields, D~namic Ana1xsis to Establish Normal Shock and Vibrationof Radioactive aterial Shlpping Packages, NUREG/CR-l685, Volume 3,(HEDL-TME 80-91), Quarterly Progress Report (July r - September 30,1980), Hanford Engineering Development Laboratory, April 1981.4

13. S. R. Fields, Dynamic Analysis to Establish Normal Shock and Vibration ofRadioactive Material Shippin Packa es, NUREG/CR-l685, Volume 4, (HEDL-TME80-92 , Quarterly Progress Report October 1 - December 31, 1980), HanfordE.ngineering Deve-Ioprnent Laboratory, July 1981.14. S. k. Fields, Dynamic Analysis to Establish Normal Shock and Vibration ofRadioactive Material Shippin Packages, NUREG/CR-2146, Volume 1, (HEUL-TME81-15 , Quarter y Progress eport January 1 - March 31, 1981), HanfordEngineering Development Laboratory, November 1981.15. S. k. Fields, Dynamic Analxsis to Establish Normal Shock and Vibration ofkadioactive Material Shippln -Packa es, NOREG/CR-2146, Volume 2, (HEDL-TME83-8 , Quarter y Progress eport April 1 - June 30, 1981), HanfordE.ngineering Development Laboratory, July 1983.NOTICE UF ERRORS IN PREVIOUS REPORTSErrors were found in three of the above previously published Quarterlyreports. These reports are Volumes 2, 3 and 4 of NUREG/CR-1685 (HEDL-TME80-72, HEDL-TME 80-91 and HEDL-TME 80-92, respectively). In these reports,all frequencies are angular frequencies and should be reported in units ofraaians/second rather than in units of Hz. This applies to all figures withfrequency as the abscissa, and to all references to frequency in the textsof the reports.5

TECHNICAL APPROACH AND RESULTS1.0 MODEL DEVELOPMENT1.1 CASK-RAIL CAR DYNAMIC SIMULATOR (CARDS)A two-dimensional, multi-degree-of-freedom model of a spent fuel shippingcask-rail car system was developed. A sketch of the idealized cask-rail carsystem modeled is shown in Figure 1, and the spring-mass model of this systemis shown in Figure 2. This model was given the name CARDS: An acronym forCask-~ail Car Qynamic ~imulator.Each of the masses in the cask-rail car model of Figure 1 is free to translatehorizontally (front to back) and vertically, and to rotate about itsaxis normal to the plane of the illustration. The system is excited byimpact with one or more cars (mass MF) at the front coupler. One possibleorientation of the system after impact is shown in Figure 3, and a comparisonwith the initial state is illustrated in Figure 4. Figure 5 is obtained bysuperimposing Figures 2 and 3. (See Appendix I NOMENCLATURE OF TERMS fordefinition of terms used in this report.)The model consists of twelve equations of motion, one derived for each degreeof freedom (generalized coordinate), and supplementary auxiliary equations.There are two general approaches that could have been used to derive theequations of motion for this dynamic system. The first is known as theforce-acceleration method and the second is known as the energy method. Thefirst method is also sometimes referred to as the method of dynamic eguili~rium,while the second method may be referred to as the Lagrange-equat~method. The force-acceleration method consists of analyzing the forces andthe torques applied to the system and relating them to the accelerations.In the energy method one sets up the energy expressions for the system andapplies Lagrange1s equation to get the equations of motion. The energy orLagrange-equation method was used for this study.The equations of motion were derived from an energy balance (expressed ingeneralized coordinates) on the system. This energy balance is sometimesknown as the law of virtual work, which states that the work done on thesystem by the external forces (virtual work) during a virtual distortion (asmall change in one of the generalized coordinates) must equal the change ininternal strain energy. The work done by external forces includes the workdone by external loads, by inertia forces, and by damping or dissipationforces. The energy balance on the system may be written asoW + oW. + oW = 0U ( 1)e ln c7

where:oWe = Work done by external loadsoWin = Work done by inertia forcesoW c = Work done by damping forcesoU = Change in internal strain energy (potential energy)For a generalized coordinate qi(2)aW coW = - oq. (3)c aqi 1oUaU= ~ oqi1(4)andoW. ln=d-err (~) aq.1 / 0 qi +( ~~ i)Oqi(5 )where:K = t 1- M X 22 r rr=(6)• aX= '} MX r (7)jaKaq. r r .1 t=I- aq. 18

(8)~ubstituting (2), (3), (4) and (5) into (1) gives(9)or( 10)where:t = Timeqi = A generalized coordinateqi = Time rate of change of qiK = Kinetic energyU = Strain energyWcWe= Work done by damping forces= Work done by external loadsThis equation is one form of Lagrange's equation. When appropriate expressionsare written for K, U, W~ and We' all in terms of the generalizedcoordinates ql, q2, ... , qn' dlfferentiated as indicated and substituted intothe above expression, equations of motion are obtained. There will be oneequation of_motion for each of the n coordinates or degrees of freedom. Inall cases considered, aK/aqi is zero, since kinetic energy is a function ofvelocity rather than displacement. For example, consider an energy balanceon the cask (i.e., the mass Mp), and let the generalized coordinate be thevertical displacement Yp, i.e.,q. = Y ( 11)1 P9

therefore( 12)( 1 M x·2 +.l M Y·2 + ) = M Y ( 13)Ipp ~pp ... ppand( 14 )Also~ = __0__oypoyp(US2Y + US3Y) ( 15)where:( 16)and( 17}Therefore( 18)10

andFinally,dwaye = a~ (WC52Y + WC53Y) (20)p pwhere:d1 CR 6 RC ) d1p PR 6 px [(Y RC- 1 - (Y -CR 6 RC ) lp PR 6 p)J (21)WC52Y = -C 52[dt (Y RC - - dt (Y - )JdWC53Y = -C 53edt (Y RC - dt (Y )Jd+ 1 CF 6 RC ) p + 1 PF 6 px [(Y RC- (Y )J (22)+ 1 CF 6 RC ) p + l PF 6 pandThere is no work done by external loads, soaW e- = 0 (25)aY p11

The equation of motion for the cask is then obtained by substitution of theabove terms in Lagrange's Equation [Eq. (10)J to gived 2 yM ~ - 0 + DUS2 + DUS3 - DWS2 - DWS3 = 0 (26)P dtThe twelve derived equations of motion are:(1) The Package or Cask..MpXp = (k S1+ k S4 )[(X RC+ ZRC6RC) - (Xp - Zp6p)J. . . .+ + C S4 )[X RC+ ZRC6RC) - (X - 6 )J(C S1 p Z p p. .- (W p1 + Wp4)~pRsgn(Xp- X (27)RC )- (Y p - 1 PF6 p )J.+ C S3[(Y RC.- 1 CF6 RC). .+ C S2[(Y RC+ 1 CR6 RC).- (Y p +.1 PR6 p )J. .- (Y p- 1 PF6 p)J (28)Ip6 p = - (k S1+ k S4 )Zp[(X RC+ ZRC6RC) - (X p - Z p 6 p )J+ kS21PR[(YRC + 1 CR 6 RC ) (Y p+ 1 PR 6 p )J- kS31PF[(YRC - 1 CF 6 RC ) - (Y p - 1 PF 6 p )J. . . .- (C Sl+ C S4 )Zp[(X RC+ ZRC6RC) - (X p - Z p 6 p)J. . .+ CS21pR[(YRC + 1 CR 6 RC ) - (Y p+ ~pR6p)J. . . .- CS31pF[(YRC - 1 CF 6 RC ) - (Yp - 1 pF 6p)J (29)12

(2) The Rail CarMRCX RC= - (k Sl+ k S4 )[(X RC+ ZRC6RC) - (Xp - Z p 6 p )]- kSS[(X RC - ZRC6RC) - X TR ] - k S8 [(X RC - ZRC6RC) X TF ]. . . .- kSCARS(XRC - X F ) - (C S1 + C S4 )[(X RC + ZRC6RC) - (X p - Z p 6 p )]. .. . . .- CSS[(X RC - ZRC6RC) - X TR ] - C S8 [(X RC - ZRC6RC) - X TF ]. .+ (W p1 + Wp4)uPRsgn(Xp - X RC )(30)..MRCY RC= - k S2[(Y RC+ t CR6 RC) - (Y p + t pR 6 p )] - k S3[(Y RC t CF6 RC)- (Y p - t pF 6 p )] - k S6(Y RC+ t RC6 RC) - k S7(Y RC- t RC6 ) RC. . .. . .- C~2 [(Y RC+ t CR6 RC) - (Yp + t pR 6 p)] - C S3[(Y RC t CF6 RC). . . . . .- (Y p - t pF 6 )] - pC S6(Y RC+ t RC6 RC) - C S7(Y RC t RC6 RC).•a CPL- UCPLBcPLsgn(YRC - tCPL6RC) IkSCARS(XRC - XF) I (31)IRC6RC = - (k S1+ k S4 )ZRC[(X RC+ ZRC6RC) - (Xp - Z p 6 p )]- k S2 t CR [(Y RC+ t CR 6 RC ) - (Y p + t pR 6p) + kS3tCF[(YRC t CF 6 RC )- (Y p - t pF6p)] + kSSZRC[(XRC - ZRC6RC) - X TR ] - kS6tRC(YRC + t RC 6 RC )+ kS7tRC(YRC - t RC6RC ) + kS8ZRC[(XRC - ZRC6RC) - X TF ]. . . .- (C Sl+ C S4 )ZRC[(X RC+ ZRC6RC) - (Xp - Z p 6 p )]. . .. ..- CS2tCR[(YRC + t CR 6 RC ) - (Yp + t pR6 p )] + CS3tCF[(YRC t CF 6 RC ).. ...- (Y p - t pF6 p )] + CSSZRC[(XRC - ZRC6RC) X TR ]13

. .- C S6 1 RC (YRC - 1 RC 6 RC ) + CS71RC(YRC 1 RC 6 RC ). . .+ CS8ZRC[(XRC - ZRC6RC) - XTFJ. . I IaCPL+ lJCPL1cPLsgn(YRC - 1CPL6RC) BCPL kSCARS(XRC - XF)+ (ZCDGO + 1CPL6RC)kSCARS(XRC - X~)(32)(3) The Front and Rear Trucks.. . . .MTRX TR = k S5 [(X RC ~ ZRC6RC) - XTRJ + C S5 [(X RC - ZRC6RC) - XTRJ.- lJTRWXTRsgn(XTR) . BRAKER (33).. . . .MTFX TF = k S8 [(X RC - L RC 6 RC ) - XTFJ + C S8 [X RC - ZRC6RC) - XTFJ.- lJTFWXTFsgn(XTF) . BRAKEF (34 )(4) The Anvil Train (Four Loaded Hopper Cars).. .MFX F= kSCARS(XRC - X F ) - k FF2 (X F - X F2 ) - lJFWFsgn(XF) . BRKIRC (35).M F2 X F2= k FF2 (X F - X F2 ) - kF2F3(XF2 - X F3 ) - lJF2WF2sgn(XF2) . BRKF2 (36).. .M F3 X F3= kF2F3(XF2 - X F3 ) - kF3F4(XF3 - X F4 ) - lJF3WF3sgn(XF3) . BRKF3 (37).. .M F4 X F4= kF3F4(XF3 - X F4 ) - lJF4WF4s'gn(XF4) . BRKF4 (38)14

See Appendix I, NOMENCLATURE OF TERMS, for definitions of the terms used inthese equations.The energy method was used in this study because it is a convenient andefficient process for deriving the equations of motion of the cask-rail carsystem. Specifically, several reasons for its selection are:(1) It has the advantage that, for a multi-degree-of-freedom system, theequations that describe the motion of the system are simplified andreduced in number because all the internal forces that do no work willnot appear in the equations.(2) To express the results of the study as acceleration response spectra,it is necessary to relate maximum system response to system frequency.One way of accomplishing this is to use the modal method of analysis,which is considered to be an energy method because the modal equationsare derived using the method outlined above. In the modal method,responses in the normal modes are determined separately and thensuperimposed to provide the total response. It can be shown that, bythe use of this approach, each normal mode may be treated as an independentone-degree system. However the modal method was not used inthis study. Independent one-degree-of-freedom (l-DOF) systems wereused to relate system response to system frequency, but the techniqueused was not the modal method. [See Section 1.2, CASK-RAIL CAR RESPONSESPECTRUM GENERATOR MODEL (CARRS)].(3) Common practice associates matrix formulation (stiffness matrices, etc.)with the alternate method. This is not always necessary; nevertheless,it is common to set up a problem in matrix notation when using theforce-acceleration method. This is not the case with the energy method,although each method produces a system of differential equations ofmotion that can be expressed in this form. The formulation of theequations of motion using the energy method requires more mathematicalmanipulation, which might be considered by some to be a disadvantage;however, in this study, this was felt to be a small price to pay tomaintain a close feel for the system attributes and to be able tosubdivide the equations of motion into their various energy components.(4) The system simulation model is set up in terms of the equations ofmotion, which are subdivided into the various energy terms. Thisfacilitates modification of the model at any time with a minimum ofeffort. This provides extreme flexibility in model construction.Both the energy methou and the force-acceleration method are only alternatemethods of formulating the equations of motion of the cask-rail car system.They are not methods for solving the system of differential equationsobtained.~ecause of the complexity of the system of equations and the factthat the equations are non-linear, a numerical method of integration wasused in this study.15

The entire model defi~ition was written in the Advanced Continuous SimulationLanguage (ACSL).ll) ACSL was developed for the purpose of modelingsystems described by time-dependent, non-linear differential equationsand/or transfer functions. Program preparation can either be from blockdiagram interconnection, conventional FORTRAN statements, or a mixture ofboth. The ACSL program is intended to provide a simple method of representingcomplex mathematical models on a digital computer. Working from asystem of equations describing the problem or from a block diagram, the userwrites ACSL statements to describe the system under investigation. Statementsdescribing the model do not need to be ordered, since the ACSL processorwill sort the equations so that no values are used before they have beencalculated. This operation of the language is in contrast to the usualdigital programming languages like FORTRAN, where program execution dependscritically on statement order.All integration in an ACSL program is handled by a centralized integrationroutine. The user has a choice of four numerical integration algorithms:(1) The Adam's-Moulton variable-step, variable-order,(2) The Gears-Stiff variable-step, variable-order,(3) The Runge-Kutta second-order, and(4) The Runge-Kutta fourth-order.The Runge-Kutta fourth-order algorithm was used in the model developed forthis study.A listing of the CARDS Model is presented in Appendix IV.1.1.1 Rail Car Coupler and Draft Gear Subsystem SubmodelThe rail car coupler and draft gear subsystem affects the response of thecask-rail car system more than any other component because the shock ofimpact is attenuated and transmitted to the cask-rail car system throughthis device.A calculation sequence was developed to simulate the behavior of the couplersubsystem for the cask-rail car and the lead car in the group it impactsduring humping operations. This coupler submodel determines the displacementsof the springs and dampers (dashpots) during normal operating conditions,and the displacements and other conditions when one or more of thesecomponents bottom out at their limits of travel. The submodel was developedas a simplified preliminary model to develop and test the simulation of acoupler with a friction draft gear. It was given the name CARDT, which isan acronym for Cask-Rail Car Dynamic Test model. Later, after validation ofCARDT by comparlng calculated-results-with some experimental data, the basicfeatures of the submodel were incorporated into CARDS.16

Friction draft gears consist of springs and dampers in parallel; therefore,CARDT is based on the spring and damper arrangement shown in Figure 5(a).The equations of motion for the simple rail car-coupler subsystem model ofFigure 5 are(39)and(40)where:X =RCDisplacement of the hammer car (in.)X F= Displacement of the struck car (in.)M =RCMass of the hammer car, including lading [lb(force)-s2/in .]M = Mass of the struck car, including lading [lb(force)-s2/in .]Fk = Total equivalent spring constant of the combined draftTgears [lb(force)/in.]An equivalent spring representing the draft gears separating the cars isobtained by combining the spring and damper of each draft gear into a singleequivalent spring [Figure 5(b)] and then reducing these series-connectedsprings to a single spring [Figure 5(c)].When a force is applied to a parallel arrangement of a spring and damper,such as that representing the draft gear on the hammer car in Figure 5(a),the forces and displacements are defined, respectively, by(41)and(42)17

where:Xl= Total force applied to the draft gear on the hammer car[lb(force)]= Force causing displacement of the spring [lb(force)]= Force causing displacement of the damper [lb(force)]x = Total travel or displacement of the draft gear on thehammer car (in.)= Displacement of the spring (in.)X10 = Displacement of the damper (in.)The force on the spring is(43)or, since X = Xl(44)where:Spring constant of the spring in the hammer car draft gear[lb(force)/in.]According to Roggeveen,(2) in a friction draft gear the friction force iscaused by the spring force and is, therefore, proportional to it. With thisin mind, the friction force or force on the damper was defined as.F Dl= \.IoF1sgn(X) (45)where:\.10 = A multiplying factor corresponding to a coefficient offrictionsgn(X) = Signum function or sign function18

The signum function is defined as..+1 X > 0sgn(X) = o x = 0 (46).-1 X < 0where:X = Total relative velocity of displacement or travel of thedraft gear (in./s)Equation (45) implies that frictional damping in the draft gear is due to thesliding of two surfaces with a friction coefficient of ~D, pressed togetherby the spring force Fl. Equation (41), which defines the total force appliedto the draft gear, may now be written as.= F l + ~DFlsgn(X) (47)F Tl.or = Fl[l + ~Dsgn(X)J (48)F TlUsing the definition of Fl from Equation (44), the equation for the totalforce becomesF n.= klX[l + ~Dsgn(X)J (49)Corresponding equations for the draft gear on the struck car areFT2 = F2 + F D2(50)XI = X = X ( 51)2 02(52)or (53)19

.and F T2= k 2X' [1 + ~Dsgn(X')] (54)where:FT2 = Total force applied to the draft gear on the struck car[lb(force)]F2 = Force causing displacement of the spring in the struckcar draft gear [lb(force)]F02 = Force causing displacement of the damper in the struckcar draft gear [lb(force)]XI= Total displacement or travel of the graft gear on thestruck car (in.)= Displacement of the spring in the struck car draft gear(in. )= Displacement of the damper in the struck car draft gear(in. )The coupler subsystem of Figure 5(a) can now be reduced to the equivalentarrangement shown in Figure 5(b). The total forces acting on the draft gearsmay now be expressed in terms of the spring constants of the equivalentsprings(55)and(56)where:.= kl[l + ~Dsgn(X)] (57)k RCDG.,= kl[l + ~Dsgn(X)] (58)k FDG20

For two springs in series, the total force applied is the same as that oneach spring,(59)and the total relative displacement or travel of the two springs is equal tothe sum of the relative displacements of each of the springs,x = X + XI (60 )TFor a single equivalent spring, the total force may be defined as(61 )where:XT= Total relative displacement of a single spring representingboth draft gears (in.)kT = Spring constant of the single equivalent spring[lb(force)/in.]Solving Equations (55), (56) and (61) for tne displacements and substitutinginto Equation (60) gives(62)but since Equation (59) is true, Equation (62) may be reduced to1 _ 1 + _1_~- k kRCDG FDG(63)or21

kRCOGkFDGkRCOG + kFOG(64)Before this definition of kT can be used for the s~bmode1 of Figure 5(c),bot~ kRCOG and kFOG must be expressed in terms of XT rather than as functionsof X and X'. The total travel of the combinpd draft gears may be expressedas(65)and the velocity as(66)Combining Equations (55) and (61) gives the relationship between X and XT,(67)and combining Equations (56) and (61) gives the corresponding relationshipbetween X' and XT,X' =~X T(68)k FOGDifferentiating Equations (67) and (68) with respect to time gives• k •X=·_-XT(69)k RCOGTandX I-kk T X T (70)FOG22

Substituting from Equations (69) ~ndboth kRCOG and kFOG functions of XT,(70) into Equations (57) and (58) makes.= kl[l + uosgn(kTXT/kRCOG)] ( 71)k RCOG.= k 2 [1 + uosgn(kTXT/kFOG)] (72)k FDGbut, since only the sign and not the magnitude of XT is of interest andsince kT' kRCOG and kFDG are always positive,k RCOG·= kl[l + Uosgn{X T )] (73)andk FOG·= k 2 [1 + Uosgn{X T )] (74)Equations (73) and (74) define the equivalent spring constants of the draftgears in their "active" state, i.e., when the total displacement liesbetween its upper and lower limits. When these limits are reached, thedraft gears go "solidi', i.e., they behave like a solid beam with propertiesconsistent with the structural characteristics of the draft gears and railcars. Consequently, the definitions of kRCOG and kFRG must be modified torepresent the transition from the "active" to "so lid' states. This isaccomplished by branching within the submodel equivalent to the following:·k RCOG = kl[l + uosgn{XT)]andk FOG= k SOG2(76)23

where:XTL, XTU= Lower and upper limits, respectively, on the travel ofthe combined draft gears (in.)kSDG1, kSDG2 = Spring constants of the "solid" draft gears on thehammer car and struck cars, respectively [lb(force)/in.]In the submodel, this branching is accomplished by the use of switchingfunctions. In Fortran notation,KRCDG=RSW(XT.LT.XTU.AND.XT.GT.XTL,Kl*(l.+MUD*SGNF(DXT)),KSDG1) (77)andKFDG=RSW(XT.LT.XTU.AND.XT.GT.XTL,K2*(1.+MUD*SGNF(DXT)),KSDG2) (78)where:andRSW( ) = A "real switch" function in ACSL (Advanced ContinuousSimulation Language)SGNF ( ) = A specially constructed "signum function"As a simple general example of how the real switch function works in ACSL,letR = RSW(A,B,C).If A is TRUE, R = B,Otherwise R = C.The foregoing has been a presentation of the development of the coupler subsystemsUbmodel. The same general approach was apg1ied to the suspensionsubsystem submodel since a Barber stabilized truckt ) utilizes frictiondamping where friction is proportional to the load. (See Section 1.1.2,Suspension Subsystem Submodels.)The coupler submodel described here was used to simulate an actual impactbetween two loaded 70-ton cars at ~6 mph. The calculated results are24

presented in Figures 6 and 7 as coupler force as a function of ~ime duringimpact. Results from the impact test, as reported by Baillie,( ) are alsopresented in Figures 6 and 7 for comparison.The results obtained from the model agreed reasonably well with the actualresults for the periods when the draft gears were "active", but deviatedconsiderably for the p~riod when the draft gears became "solid" after bottomingout. Roggeveen l5 ) simulated the same test using an analogue computerand obtained the same general trend of results. He concluded that thelower peak force during the actual test could be attributed to energy dissipationdue to lading slip or cargo shift, and developed a model thatdivided the masses of each car into two masses, one for the car and one forthe lading. This "two lump" approach of Roggeveen's was not used. In itsplace, an approach was used in which car-to-car characterization functionswere developed to characterize the behavior of rail cars and their draftgears during the "solid" state of the draft gears. The "solid" state of adraft gear refers to that state after bottoming out when the draft gearbehaves as a solid beam. This is in contrast to the draft gear's "active"state which is the normal condition before the draft gear spring has reachedits limit of travel. A characterization function defines a pseudo springconstant or resistance function for the draft gear for its "solid" state,which accounts for dissipation of a portion of the total kinetic energy ofthe system due to cargo shifting and/or deformation of the cargo or rail carduring this state. The spring constant defined is unique in that itincreases gradually at first while the cargo shifts or deforms easily, butthen rises sharply as the cargo compresses or stiffens. An upper limit isimposed on the spring constant during compression which represents near totalcompaction of the cargo. Energy dissipation due to crushing and deformationof the cargo during the "solid" state is simulated by removing a large fractionof the potential energy stored in the spring before the draft gearrebounds or recovers at zero relative kinetic energy of the two coupled cars.A car-to-car characterization function was first developed for CARDT andthen expanded and installed in CARDS. This function was developed to avoidhaving to model each car in a train in detail.The first step in the development of a car-to-car characterization functionwas linked to the development and application of a model validation algorithumbased on Theil's inequality coefficients. (See Section 4.0, MODELVALIDATION). A Theil's inequality coefficient (TIC) is a figure of meritcomputed from comparisions of predicted and measured time-varying (series)values of a response variable. A TIC ranges in value from 0 (indicatingequality or perfect agreement) to 1 (indicating maximum inequality orpoorest agreement).Simulation runs were made to define a spring constant for a draft gear inits "solid" state. This spring constant was developed by varying certainparameters and conditions to minimize a Theil's inequality coefficient forcomparision of calculated and measured time-varying values of coupler force.The system simulated was the impact test wh~r~ two gravel-filled 70-tonhopper cards collided at ~6 miles per hour.l 4 ) The simulation runs were25

ased on "solid" draft gear spring constants that were allowed to vary asfunctions of the relative displacement(79)beyond the maximum value of Xl for the Ilactive" state. The spring constantsincreased in magnitude as XT increased beyond this "active" limit.The spring constants were expressed as the products of pre-selected basevalues and a multiplying factor that varied as a function of XT beyond itsactive limit, as shown in Equations (80) and (81), and conditions (82).k SDGl= kSDG10 ~(XT)(80)k SDG2= kSDG20 ~(XT) (81)where:kSDG10' kSDG20~(XT)= base spring constants corresponding to krespectively [lb(force)/in.]SDGl= a multiplying factor, whereand k SDG2'~(XT) = 1.0, when X T = 5.6 in. }~(XT)> 1.0, when Xl > 5.6 in.(82)The lower limit on the base "solid" state spring constants was set at thevalue of the "active'" state spring constant. The lower limit on the multiplyingfactor was 1.0, and the upper limit was an extrapolation from anarbitrary upper value of 6.35 in. set for XT.The time-varying coupler force, calculated using Equations (80) and (81), wascompared with Baillie's data in Figure 8. The calculated coupler force vstime curve had the characteristic shape of the experimental curve, but bothits magnitude and duration were substantially larger than those of theexperimental curve. It was determined that, if the "solid" draft gear springconstants were bounded at some upper value less than that reached at zerorelative velocity (i.e., dXT/dt = a), the peak coupler force would bereduced, but the duration would be increased. It was further determinedthat the duration could then be reduced by extracting a suitable fraction of26

the potential energy stored in the springs. To accomplish these two effects,Equations (80) and (81), and conditions (82), were modified as follows:.= kSOG10,(XT)[1 + ~XTsgn(XT)] (83)k SDGl.k SDG2= kSDG20,(XT)[1 + ~XTsgn(XT)J(84)and,(XT) = ,( X T)Lwhen X T~ 5.6 in.,( XT) = ,( XT) when 5.6 < X T< 6.35(85),( XT) = ,(XT)U when XT~6.35 in.where:~Xl= A multiplying factor representing the extent of energydissipation (0 ~ ~XT ~ 1).When the draft gears bottom out and enter their "solid" state, the relativedisplacement XT no longer represents the travel of the combined draftgears. The terms XRc and XF are the horizontal displacements of thecenters of gravit~ (cg) of the hammer car and anvil car, respectively.Ouring the "solid" state of the draft gears, the cargo shifts or displaces,causing a shift or change in these displacements even though the actualtravel of the draft gears during this period may be very slight. Consequently,the coupler force between the cars becomes a function of theresistance of the cargo to shift or deformation. A load-deflection curvefor the cargo during this period would be based on cargo displacement relativeto that of the rail car (i.e., displacement of the cg) and wouldproduce a pseudo spring constant with the characteristics of the "solid"draft gear spring constants described in the previous paragraph. It isassumed that no cargo shifting or deformation occurs during the "active"state of the draft gears. This pseudo spring constant or "solid" draft gearspring constant also contains a term that accounts for the dissipation of alarge portion of the energy required to shift or deform the cargo. Normally,a spring would restore to the system its energy of compression. In cargoshifting and deformation, energy is dissipated due to friction and due topermanent deformation of the cargo. Therefore, in the model, when the cargois no longer compelled to move in the direction of greater compaction, theenergy storeo in the spring is discarded from the system by a substantialreduction in the spring constant for the recovery phase. This is accomplishedby adjusting the parameter ~XT. During the compaction or shifting27

of the cargo, when the relative velocity XT is positive, ~XT is set at uor some small fraction. At the end of compaction, when the spring wouldnormally restore the energy of compaction to the system and when XT isnegative, ~XT is set at some large fraction. ~XT is defined by~XT= ~XTC.when X T> a (Compaction)(86)when ~ a (Recovery)~XT = X~XTE Twhere:~XTC~XTE= An energy dissipation coefficient for cargo compaction= An energy dissipation coefficient for the cargo recovery phaseThe equivalent spring constants of the draft gears in both their "active" and"solid" states may be summarized by restating Equation (75) and combiningEquations (76), (83) and (84) to give.k FDG= k 2[1 + Uosgn(X T)](75)for the lI active ll state, andk RCDG = kSDG10(XT) [1k FDG = kSDG20(XT) [1.+ UXTsgn(XT)J.+ UXTsgn(XT)]for the II so 1id ll state.28

Using the above expressions for the spring constants of the draft gears inthe CARDT model. additional runs were made to simulate the 6 mph impact·between the two gravel-loaded 70-ton hopper cars discussed earlier. Duringthese runs. values of the parameters kSDG10. kSDG20. ~(XT). ~XTC and~XTE were adjusted to obtain a coupler force vs time curve that comparedreasonably well with the actual data reported by Baillie(4) for thisexperiment. Final values of these and other pertinent parameters are summarizedin Table 1. The parameter ~(Xl) is presented in Figure 9. Resultsof these simulation runs are compared with experimental results in Figures 10through 13. Coupler forces. relative displacements of the centers of gravityof the cars. relative velocities and relative accelerations are compared inFigures 10. 11. 12 and 13. respectively. GOOd comparisons were obtained upto ~0.076 second after impact. Beyond this time the response variablesdeviate as shown. indicating that further adjustments in the parameters arerequired. The experimental coupler force peaks at about 0.07 second whilethe calculated force peaks at ~0.085 second. The calculated coupler forceas a function of calculated relative displacement is presented in Figure 14.This load-deflection curve for the single equivalent spring separating therail cars encompasses both the "active" and "solid" states of the draftgears. The shape of th~ cyclic cur~;)of Figure 14 is not unlike the curvespresented by Kasbekar(6) and Scales\ for standard draft gears.It was noted that a lower value of the spring constant for the "solid" draftgear lowers the peak coupler force and increases its duration (i.e •• broadensthe peak). while a higher spring constant increases the peak force anddecreases the duration. Tile calculated coupler force curve may be "shaped"to approach that of the experimental curve by the judicious adjustmentof the parameters kSDG10. kSDG20. ~(XT). ~XTC and ~XTE. The firstthree parameters tend to raise and lower the peak force with a corresponaingnarrowing and broadening of its duration. The last two parameters.when used with the sign function sgn(XT). cause the coupler force to dropto a level consistent with the dissipation of energy due to cargo shiftingand deformation. The width of the pulse then depends upon the time at whichXT goes negative.After a careful study of the differences between the calculated and measuredvalues of coupler force. relative displacement. relative velocity. and relativeacceleration compared in Figures 10. 11. 12 and 13. respectively. it wasdeterminea that two adjustments were necessary to obtain better agreement.The first adjustment made was to the energy dissipation coefficient. ~XTE.~XTE was changed from a value of 0.9 to 0.95 (~ee 1able 1). This drops thecoupler force to a lower value after the veloclty XT goes negative (cargorecovery phase).The second adjustment made was in the argument of the sign functions inEquations (87) and to the control variable for Equatio~s (86). As statedearlier. the width of the coupler force pulse depends upon the time at whichXl goes negative. The velocity XT cannot be altered since it is determinedfrom the equations of motion of the system; however. the argument of29

the sign functions and the control variable for Equation (86) can be redefinedto produce the desired results. For this purpose, an "adjusted"relative velocity of displacement or travel of the centers of gravity ofthe two rail cars, XTA, was used and Equations (87) and (86) changed to.k RCDG = kSDG10cP(XT) [1 + IJXT sgn(X TA )](88).or= kSDG20cP(XT) [1 + IJXTsgn(XTA)]k FDGandwhenX TA> 0 (Compaction)(89)when X TA~ 0 (Recovery)where:.XTA = Adjusted relative velocity of displacement or travel ofthe cgs of the two rail cars (in./s)The adjusted relative velocity is defined as(90)or(91)where:An adjustment factor or relative velocity to regulatethe relative velocity XT (in./s)The function of ~LA is to make the argume~t and control variable, XTA, gonegative before XT. A constant value of XLA wou}d give a time plot of ~TAsimilar to that shown in Figure 15. Therefore, XLA becomes an additionalcontrol variable that can be used to vary the size of the pulse of thecoupler force.curve by "shaving" slices from its back side. Increasing themagnitude of XLA would result in larger slices being removed from the pulse.A negative value of ~A would add slices to the pulse.30

. .The adjusted relative velocities, XTA and XLA, may be related to the velocitiesof the rail cars (not the cgls) and the velocities of the cargos on therail cars, respectively, as follows. The velocity of the cg of the hammercar is defined as(92)and the velocity of tIle center of gravity of the anvi 1 car as(93)where:MFMRC= Mass of the anvi 1 car (M)= Mass of the hammer car (M)MLF = Mass of the lading or cargo on the anvi 1 car (M)MLRC = Mass of the lading or cargo on the hammercar (M)XRC = Velocity of the cg of the hammer car and its cargo (LIe)XF = Velocity of the cg of the anvil car and its cargo (Lie)XCRC = Velbcity of the cg of the empty hammer car (Lie).XCF = Velocity 0: the cg of the empty anvi 1 car (Lie)MrF = Total mass of the anvil car and its cargo (M)(94)MTRC = Total mass of the hammer car and its cargo (M)= t-Rc + ttRC (95)31

The relative velocity of displacement or travel of the centers of gravity ofthe two loaded rail cars is defined by(96)Substitution from Equations (92) and (93) into Equation (96) gives(97)Replacing XTin Equation (91) with the above gives(98)Assuming that XLA may be expressed in terms of the velocities of thecargos and their mass fractions as(99)Then Equation (98) may be rewritten as(100)or( 101)32

Equation (101) states that the adjusted relative velocity of the centers ofgravity of the two rail cars is equal to the difference between the productsof the mass fractions of the cars and their absolute velocities, if theadjustment factor or relative velocity ~I A is defined as the differencebetween the products of the mass fractions of the cargos and their absolutevelocities. The velocity ~LA may be considered to be the adjusted relativevelocity of the cargos on the two rail cars.The expressions for the spring constants of the draft gears in the CARDTmodel were replaced by Equations (88) and (89), and the simulation of the6 mph impact between the two gravel-loaded 70~ton hopper cars was repeated.A constant value of 30 in./s was assumed for XLA. Results of this simulationrun are compared with the results reported by Baillie(4) in Figures 16through 19.Coupler forces, relative displacements of the centers of gravity of the cars,relative velocities and relative accelerations as functions of time are comparedin Figures 16, 17, 18 and 19, respectively. The calculated couplerforce as a function of calculated relative displacement is presented inFigure 20, and the experimental coupler force as a function of the experimentalrelative displacement is presented in Figure 21. The comparisonsbetween the calculated and experimental response variables show some improvementover those shown in Figures 10 through 13. The "goodness" of the comparisonshas been expressed in terms of Theil's inequality coefficients foreach response variable and Theil's multiple inequality coefficient for thesimultaneous comparison of all the response variables (see Section 4, MODELVALIDATION) •The CARDS model was modified to include equations equivalent to Equations(75), (88) and (89), and the function presented in Figure 9. Sets ofequations were written to represent the linkage between the cask-rail car(hammer car) and the first ballast-filled anvil car, and the linkages betweenthe remaining three ballast-filled anvil cars. However, an additional controlvariable was required since the cargo of the cask-rail car (the cask)is considered as a separate mass with its own equations of motion. Also,the trucks on the rail car are considered as separate masses with their ownequations of'motion. Consequently since the character of the cask-rail caris known and modeled accordingly, that portion of the car characterizationfunction for the hammer car-anvil car linkage need not include the effectsof cargo compaction and energy dissipation. To accomplish this, the controlvariable ReOR was introduced to provide control over the draft gear springconstant during the "so lid" state. RCOR was added as a restriction onEquation set (88) as follows:k FDG.= kSOG20~(XT) [1 + ~XTsgn(XTA)J(102 )33

whenX T.s. X TLor X T~ X TUandRCOR = 0andk RCDGk FDG= kSDG10= kSDG20ct> (XT )[1.+ ).I XTsgn(X T A)]}(103)whenXT .s. XTL or XT ~ XTUandRCOR =where:RCOR = cask-rail car override variable, with the control functinnReOR = 1.0, to override rail car characterization functionRCOR = 0, to activate rail car characterization functionRCOR is a control variable that is set at 1 since the cargo on the cask-railcar (the cask) is considered as a separate mass with its own equations ofmotion. The adjustment factor XLA is an input parameter. Similar equationsand conditions were defined for the linkages between the other anvilcars in the train; however, the control variables equivalent to RCOR wereset equal to O.34

When the cask-rail car strikes one or more anvil cars, it will tend to rotateabouts its center of gravity such that the striking or front end will tendto move downward and the far or rear end will move upward. This rotationalor pitching motion is opposed by the damping in the suspension subsystems,and by frictional damping due to the vertical sliding motion of the couplerface on the cask-rail car against the coupler face on the adjacent anvil car.The frictional force at the coupler faces is represented as a vertical dashpotin Figure 22.The energy dissipated as frictional work at the coupler faces was defined as(104 )where:WCRF= Energy dissipated as frictional work, [lb(force)-in.]FYRF = Frictional force opposing movement of sliding couplerfaces [lb(force)]YCPL = Vertical displacement of coupler face on cask-rail car,(in. )The frictional force FYRF was defined by the expression( 105)where:IFCPL I = Absolute value of force applied to coupler facesperpendicular to the sliding surfaces [lb(force)].YCPL = Vertical velocity of coupler face on cask-rail car (in./s)(Coupler on anvil car is assumed to be stationary.)A multiplying factor representing the fraction of F CPL6CPL = actually applied to the moving coupler facesUCoefficient of friction for the sliding of the two couplerCPL = faces against each othersgn(YCPL) = Signum function or sign function of YCPLa.CPL = A factor to allow the damping term to vary as a functionof the absolute value of FCPL raised to the factor power35

The force applied to the coupler, FCPL, is the coupler force, i.e.,FCPL = kSCARS (~C- XF)(106)where:kSCARS = Spring constant of an equivalent single spring representingthe draft gears on cask-rail car and first anvilcar [lb(force)/in.]~C = Horizontal displacement of cask-rail car (in.)XF= Horizontal displacement of first anvil car (in.)The equivalent spring constant, kSCARS' is actually kT, the spring constantdefined by Equation (64) as a function of the equivalent spring constantsrepresenting the draft gears on each car.By combining Equations (104) and (105), the energy dissipated as work may beexpressed as(107)orwhere:(108 )YRC= Vertical displacement of the cg of the cask-rail car (in.)eRC = Angle of rotation of the XRC and YRC axes about anaxis perpendicular to the XRC - YRC plane through the cgof the rail car (rad)= Horizontal distance from vertical centerline of cask-railcar to coupler face (in.)Differentiating Equation (108) with respect to each of the generalized coordinatesof the system yields36

(109 )and(110 )These terms were included as energy dissipation terms in those equations ofmotion of the system that define the vertical and angular accelerations,YRC and eRC, respectively. Although the coupler force, FCPL, is a functionof XRC and XF, similar dissipation terms were not derived from Equation (108)for these coordinates since it was felt that an energy dissipation term forvertical motion in the equations of motion defining the horizontal accelerationsdid not seem appropriate. However, since the existence of these dissipationterms is indicated by the use of the energy method, further studyshould be made to determine if these terms are significant.1. 1.2 Suspensio~ Subsystem Submode1The rail car suspension subsystem is important since it controls thevertical and rotational movement of the car during and after impact. Likethe coupler subsystem, suspension subsystems consist of springs and damp~r~in parallel, as i11u~trated in Figure 22. In a Barber stabilized truck,(3)the stabilizing or damping friction force is proportional to the load on thetruck. Therefore, the spring constants for the equivalent springs shown inFigure 22 are defined by equations similar to those for the draft gears,i .e. ,Y RC56> YRCMAX (111)or ~ YRCMAX (112)Y RC56and Y RC78 > YRCMAX (113)or ~ YRCMAX (114)Y RC7837

where:u 6'u = Factors that allow the damping term to vary as a function of7the absolute value of the velocity raised to the factor power= Spring constants for the equivalent springs representingthe rear and front suspensions, respectively [lb(force)/in.]= Spring constants of the combined springs in the rear andfront suspensions, respectively, in their "active" state[lb(force)/in.]= Spring constants of the combined springs in the rear andfront suspensions, respectively, in their "solid" state,i.e., after they have bottomed out [lb(force)/in.]= Vertical displacement velocities of the rail car at the rearand front suspensions, respectively (in./s)YRCMAX = Maximum downward vertical displacement of the rail car (thepoint at which the suspension springs bottom out or go"solid") (in.)YRC56' YRC78 = Vertical displacements of the rail car at the rear and frontsuspensions, respectively (in.)8 6 ,8 7= Multiplying factors corresponding to coefficients of frictionfor the dampers in the rear and front suspensions, respectively= Multiplying factors representing the fraction of the load onthe respective suspensions that is applied perpendicular tothe sliding surfaces of the damper. .sgn(YRC56), sgn(YRC78) = ?ignum functions,or sign functions of YRC56 andYRC78' respectively.The signum function is defined as follows for an argument YY > 0.sgn( Y) = Y = 0 ( 115)Y < 038

Equations (111) and (113) differ from those of the draft gears in two ways.First, the sign of the second term is opposite to that of the draft gearequations. This is necessary since the sign convention used for the modelis positive horizontal displacement to the right and positive verticaldisplacement upward. With this convent-ion, the velocity of the verticaldisplacement is negative downward in the direction of the load compressingthe suspension subsystem. A negative value of this velocity in Equations(111) and (113) will result in the addition of the terms in the brackets.The net result is that the equivalent springs for the suspension subsystemswill be stiffer during compression than during relaxation or lifting. Thesecond way in which Equations (111) and (113) differ from those of the draftgears is due to the multiplying factors 66 and 67. These factors are relatedto the action of the so-called "side springs" that apply the force perpendicularto the sliding surfaces of the damping device. These factors representfractions of the force on the respective suspension subsystems whichare actually applied to the sliding surfaces for damping. The action of thevelocity terms in Equations (111) and (113) is to augment the friction factors~D6 and ~D7. They act in conjunc~ion with the load fractions 66 and67 and the friction factors to regulate the amount of energy lost due to theforces exerted on the friction surfaces by the side springs. The absolutevalue of the velocity multiplied by a sign function with the velocity as theargument is equivalent to the vertical velocity; therefore, the second termin Equations (111) and (113) is equivalent to a viscous damping term. However,due to the presence of the factors a6 and a7, greater latitude thaneither pure viscous or pure frictional damping is possible.1. 1.3 Pitching Moment Caused by the Offset of the Coupler and the Centerof Gravity of the Rail CarThe CARDS model contains a term representing the pitching moment caused bythe offset of the coupler and the center of gravity of the rail car. Thisterm is part of the equation of motion defining the angle of rotation of thecar.Figure 23 is a simplified sketch of the rail car portion of the CARDS modelthat shows how the rotation of the rail car about a lateral axis passingthrough its center of gravity is enhanced by the moment of the coupler forceabout the axis. The moment about the center of gravity is~CCG= ZCDGDUSCAR ( 116)where:ZCDG = Vertical distance between the line of force and the cgof the rail car (in.)DUSCAR = Coupler force [lb(force)]39

The coupler force is defined by( 117)The vertical distance, ZCDG' is defined by( 118)where:ZCDGO = Distance between the centerline of the draft gear and thec9 of the cask-rail car (in.)9. CPLe RC= Horizontal distance from the vertical centerline of thecask-rail car to the coupler face (in.)= Angle of rotation of the cask-rail car about the lateralaxis through its cg (rad)The pitching moment, MRCCG, was added to the equation of motion that definesthe angle of rotation of the cask-rail car, i.e.,(119 )where:DUSi= i-th force on the rail car [lb(force)]9.i = Distance from the rail car cg to the line of the appliedi-th force (in.)1.1.4 Cask-Rail Car Bending SubmodelThe CARDS model contains a submodel to simulate bending of the cask-rail car(hammer car); however, although a spring arrangement to represent bending ofthe car was developed and incorporated into the model, it has never been40

used or tested. At present, the bending submodel is isolated from the restof the model by the use of switching functions that are in the deactivatemode.The bending submodel remains isolated since time did not permit a study ofsome potential problems affecting superposition. The system of equationsthat define the present rail car model is based on the rotation (front toback pitching) of a rigid, nonbending rail car. The displacement at allsupport points on the rail car (cask to rail car and rail car to trucks) arefunctions of the vertical displacement of the center of mass of the railcar, angle of rotation, and a constant (nonbending) distance from the centerof mass to the support points. When bending of the rail car occurs, thecenter of mass and, therefore, the vertical displacement are no longerlocated on a straight line and can no longer be related to the support pointssimply as a function of the distance and angle of rotation. If the incrementof displacement due to bending is small, the present bending submodel may beused with little error. If the effect of bending is large, modificationswill be necessary to assure that the displacements of the support points arecorrectly represented.It was felt from the start that bending of the cask-rail car would be slightand that the effect on system response would be small. Subsequent comparisonsof measured and calculated response variables have tended to re-enforcethis belief. However, a bending submodel was developed and, although it hasnever been usea or tested, the approach to its development is presented herefor the recoro.The approach used is based on the representation of a beam with lumped massesas a far-coupled spring-mass system.~8) The proper spring arrangement torepresent bending of the rail car was established by considering the railcar as a beam, and defining a stiffness coefficient kij to be a forceapplied at point j to produce a deflection equal to unlty in the directionof the force, while point i is restrained against translation (zero deflectionat i). The coefficients kij represent a force system that is capableof translating point j a unit amount while preventing the translation ofpoint i. For example, in Figure 24, application of the force kll at position1 to give a deflection Yl = 1, while preventing translation or deflectionsat the other load positions, causes the reactions kRl' k31' k21, andkFl at the rear support R, positions 3 and 2, and the front support F,respectively. Similar application of forces k33 and k22 yields the reactionsshown. Because of Maxwell's reciprocal lawand(120)( 121)Relating the mass or load positions to the reactions, the bending submodelof the beam (rail car) may be represented by the far-coupled spring-mass41

system shown in Figure 25(a). If the front and rear supports are mounted onsprings (suspension system), the bending submodel is represented by thespring-mass arrangement of Figure 25(b).The stiffness coefficients or spring constants, kij, for the bendingsubmodel are obtained from a determination of fleXlbility influence coefficients.The influence coefficients are determined, as shown in Figure 26,by placing a unit load at one load position at a time (positions 1, 2 and 3in Figure 26) and making use of the area-moment method to determine thedeflections 0i". These deflections are superimposed and then combinedwith the actua1 loads (F i ) at the positions to obtain the total deflections(122 )(123)and(124)When this system of equations is solved for the loads, three equations ofmotion are obtained. The coefficients of Yl, Y2 and Y3 in these equationsof motion are combinations of the 0ij, and can be shown to be equal to theappropriate kij. Equations for the Dij and the kij, in terms of the locationsof the support points and other rail car parameters, have been programmedinto the model.The springs representing bending have been incorporated into the cask-railcar model, as shown in Figure 27.Modeling the Anvil TrainOuring humping operations, the cask-rail car may impact "n" loaded carsmaking up a train. The CARDS model consists of the cask-rail car (hammercar) and four "anvil" cars in an "anvil train" as shown in Figures 28 and 29.Although any number of anvil cars may be considered in the anvil train, onlyfour are in the model at present to be consistent with the make-up of thetrain used in the humping tests conducted at the Savannah River Laboratoriesfrom June 8, 1978 to August 3, 1978.The model of the anvil train consists of the four masses, MF, MF2, MF3 andMF4' each representing a single loaded car and each separated from theother by a coupler. The equations of motion for the four anvil cars are:42

.MFX F= kSCARS(XRC - X F ) - k FF2 (X F - X F2 ) - ~FWFsgn(XF) . BRKIRC (125).M = kF2F3(XF2 - - kF3F4(XF3 - - ~F3W3sgn(XF3) . BRKF3 (127)F3 X F3 X F3 ) X F4 ).M = kF3F4(XF3 - - kF4W4sgn(XF4) . BRKF4 (128)F4 X F4 X F4 )The terms in Equations (125) through (128) are defined as follows:M F, M M F3and ~4F2 ,= Masses of anvil cars 1 through 4,respectivelyBRKIRC, BRKF2, BRKF3 and BRKF4 = Brake switches for anvil cars 1 through 4,respectively. (Brakes are on and lockedwhen equal to 1 and off when equal to 0.)= Spring constants of equivalent springsrepresenting the draft gear combinationsbetween cars [lb(force)/in.JX F, X X F3and X =F2 ,F4Horizontal displacement of anvil cars1 through 4, respectively (in.)W F, W W F3and W =F2 ,F4Weights of loaded anvil cars 1 through 4,respectively [lb(force)J~F' ~F2' ~F3 and ~F4 = Coefficients of friction for sliding contactbetween the tracks and the wheels ofanvil cars 1 through 4, respectivelyThe size of the anvil train may be increased by adding additional equationsbetween the equations for the first anvil car [Equation (125)J and the lastanvil car [Equation (128)J. Also, appropriate auxiliary equations for thespring constants, etc. must be added to the model. The size of the anviltrain may be easily varied by using switches as multipliers of the springconstants of the equivalent springs representing the couplers separating thecars. Cars may be switched into or out of the train, as desired, by simplysetting these switches either to 1 or to 0, respectively.43

Some results of a simulation of Test 3 of the humping tests at Savannah RiverLaboratories are presented in Figures 30 and 31 to illustrate how the shockof impact is propagated through the train. The coupler force between carsas a function of time after impact is presented in Figure 30, and Figure 31shows the corresponding horizontal displacements or travel of each car alongthe track. Rebounding and multiple collisions of the cars in the train, withenergy dissipation, are illustrated in these two figures. Figure 30 showsfour force peaks in rapid succession initially, due to successive bottomingof the draft gears at impact. Friction in the draft gears and at the slidingcontacts between the wheels and the track continually dissipates the energyin the system, resulting in a weakening of the force peaks after the firstcycle. Some rebounding of the cars due to release of potential energy storedin the draft gears appears to occur during the first cycle, which accountsfor the dips in the displacement curves in Figure 31. The dip in the displacementcurve for the hammer car is more prominent than those for the othercars because it was the only car that did not have its brakes on and locked.This simulation of Test 3 was conducted prior to final validation of thecask-rail car portion of the CARDS model. The validation was carried outusing the coupler forces recorded during each of the tests as the shockforces causing vibration of the respective systems. (See Section 4.0,MODEL VALIUATION.) Time did not permit a repetition of this simulationafter validation in which the coupler force for Test 3 would be calculatedalong with other variables that describe the response of both the cask-railcar and the anvil train.1.2 CASK-RAIL CAR RESPONSE SPECTRUM GENERATOR (CARRS)Equations of motion were derived for equivalent single degree-of-freedom(l-DOF) representations of the relative horizontal, vertical and rotationalmotion between a radioactive material shipping package and its rail car(support). These equations of motion (EOMs) were used to construct CARRS(Cask Rail Car Response Spectrum Generator), a model to generate frequencyresponse spectra using calculated results obtained from the CARDS (Cask RailCar Qynamic ~imulator) model. -- Response spectra for the cask-rail car system are obtained by converting thecoupled EOMs for the cask in the CARDS model into EOMs for equivalent independentl-DOF systems. The pro~edure for making this conversion is patternedafter that of Harris and Crede.l 9) Equivalent independent l-DOF equationsdescribing the relative horizontal, vertical and rotational motion betweenthe cask and rail car will now be derived using this procedure.In the CARDS model, the equation of motion for vertical motion of the caskis expressed asMY = - DUS2 - DUS3 + DWS2 + DWS3 (129)p p44

where:DUS2 = -k S2[(Y RC + 1 - (Y p + 1 SCR S RC ) pR p)J (130)DUS3 = -k S3[(Y RC- - (Y p - )J ( 131 )1 CF S RC ) 1 pF S p· . . .DWS2 = C S2[(Y RC + 1 - (Y p + 1pRS CR s RC ) p)J (132 )· .DWS3 = C S3[(Y RC- - (Y p - )J (133 )1 CF s RC ) 1 pF S pA sketch of the spring-mass model of the cask-rail car system is shown inFigure 2. A nomenclature of terms used in all the equations is presentedin Appendix 1. Combining Equations (129) through (133) gives.- (Y p - 1pF S p )J + C S2 [(Y RC· . .+ C S3[(Y RC- 1CF S RC ) - (Y p.+ 1CR s RC ) -.- 1pF S p )J.(Y p +.1pR S p )J (28)Let the relative vertical displacement be defined as(134 )The relative vertical velocity and acceleration are( 135)and( 136)Substituting from Equations (134) through (136) into Equation (28) andrearranging gives45

. . . . . .+ - )J + - - i pF 6p)J (137)C S2[Y d+ (i CR6 RCi pR 6 p C S3[Y d(i CF6 RCFurther rearrangement of Equation (137) yields an EOM in terms of the relativedisplacement Yd..MpY d+ (k S2+ k S3)Y d+ (C S2+ C S3)Y d= MpY RC+ (k S3i CF- kS2iCR)6RC+ (k S2 i pR - kS3ipF)6p.+ (C S2 i pR - CS3ipF)6p (138)The cask-rail car configuration used in Tests 1 and 4 conducted at theSavannah River Laboratories (SRL) is defined in Table 2 and Figure 32.Measurements before the tests show that, for this configuration, the cask isnot centered on the rail car (along its length) (see Figure 2), i.e.,However, the lengths ipR and ipF are equal. Using this information,Equation (138) may be rewritten as. ..MpY d+ (k S2+ k S3)Y d+ (C S2+ C S3 )Y d= MpY RC+ (k S3 i CF - kS2iCR)6RC+ (k S2 - kS3)ipR6p(140)46

If it is assumed thatandkS2 :: kS3CS2 :: CS3( 141 )(142 )then Equation (140) may be expressed as.. . ..MpY d + (k S2 + k S3 )Y d + (C S2 + C S3 )Y d :: MpY RC + kS2(~CF - ~CR)eRC + 0+ CS2(~CF - ~CR)eRC + 0.(143)Dividing Equation (143) by Mp and introducing the frequency(144)gi vesIf the cask had been mounted at the center of the rail car (i.e., if thecenter of gravity of the cask had been placed to coincide with that of therail car), then 1CF would have been equal to ~CR and Equation (145) would bereduced to(146 )Equation (146) is an EOM for an equivalent single-degree-of-freedom (l-DOF)representation of the cask-rail car system with support (rail car) motion Y RC .When ~CF :: ~CR, the EOM for vertical motion is uncoupled from that for rotationalmotion of the rail car. However, since the cask was not centered onthe rail car in Tests 1 through 4, Equation (145) must be used to determinethe response spectra for these tests.47

The CARDS model equation for horizontal motion of the cask isMpX p= -DUSl - DUS4 + DWSl + DWS4 + DWPl + DWP4 (147)where:DUSlDUS4DWSl =DWS4 =DWPl =DWP4= -kSl[(X RC + ZRC9RC)= -k S4 [(X RC + ZRC9RC). .CS1[(X RC + ZRC9RC). .C S4 [(X RC + ZRC9RC).-~PRWplsgn(Xp.= -~PRwp4sgn(Xp- (Xp - Zp9p)J(148)- (X p - Zp9p)J( 149).- (Xp - Zp9p)J (150). .- (Xp - Zp9p)J (151).- X RC ) (152 ).- X RC ) (153)Combining Equations (147) through (153) gives. . . .+ (C 51+ C S4 )[X RC+ ZRC9RC) - (Xp - Zp9p)J. .- ~PR(Wpl + W p4 )sgn(X p - X RC ) (154 )Let the relative horizontal displacement be defined as(155)The relative horizontal velocity and acceleration are then(156)48

and( 157)Substituting from Equations (156) through (157) into Equation (154) andrearranging gives. .MpX RC- MpX d= (k Sl+ K S4)X d+ (C Sl+ C S4)X d+ ~PR(Wpl + W p4 )sgn(X d). .+ (k S1+ k S4 )(ZRC SRC + ZpSp) + (C Sl+ CS4)(ZRCSRC + Zpsp) (158)Aaditional rearrangement of Equation (158) yields an EOMrelative displacement XdMpX d+ (k Sl + k S4 )X d + (C S1. .+ C S4)X d+ ~PR(Wpl + W p4 )sgn(X d)in terms of the. .- (C S1 + C S4 ) (ZRCSRC + ZpSp) (159)Uividing Equation (159) by Mp and introducing the frequency(160)gives( 161 )49

Now, ifZRC = Zp = 0 (see Figure 2) (162)that is, if the tiedown attachment points on the cask and rail car arelocated on horizontal lines through their respective cgls, then Equation (161)would reduce to(163)Equation (163) is an EOM for an equivalent l-DOF representation of the caskrai1 car system with support (rai 1 car) mot ion ;(RC' When both ZRC and Zp areequal to zero, the EOM for horizontal motion is uncoupled from those forrotational motion of the cask and rail car. Since part of the tiedown configurationfor the cask-rail car system used in the experiments is embodiedin the cask base, framework, chocks and horizontal load cells, it does notseem likely that ZRC and Zp are zero; therefore, Equation (161) probablyshould be used to determine the response spectra for horizontal motion.Under certain special conditions, and if(164)andZRC = Zp = 0 , (162)the vertical response spectra may be obtained from the solution of Equation(146) and the horizontal response spectra from Eqyption (Jp3). This isaccomplished by determining the support motions, YRC and XRC' either frommeasurements from experiments or from simulations using a model such asCARDS. If the support motions are in no way influenced by the packagemotion, as in the case of earthquake analysis where the groHnd motion is notsignlficantly influenced by structure motlon, then Y RC and XRC may be inputinput to Equabons (146) at:l.d (163)., respectlVely, and the equations solvedfor the maximum values of Yd and Xd at various values of the frequencieswx and wy. One plot of maximum response vs frequency is generated for eachlevel of damping defined by the last term on the left-hand side (LHS) ofEquation (146) and the last two terms on the LHS of Equation (163),respectively.50

For the cask-rail car configurations being considered, the support or railcar motion is strongly influenced by the motion of the cask. Results fromthe CARDS simulation of Test 3 will now be used to justify this statement.This simulation run produced results as functions of time which agreed verywell with experimental measurements, in terms of both shape and magnitude ofthe time plots. The equations in the CARDS model that define the verticalmotion of the cask and rail car areandMpY p = - DUS2 - DUS3 + DWS2 + DWS3 (129)MRCY RC= DUS2 + DUS3 - DUS6 - DUS7 - DWS2 - DWS3 - DWS6 - DWS7 + DWCRF (165)respectively.Combining Equations (129) and (165) givesMpY p - DUS6 - DUS7 - DWS6 - DWS7 + DWCRF (166 )where:( 167)DUS7 = k S7 (Y RC - iRCe RC ) (168). .DWS6 = C S6 (Y RC + iRCe RC ) (169). .DWS7 = C S7 (Y RC - iRCe RC ) (170)DWCRF = I IQCPL·-~CPLaCPL DUSCAR sgn(Y RC - iCPLeRC)DUSCAR = Coupler force.( 171)The terms DUS2, DUS3, DWS2 and DWS3 are defined by Equations (130) through(133), respectively.In the Test 3 simulation run, at the time when the vertical accelerationof the rail car (support) YRC is a maximum (0.116 s), these force termshave the numerical values shown in Table 3. Using these values in Equations(129) and (166) gives51

-DUS2 = -44754.6-DUS3 = 54094.7+DWS2 = 17889.5+DWS3 = 4904.6MpYp = 76285.6 = LF yp (172)and-M p yp = -76285.6-DUS6 = -74418.0-DUS7 = 51971.8-DWS6 = 0.0-DWS7 = 0.0+DWCRF = 0.0M = -98731.8 =RC Y RCLF yRC(173)It is clear that, if the force MpYp were not included in the summation ofEquation (173) (i.e., if the cask were cut loose or isolated from the railcar), the deceleration of MRCjthe rail car or support) would be substantiallyreduced. The force MpYp is the following fraction of the sum of theabsolute values of all the vertical forces acting on the rail car.IMpYp I 76285.6EJVertical Forces I = 202675.4 = 0.376(174)This shows that the vertical motion of the cask stron ly influences thevertical motion of the rail car support.The influence of the horizontal motion of the cask on the horizontal motionof the rail car may be determined in the same way. The equations in theCARDS model that define the horizontal motion of the cask and rail car areanaMpX p= - DUSl - DUS4 + DWSl + DWS4 + DWPl + DWP4 (147)MRC~C = DUSl + DUS4 - DUS5 - DUS8 - DUSCAR - DWSl - DWS4+ OWS5 + DWS8 - OWPl - DWPR (175)respectively.Combining Equations (147) and (175) gives52

where:MRC~C = - MpX p - DUS5 - DUS8 - DUSCAR + DWS5 + DWS8 (176)DUS5 = k S5 [(X RC - ZRC6RC) - XTRJ (177)DUS8 = k S8 [(X RC - ZRC6RC) - XTFJ (178). . .DWS5 = -C S5 [(X RC - ZRC6RC) - XTRJ (179). . .DWS8 = -C S8 [(X RC - ZRC6RC) - XTFJ (180)DUSCAR = kSCARS(XRC - X F ) (If ca~culated coupler (181)force 1S used.)= DUSX4 (If measured coupler force is used.) (182)The terms DUS1, DUS4, DWS1, DWS4, DWPl and DWP4 are defined by Equations(148) through (153), respectively.In the Test 3 simulation run, at the time when the horizontal accelerationof the rail car XRC is a maximum (0.057 s), these force terms have thevalues shown in Table 4. Using these values in Equations (147) and (176)gives-DUSl-DUS4+DWSl+DWS4+DWPl+DWP4MpX p=======-221589.00.0-57230.0-57230.0-23200.0-23200.0-382449.0 = EF Xp (183)and-MpXp-DUS5-DUS8===-DUSCAR =+DWS5 =+DWS8 =MRCX RC=382449.031802.731802.7-1160000.034563.834563.8-644818.0 = EF XRC(184)53

From this it appears that, if the force MpXp were removed from the summationof Equation (184) (i.e., if the cask were cut loose or isolated fromthe rail car), the deceleration of ~C .. (the rail car or support) would besubstantially increased. The force MpXp is the following fraction of thesum of the absolute values of all horizontal forces acting on the rail carIMpXpI _ 382449 = 0.233 ( 185)7E"IH~0-r7i~zon~ - 1644182This shows that the horizontal motion of the cask strongly influences thehorizontal motion of the rail car (support); however, since thrs-fraction issmaller than that of Equation (174), it appears that the cask affects thevertical motion of the support to a greater degree.To confirm this conclusion, the CARDS model was adjusted to disconnect allcomponents that tend to decrease the magnitude of the deceleration of therail car (i.e., the cask and trucks), and a simulation run was made todetermine the horizontal acceleration of the rail car. The experimentallymeasured coupler force was used in this simulation. The results of thissimulation are compared, in Figure 33, to the calculated and experimentalresults for the complete cask-rail car system. It is evident that the calculatedand experimental results for the full system compare well, but thedeceleration of the lIisolated ll rail car is substantially greater. Thedeceleration of the lIisolated ll car, as might be expected, follows the couplerforce curve. The experimental data used in this comparison contained highfrequency noise that had to be filtered out before comparisons could be made.Filtering of these high frequency noise (>100 Hz) components from the experimentaldata was accomplished using the Fast Fourier Transform (FFT) program.(See Section 4.0, MODEL VALIDATION.)Earlier in this section, EOMs were derived for l-DOF representations of thecask-rail car system for determination of the response spectra in terms ofthe relative motion between the cask and rail car in both the vertical andhorizontal directions. It was shown that, for special orientation of thecask on the rail car, the EOMs could be uncoupled from the rotational orpitching components of motion. Unfortunately, the cask-rail car configurationsused in the tests at SRL were not arranged to provide for thisuncoupling. Consequently, the EOMs that must be used to generate thedesired response spectra are Equation (145),(145 )for the relative vertical motion [or Equation (140) if kS2 f kS3J, andEquat i on (161)54

(161)for the relative horizontal motion. The uncoupled equivalent of Equation(145) is Equation (145) without the last two terms on the right hand·side (RHS) [see Equation (146)J. The uncoupled equivalent of Equation (161)is Equation (161) without the last two terms Dn its RHS [see Equation (163)J.How important are the rotational terms in Equations (145) and (161)? Toanswer this, the RHSs of each equation were evaluated using input data andresults from the same simulation run (using the CARDS model) from which theresults of Tables 3 and 4 were obtained. The RHS of Equation (145) may beexpressed as(186 )and that of Equation (161) asThe frequencies are defined byandw 2 (ky = S2+ k ) S3 (144)M p2(k + k Sl S4)Wx =M(160)pUsing the values given in Table 5,w2 -2y = 966.2 s-1W Y = 31.08 s55

andRHS(145) = -353.9 in./s 2 + 131.3 in./s 2 - 120.5 in./s 2= -353.9 in./s 2 + 10.8 in./s 2The last two terms of RHS(145) only contribute about 3% of the total.Similarly, using the values given in Table 6and2 -2Wx = 5072.5 s-1Wx = 71.22 sRHS(161) = -4180.5 1 . n. / s 2 110.9 in./s 2 - 47.9 in./s 2= -4180.5 in./s 2 158.8 1 . n. / s 2The last two terms of RHS(161) contribute about 4% of the total. Sincemaximum displacement occurs at zero velocity and maximum velocity occurs atzero displacement, the net magnitudes of the last two terms in the RHSs ofEquations (145) and (161) should remain nearly constant. Consequently, thepercentages of the contributions should increase as the magnitudes of thevertical and horizontal accelerations of the support decrease from theirmaximum values. At this time, it is not clear how the variation of therotational components would affect the values of Yd and Xd.The vertical motion of the cg of the rail car was never measured during theexperiments; however, measurements of the vertical acceleration were madefor the car structure at the struck end, far end, and above the truck centerat the struck end, using two piezoelectric (PE) accelerometers and onepiezoresistive (PR) accelerometer. Apparently the vertical rail car motionat these locations was at a frequency that was outside the range that couldbe recorded by a PE accelerometer, so the data recorded could not be used.However, piezoresistive accelerometers are capable of measurements at thesefrequencies. The only PR accelerometer was located on the car structure atthe struck end; however, the data recorded by this accelerometer was uselessdue to a considerable amount of noise that could, not be filtered out. Theoutput of this instrument was processed using the Fast Fourier Transform(FFT) program to filter out the high noise components, but to no avail. Itwas though~.that, if these data were judged to be valid, they might be usedto replace YRC in a modified version of Equation (186). To accomplishthis, the vertical displacement of the rail car at the struck end (seeFigures 2 through 4) is defined as56

(188)and the acceleration as(189 )Solving Equation (189) for YRC gives(190)Substitution from Equation (190) into Equation (186) givesRHS(145)Since the data from the PR accelerometer were not valid, then responsespectra could not be obtained from Equation (145), using the experimentallymeasured support motion V R C78. However, if th~se data had been valid andif the rotational terms are small compared to YRC78, then Equation (191)could have been reduced to the approximationRHS(145) = Y (192)RC78It was established earlier that the last two terms of RHS(145) [Equation(191)J are quite small, but from Table 5,J!.RC= 264 in.2eRC = -6.89 rad/sandY RC78= 1465.5 in./s 257

iRC~RC = (264)(-6.89) = -1819 in./s 2The magnitude of this product is larger than that of YRC7~herefore, ifa measured value of YRC78 had been used to generate the response spectra,it would have had to be accompanied by a measurement of aRC. No suchmeasurement was made, so Equation (192) still would not have been valid.The horizontal acceleration of the cg of the rail car also was not measuredduring the experiments, but measurements were made using both a PE and a PRaccelerometer at the struck end, and a PE accelerometer at the far end. Onlythe PE accelerometer at the struck end appears to have failed to provide gooddata. Since the data from the other two accelerometers appeared to be valid,they were used for XRc in Equation (187). The horizontal displacement ofthe rail car at the struck end is defined by(193)and the acceleration by(194)Solving Equation (194) for X RCgives(195)Substituting ~C from Equation (195) into Equation (187) gives(196)58

Earlier, it was determined that the last two terms of this equation are smallcomp.ftred to XRC. If it can be shown that t~e second term is small compaf.edto ~C78' then it would justify the use of ~C78 as an approximation of XRc.From Table 6, 2Rc = 18.0 inches. The output from the CARDS simulation ofTest 3 shows that the maximum value of aRC occurs at 0.104 second.At this time,., 2eRC = -11.4 rad/sandX RC= -2036 in./s 2ZRC6RC = (18)(-11.4)= -205.2 in./s 2Substituting these values into Equation (194) givesX = 2036 + 205.2RC78= -1830.8 in./s 2The second term is ~ll% of the absolute value of x RC78• If this percentageis deemed small enough then the measurements of X RC78may be used as anapproximation of XRC 'and Equation (196) may be reduced toRHS(161) = ~C78 (197)The horizontal displacement and acceleration of the far end of the rail carare defined by(198)59

and.. ..X RC56 = X RC ZRCeRC(199)respectively. Since the RHSs of these equati~ns are the same as those ofEquations (193) and (194), XRC56 is equal to XRC78 and the same conclusionsapply.Finally, to determine response spectra using Equations (145) and/or (161), aspecial compatibility condition must exist between the RHS and left handside (LHS) of each equation. This compatibility condition requires that ifthe RHS is determined at a particular frequency, then the relative responsemay be determined from the LHS only at that same frequency. In other words,the relative response cannot be determined from the LHS for various frequencieswhile using a RHS determined from a different frequency. This issupported by the previous discussion of the influence of the cask and truckson the rail car (support) motion. Changes in the tiedown spring constantschange the frequencies and the response of the rail car to cask motion.Isolation of the car from the cask and trucks may be accomplished by settingthe appropriate spring constants equal to zero. The effect of this isillustrated in Figure 33.The RHS forcing functions obtained from CARDS contain frequencies, orvariables that are contained in the frequencies, corresponding to the frequencieson the LHSs of the respective l-DOF EOMs. Therefore, when thefrequencies on the LHSs are set at successively different values and runsmade using the time-varying RHSs determined for a specific frequency, itwould seem that an incompatibility exists. However, if it is assumed that ashaker table in a vibration testing facility is given motion matching theappropriate RHS forcing function, then the response of a device described bythe respective l-DOF EOMs may be studied. The shaker table (support) wouldbe given time-varying accelerations or motions equal to the RHSs, i.e •where:..Y S= RHS(145) (200)..X = RHS(161) (201)sYS = Vertical acceleration of the support or shaker table (L/e 2)XS = Horizontal acceleration of the support or shaker table (L/e 2)60

Comparing Equations (186) and (200), YS may be expressed as2w YYS = YRC + -2-( R. CF (202)Similarly, comparison of Equations (187) and (201) yieldsSince kS2 might not be the same as kS3' and CS2 may be different than CS3' amore general equation of motion may be obtained from Equation (140), i.e.,(204)or(205)where, in this case,(C S3 R. CF - C S2 R. CR) • (C S2 - C S3 )(206)+ M pe RC + M pR.pRe p61

Assuming Xs and YS to be the motion of a support not influenced by the deviceattached to it, the response spectra of the device may be determined byvarying the frequencies on the LHSs of Equations (161) and (205).The experiments at SRL were run with two casks and four tiedown configurations(see Figure 32). Experiments or tests may be identified according toparticular combinations of these masses and "springs," and frequencies determined.The maximum relative responses may be determined from Equations (145)and (161) using these frequencies and the appropriate measurements availablefor their respective RHSs. These could then be compared to the correspondingcalculated maximum responses at the same frequencies, using calculatedresponse data for the RHSs of Equations (145) and (161).An equivalent independent l-DOF equation describing the relative rotationalmotion between the cask and rail car was also derived usTn9~same procedureused to get Equations (145) and (161). In the CARDS model, the equationof motion for rotational motion of the cask is expressed asI p 6 p = Zp(DUSl + DUS4 - DWSl - DWS4) - t pR (DUS2 - DWS2)+ t pF (DUS3 - DWS3) (207)The terms DUS1, OUS4, DWSl and OWS4 are defined by Equations (148) through(151), respectively, and the terms OUS2, OUS3, OWS2 and OWS3 are defined byEquations (130) through (133), respectively. Combining these Equations withEquation (207) givesI p6p = - Zp(k Sl+ k S4 )[(X RC+ ZRC6RC) - (X p - Zp6p)]+ kS21PR[(YRC + 1 CR 6 RC ) (Y p + 1 PR 6p)J- kS31PF[(YRC - t CF 6 RC ) - (Y p t pF 6p)]. . . .- Zp(C Sl+ C S4 )[(X RC+ ZRC6RC) - (X p - Z p 6 p )]. . . .+ CS2tpR[(YRC + t CR 6 RC ) - (Yp + t pR 6p)]- C S3 t pF [(YRC - tCF~RC) - (Y p - tpF~P)] (208)Let the relative horizontal displacement be defined as62(209)

The relative rotational velocity and acceleration are then(210 )and(211 )Combining Equations (208) through (211) gives, after muchfollowing EOM in terms of the relative displacement edalgebra,the(212)The frequency we is defined by(213)The term ~eis a damping coefficient defined as(214)The remalnlng term, $e' is a coupling term. It is expressed in terms of thecoordinates X~C' YRC' and eRC describing the motion of the rail car, and thetwo remaining coordlnates Xp and Yp describing the horizontal and verticalmotion of the cask. This coupling term is defined as63

+ kS2ipR[(YRC + iRCS RC ) - YpJ- kS3ipF[(YRC - iCFS RC ) - YpJ. . .- Zp(C Sl + C S4 )[(X RC + ZRCSRC) - XpJ. . .+ CS2ipR[(YRC + iCRS RC ) - YpJ. . .- CS3ipF[(YRC - iCFS RC ) - YpJ } / Ip (215)Equations (161)~ (204) and (212) are independent l-DOF EOMs with forcingfunctions defined by the right hand sides (RHSs) of the respective equations.As stated earlier~ if it is assumed that the RHS of each l-DOF EOM representsthe time-varying acceleration of a platform supporting a l-DOF device definedby the left hand side (LHS) of the respective EOM~ then the response of thedevice to various platform or support motions may be studied. The RHSs ofEquations (161) and (204) are defined by Equations (203) and (206)~ respectively.The RHS of Equation (212) is defined by(216)The l-DOF EOMs of the cask-rail car system may now be summarized as follows:(205)(217)and(218)where: as = Rotational acceleration of support or shaker table (1/9 2 )64

Assuming that the motion of a support is not influenced by the deviceattached to it, the response spectra of the device may be determined byvarying the frequencies on the LHSs of Equations (205), (217) and (218).Equations (205), (217) and (218) were used to construct the response spectrumgenerator model CARRS. The support accelerations, defined by Equations(203), (206) and (216), are determined as functions of time by theCARDS model during a simulation and are written on a file to be read laterby the CARRS model to generate the response spectra.Response spectra are generated by the CARRS model in the following manner.Time-varying support accelerations (the RHSs of the l-DOF EOMs in CARRS) areread from the file created by CARDS until arrays are filled. These arraysare then accessed at each time interval as the transient progresses. Acommon frequency is then set for the LHSs of the l-DOF EOMs. The supportaccelerations are then traversed over the complete transient and the relativehorizontal, vertical and rotational accelerations computed. The frequencyon the LHSs of the l-DOF EOMs is then set at a different value, the integratorsare re-initialized, and the transient traversed again to obtain newvalues of the relative accelerations. This procedure was repeated for frequenciesof 2, 5 and 10 through 260 rad/s in 10 rad/s increments. The entirefrequency range was covered, for a particular set of support accelerations,by successive CARRS runs chained together as one run. A set of maximum orpeak relative accelerations for each frequency was automatically determinedby CARRS. Response spectra were then obtained by plotting the absolutevalues of these maximum accelerations against the frequency.A listing of the CARRS model is presented in Appendix V.65

2.0 TEST DATA COLLECTION AND REDUCTIONShock and vibration data gathered from the cask-rail car humping tests conductedat the Savannah River Laboratories in July and August of 1978 werereduced and analyzed to be used for validation of the CARDS model.A summary of the configurations and conditions of these completed tests ispresented as Table 2. For convenience, this summary has been transformedinto a 4-dimensional morphological space as shown in Figure 32. The fourdimensions are rail car design, cask design, tiedown configuration and typeof coupler. Entries at each of these levels or dimensions are linkedtogether, if they are related, by lines representing the tests identified bytest numbers.To collect and reduce data for model validation, transducers sensitive toforce, displacement, and acceleration were mounted on the shipping container,tieaowns, and rail car in positions that corresponded to those in the analyticalmodel. Following data reduction, the empirical data, together with thecorresponding analytical data, were analyzed to allow modification and verificationof the model. A simplified flow diagram of the procedure from datacollection through model verification is shown in Figure 34.The locations, types, and ranges of selected transducers were based on preliminaryanalytical results. Since the dynamic model described in theprevious section simulates the longitudinal, vertical and rotational motionof the cask-rail car system, four additional data locations were required.These locations, on each set of trucks and on the car bed immediately abovethose trucks, were expected to produce accelerations in the ranges of +120 gand +150 g, respectively, within a frequency band of 3 to 1100 Hz. TheserequTrements fell within the scope of previously planned instrumentationsupport.The test plan specified 26 data channels plus a voice channel and timingchannel with a FM-multiplexed into two channels of information on the testvehicle. The two channels were transmitted via a radio frequency link to aSandia-supplied ground station, where they were recorded on both magnetictape and oscillograph.Oscillographic data give on-line quick-look data for test data verification.The magnetic tape recordings, because they represented the only reproducibleform of all the test data, were reproduced under laboratory conditions atSandia following the tests. Once copies of the original data tapes weremade, they were demodulated to their original analog form and remodulated andrecorded in a wide-band FM format compatible with equipment at the HanfordEngineering Development Laboratory (HEDL). Following this re-recording, thetapes containing all the experimental data and timing information were sentto HEDL for data reduction and analysis.67

Data reduction consisted of reducing all data channels, with the aid of theappropriate calibration information and timing tracks, to a set of timeamplitudedigital records of the experimental data. This step was performedon an existing Time-Data system, producing digital records compatible withDigital Equipment Corporation PDP-ll series computers.Digital data flowed between the Time-Data system and the existing PDP-ll/34for various forms of data analysis, and between the PDP-ll/34 and BoeingComputer Service's (BCS) Cyber 74 and Univac 1140/44 for model verification.Initial data reduction consisted of conventional normalization of data amplitudewith respect to calibration information. Digital and analog recordingsof the time domain record were prepared for comparison with the originalon-line oscilloyraphic recordings. Simultaneously, the power spectra ofeach information channel were generated.Data analysis and model verification, where practical, employed existingsoftware. Software systems available included:Time-Data:TSL (Time Series Language)software system.- Time-Data proprietary analysisPDP-ll/34:SPAkTA:SSP:RT-ll:R5X-llM:SPS-Basic (Scientific Programming System) - Tektronixoperating system with graphical as well as analysiscapabilities.DEC RT-ll buffer oriented interactive system.(Scientific Subroutine Package) DEC RT-llsubroutines.FortranDEC operating system; digital information transfer to BCS.DEC operating system; multi-user operating system forspecial verification and analysis software.These softwar'e systems, together with the communications 1ink to theanalytical model at BCS, processed the data to be used later for modelvalidation.Early in the study, it was decided to exercise the data reduction and modelverification techniques to be used. For this purpose, data were synthesizedemploying a preliminary version of the CARDS model. (See Section 1.0, MODELDEVELOPMENT, and Figures 2, 3 and 4.) Arbitrary values were used for someof the spring constants, damping factors, masses and dimensions. The model(shown in Figures 2, 3 and 4) produced instantaneous acceleration, velocityand displacement of three locations at O.Ol-s intervals for a total intervalof 2 seconds.68

The parameters employed in this exercise were:XRCYRC56YRC78DXRCDYRC56D2XRCD2YR56D2YR78- Horizontal displacement at center of rail car- Vertical displacement at rear of car above support(rear truck)- Vertical displacement at front of car above support(front truck)- Derivative of XRC, or velocity- Derivative of YRC56, or velocity- Second derivative of XRC, or acceleration- Second derivative of YRC56, or acceleration- Second derivative of YRC78, or accelerationImpact was assumed to be at the "front-end" of the car.Data obtained experimentally are generally acceleration, but by employing theproper boundary conditions to establish the constants of integration, boththe velocity and displacement data can be derived. Because of this, thedisplacement, velocity and acceleration data derived from the model areassumed equivalent to that obtained experimentally.Initially, the acceleration d~ta for the three positions were operated on byFast Fourier Transforms (FFT)\lO) producing the frequency domain equivalentof original time-domain data. The results of this process (shown in Figure35) are the same as those derived from a spectrum analyzer--powerspectral density.The inverse FFT, which transforms the frequency domain data to its timedomainequivalent, offers an ideal filtering ability. If the bandwidth ofthe information is reduced, the time-domain information is altered, as shownin Figure 36.The example given is where the vertical acceleration on the struck end(D2YR56) is limited to 75% and 50% of the total bandwidth of 50 Hz. Itshould be noted that, as the higher frequency information is deleted (as inthe 50% bandwidth case), the instantaneous peak acceleration value isaltered. This process, if improperly used, co~ld misrepresent theinstantaneous peak forces in a system. Similarly, if one were to attempt tofind similarities between filtered time-domain waveforms, the nature of thefiltering would have to be comparable.69

Discrete Fourier transform methods assume a repetitive function of timeconvolved with a rectangular window that covers the interval of the timedomainsample. The results of this assumption are both beneficial anddetrimental. The benefit is that a non-recurrent wave, such as the responseto impact may be objectively analyzed. The detriment is that an artifactleakage(lO)may occur if the time-domain constituents are not harmonicallyrelated to the sample window.A method of minimizing this "leakage" is to shape the time-domain informationwith a cosine or Hanning window, as illustrated in Figure 37. The Hanningweighting,A = 0.5(1 - 2nt/T) for t = 0 to T,while reducing the leakage, preserves the amplitude information in the frequencydomain. The amplitude of frequency domain parameters, when shapedwith the Hanning window, is scaled by 0.5 if the information is uniform inthe sample interval.The example shown in Figure 37 illustrates that the spectral information forboth the weighted and original data are similar, while their correspondingtime-domain representations are quite different.These simple exercises in data analysis illustrate some of the fundamentaltechniques used for the analysis of the experimental data and, ultimately,for model verification.Because of the restrictions of the data analysis techniques, it would be purechance that data generated analytically and that obtained experimentallywould be comparable in their time-domain form. The technique that wasinitially employed to reduce the experimental data is as follows:Digitize all acceleration information with attention given to a•consistent time scale with respect to impact•••Assure that the time sample t for each digital representation conformsto t < 1/2fh, where fh is the highest frequency of interestin the measurementScale the time-domain information with the Hanning windowRepeat the operation for data generated from the analytical modelOnce the power spectra are in the same form, the model's parameters may beadjusted to force agreement.70

Instrumentation configurations were developed to be compatible with the railcar-cask tiedown system being tested. The instruments, together with themechanical configuration they support, are illustrated in Figures 38 through41. A brief description of this instrumentation is given in Table 7. Theaata acquisition techniques described in the opening paragraphs of thissection were employed.As during the II pre liminary tests ll , high-speed photogrametric instrumentation(high-speed movies) recorded the coupling action of the rail car under test,as well as the interactions of the rail car, shipping cask, and the tiedownmechanism. In addition, still photographic records were made of the instrumentation,rail car, shipping cask, and tiedown assembly.During these impact tests, the velocity of the rail car under test wasaccurately measured just prior to impact. The technique employed was tobreak glass wands with a protrusion extending from the moving rail car.Since the wands were of known separation, the elapsed time between the rodsallowed accurate velocity measurements. These values agreed with those fromradar measurements.As expected, some data acquisition channels failed during tests. Also, someestimated peak amplitudes (used during calibration of the systems) were toolarge or too small producing either data that was on the same order of magnitudeas the background noise or was clipped off at the saturation level ofthe system. Although these problems voided the data on the affected channelsand reduced the amount and variety of data available for model validation,the model validation task was successfully completed. (See Section 4.0,MODEL VALIDATION.)A further shakedown of the data reduction methods used was undertaken byanalyzing representative data derived from Test 1, an 8.3 mph impact of a70-ton SCL (Seaboard Coastline) rail car with a standard coupler, a 40-tonshipping cask, and tiedown configuration IIA II . This configuration and thelocation of the instruments are shown in Figure 38.Initial analysis consisted of digitizing the analog ~ignals at 5.12 kHz*which, according to the Nyquist sampling theorem,(lO) will accuratelydefine and preserve frequencies up to 2.56 kHz. This is consistent with the2.5 kHz band width of information obtainable from the employed wide-band FManalog recordings made at 7-1/2 IPS (IRIG intermediate band). Further, themaximum frequency of information was estimated by specialists at the SandiaLaboratories to be no greater than 1100 Hz (with instrument 7 the singleexception at 2.56 kHz).*kHz = kilohertz71

For this initial effort, every second data point from the digitized timedomainrecord was employed for analysis and presentation. This data selectionprocess results in an effective sampling rate of 2.56 kHz, whichpreserves information content up to 1.28 kHz.The data reduction effort produced the following results:• Raw time-domain data and their peak excursion values• Filtered time-domain data and their peak excursion values• Instant Fast Fourier Transform (FFT) for both unfilteredand filtered data• Relative spectral energy content of filtered and raw data• Example transfer functionsTable 8 summarizes the measured and reduced parameter values from thetime-domain information.Raw time-domain data (one example is illustrated in Figure 42) are the first400 ms* (1024 samples of 0.39 ms/sample) following initial displacement asmeasured on instrument No.4, Figure 43. These data were transformed intotheir frequency domain equivalent using the Fast Fourier Transforms (FFT)discussed earlier. The resulting spectra, corresponding to the time-domainwaveform of Figure 42, is a measure of the frequency content of the waveform.These spectra are shown in Figure 44.The representation of spectra content covers a range form DC (Oth harmonic)to 1.28 kHz (512th harmonic), where a harmonic division is 2.5 Hz.The units of measure of these instant FFTs are gI s /1HZ for acceleration ork-lb/IRZ.** As in an electronic spectrum analyzer, the total harmoniccontent over a finite band width (2.5 Hz) must be reported at a singlepoint; therefore, a normalizing factor K is applied. To permit the magnitudespresented here to be compared with those derived bY(91h)er methods ofanalysis, a test was developed around Parseval's formula:*ms = milliseconds**k-lb//RZ = kilopounds per square root of hertz.72

where:f(t) = Time-domain informationF(w) = Fourier Transform of f(t)K = Applied scale factor (previously mentioned)A unity magnitude sine wave was synthesized such that the sample window wasequal to an integral number of periods. The resulting integral of thesquared instant FFT, when compared to the integral of the original inputwave square, revealed that:1 2K = .....----;:--;-;-----,~ =No. of Harmonics No. of Input SamplesSince K is associated with F2(w) or average power spectras, the employedinstant FFTs have an applied scale factor of lIAr. In the presented exampleof 512 harmonics of instant FFTs, a scale factor of l/~, or 0.0442, hasbeen incorporated.One of the objectives of this empirical data analysis was to provide informationto validate the analytical model. It was determined that, by analyzinga narrow band of frequencies rather than the entire spectrum, a first-ordersolution would be more easily obtained. Further, if the energy content ofthat narrow band represented the major portion of the total energy, furtheranalysis might be minimized. Using the symmetric properties of the FFT, idealfiltering was performed by truncating the frequency at the 100th harmonic (250Hz) and performing an inverse FFT.Table 9 compares the energy in the band-width limited spectra to the energy ofthe entire spectra, for a selected example of acceleration data. These dataare shown as unfiltered time-domain information in Figure 42, and as filteredtime-domain data in Figure 44. It is apparent that the time-domain peak valuesmay be significantly reduced when the eliminated high frequency energy representedan appreciable portion of the entire spectrum. Note that this energyrelationship ,is a necessary but not sufficient condition to cause the peakvalue variations.Also related to the limited band width energy distribution is the range ofeffectiveness of a transfer function H(w). Transfer functions are essentiallyratios of corresponding instant FFTs derived from the input and outputof the system. For a linear, time-invariant system:H(f) = V(f) = Transfer functionX( f)73

where:X(f) = Complex frequency domain input functionY(f) = Complex frequency domain output functionThis function represents the system's output response to an input stimuli ofa single frequency. If incomplete parameters are employed to represent thesystem1s response, the response is incompletely characterized. However, thesystem is accurately characterized over that limited range. The data presentedhere consider the band of frequencies DC to 250 Hz. The assumptionwas made that system noise was above 250 Hz, but no attempt has been made tocharacterize or to quantify that noise.The above transfer function obviously is dependent on the input and outputspectra being over the same range; hence, windowing or filtering may benecessary. It is conceivable that a matrix of transfer functions, appropriatelywindowed, will permit the data to verify the model in a piece-wiselinear fashion. At the minimum, it should give insight into the nature ofthe required model modification.Figures 45 and 46 illustrate the transfer function magnitude relating theenergy transfer from instrument 22 to 11 and from instrument 11 to 9 over thefrequency range DC to 250 Hz. This corresponds to the vertical transfer ofenergy from the far end of the car on its structure, to the far end of thecask; then to the struck end of the cask. These figures show that IHI > 1.Therefore, the energy is transferred from 9 to 11 (from the struck end tothe far end) rather than the direction shown (11 to 9).In a similar fashion, Figures 47 and 48 illustrate the longitudinal energytransfer characteristics from Instruments 12 to 10 and 10 to 8. Againobserving the value of IHI relative to 1, general characteristics of energycouplings directions are revealed. In this case the direction is related tofrequency in a complicated manner relative to the simple paths assumed.The results of these efforts illustrate the techniques that were employedfor data reduction. They show the applicability of analyzing the band widthlimited data as a first step towards model verification.A meeting to discuss the quality of the data obtained from the SRL rail carimpact tests was held at the Sandia Laboratories in Albuquerque, New Mexicoon Oecember 4, 1979. It was learned that data on the vertical accelerationof points on the rail car, and on the horizontal acceleration of the trucks,were lost due to the use of piezoelectric (PE) accelerometers. Theseaccelerometers were not functional at the frequency range of the rail carand truck responses to be measured.Measurements of vertical acceleration were made for points on the car structureat the struck end, far end, and above the truck center at the struckend using two PE accelerometers and one piezoresistive (PR) accelerometer.74

Apparently the frequency of the vertical rail car motion at these locationswas outside the range of the PE accelerometers, so the data recorded couldnot be used. A PR accelerometer is capable of measurements at these frequencies.The vertical acceleration of the rail car structure at the struckend was monitored using a PR accelerometer, but these data were lost due toeither II clipping ll(over-ranging) or substructure II no ise ll •The horizontal accelerations of the rail car and cask and the verticalaccelerations of the cask were recorded without difficulty. These data wereadequate for the successful validation of the CARDS model. (See Section 4.0,MODEL VALIDATION.)75

3.0 COLLECT PARAMETER DATAA literature search was made to collect data on key parameters to be used inthe CARDS model for model validation (see Section 4.0, MODEL VALIDATION) andfor the parametric and sensitivity analysis (see Section 5.0, PARAMETRIC ANDSENSITIVITY ANALYSIS). Data collected included characteristics of flat bulkheadrail cars (i.e., dimensions, weights, etc.), data on rail car suspensionsystems, data on draft gears (couplers), and data on heavy shielded spentfuelshipping casks and their tiedown systems.Dimensions, weights and other data that make up specifications for thedesign, fabrication and construction of a 50-ton flat bulkhead car wereobtained from the Association of American Railroads (AAR).( IZ} These datawere supplemented by drawings supplied by Savannah River Laboratories of theflat bulkhead car used in the coupling tests.Load-deflection characteristics and the arrangement of springs in rail carsuspension systems were obtained from AAR specifications (References 13 and14, respectively). The load-deflection characteristics are given for helicalsprings, in terms of spring diameter and number of turns. These must berelated to the proper height, number and grouping for a suspension systembefore they can be translated into a spring constant for that particularsystem.Kasbekar et al.,(6) present a piece-wise linear load-deflection c~rve foran M-901E draft gear obtained from tests performed by the AAR.(15jRoggeveen(2) implies that a spring constant of ~6.25 x 104 lb(force)/in. maybe acceptable for a draft gear in a coupling situation.Weights, dimensions and other data on some heavy shielded spent fuel shippingcasks and their tiedown systems are available in Reference 16 and in safetyanalysis reports for the National Lead Industries NLI 1/2, and Nuclear FuelServices NFS-4 shipping casks.It was noted that the sources of parameter data in the literature, in turn,usually refer to publications of the Association of American Railroads (AAR)as the source of their information. Therefore, several individuals in theAAR were contacted to obtain information on rail car suspension subsystemand coupler subsystem components. In particular, information was sought onthe damping devices in these subsystems, including the side-springs in thesuspension subsystem spring groups. Also, AAR specifications were obtainedthat contained a broad spectrum of pertinent information on flat bulkheadcars and other types of cars suitable for hauling heavy radioactive materialpackages.ENSCO, Inc. was retained to provide parameter data on the railway equipmentused in the coupling tests conducted at the Savannah River Laboratories, andon equipment that may be encountered in future studies. In addition, ENSCOsupplied data from similar independent experiments conducted in the past tosupplement the SRL data for model validation. Information on draft gearmodeling, cargo shifting, and on the mix of rail car types present in ananvil train were also provided.77

The parameter data supplied by ENSCO were used in the CARDS model to establisha base case to be used in model validation and in the parametric andsensitivity analyses. These data are clearly presented in the listing ofthe CARDS model in Appendix IV. It should be pointed out here that some ofthese data required adjustment during the subsequent model validation runs,as the model was being tuned to the particular test analyzed. The adjusteddata are also clearly noted in the model listing.78

4.0 MODtL VALIDATIONThree model validation techniques or algorithms were used, at various pointsthroughout the study, to assess the "goodness" of agreement between timevaryingresponse variables measured during humping or coupling experimentsand their counterparts calculated using the CAROl and CARDS models. Thesetechniques are:1) A statistical technique for comparing, in the time domain, thedifferences between predicted and measured values of a timevarying response variable2) A spectral analysis technique that maps the predicted and measuredvalues of a response variable into the frequency domain forcomparison3) A straightforward visual comparison of the time-varying responsevariables in the time domain4.1 THEIL·S INEQUALITY COEFFICIENTSThe first mOdel validation algorithm used is a statistical technique forcomputing a figure of merit from comparisons of time-varying values (series)of preaictea and actual outputs. Statistical techniques available fortesting the "goodness" of fit of mOdels to actual system behavior includeanalysis of variance, the Chi-square test, factor analysis, KolmogorovSmirnov tests, nonparametric test, r~qr~ssion analysis, spectral analysis,ana Theil·s inequality coefficients.t17 ) The technique based on Theil· sinequality coefficients was selected. It was first programmed into theCARUT model and demonstrated successfully, and then included in the CARDSmoael. This technique was chosen as one of the three validation algorithmsconsidered for three reasons:1) It represents a simple addition to the dynamic model2) It produces one number or figure of merit (the inequality coefficient)that reflects the degree of agreement between the model andthe system modeled3) It may be expanded to measure the degree of agreement based on "n"output variables by using Theil's multiple inequality coefficient79

Theil1s inequality coefficient is defined asn(* L(Y Pi - YAi)2) 0.5TIC ::: (219)nY2fs + pi I: Y Ai0 Lwhere: n ::: Number of sampling points, and... , ... , YYPl' Yp2 ' Yp3 , Ypi ' pn... , ... ,YA1' YA2 ' Y A3 , YAi ' VAn(* n 2) 0.5are the values of output variable Y at discrete points in time (a timeseries). Ypi and YAi are the corresponding predicted and actual values,respectively, of the output variable Y. The values of TIC from Equation(219) will vary between the following two extremes:TIC ::: 0 when Ypi ::: YAi for all i (Thecase of equality or perfectagreement)TIC :::(The case of maximum inequalityor poor agreement)Theil's multiple or overall inequality coefficient (TMIC) is a figure ofmerit based on the number of observations or data points, the values ofseveral output or response variables selected at discrete points, and thetwo-variable inequality coefficients (TICs) defined by Equation (219). Thetwo-variable (calculated and experimental vpri~ble values) inequality coefficientsare combined to generate the TMIC.\17J The TMIC is defined byTMIC::: (PPO+PXO)TICO+(PPV+PXV)TICV+(PPA+PXA)TICA+(PPF+PXF)TIC (220)(PPO+PXO+PPV+PXV+PPA+PXA+PPF+PXF)where:PPO (221 )80

PXD = JX T;2 (222)PPVPXVPPAffX T= nPI = XT~= JX~2(223)(224)(225)PXA = jXT;2 (226)PPF = J~~L (227)PXF = J~~LX (228)The terms in these equations areTMICTIC,TICD,TICV,TICAFCPL,FCPLXXT,XTX= Theil's multiple inequality coefficient= Theil's two-variable inequality coefficients forcomparison of calculated and experimental values ofcoupler force, relative displacement, relative velocity,and relative acceleration, respectively= Calculated and experimental coupler forces,respectively [lb(force)]= Calculated and experimental relative displacements,respectively (in.)= Calculated and experimental relative velocities,respectively (in./s)81

= Calculated and experimental relative accelerations,respectively (in./s/s)n = Number of observations or sampling pointsEquation (220) is a corrected version of the equation presented in Reference17. A correction was made to this equation when it was discovered,after an evaluation, that a factor of 2 in the denominator was a mistake.This factor was removed. Equations (220) through (228) were added to theCARDT model for calculation of the TMIC during the simulation discussed inSection 1.0, MODEL DEVELOPMENT. The values of TMIC from Equation (220) willvary between the following two extremes:TMIC = 0 (The case of equality or perfect agreement)TMIC = 1 (The case of maximum inequality or poor agreement)The model validation algorithm based on Theil's inequality coefficients(TIC) was tested by comparing actual values of some time-varying responsevariables, recorded follqwing a 6-mph impact between the two 70-ton hoppercars loaded with gravel,t 4 j with values calculated using the CARDT model.(See Section 1.1.1, Rail Car Coupler and Draft Gear Subsystem Submodel.)Theil's inequality coefficients for the response variables of Figures 16, 17,18 and 19, in the time domain, are presented as Figures 49, 50, 51 and 52,respectively. Theil's multiple inequality coefficient for the time domainis presented in Figure 53. The final value of the multiple coefficient ofFigure 53 is ~0.106. which indicates that the model accomplishes a reasonablygood simulation of the experiment. However, it is also an indicationthat further refinements and adjustments are possible to drive TMIC as closeto 0 as possible. The values of TMIC presented in Figure 53 are low by afactor of 2. This is due to the factor of 2 error discovered in the literatureversion of Equation (216). This error was not discovered until afterthe CARDT simulation was completed. The final value of TMIC in Figure 53should be about 0.212 rather than 0.106.The shape of -the TIC vs time curve of Figure 49 may be explained as follows.The maximum value of TIC of about 0.74 is due to a perturbation in theexperimental data during the first 0.002 second after impact (see Figure 16).During this time period, the measured coupler force rises from 0 to~50.000 lb(force) at 0.002 second after impact, and then drops back to 0during the following 0.001 second. The calculated coupler force variesgradually during this period. Consequently, due to the differences betweenthe values of the calculated and measured couplerforces and the small numberof data points for comparison, the TIC calculated for this period amplifiesthe poor initial agreement between the model output and experimental data.Further examination of Figures 16 and 49 reveals a quick recovery by TIC asit drops to its lowest value (best agreement) of about 0.0684 just beforethe next major perturbation in the measured coupler force at about 0.053second.82

This perturbation causes a short sharp rise in TIC followed by a shortrecovery period. The draft gears then bottom out, and large differencesbetween measured and calculated values of coupler force during the draftgears' II so 1id li state result in an increase in TIC to about 0.25. TIC thenrecovers to some extent at rebound to a value of about 0.12, and then levelsoff at a final value of about 0.212 when the draft gears re-enter theirlI ac tive li state.4.2 FAST FOURIEk TRANSFORMSThe second model validation algorithm chosen for use with the CARDS model isbased on spectral analysis. This algorithm was transformed into the computerprogram FFT (Fast Fourier Transform) as part of the data collection andreduction tasK. (~listing of FFT is presented in Appendix VI). FFT convertsthe displacement, velocity and acceleration response of a cask-railcar system from the time domain to the frequency domain and allows theresponse spectra to be determined directly from either model output or fromtest data. An example of response spectra produced by FFT from test data ispresented as Figure 44. Additional examples may be found in References 18and 19.Originally, it was intended that FFT would be used as a subroutine in theCARDS model; but, due to certain incompatibilities with ACSL (AdvancedContinuous Simulation Language), it was used instead as a separate programfor processIng model output as if it were the recorded output from anexperiment. FFT was used only to a limited extent for model validation.Its primary uses were to map response variables from the time domain intothe frequency domain and to filter out the high frequency noise in the testdata. [See Section 1.2, CASK-RAIL CAR RESPONSE SPECTRUM GENERATOR (CARRS)].4.3 VISUAL COMPARISON OF RESPONSE VARIABLESThe third technique used to assess the Ilgoodness li of agreement betweenmeasured and calculated response variables was a straightforward visualcomparison of plots of the response variables in the time domain.As the study progressed, after the CARDS model had been modified and tunedto account for flaws in some of the test configurations, this technique wasfound to be adequate and was used exclusively for the comparison of measuredand calculated response variables.4.4 FREQUENCY RESPONSE SPECTRAA fourth technique was developed for both model validation and for theparametric and sensitivity analysis discussed in Section 5.0. However, forreasons stated in Section 1.2, this technique was not used for model validation.This technique is based on the transformation of the multi-degree-offreedomrepresentation of the cask-rail car system into an equivalentsingle-degree-of-freedom representation. [See Section 1~2, CASK-RAIL CAR83

RESPONSE SPECTRUM GENERATOR (CARRS)]. Theoretically, the single degree-offreedom(l-DOF) representation of the system (CARRS model) may be used togenerate frequency response spectra for both the test configurations andtheir simulations (using the CARDS model). The II goodness ll of agreement ofthese spectra would be a measure of how well the CARDS model simulates thetests. Horizontal and vertical accelerations measured at various points onthe cask-rail car systems of the tests would be used as the forcing functionsin the CARRS model to generate "measured or experimentally derived" frequencyresponse spectra. Calculated accelerations (forcing functions) obtainedfrom the CARDS model simulations of the tests would then be used to generatethe corresponding "calculated" spectra to be compared to the IImeasured orexperimentally derived" spectra. However, for the reasons discussed inSection 1.2, the "experimentally derived ll spectra for relative verticalmotion could not be generated. Specifically, these spectra could not begenerated because all measurements of the vertical accelerations of the railcar structure were lost. The lIexperimentally derived" spectra for relativehorizontal motion could have been generated but, since visual comparisons ofthe horizontal accelerations for Test 3 were good, it was decided that thesevisual comparisons would be sufficient.4.5 MODEL VALIDATION AND RESULTSDuring the development of the CARDS model it was noted that, although thetime-domain plots of some measured and calculated response variables weresimilar in appearance, they were offset sufficiently to yield values oftheir inequality coefficients (TICs) that suggested poor agreement. In somecases, the model was "tuned" to identify the parameter or parameters causingthe offset and to determine the values of these parameters that would bringthe plots closer together. This IItuning" process consisted of varying thevalues of selected parameters one at a time while holding the others constantat their base case values, and computing values of Theil's multiple inequalitycoefficient (TMIC). A minimum value of TMIC would be obtained for theIIbest" value of a given parameter. One of the first parameters investigatedwas the time shift required to obtain the best fit when values of calculatedand experimental response variables were superimposed. Early in the study,an initial comparison of the time-varying calculated and experimental couplerforces showed that the ramps and peaks of the experimental curve lagged considerablybehind those of the calculated curve. Since the starting time forthe CARDS simulation is the time at which the coupler begins to travel, thissuggested that perhaps the recording device installed for the experiment wasactivated by almost imperceptible movements of the coupler mechanism priorto significant compression. Frame by frame examination of the high speedfilm of this portion of Test 3 showed that, from the instant of initial contactbetween the couplers to the first sign of draft gear travel, 9 frameswere exposed. At 400 frames per second, this meant that 0.0225 second hadelapsed over this interval. A shift of the results by this amount of timeproduced much better agreement between the times at which the various eventsoccurred. This time shift represents a suspected lag between the time therecording device was activated and the time at which the coupler actuallybegins to travel. A final value of this time lag was established by trying84

a number of values while evaluating Theil's two-variable inequality coefficientfor the coupler force, and Theil's multiple inequality coefficient.Minimum values of these coefficients (indicating the best agreement) occurredfor a time shift of 0.038 second. The time shift of 0.038 second fixed thecommon zero point on the time traces of the experimental data for furthercomparisons.4.5.1 Comparison of Measured and Calculated Results for Test 3In Reference 20 it was shown that results obtained from a CARDS simulationof Test 3 of the SRL coupling tests were in good agreement with experimentalresults except for tne vertical acceler~tions of the cask. In the followingreporting period,(2l) ENSCO, Inc. completed a study to provide parameterdata on the railway equipment used in the coupling tests at SRL. These datawere inserted in the CARDS model to establish a base case for model validationand for planned parametric and sensitivity analyses. Additional simulationruns were made to obtain new calculated results to be compared with theexperimental results.At first, the new data resulted in less agreement between the calculatedand experimental results than had been obtained previously. The calculatedand experimental values of the vertical acceleration of the cask at the farend did not show acceptable agreement when compared both visually and quantitatively.After modifications were made to the model, based on a reviewof high speed films of the tests and of system structural features, adramatic improvement in the agreement was realized (especially in the visualcomparisons). The high speed films of Test 3 showed that water was ejectedfrom the collar around the cask at the far end at impact (rain water hadcollected under the collar during a rain storm the night before the test).It was also recalled that a rubber gasket or shim was used under the collar.This suggested that the rubber, or a gap, or both, could cause both anincrease in the magnitude and frequency of the acceleration readings at thefar end, precisely the characteristics needed to achieve agreement. Doubleintegration of the measured accelerations gave displacements that confirmedthis conclusion. Therefore, a nonlinear stiffness coefficient was devisedfor the rear tiedowns that was assumed to consist of a series combination ofan initial gap between the cask and its collar, a rubber shim, and then theintended tiedown structure. A corresponding damping coefficient was alsodevised.As in the preliminary assessment of Reference 20, the latest assessment ofhow well the CARDS model simulated the behavior of the cask-rail car systemfor the conditions of Test 3 of the SRL experiments was made by comparing,for two cases, both visually and quantitatively, the calculated and experimentalvalues of coupler force, the longitudinal force of interaction betweenthe cask and rail car, the horizonal acceleration of the rail car, the horizontalacceleration of the cask, the vertical acceleration of the cask atthe far end, and the vertical acceleration of the cask at the struck end.Also, in this latest assessment, the calculated vertical displacements ofthe cask were compared to those obtained by double integration of the85

measured vertical accelerations of the cask. In both cases, the couplerforce was the force of excitation causing the system to vibrate. In thefirst case (Case 1), the experimentally measured coupler force was used. Inthe second case (Case 2), the coupler force used was that calculated by theCARDS mOdel. Visual comparisons are presented in Figures 54 through 60 forCase 1, and in Figures 62 through 68 for Case 2. To supplement these comparisons,calculated vertical tiedown forces are presented in Figure 61 forCase 1, and in Figure 69 for Case 2. Quantitative comparisons of each pairof individual response variables were made using Theil's two-variableinequality coefficients. A simultaneous quantitative comparison of all theresponse variables was made using Theil's multiple inequality coefficient.The quantitative comparisons are summarized in Table 9. Theil's two-variableinequality coefficients and Theil's multiple inequality coefficient are discussedin Section 4.1.The Theil·s inequality coefficients in Table 9 show that good agreementbetween calculated and experimental results was obtained for all but thevertical accelerations. The vertical accelerations of the cask producedtwo-variable inequality coefficients above 0.5 (Theil's inequality coefficientsare zero at perfect agreement and 1 at the poorest agreement). However,Figures 58, 59, 66 and 67 show that good visual agreement existsbetween the vertical accelerations. Both the magnitude and frequency ofthese plots are in good agreement. It appears, however, that better quantitativeagreement could be obtained if the calculated vertical accelerationat the far end (Figures 58 and 66) could be made to shift ~.025 secondforward on the time scale, and if the calculated vertical acceleration atthe struck end (Figures 59 and 67) could be shifted ~0.02 second backwardon the time scale. Theil's multiple inequality coefficient for Case 1 is0.059, and that for Case 2 is 0.214.The plots of calculated vertical acceleration of the cask at the far end inFigures 58 and 66 are shaped by the nonlinear stiffness coefficient devisedfor the rear tiedowns. Initially, then the cask accelerates freely upwarddue to the loose fit of the collar, but then it soon encounters the rubbercushionedcollar and decelerates rapidly. The stiffness coefficient of therubber shim varies with relative displacement; therefore, the frequencyvaries. The structural damping of the collar varies in a manner similar tothat of the stiffness coefficient.The vertical displacements of the cask are presented in Figures 60 and 68.These figures compare the calculated vertical displacements with thoseobtained by double integration of the measured vertical accelerations of thecask. Figure 60 presents the comparisons of Case 1 results, and Figure 68the comparisons of Case 2 results. Both of these figures show good agreementup to about 0.1 second, and then the calculated a.nd "experimental" displacementcurves show substantial separation.86

4.5.2 Compari50n of Measured and Calculated Results for Tests 10 and 11An assessment of how well the CARDS model simulates the behavior of thecask-rail car system for the conditions of Tests 10 and 11 was made by comparingthe calculated and experimental values of the longitudinal force ofinteraction between the cask and rail car, the horizontal acceleration ofthe rail car, the horizontal acceleration of the cask, and the verticalacceleration of the cask at the far end. The coupler force measured duringthese tests was used as the force of excitation causing the system simulatedby CARDS to vibrate. This coupler force is shown in Figures 70 and 76 forTests 10 and 11, respectively.The cask-rail car system used in Tests 10 and 11 consisted of a 70-ton caskmounted on a flat bulkhead rail car with standard couplers. (For test configurationsand conditions, see Table 2 and Figure 32.) The cask used inthese tests was a rectangular box-shaped 70-ton cask used for onsite shipmentsat SRL. The rail car was the same one used in Test 3. When the baseof the cask was placed in contact with the bumper beams between the cask andthe load cells, its vertical centerline (fore and aft) fell almost 8.0 feetforward [toward the struck end (SE)] of the rail car centerline. This offsetplaced the far end (FE) of the cask almost directly over the center ofgravity of the rail car.For Test la, the calculated longitudinal force of interaction between thecask and rail car, the horizontal acceleration of the rail car, the horizontalacceleration of the cask, and the vertical acceleration of the cask atthe far end are compared with corresponding experimental data in Figures 71,72, 73 and 74, respectively. All of these response variables compare wellwith their experimental counterparts, except for the vertical accelerationof the cask at the far end. The peak values of the calculated verticalacceleration of the cask in Figure 74 are substantially lower than the peakson the plot of the experimental data. There is evidence indicating that theexperimental data may be in error. First, these vertical accelerations ofthe cask are compared, in Figure 74, to the calculated vertical accelerationof a point on the rail car over the trucks at the far end. The agreementbetween this calculated vertical rail car acceleration and the experimentaldata for the vertical acceleration of the cask is better than that betweenthe calculated and experimental values of the vertical accelerations of thecask. This would mean that the far end of the cask was pitching as much asthe far end of the rail car. This does not seem reasonable in view of thestatement made earlier that the far end of the cask was located almostdirectly above the center of gravity (cg) of the rail car. There is rotationabout the cg of the rail car, but the vertical motion of the rail car at thispoint is substantially less than that of the rail car over the trucks at thestruck and far ends. The second piece of evidence which indicates that theexperimental data from Test 10 may be in error is found by moving forward inthe text to Figure 80 where the vertical acceleration of the cask at the farend, calculated for Test 11 conditions, is compared to the same verticalacceleration measured during Test 11. Figure 80 shows that very good agreementexists between the calculated and experimental values of this acceleration,and that they both differ substantially from a superimposed plot of87

the vertical acceleration of a point on the rail car over the trucks at thefar end. The only changes made to CARDS in proceeding from the simulationof Test 10 to the simulation of Test 11 were 1) the impact velocity wasincreased from 8.0 miles per hour to 11.2 miles per hour, and 2) the couplerforce recorded during Test 11 (Figure 76) replaced that from Test 10(Figure 70) as the force of excitation applied at the coupler. None of thestructural parameters of the cask-rail car system were changed.Two key assumptions were made when the parameters were prepared for insertioninto CARDS for the simulation of Tests 10 and 11. First of all, it wasassumed that the vertical components of the tiedowns were tight. This is incontrast to the simulation of the cask-rail car system of Test 3 where somelooseness, and the installation of rubber bushings in the collar at the farend of the 40-ton Hallam cask, required the use of a nonlinear stiffnesscoefficient to represent the vertical component of the tiedown structure(see Section 4.5.1). The 70-ton cask used in Tests 10 and 11, unlike the40-ton Hallam cask used in the rest of the tests, did not require a cradlestructure that became part of the tiedown structure. The 70-ton cask wasbolted directly to the rail car structure. The assumption of tight verticaltiedowns for Tests 10 and 11 appears to be justified by the good agreementbetween the calculated and experimental values of the vertical accelerationof the far end of the cask, for Test 11, as shown in Figure 80.The horizontal component of the tiedowns, in Tests 10 and 11, consisted of arigid welded stop to restrain the cask from moving longitudinally. Initially,it was assumed that the stiffness coefficient of this horizontalcomponent was constant. Several values, ranging up to 5 x 10 6 lb/in.,were tried; however, none of these trial simulations produced results thatmatched the experimental data. These simulations suggested that a nonlinearstiffness coefficient was required for the horizontal component of the tiedowns.Consequently, this was the second assumption made for the simulationof Tests 10 and 11. It was assumed that a constant stiffness coefficient of1.0 x 105 lb(force)/in. was valid up to a relative displacement betweenthe cask and rail car of ~0.2 in. and that, after this initial movement,the tiedowns yielded and could be represented by the nonlinear stiffnesscoefficient shown in Figure 75. This stiffness coefficient was establishedfor Test 10 and used, without change, for the simulation of Test 11.For Test 11, the calculated longitudinal force of interaction between thecask and rail car, the horizontal acceleration of the cask, and the verticalacceleration of the cask at the far end are compared with experimental datain Figures 77, 79 and 80, respectively. The calculated horizontal accelerationof the rail car is presented in Figure 78. In the comparisons forTest 10, this acceleration was compared to data from instrument 12. However,in Test 11 the data from instrument 12, and from all other instrumentsmeasuring the horizontal acceleration of the car, were not suitable for use,so no experimental data are shown in Figure 78. Except for the horizontalacceleration of the car, all of the response variables listed above comparewell with the corresponding experimental data.88

There is some uncertainty with regard to the measured coupler force shownin Figure 76. The experimental traces show that, from ~0.2 s to ~0.5 s,this coupler force leveled off at a value of ~200,OOO lb(force) ratherthan O. In contrast, the coupler force measured for Test 10 dropped to zeroforce after ~0.25 s. It is not known whether or not this failure to dropto zero, as would be expected, is due to a faulty instrument and, if so, atwhat point along the trace the instrument went awry. A comparison of thecoupler force plots in Figures 70 and 76 suggests that the instrument forTest 11 might have experienced some difficulty at ~0.2 s.The experimental acceleration data used in the above comparisons containedhigh frequency noise that had to be filtered out before the comparisons couldbe made. As indicated in Figures 72 through 74, and Figures 78 through 80,the horizontal acceleration data were filtered at 100 Hz and the verticalacceleration data at 50 Hz. Filtering of the high frequency noise componentsfrom these data was accomplished using the FFT (Fast Fourier Transform)program. (See Section 4.2.) - - -4.5.3 Comparison of Measured and Calculated Results for Tests 13, 16and 18The validation of the CARDS model was completed with the comparison ofmeasured results from Tests 13, 16 and 18 with corresponding results calculateausing the CARDS model.An assessment of how well the CARDS model simulates the behavior of the caskrailcar systems used in these tests was made by comparing calculated andmeasured values of the horizontal force of interaction between the cask andrail car, the horizontal acceleration of the rail car, the horizontalacceleration of the cask, the vertical acceleration of the cask at the farend, and the vertical acceleration of the cask at the struck end. Thecoupler force measured during these tests was used as the force of excitationcausing the system simulated by CARDS to vibrate. This coupler force isshown in Figures 85, 93 and 99 for Tests 16, 13 and 18, respectively.The cask used in Tests 13, 16 and 18 was the 40-ton Hallam cask used inTest 3 (see Figure 32 and Table 2). Unlike the box-shaped 70-ton cask usedin Tests 10 and 11, this cylindrical cask was mounted on and secured to acradle structure that served as part of the tiedown structure. In Test 3,this cradle structure was fastened to a rail car with bolts, but in Tests 13,16 and 18, it was fastened to a different rail car (a different one for eachof these three tests) with cables. As reported in Section 4.5.1, goodagreement between the calculated and experimental results for Test 3 wasobtained only after allowance was made for slack in the vertical tiedownstructure at the far end (opposite the struck end of the car). This slack,or looseness, in the tiedowns was evident in high speed films of Test 3.The films showed rain water being ejected from the collar at the far end ofthe cask at impact. Also, it was recalled that a rubber shim had beeninstalled between the collar and the cask. When this gap and rubber shimcombination was considered as part of the tiedown structure, and an appropriatenonlinear stiffness coefficient devised, good agreement between the89

calculated and experimental results was obtained. This same nonlinearrepresentation of the stiffness coefficient for the vertical component ofthe rear tiedowns was used, without change, in the simulations of Tests 13,16 and 18.In Tests 10 and 11, the lO-ton cask was bolted directly to the rail car. Asshown in Figure 32 and Table 2, the same rail car was used in Tests 3, 10and 11. This rail car was a Seaboard Coastline (SCL) flat, bulkhead carwith standard couplers. For Tests 13 and 16, an 80-ton flat rail car withthree-wheeled trucks was used. The 80-ton rail car was equipped with astandard coupler on one end for use in Test 16, and a 15-in. travel end-ofcar(EOC) cushion device on the opposite end for use in Test 13. This lattercar is referred to as the 80-ton Union Carbide car because the Union CarbideCorporation converted it for transporting canisters placed in ~ w~lded,II saw-toothed ll rack superstructure added to the top of the car. t22 ) ForTest 18, a SCL flat bulkhead car with a cushion underframe coupling mechanismwas used. The principal difference between this car aQd the one used inTests 3, 10 and 11 was in the coupling mechanism used. t22)The CARDS model is a complex two-dimensional, multi-degree-of-freedom modelthat determines the horizontal, vertical and rotational motion of both thecask and its rail car following impact with an anvil train during couplingoperations. Results of a parametric and sensitivity analysis, using CARDSand the cask-rail car configuration of Test 3, showed that the relativevertical and rotational accelerations (of the cask relative to the rail car)are highly sensitive and sensitive, respectively, to the horizontal distancebetween the cgs of the cask and rail car. (See Section 5.0, PARAMETRIC ANDSENSITIVITY ANALYSIS.) This horizontal distance, given the parameter namelOCR in Section 5.0, is highlighted in Figures 2 and 81 through 84.Figures 81, 82, 83 and 84 are sketches of the cask-rail car configurationsused in Tests 3 and 18, 10 and 11, 13, and 16, respectively. These figuresidentify not only 10CR and the casks and rail cars used in the tests, butalso the types of couplers and tiedowns used.The simulations of Tests 13, 16 and 18 were initially guided by comparisonsof measured and calculated values of the horizontal force of interactionbetween the cask and the rail car. In the CARDS model, this force is definedby the equation,(229)where:DUSLF = Horizontal interaction force [lb(force)]90

kSl and kS4 = Stiffnesses of the horizontal components of the rearand front tiedowns, respectively, between the cask andrail car [lb(force)/in.]~CXplRc= Horizontal displacement of the cg of the cask-rail car( in. )= Horizontal displacement of the cg of the cask or package( in. )= Vertical distance from the horizontal centerline of thecask-rail car to its top and bottom surfaces (in.)Zp = Vertical distance from the horizontal centerline of thecask to its top and bottom surfaces (in.)eRC = Angle of rotation of the XRC and YRC axes about anaxis peripendicular to the XRC - YRC plane through thecg of the rail car (rad)ep = Angle of rotation of the Xp and Yp axes about an axisperpendicular to the Xp - Yp plane through the cg ofthe cask or package (rad)Initial comparisons revealed poor agreement between the calculated and measuredvalues of this force. Specifically, after the peak forces followingthe impact pulses of Tests 13 and 16, the calculated results included somesubstantial negative values of this force while the measured results includedonly a few small negative values.Of the three tests, Test 16 was the most similar to Test 3, a test simulatedsuccessfully earlier in the study (see Section 4.5.1). The horizontal interactionforce calculated for Test 3 did not show this tendency to negativevalues, so it was concluded that reasons for the differences in the resultsmight be found by examining the differences in the cask-rail car systemsused in these two tests. The primary differences between the cask-rail carsystems of Test 3 and Test 16 are (see Figures 32, 81 and 84 and Table 2):1) A 70-ton SCL flat, bulkhead rai 1 car was used in Test 3. InTest 16 the 80-ton Union Carbide rail car was used. Both of thesetests were conducted with standard couplers.2) In Test 3, the cg of the cask was located 49.0 in. forward of thecg of the rail car. In Test 16, the cg of the cask was located18.25 inches aft of the cg of the rail car (see Figures 81 and 84)3) Bolted tiedowns were used for vertical restraint in Test 3. InTest 16, cable tiedowns were used.91

The major difference between the cars used was in the car weights. Theaverage weight of the loaded 80-ton Union Carbide car (designated asOROX805), based on weights measured prior to Tests 6 through 9 and Tests 12through 16, is 160,105 lb. Only the 40-ton cask was used with this car, sosubtracting the weight of this cask gives a car weight (which includes thecaskcradle) of about 80,105 lb. The lO-ton SCL rail car used in Tests 1through 5 and in Tests 10 and 11 was designated as ACLl8498. The loadedweight of this car, measured prior to Tests 10 and 11, was 222,920 lb.Subtracting the weight of the lO-ton cask gives a car weight of about82,920 lb. This means that the rail car used in Test 16 was about 3.4%lighter than the rail car used in Test 3. A lighter car would deceleratefaster, resulting in less horizontal displacement of the car (i.e., XRc inEquation (229) would be smaller). This would produce a greater tendencytoward negative values of the horizontal interaction force; however, it wasfelt that the difference in the car weights was too small to account for thelarge negative values obtained from the model.The location of the cask along the length of the rail car has little effecton the horizontal force of interaction. This is evident from the results ofthe parametric and sensitivity analysis reported in Section 5.0. In Figures130 and 131, the horizontal distance between the vertical centerlinesof the cask and rail car, 10CR' is listed in the eighth and tenth positions,respectively, out of ten parameters ranked according to their influenceon the horizontal tiedown force. The only parameters ranked belowlOCR (that is, in positions indicating less influence) are the stiffnesscoefficients of the vertical components of the tiedowns, and two compositeparameters representing variations of these coefficients.The remaining difference between the cask-rail car systems of Tests 3 and 16that might account for the differences in the calculated values of the horizontalinteraction force is in the type of tiedowns used. The effect of thetype of tiedowns used on the horizontal interaction force is primarily dueto the stiffness coefficients of the horizontal components of the tiedowns[see Equation (229)J. It was reasoned that, because cables instead of boltswere used for vertical restraint in Test 16, the cask (and its cradle)apparently tended to shift longitudinally during impact and did not returnto its original position. This was because the restoring "spring" action or"chocking" effect of the vertically oriented bolts was missing. Instead,energy was dissipated during the shifting of the cask.The equations in the CARDS model that define the stiffness coefficients ofthe horizontal components of the tiedowns were modified to account for thisloss of energy due to shifting of the cask. Previously, these stiffnesscoefficients were computed in a calculation sequence that set the coefficientseither to their high or low values, or to the sum of their high andlow values, depending upon conditions related to the movement of the cask(and its cradle). This procedure was retained, but the values computedwere modifiea as follows. Let the unmodified values be expressed as92

(230)and(231 )These coefficients were modified using the expressions(232)and(233 )where:d~PRCdt= Relative velocity of cask-rail car combination (in./s)dX p~ = Velocity of the cask (in./s)dX RC~ = Velocity of the rail car (in./s)M and ~S4 = Energy dissipation factors for k Sland k S4' respectivelykSlsgn(A) = Sign functionA > 0d~PRC= A = 0 where A = dtA < 093

The values of the energy dissipation factors used depend upon the conditionsencountered and imposed, i •e. ,Similarly,M [if dX RPRCkSl = MkS1F dt < a and cable tiedowns used] (234)MkSl = a [otherwise]M kS4[. dX RPRC= M lf dt < a and cable tiedowns used] (235)kS4FMkS4 = a [otherwi se ]MkS1F and ~S4F = Arbitrary factors currently set at 0.5The above representation of the stiffness coefficients in CARDS produced agood comparison of the calculated and measured values of the horizontal forceof interaction between the cask and rail car of Test 16 (see Figure 86), andreasonable agreement in comparisons of four additional response variables(see Figures 87, 88, 89 and 90).When the above equations and factors were used, without change, to determinethe stiffness coefficients kSl and kS4 for Tests 13 and 18, improvementsin the comparisons of the calculated and measured results for these testswere also realized (see Figures 93 through 104).The stiffness coefficients defined by Equations (232) and (233) generatehysteresis-type curves. Figure 91 is a load-deflection curve generated forthe horizontal component of the tiedown at the far end during the simulationof Test 16, and Figure 92 is the corresponding plot of the stiffness coefficientkSl as a function of the relative displacement, Xp - XRC.Figure 87 shows three plots of the horizontal acceleration of the rail carduring Test 16. The solid line is a plot of the calculated acceleration,the dashed line is a plot of the measured acceleration, and the dash-dotline is a plot of the calculated acceleration of the rail car with no cask.The calculated and measured values of the acceleration of the loaded railcar show poor agreement. During the peak pulse, the calculated accelerationis only about one-fourth of the measured acceleration. The peak accelerationof the unloaded rail car is about one-half that of the measured accelerationduring the same time period. There is strong evidence that suggests thatthe measured values of the acceleration may be in error. In Figure 33, valuesof the horizontal acceleration of the loaded rail car, measured duringTest 3, were compared with calculated values for both the loaded and unloaded94

ail car (an unloaded rail car is defined as one without both the cask andthe trucks). The purpose of this earlier comparison of results was to showthat the horizontal motion of the cask strongly influences the horizontalmotion of the rail car. These earlier comparisons showed that the calculatedand measured results for the "loaded ll system compare very well, and that thedeceleration of the "isolated" or "unloaded" rail car is substantiallygreater. It was also shown that the deceleration of the unloaded car followsthe coupler force curve. When the results in Figure 87 are compared withthose of Figure 33, the following facts may be noted:1) The measured and calculated accelerations in Figure 33 are in veryclose agreement2) The peak calculated accelerations of both the loaded and unloadedrail cars in Figure 87 are consistent with those in Figure 333) The calculated accelerations of the unloaded rail car in Figures 87and 33 follow the respective coupler force curves for Tests 16and 34) The coupler force curves for Test 3 (see Figure 54) and forTest 16 (see Figure 85) are not identical, but they are verysimilar and their peak values are in the neighborhood of1.1 x 10 6 lb(force).In addition to these facts, further evidence is suggested by the comparisonof the measured and calculated values of the horizontal acceleration of thecask in Figure 88. This figure shows that very good agreement between themeasured and calculated values was realized. It seems doubtful that suchgood agreement could be obtained for the horizontal acceleration of the caskwhile the measured and calculated values of the horizontal acceleration ofthe rail car show such poor agreement. It was shown earlier, in Section 1.2,CASK-RAIL CAR RESPONSE SPECTRUM GENERATOR (CARRS), that the horizontal motionof the cask strongly influences the horizontal motion of the rail car.Measured and calculated values of the vertical acceleration of the caskat the far end are compared in Figure 89. Only fair agreement was realizedsince the peak values of the calculated acceleration are about 50% or 60%greater than the measured accelerations, and the frequency is lower. However,the calculated results appear to be consistent with the correspondingresults for Test 3 (see Figure 58), while the measured results are about afactor of 2 less than those obtained from Test 3. The press of time ruledout an in-depth analysis of these differences that might have led to theirverification or to some justification for modifications to the model thatwould have produced better agreement.Figure 90 compares measured and calculated values of the~vertica1 accelerationof the cask at the struck end. Here again, only fair agreement wasrealized. Comparisons with Test 3 results, in this case, do not show any95

esemblance or consistency. In fact, it appears that there is better a~reementbetween the measured and calculated values for Test 16 than there 1Sbetween corresponding values from Test 16 and Test 3. For example, thefrequencies of both the measured and calculated values of Test 16 are higherthan those of Test 3, and are consistent with one another. However, thefrequency of the calculated results is higher than that of the measuredresults.Although time did not permit an in-depth analysis to find a reason for thedifferences in the vertical accelerations of the cask obtained for thecask-rail car systems used in Tests 3 and 16, it should be pointed out againthat one of the three primary differences between the cask-rail car systemsused in these tests is the parameter 10CR' the horizontal distance betweenthe vertical centerlines of the cask and rail car. In Test 3, the cg of thecask was located 49.0 in. forward of the cg of the rail car whereas, inTest 16, the cg of the cask was located 18.25 in. aft of the cg of the railcar (see Figures 81 and 84). It is not certain what effect this has on thevertical accelerations; however, the results of the parametric and sensitivityanalysis show that both the maximum absolute relative vertical accelerationof an equivalent single-degree-of-freedom model of the cask-rail carsystem of Test 3 and the maximum vertical acceleration of its support arehighly sensitive to 10CR (see Table 17 and Figures 125 and 128).It was stated earlier that when Equations (230) through (235) and thearbitrary factors MkS1F and MkS4F were used, without change, to determinethe stiffness coefficients kSl and kS4 for the cask-rail car systemsused in Tests 13 and 18, improvements in the comparisons of the calculatedand measured results for these tests were also realized. For these tests,time did not permit further analysis beyond this stage; consequently, comparisonsof measured and calculated values of response variables for thesetests are presented, as developed, in Figures 94 through 104. Figures 94through 104 show that, even though no further work was done, the calculatedand measured results for these tests are in reasonable agreement.96

5.0 PARAMETRIC AND SENSITIVITY ANALYSISA parametric and sensitivity analysis was conducted to identify those parametersthat significantly affect the normal shock and vibration environmentand the response of the cask-rail car system. Frequency response spectrawere generated for the horizontal, vertical and rotational accelerations ofa radioactive material shipping package (cask) relative to the accelerationsof its support (rail car). Generation of the response spectra was coupledto a parametric and sensitivity analysis to assess the effects on theresponse spectra (and on selected response variables) of varying certainselected parameters.Parameters are usually varied to study the effect on one or more responsevariables (RV) or figures of merit (FOM). This is termed a parametric analysis.Aparametric analysis is usually coupled to a sensitivity analysis.The objectives of a sensitivity analysis are to arrive at a measure of howsensitive the RVs or FOMs are to changes in the parameters, and to rank theparameters according to their influence on the RVs or FOMs. The determinationof the response spectra, an assessment of the changes in these spectradue to the variation of the parameters, and the identification of the mostinfluential parameters constitutes a parametric and sensitivity analysis.Details of the sensitivity analysis and the ranking of parameters will bepresented and discussed later.Equivalent single-degree-of-freedom (l-DOF) equations of motion (EOMs) werederived to generate the response spectra [see Section 1.2, CASK-RAIL CARRESPONSE SPECTRUM GENERATOR (CARRS)]. These l-DOF EOMs have forcing functionson their right-hand sides that are equivalent to the motions of a support(or shaker table in a testing facility). These support motions, andthe l-DOF EOMs, are derived from the equations of motion used in the CARDSmodel. (See Sections 1.1 and 1.2.) .Parameters are varied in the CARDS model to produce IIsupportll accelerationsas functions of time. These time-varying support motions are then used inthe l-OOF EOMs of the CARRS model to generate the horizontal, vertical androtational accelerations of the cask relative to the actual acceleration ofthe rail car. The actual rail car acceleration is not the same as the supportacceleration. Detailed derivations of the horizontal, vertical androtational accelerations of the support, along with derivations of the l-DOFEOMs in terms of the corresponding relative accelerations, are presented inSection 1.2.Frequency response spectra were generated using the CARRS model (Section 1.2)and results obtained from the CARDS model (Section 1.1). Two sets ofresponse spectra were generated. The first set, des i gnated as II pre 1imi naryll,was generated for five preliminary or exploratory cases. A second set ofresponse spectra, designated as IIrequestedll, was generated for 23 cases (inaddition to a base case) based on conditions and parameters specified orrequested by the US Nuclear Regulatory Commission. The five II pre liminary"97

cases are defined in Table la, and the "requested" cases are defined inTables 11 through 13. The procedure used to generate the response spectra,using CARDS and CARRS, is described in Section 1.2.The cask-rail car system simulated by CARDS for the parametric and sensitivityanalysis was the Test 3 configuration shown in Figures 1 and 81.The preliminary cases defined in Table 10 differ due to only three of theconditions listed. The only difference between Cases 1 and 2 is due to thecondition of the rear tiedowns. Case 1 represents the actual condition ofthe rear tiedowns in Test 3 of the coupling tests conducted at SRL. It wasstated earlier in Section 4.5.1 that ENSCO, Inc. had completed a study toprovide parameter data on the railway equipment used in the coupling testsconducted at SRL. These data were used to establish the base case for thesimulation of Test 3 using the CARDS model. After experiencing difficultyin matching the vertical acceleration of the cask at the far end (as determinedusing the CARDS model) with that measured during the test, high speedfilms of Test 3 were examined for some indication of the reason for the mismatch.The films showed that water (rain water collected during a rain stormthe previous night) was ejected from the collar around the cask at the farend. It was also recalled that a rubber bushing or liner had been installedbetween the cask and the collar. These conditions indicated a possible loosefit between the cask and the collar. Because this cask and collar combinationis part of the tiedown system at the far end, it was concluded that themismatch of results was due to looseness in the rear tiedowns. This wasconfirmed by integrating the cask acceleration recorded during the test twicewith respect to time to get cask displacement, and then comparing this displacementto the calculated displacement (see Figures 60 and 68). It wasfound that the calculated displacement matched the "integrated-measured"displacement reasonably well only by assuming an initial "free" or looserear tiedown, followed by contact with a rubber bushing, and finally followedby "so lid" contact with rubber compressed against the collar.Case 2 in Table 10 re resents a condition where neither slack nor a rubberushlng eXlsts ln the rear tledowns, l.e., t e rear tledowns are as tlrht asthe front tiedowns. This case is, in effect, the base case for Cases ,3,4 and 5. Case 2 represents a set of conditions including:1) No looseness in the vertical component of the rear (or front)tiedowns2) The cask centerline is positioned 4 ft forward of the rail carcenterline3) The time-varying coupler force is that measured during the SRLtests4) D?mping in the equations of motion in the CARDS model includes bothV1SCOUS (structural) damping and damping due to friction opposingthe horizontal motion of the cask relative to the rail car98

5) Damping in the l-DOF EOMs in the CARRS model is the same as \of Condition (4) above.Case 3 differs from Case 2 due to a change in Condition 5) above, i.e.,there is no damping of any kind in the l-DOF EOMs in CARRS. The only differencebetween Case 4 and Case 2 is also due to a change in Condition 5),however, in Case 4, there is viscous (structural) damping only. Finally,Case 5 differs from Case 2 due to Condition 2), i.e., the cask is centeredfore and aft on the rail car rather than being shifted 4 ft forward of thisposition, as in the SRL tests.Results for the "preliminary" cases are presented in the form of "support"accelerations as functions of time, and maximum absolute relative (MAR)accelerations as functions of frequency.- The MAR accelerations are theresponse spectra.The support accelerations [defined by Equations (203), (206), and (216)J forthe preliminary cases defined in Table 10, calculated by CARDS, are presentedin Figures 105, 106 and 107. Figure 105 is a plot of the horizontal accelerationof the support for the equivalent l-DOF system, as a function oftime, for Cases 2, 3 and 4. Figures 106 and 107 are the corresponding plotsfor the vertical and rotational accelerations of the support, respectively.The support accelerations for Cases 1 and 5 are different than those shownin Figures 105, 106 and 107 because the differences in Conditions (1) and (2)in Table 10 required separate CARDS simulations, which produced differentresults. The support accelerations of Figures 105, 106 and 107 are presentedas typical examples of the RHS forcing functions used in the l-DOF EOMs inCARRS.The response spectra generated by the CARRS model, for the "preliminary"cases defined in Table 10, are presented in Figures 108, 109 and 110.Figure 108 consists of plots of the maximum absolute relative (MAR) horizontalacceleration of the equivalent l-DOF system as a function of frequency[see Equation (161)J. Figures 109 and 110 are the corresponding frequencyplots of the maximum absolute relative vertical and rotational accelerations,respectively. In Figure 108, Cases 3 and 5 produce almost identical plotswith the highest accelerations over the range of frequencies considered.These plots have a common maximum value of the maximum (maximax) absoluterelative horizontal acceleration of about 8500 in./s2 at a frequency of250 rad/s. The significance of the identical plots produced by Cases 3 and5 is that the only difference between these cases is the positioning of thecask on the rail car (see Table 10). Case 3 has the cask centerline positioned4 ft forward of the rail car centerline, while Case 5 has the caskcentered fore and aft. The conclusion may be drawn that this difference inthe location of the cask on the rail car has little effect on the maximumabsolute relative horizontal acceleration over the range of frequencies considered.However, the location of the cask on the rail car has a greateffect on the maximum absolute relative vertical acceleration, as shown inFigure 109. A maximax absolute relative vertical acceleration of about99

~~, at a frequency of 50 rad/s, is obtained for Case 3, while the~m (not maximax) absolute relative vertical acceleration obtained for5 is less than 100 in./s2 over the entire frequency range. It should~ointed out here that these accelerations are the relative vertical.celerations of the cg of the cask relative to the cg of the rail car ..here are higher relative vertical accelerations at other locations on thecask. Results from the CARDS model show that, for the centered cask case(Case 5), the absolute relative vertical accelerations of the cask at thetiedown attachment points are ~280 in./s2, while the corresponding absoluterelative vertical acceleration at the cg is ~62 in./s~. The absoluterelative vertical accelerations at the tiedown attachment points are almost5 tlmes greater than the correspondlng accelerations at the cg.The plots for Cases 1 and 2 in Figure 108 are close together, which indicatesthat looseness in the vertical component of the rear tiedowns haslittle effect on the maximum absolute relative horizontal acceleration. Incontrast, the plots for Cases 1 and 2 in Figure 109 are widely separated,indicating that this looseness in the rear tiedowns produces significantlyhigher values of the maximum absolute relative vertical acceleration at allfre~uencies. Vertical looseness in the rear tiedowns also produces substantialy greater maXlmum absolute relative (MAR) rotational accelerations, asshown in Figure 110. Figure 110 shows widely separated plots for Cases 1and 2, with Case 1 having the higher accelerations over the range offrequencies considered.The effect of frictional damping opposing the horizontal motion of the caskrelative to the rail car is illustrated by the plots for Cases 2 and 4 inFigures 108, 109 and 110. In Figure 108, separation of the plots forCases 2 and 4 shows that frictional damping decreases the MAR horizontalacceleration over most of the frequency range. The lower plot in Figure 108consists of the results for Case 2, the case where frictional damping ispresent along with viscous (structural) damping. The results of Case 4 arepresented as the upper plot in Figure 108. This case has viscous dampingbut no frictional damping. Frictional damping has little effect on the MARvertical acceleration and on the MAR rotatlonal acceleratlon, as lndlcatedby the superposition of points on the plots for Cases 2 and 4 in Figures 109and 110, respectively.The 23 cases IIrequestedli are defined in Tables 11, 12 and 13. These casesare defined in terms of the requested conditions in Table 11, and in termsof the requested parameters in Tables 12 and 13. The parameters used in thedefinitions of Tables 12 and 13 are defined in NOMENCLATURE OF TERMS, AppendixI. Some of these parameters are also shown in Figure 2, 3 and 4. Itshould be noted that, among the conditions specified in Table 11, the couplerforce used for all the cases was that measured during Test 3 of the humpingtests.Table 11 shows that the conditions are the same for all the IIrequestedlicases and that, except for one condition, the cases would be the same asIIpreliminaryli Case 4. The requested cases do not include frictional dampingopposing the horizontal motion of the cask relative to the rail car in theEOMs in the CARDS model.100

The requested parameters were divided into two groups. The first group consistsof five parameters designated as IIpure ll parameters. The second groupcontains eight parameters designated as IIcomposite" parameters. The groupof pure parameters includes individual parameters, but has been extended toinclude sets of parameters that are closely related. The two sets includedin this group are {k x }' a set of stiffness coefficients consisting of thosefor the horizontal components of the rear and front tiedowns and {k y }, a setof stiffness coefficients consisting of those for the vertical components ofthe rear and front tiedowns. Composite parameters consist of unrelatedparameters, or related parameters that are varied by differing amounts. Forexample, the composite parameter CPl defined in Table 13 consists of thestiffness coefficients of both the horizontal and vertical components of thetiedowns. The stiffness coeTTicients of these components are considered tobe unrelated because of their differences in orientation. Pure parametersana definitions of their cases are presented in Table 12. Composite parametersand definitions of their cases are presented in Table 13.The definitions of the cases are expanded in Table 14 in terms of the numericalvalues of the parameters. It should be noted that there are high andlow values of the stiffness coefficients of the horizontal components of thetiedowns. The low value represents the stiffness coefficient of a tiedownconsisting of such devices as cables, chains, bolts, etc, which provideconstraint while the cask and frame combination is free to move betweenchocks. The high value represents the stiffness coefficient of a chock.The actual stiffness coefficient used when the chock is encountered is acombination of these two values.The results for the IIrequestedll have been presented in the form of IIsupportllaccelerations as functions of time, and MAR accelerations as functions offrequency. In addition, the forces in the horizontal and vertical componentsof the tiedowns at both the struck and far ends have been presented as functionsof time. The horizontal, vertical and rotational accelerations of theIIsupportll were presented as functions of time (for the base case and Cases1, 2, C, D, and 3 through 8) in Figures 2 through 16 in Reference 23, and(for the base case and Cases 9 through 21) in Figures 2 through 19 in Reference24. The forces in the tiedowns, for Cases 1, 2, C, D, and 3 through21, were presented as functions of time in Figures 20 through 63 in Reference24. The MAR accelerations were presented as functions of frequency(for the base case and Cases 1, 2, C, D, and 3 through 8) in Figures 17through 31 in 'Reference 23, and (for the base case and Cases 9 through 21)in Figures 64 through 81 in Reference 24. Only those plots for the basecase and Cases 7 and 8 are rresented here as examples. The bulk of theresults will be summarizedater in some special tables and figures.The support accelerations (for the base case and Cases 7 and 8), as functionsof time, are presented in Figures 111, 112 and 113, and the correspondingtiedown forces are presented in Figures 114 through 117. The correspondingMAR accelerations as functions of frequency (the response spectra) are shownin Figures 118, 119 and 120.101

In Reference 23, plots of the MAR horizontal accelerations as functions offrequency are presented in Figures 17, 20, 23, 26 and 29. Correspondingplots of the MAR vertical accelerations are presented in Figures 18, 21, 24,27 and 30, and the corresponding MAR rotational accelerations are presentedin Figures 19, 22, 25, 28, and 31.Figure 20 in Reference 23 is almost identical to Figure 26 of the samereference, which indicates that Cases C and D produce MAR horizontal accelerationsnearly equal to those produced by Cases 5 and 6. Tables 12, 13 and14 show that, in Cases C and D, the stiffness coefficients of both the horizontaland vertical components of the tiedowns were varied and that, inCases 5 and 6, only the stiffness coefficients of the horizontal componentswere varied. This indicates that the stiffness coefficients of the verticalcomponents have little, if any, effect on the MAR horizontal acceleration.In Figure 29 of Reference 23, the plots for the base case and Cases 7 and 8are very close together. Tables 13 and 14 show that the only parametersvaried in Cases 7 and 8 were the stiffness coefficients of the verticalcomponents of the tiedowns. Therefore, this confirms the previous conclusionthat these coefficients have little effect on the MAR horizontalaccelerations.Figures 21 and 30 in Reference 23, although far from identical, are similar.These figures contain plots of the MAR vertical acceleration vs frequencyfor the base case and Cases C and D, and Cases 7 and 8, respectively. Thesimilarity of these plots is an indication that a similarity exists betweenCases C and D and Cases 7 and 8. Tables 12, 13 and 14 show that, in Cases Cand D, the stiffness coefficients of both the horizontal and vertical componentsof the tiedowns were varied and that, in Cases 7 and 8, only thestiffness coefficients of the vertical components of the tiedowns werevaried. It may be concluded from this that the MAR vertical acceleration ismoderately affected by the stiffness coefficients of the horizontal componentsof the tiedowns.Figure 28 in Reference 23 contains plots of the MAR rotational accelerationfor the base case and Cases 5 and 6. These plots, although not identical,are close together compared to those in Figures 19, 22, 25 and 31 in the samereference. Recalling that, in Cases 5 and 6, only the stiffness coefficientsof the horizpntal components of the tiedowns were varied, this indicates thatthese coefficients only moderately affect the MAR rotational acceleration.This may be confirmed by comparing Figures 22 (Cases C and D) and 31 (Cases7 and 8) of Reference 23. This comparison suggests that Cases C and Dproduce nearly the same results as those obtained from Cases 7 and 8. Theonly parameters that are not common to these two sets of cases are thestiffness coefficients of the vertical components of the tiedowns.A crossover or change of position of the plots, over the range of frequenciesconsidered, is evident in Figures 17, 20, 23, 26, 27 and 28 in Reference 23.This change of position also occurs over a very short frequency span at thehigh frequency range in Figure 21 (Reference 23). As an example of how theplots change position, consider Figure 23 (Reference 23). In this figure,102

over the range of frequencies from 2 rad/s to ~100 rad/s, Case 3 is representedby the lower plot and Case 4 by the upper plot. Between 100 rad/sand 130 rad/s, the plot representing the base case becomes the upper plot,and the Case 4 plot becomes the middle plot. Over the frequency rangebetween 130 rad/s and 260 rad/s, the Case 3 plot becomes the upper plot, theCase 4 plot becomes the lower plot, and the base case plot occupies themiddle position again. It is not clear at this time whether this changingof position is due to the frequency used in the l-DOF EOMs in CARRS orwhether it is due to the variation in the support accelerations produced byCARDS for the various cases.The MAR acceleration plots in References 23 and 24 are the accelerationresponse spectra for paired cases compared to the base case. These spectraare concentrated on three plots (presented in this report as Figures 121,122 and 123), one for each of the three MAR accelerations, to show how thevarious spectra lie with respect to a band bounded by ±50% values of thebase case spectra. The horizontal spectra are well behaved, that is, all ofthe spectra lie within the band; however, the vertical and rotational spectrado not conform as well. Seven cases fall outside the band for the verticalspectra, and ten cases fall outside the band for the rotational spectra.These cases, and the parameters they represent, are:Vertical Spectra Rotational SpectraCase Parameter Case ParameterC CPl C CPl7 {k y} D CPl8 {k y} 3 CP211 i OCR4 CP213 CP6 7 {k y}18 i OCR10 CP419 i OCR11 i OCR13 CP620 CP821 CP8These cases and their parameters are defined in Tables 12 and 13. It shouldbe noted that, for the vertical spectra, the "pure" parameters {ky},iOCR, ipR and ipF seem to be dominant since CPl consists of {k } and theless dominant {k x} while CP6 consists of iPR and ipF for a cas~ centered onthe rail car. The same "pure" parameters appear to be dominant for therotational spectra. The additional parameters affecting~ the rotationalspectra are CP2, which consists of {k y} and the less dominant {k x } and Wp,CP4 which consists of the elements of {k y } varied individually, and CP8 whichconsists of {k y}, {k x}' Wp~ and the stiffness coefficients of the horizontaland vertical components of-the springs between the rail car and its trucks.103

In the last five paragraphs, an attempt was made to interpret the differencesevident in the response spectra of Figures 17 through 31 (in Reference 23)in terms of the parameters varied. A better picture of the effects due tovariation of the parameters was obtained for these and subsequent simulationsfrom a sensitivity analysis. As stated earlier, parameters are usuallyvaried to study the effects on one or more response variables (RV) or figuresof merit (i.e., a parametric analysis). It was also stated that a parametricanalysis is usually coupled to a sensitivity analysis. The objectives of asensitivity analysis are to arrive at a measure of how sensitive the RVs areto changes in the parameters, and to rank the parameters according to theirinfluence on the RVs.A sensitivity analysis was used to determine the sensitivities of selectedRVs to parameter variations. Results of this sensitivity analysis are presentedin Tables 15 through 19 of this report, in Figures 32 through 41 inReference 23, and in Figures 85 through 111 in Reference 24. For thissensitivity analysis, three sets of RVs were chosen:1) The peak (or maximum) absolute values of the support accelerations.. .. ..determined by the CARDS model, i.e., IXslmax' IYslmax and leslmax2) The maximum values of the maximum absolute relative accelerations(or "maximax" absolu~e relati~e accelerations)* determined by theCARRS model, i.e., IXdl ,IYdl and Ilid Imax max max3) The peak or maximum values of the forces in the horizontal componentsof the tiedowns (DUS1~ax and DUS4m x) and in the verticalcomponents of the tiedowns lDUSJmax and BusJmax), as determined bythe CARDS mode 1.Absolute peak support accelerations were selected as RVs for the sensitivityanalysis because the support accelerations are the only output variablestrOduced by the CARDS model that are used in the CARRS model. They are, inact, essential variables because they are the forcing functions on the RHSsof the l-DOF EOMs of the CARRS model [see Equations (145), (161) and (212)in Section 1.2J. The effects of changes in the parameters used in CARDS arepropagated through the support accelerations to the l-DOF EOMs in CARRS. Themaximax absolute relative accelerations were selected as RVs because they*The response spectra of Figures 17 through 81 in Reference 23 and Figures64 through 81 in Reference 24 are obtained by plotting the maximumabsolute values of the relative accelerations obtained from CARRS runs foreach of the frequencies shown. The maximax absolute relative accelerationsare the maximum values of the maximum absolute relative accelerationsplotted in Figures 17 through 31 (Reference 23) and Figures 64 through 81(Reference 24).104

epresent the ultimate FOMs of the study, i.e., the response spectra of thecask-rail car system (represented as an equivalent l-DOF system in CARRS)resting upon a support with accelerations (motions) determined by CARDS. Themaximum forces in the tiedown components were selected as RVs because theyrepresent the loads imposed on the tiedowns due to the parameter changes.The sensitivity of a RV to changes in the parameters may be defined in anumber of ways. In this study, the sensitivity is expressed as the contributionof each parameter to the total change in a RV, i.e.,tI(RV) = [a (RV)] tIP + [a (RV)] tiP + ••• + [a(RV)] aP(236)aP 1 aP 2l 2 nwhere:tllRV) = Total change in the RVtlP n = Variation or change of the n-th parameter about its basecase valueTerms in brackets = Influence coefficients (partial derivatives)Influence coefficients are defined as the rate of change of a RV with respectto a parameter, say Pl' obtained by varying Pl about its base case valuewhile holding all other parameters at their base case values, i.e.,Coefficient of InflUenCe] [a(RV)] (237)of Parameter P lon = aP[Response Variable RVlP , P , ... , Pn2 3The sensitivity of the RV to the parameter P~Sensitivity of RV] = [a(RV)] tiP[ to Parameter P(238 )~ nnnNormally, the variations in Equation (236) are taken to be very small; however,in studies of this type, extreme latitude is justified if the RV vs Pplots are well-behaved and if piece-wise linear approximations are used.In Figures 32 through 41 of Reference 23, Figures 95 through 111 in Reference24, and in the example plots of Figures 134 through 136 in this report,the slope of a plot is an indication of the magnitude of the influence of theparameter ratio on the RV, and of the sensitivity of the RV to the parameterratio. The greater the slope, the greater the influence of the parameter105

and the greater the sensitivity. The plots in these figures are graphicalrepresentations of Table 15 since the values of the response variablesplotted are those shown for the base case and the various cases defined inTables 12, 13 and 14. The effects of the parameters on the RVs, expressedas influence coefficients and as the contribution of each parameter to thetotal change (sensitivity) in a RV, were determined using the results fromTable 15 and the figures in References 23 and 24. In this study, influencecoefficients were obtained by using a weighted average of the slopes of thestraight line segments of plots equivalent to the appropriate figures inReferences 23 and 24 (and the example Figures 134 through 136). As anexample, consider the coefficient of influence of the cask weight, W, onthe absolute peak horizontal acceJ~ration of the support, IXsl max • ~he slopeof the first line segment of an IXslmax plot equivalent to that in Figure 32of Reference 23, but in terms of the cask weight rather than the ratio, isSlope Seg 1 (239)4189 - 4663=----,,-------.-(8 x 10 4 ) - (4 x 10 4 )= -0.01185 in./[lb(force)·s2]The slope of the second line segment isSlope Seg (240), {k S2' k S3} , etc.= __.::-38=--4:...,:3-;:---_4:....:1.;::;..8=--9__"...(1.6 x 10 5 ) - (8 x 10 4 )= -0.004325 in./[lb(force)·s2]The approximate total influence coefficient for the combined line segmentsis taken to be the weighted average slope (WAS)106

(241)(242)4 4= (-0.01185)(4 x 10 ) + (-0.004325)(8 x 10 )(4 x 10 4 ) + (8 x 10 4 )= -0.006833 in./[lb(force)-s2]This same procedure was used to obtain the influence coefficients for theinfluence of the various parameters on the remaining absolute peak supportaccelerations, and on the maximax absolute relative accelerations. Theinfluence coefficients obtained are presented in Table 18.Table 15 is a summary of the results of the parametric and sensitivityanalysis in terms of the values of the selected RVs at the base case and atthe other 23 cases considered. This table shows the differences between thevalues of the RVs at the base case and the values of the RVs at the othercases. These differences are also presented as a percent difference fromthe ~ase case (%OFB). - The parameters are ranked according to how sensitive the response variablesare to the parameter changes. In Table 16, the parameters are ranked bysensitivity expressed as the absolute value of the percent difference fromthe base case, I%DFBI, obtained from Table 15. These rankings are graphicallyportrayed in bar charts, one for each of the response variables, inFigures 124 through 133.The results presented in Tables 15 and 16, and in Figures 124 through 133,are expressed in terms of "sensitivity ranges" in Table 17. In this table,the dividing point between "sensitive" and "insensitive" was arbitrarilyselected as 40%DFB. The entire sensitivity range is divided into thefollowing five subranges:107

I%DFBI80 - 100 Up60 - 8040 - 60RangesSensiti ve 1)2)3)SubrangesResponse Variable (RV)Highly SensitiveRV SensitiveRV Moderately Sens it i ve20- 40Insensitive 4)RV Moderately Insensitive0- 205)RVInsensitiveTable 17 shows that, when this sensitivity scale is applied, the horizontalaccelerations IXsl max an~. IXdlmax fa).l into the insensitive range, while thevertical accelerations IYsl max and IYdlmax and the rotational accelerationsle'sl max and led IIII ax extend into the IIhighly sensitive ll subrange. The tiedownforces extend no higher than the "moderately sensitive ll subrange. Thevertical accelerations are sensitive to the parameters {k y}, iOCR, CPland CP6. The rotational accelerations are sensitive to the parameters {ky},CP1, CP2, CP8, iOCR, CP6, CP4 and CP3. Seven of these parameters and thelrcases are the same as those identified with the response spectra that felloutside the +50% band on the response spectra plots of Figures 121, 122 and123. They have been discussed earlier. It should be noted from Table 17that 16 s l max is also moderately sensitive to Wp' The tiedown forces aremoderately sensitive to the parameters CP2 and CP8. The vertical tiedownforces are also moderately sensitive to the vertical distance Zp'In Table H:l, the "pure" parameters are ranked by influence coefficient andby sensitivity expressed as the contribution of each parameter to the totalchange in the response variable. Table 18 shows that, for all the responsevariables except the vertical accelerations, the most influential II pure llparameter is the vertical distance Zp' The parameter that has the mostinfluence on the vertical accelerations is iOCR, the horizontal distancebetween the cgs of the cask and rai 1 car. It should be noted that, for thevertical accelerations, iOCR is divided into two parameters, iOCR(FE) whenthe cg of the cask is located on the far end side of the rail car cg, andiOCR(SE) when the cg of the cask is located on the struck end side of therail car cg. This was necessary since the slopes (rates of change of thevertical accelerations with respect to the iOCR) were nearly equal and oppositein sign. Influence coefficients derived from weighted averages of theseslopes would not have reflected the true influence of iOCR' Table 18 alsoshows that the II pure " parameter that contributes the most to the totalchanges in the horizontal accelerations (i.e., the sensitivities) is Wp, thepackage weight. This table also reveals that the parameter which mostaffects the total changes in the vertical accelerations is iOCR, and theparameter causing the greatest changes in the rotational accelerations is108

{k y }. The parameters that most affect the total changes in the tiedownforces DUSl max ' DUS4max ' DUS2max and DUS3max are Wp' {kx}' Zp and Zp'respectively. It should be remembered that the ranges of the parameters usedto arrive at the sensitivities were specified at the outset in the definitionof the cases. More meaningful values of the sensitivities are obtained ifthese ranges represent the uncertainties in the parameters.Nine of the thirteen parameters (both "pure" and "composite") varied werevaried about the base case by applying a multiplying factor to the base casevalues. This multiplying factor is expressed in terms of a parameter ratio," the ratio of the parameter value to the base case parameter value.Treating these parameter ratios as parameters, influence coefficients andsensitivities were obtained. These parameter ratio-based influence coefficientsand sensitivities are presented in Table 19. The sensitivities ofeach of the response variables to changes in the parameter ratios are illustratedin Figures 32 through 41 in Reference 23 and in Figures 95 through111 in Reference 24. Only the plots for the base case and Cases 7 and 8(Figures 34 and 39 in Reference 23, and Figure 107 in Reference 24) arepresented in this report as examples. The sensitivities of the absolutepeak support accelerations to changes in the pure parameter {k y } (Figure 34in Reference 23) are presented in Figure 134. The sensitivities of themaximax absolute relative accelerations to changes in {k } (Figure 39 inReference 23) are shown in Figure 135, and the sensitivities of the absolutetiedown forces to changes in {ky} (Figure 107 in Reference 24) are shown inFigure 136. Four of the "composite" parameters could not be expressed interms of parameter ratios. These parameters are CP3, CP4, CP5 and CP6, whichcorrespond to Cases 9, 10, 12, and 13, respectively. Consequently, thesecases are not included in Table 19, in Figures 32 through 41 in Reference 23,and in Figures 95 through 111 in Reference 24. The results in Table 19 maybe condensed as follows:ResponseVariableMost InfluentialParameter(Parameter Ratio)Parameter Ratio toWhich Response VariableIs Most SensitiveIXslmax if>(CP8) if>(CP8)IYs.lmax ,({k y }) ,[.tOCR(SE)]16s lmax ,(CP2) ,(CP2)I Xd Imax ,(Wp) if> (W p)IYdlmax if> ( {k y}) ,[ .tOCR( SE) ]16dlmax if>(CP2) if>(CP2)The sensitivities presented here are consistent with those presented inTable 17.109

CONCLUSIONS AND RECOMMENDATIONSOn the basis of the good agreement obtained between the measured and calculatedresults for Tests 3, 10, 11, 13, 16 and 18, it is concluded that theCARDS model has been validated and, therefore, is an acceptable tool for theprediction of the dynamic response of a Cask-~ail Car System (CRS) impactinga stationary train of anvil cars at speeas up to 11 mpn.A CRS is a complex system. It is conceivable that supposedly identicalCRSs may not behave the same, depending on how its subsystems and componentparts are fastened to one another, on the fabrication or assembly tolerancespermitted, etc. Perhaps a CRS that is thought to be well-defined might contain"surprises" that may cause the CRS to respond in a manner drasticallydifferent from the predicted response. When results obtained from CARDS werecompared with the measured results from coupling Tests 3, 13, 16 and 18,some, up to that time, unsuspected situations were brought to light thatsignificantly affected the agreement between the measured and calculatedresults. In Test 3, good agreement between the two sets of vertical accelerationsof the cask at the far end was obtained only after allowance wasmade for previously unsuspected slack in the vertical tiedown structure (thecradle collar portion) at the far end. The same cask-cradle combination wasused in Tests 13, 16 and 18; so this allowance was also used for these testswith good results. Also, in Tests 13, 16 and 18, the simulations were initiallyguided by comparisons of measured and calculated values of the horizontalforce of interaction for Test 16. Differences between the measuredand calculated values of this force for Test 16 were attributed to horizontalslippage between the cask and the rail car that resulted in an energyloss to the system. In these three tests, cable tiedowns were used insteadof bolted tiedowns. It was assumed that when the chocking effect due tovertically oriented bolts was no longer present, some horizontal slippageoccurred. When this energy loss or "slippage" was accounted for in themodel by modifying the stiffnesses of the horizontal components of the cabletiedowns, good agreement between the measured and calculated values of thehorizontal interaction force and four other response variables was realized.When these modifications were applied, without change, to the simulation ofthe cask-rail car systems used in Test 13 and 18, substantial reductionswere realized in the differences between the measured and calculated valuesof the five 'response variables compared.It is reconmended that simulation models such as CARDS, that have beenvalidated against experimental data, be used to establish standards for thepreparation of a CRS before shipment.111

REFERENCES1.2. R. C. Roggeveen, IIComputer Predictions of Freight Train Shock Actions, IIASME Paper 72-WA/RT-9, November 26-30, 1972.3. C. L. Combes et al., 1966 Car and Locomotive c~clo~edia, 1st Ed.,Simmons-Boardman Publishing Corp., New York, N , 1 66.4. W. E. Baillie, IIImpact as Related to Freight Car and Lading Damage, IIASME Paper 59-A-249.5. R. C. Roggeveen, IIAnalog Computer Simulations of End Impact of RailwayCars, II ASME Paper 65-RR-3.6. P. V. Kasbekar, V. K. Garg and G. C. Martin, IIDynamic Simulation ofFreight Car and Lading During Impact,1I Journal of Engineering forlndu~try, Transactions of the ASME, November 1977.7. B. T. Scales, IILongitudinal-Shock Problems in Freight Train Operation, IIASME Paper 64-WA/RR-4, 1964.8. J. M. Biggs, Introduction to Structural Dynamics. 1st Ed., McGraw-HillBook Co., New"""York, NY, pp. 87-89 and 102-104, 1964.9. C. M. Harris and C. Crede, Shock and Vibration Handbook, Volume 2(p. 31-2) and Volume 3 (p. 50-10), McGraw-Hill, New York, NY, 1961.10. R. W. Ramirez, The FFT: Fundamentals and Concepts, Tektronix, Inc.,Beaverton, OR, 1975.11. A. Papoulis, The Fourier Integral and Its Application, McGraw-Hill,New York, NY, p. 27, 1962.12. Carsor13. Helical Springs, Heat Treated Steel, Specifications M-114, Associationof American Railroads, Operations and Maintenance Department,Mechanical Division, Chicago, IL, March 1, 1973.14. Specifications for Testing Special Devices to Control Stability ofFreight Cars, Specifications 0-65 through D-76A, Association ofAmerican Railroads, Chicago, IL, January 1, 1974. ~113

REFERENCES(Cont1d)15. A. A. R. Test Data - Friction Draft Gear, Specifications M-901-E,Association of American Railroads, Chicago, IL.16. Design and Analysis Report, IF-300 Shipping Cask, NEDO-10084-1, GeneralElectric Company, Nuclear Fuel Department, February 1973.17. N. A. Kheir and W. M. Holmes, "On Validating Simulation Models ofMissile Systems," Simulation, April 1978.18. S. R. Fields and S. J. Mech, Dynamic Analysis to Establish Normal Shockand Vibration of Radioactive Materlal Shlppln Packages, Quarterlyrogress Report ctober 1, 19 8 - ecember 3 , 19 8), NUREG/CR-0766(HEDL-TME 79-3), June 1979.19.20. S. R. Fields and S. J. Mech, Dynamic Analysis to Establish Normal Shockand Vibration of Radioactive Material Shipping Packages, QuarterlyProgress Report (October 1, 1979 - December 31, 1979), NUREG/CR-1484,(HEDL-TME 80-24), August 1980.21. S. R. Fields, Dynamic Analysis to Establish Normal Shock and Vibrationof Radioactive Materlal Shlpplng Packages, Quarterly Progress Report(January 1, 1980 - March 31, 1980), NUREG/CR-1685, Vol. 1, (HEDL-TME80-51), January 1981.22. S. F. Petry, Rail Tiedown Tests with Heavy Casks for RadioactiveShipments, DP-1536, August 1980.23. S. R. Fields, Dynamic Analysis to Establish Normal Shock and Vibrationof Radioactive Material Shipping Packages, Quarterly Progress Report(July 1, 1980 - September 30, 1980), NUREG!CR-1685, Vol. 3, (HEDL-TME80-91), April 1981.24. S. R. Fields, Dynamic Analysis to Establish Normal Shock and Vibrationof Rad~oactive Materla1 Shippln Packa es, Quarterly Pro ress ReportOctober 1 - December 31, 1980 , NUREG/CR-1685, Vol. 4,(HEDL-TME 80-92), July 1981.114

A P PEN D I XINOMENCLATURE OF TERMS1-1

NOMENCLATURE OF TERMSI3RAKEF, BRAKERBRKIRC, BRKF2,I3RKF3, BRKF4CSl through CS8de pDTHP, --at' e pde RCDTHRC, crt' eRClJUSCARDUSLFDUSX4DUSl through DUS8DWCRFDWP1, DWP4DWSl through DWS8= Brake switches applied to the front and rear railcar trucks, respectively. When switches are setat 1.0, the brakes at the trucks are on and locked;when they are set at 0, the brakes are off.= Brake switches for anvil cars 1 through 4,respectively. Brakes are on and locked when setat 1.0 and off when set at O.= Damping coefficients for viscous dampers representingstructural damping at springs Sl through S8in Figures 2 and 3 [lb(force)·s/in.= Angular velocity of package or cask about an axisthrough its cg (rad/s)= Angular velocity of rail car about an axis throughits cg (rad/s)= Coupler force calculated by CARDS model[lb(force)]= Horizontal interaction force [lb(force)]= Coupler force obtained from experimental measurements[lb(force)]= Forces acting on springs Sl throu9 h S8,respectively (see Figures 1 and 3) [lb(force)]= Frictional force opposing vertical motion ofcoupler faces between hammer car (cask-rail car)and first car in anvil train [lb(force)]= Frictional forces opposing horizontal motion ofcask on rail car at rear and front attachmentpoints, respectively [lb(force)]= Viscous damping forces representing structuraldamping associated with springs Sl through S8'respectively [lb(force)]= Velocity of the cg of empty anvil car (Lie)1-3

dXOXCRC - CRC X' --crr-' CRC= Velocity of cg of the empty hammer car (Lie)= Relative horizontal velocity of l-DOF representationof package-rail car system (in./s)= Horizontal velocity of cg of anvil car and itscargo (Lie)= Adjustment factor or relative velocity to regulatethe relative velocity X T(in./s)= Horizontal velocity of cg of cask or package(in./s)dX RCOXRC, "Cit, X RCdXDXRPRC _ RPRC, at= Horizontal velocity of the cg of hammer car andits cargo (Lie or in./s)= Relative velocity of cask-rail car combination(in./s)OXT,DXTX,dX T dXrxCit' """""Crt'Xl'XTX= Calculated and experimental total relativevelocities of displacement of the cgs of tworail cars, respectively (in./s)dX TADXTA, crt' X TA= Adjusted relative velocity of displacement ortravel of the cg of two impacting rail cars(in./s)DYCPL,dY CPL'YCPLdt= Vertical velocity of coupler face on cask-railcar (in./s) (Coupler on anvil car is assumed tobe stationary.)= Relative vertical velocity of equivalent l-DOFmodel of package-rail car system (in./s)1-4

= Vertical velocity of cg of cask or package(in./s)= Vertical velocity of cask-rail car at its cg(in./s)D2THRC,2d eRC ..2' eRCdt= Angular acceleration of package or cask about anaxis through its cg (rad/s 2 )= Angular acceleration of rail car about an axisthrough its cg (rad/s 2 )= Angular or rotational acceleration of support (1/e 2 )d 2 X ..dD2XD, --2' Xdt dd2X ..FD2XF, --2' Xdt F= Relative horizontal acceleration of l-DOF representationof package-rail car system (in./s 2 )= Horizontal acceleration of cg of car(s) (mass M F)at front (struck end) of rail car (in./s 2 )D2XkC,D2XR56,02XR78,d2X ..RCLd t 2 ' "KC2d X ..RC56X_dt2 ' "1{C562d X .. RC78dt2 ' XRC78= Horizontal acceleration of cg of cask or package(M ) (in./s 2 )p= Horizontal acceleration of cg of cask-rail car2(M C) (i n•/ s )R= Horizontal acceleration of cask-rail car at supportpoint at rear truck (in./s 2 )= Horizontal acceleration of cask-rail car atsupport point at front truck (in./s 2 )1-5

= Horizontal acceleration of support (L/e 2 )D2XTR,2d X TRdt 2 '2. d Yd"D2YD, -2-' Y ddt= Horizontal accelerations of the cgs of rear (MrR)and front (MrF) rail car trucks, respectively(in./s 2 )= Relative vertical acceleration of equivalent l-DOFmodel of package-rail car system (in./s 2 )d 2 yP02YP, -2-' Y pdt= Vertical acceleration of cask or package at itscg (in./s 2 )D2YP12,D2YP34,2d Y p12..Ydt2' P122d Yp34 ..Ydt2' P34= Vertical acceleration of cask or package at reartiedown attachment point (in./s 2 )= Vertical acceleration of cask or package at fronttiedown attachment point (ir../s 2 )d 2 .. Y RC02YRC, ---2-' Y RCdt= Vertical acceleration of cask-rail car at its cg(in./s 2 )D2YR12,D2YR34,D2YR56,2..d Y RC12dt 2 'Y RC122d YRC34 ..Ydt 2 ' RC342d YRC56 ..Ydt 2 ' RC56= Vertical acceleration of cask-rail car at reartiedown attachment point (in./s 2 )= Vertical acceleration of cask-rai 1 car at fronttiedown attachment point (in./s 2 )= Vertical acceleration of cask-rail car at supportpoint at rear truck (in./s 2 )1-6

D2YR78,2d YRC78dt2'..Y RC78= Vertical acceleration of cask-rail car at supportpoint at front truck (in./s 2 )d 2 yD2YS, -:I, Y sdtFCPL, FCPLXIF CPLIFYRFIpIRCKkFDGkSCARS, kFF2,kF2F3, kF3F4kRCUGkSCARS, KSCARSKSDG1' KSDG2KSDG10, kSDG20= Vertical acceleration of support (L/e 2 )= Calculated and experimental coupler forces,respectively [lb(force)]= Absolute value of force applied to coupler faces,perpendicular to sliding surfaces [lb(force)]= Frictional force opposing movement of slidingcoupler faces [lb(force)]= Mass moment of inertia of cask or package[lb(mass)-in. 2] or [lb(force)-in.-s2]= Mass moment of inertia of rail car[lb(mass)-in. 2] or [lb(force)-in.-s2]= Kinetic energy of system [lb(force)-in.]= Spring constant of single equivalent springrepresenting combined spring and fraction damperof draft gear on first anvil car [lb(force)/in.]= Spring constants of equivalent springs representingdraft gear combinations between cars[lb(force)/in.]= Spring constant of single equivalent springrepresenting combined spring and friction damperof draft gear on hammer car [lb(force)/in.]= Total equivalent sprin9 constant for combineddraft gears of cask-rall car (hammer car) andfirst struck car (anvil car) [lb(force)/in.]= Spring constants of II so lid ll draft gears on hammerand anvil cars, respectively [lb(force)/in.]= Base spring constants corresponding to kSDGland kSDG2' respectively [lb(force)/in.]= Stiffness of structure of car(s) (MF) at frontof cask-rail car [lb(force)/in.]1-7

kSRCkS 1, KS 1kS2, KS2k~5'KS5= Stiffness of structure of cask-rail car (MRC)[lb(force)/in.]= Stiffness of horizontal component of rear tiedownbetween cask (Mp) and rail car (MRc)[lb(force)/in.]= Stiffness of vertical component of rear tiedownbetween cask (~) and rail car (MRc)[lb(force)/in.]= Stiffness of vertical component of front tiedownbetween cask (~) and rai 1 car (MRc)[lb(force)/in.]= Stiffness of horizontal component of front tiedownbetween cask (Mp) and rail car (MRc)[lb(force)/in.]= Stiffness of horizontal component of cask-railcar suspension at rear truck [lb(fcrce)/in.]= Spring constants for equivalent springs representingvertical components of rear and frontsuspensions, respectively [lb(force)/in.]kSS' KS8= Stiffness of horizontal component of cask-railcar suspension at front truck [lb(force)/in.]= Spring constant of single equivalent springrepresenting combined draft gears of hammer andanvil rail cars [lb(force)/in.]= Spring constant of spring in hammer car draftgear [lb(force)/in.]= Spring constant of spring in the anvil car draftgear [lb(force)/in.]= Spring constants of combined springs in verticalcomponents of rear and front suspensions,respectively, in their "active" state[lb(force)/in.]= Spring constants of combined springs in verticalcomponents of rear and front suspensions,respectively, in their "solid" state, i.e.,after they have bottomed out [lb(force)/in.]1-8

= Horizontal distance from vertical centerline ofcask-rail car to front tiedown attachment point( in. )R.CPL, LCPL10CR' LOCRR.pF, LPF= Horizontal distance from vertical centerline ofcask-rail car to coupler face (in.)= Horizontal distance from vertical centerline ofcask-rail car to rear tiedown attachment point( in. )= Horizontal distance between vertical centerlinesof cask and cask-rail car (in.)= Horizontal distance from vertical centerline ofcask to front tiedown attachment point (in.)= Horizontal distance from vertical centerline ofcask to rear tiedown attachment point (in.)= Horizontal distance from vertical centerline ofcask-rail car to a suspension point at a truck(in.) (2*LRC = distance between suspensionpoints)MF, MF2,MF3, MF4MkS 1, M.

MrR, MTR= Mass of rear truck on cask-rail car[lb(force)-s2/in.]= Total mass of hammer car and its cargo (M)nNCARSFq.,RCORSCARSsgn(A)Sl, S1= Number of observations or sampling points= Number of cars at front (struck end)of cask-rail car= The i-th generalized coordinate= Time rate of change of i-th generalizedcoordinate= Cask-rail car override variable, with controlfunction:RCOR= 1.0, to override rail carcharacterization functionRCOR = 0, to activate rail carcharacterization function= Composite spring connecting the cgs of cask-railcar (MRc) and car(s) at front (struck end) ofcask-car (Mf). (This spring is composed ofsprings representing the structures of MRC andMF, and is based on the assumption of rigidcouplers.)= Signum function or sign function of argument A{ ~ ~: ~ : g- 1, A < 0= Spring representing horizontal component of reartiedown between cask (MP) and rail car (MRc)= Spring representing vertical component of reartiedown between Mp and MRC= Spring representing vertical component of fronttiedown between Mp and MRC= Spring representing horizontal component of fronttiedown between Mp and MRC1-10

S5' S5S6' S6S7' S7S8' S8S9' S9S10, S10t, T= Spring representing horizontal component ofcask-rail car suspension at rear truck= Spring representing vertical component ofcask-rail car suspension at rear truck= Spring representing vertical component ofcask-rail car suspension at front truck= Spring representing horizontal component ofcask-rail car suspension at front truck= Composite spring connecting the cg of thecask-rail car to the tip of its coupler= Composite spring connecting cg of car(s) (MF)at front of cask-rail car to the tip of itscoupler= Time (s)= Angle of rotation of Xp and Yp axes about anaxis perpendicular to Xp - Yp plane throughcg of cask or package (rad)THRC, eRCTIC, TICD, TICV, TICATMICUVXFIVXRCI= Angle of rotation of XRC and YRC axes aboutan axis perpendicular to XRC - YRC planetrrough the cg of rail car (rad)= Theil's two-variable inequality coefficients forcomparison of calculated and experimental valuesof coupler force, relative displacement, relativevelocity, and relative acceleration, respectively= Theil1s multiple inequality coefficient= Potential energy or internal strain energy ofsystem [lb(force)-in.]= Initial velocity of car(s) (MF) at front ofcask-rail car (in./s)= Initial velocity of cask-rail car (MRc) (in./s)= Work done on system by damping forces[lb(force) ·in.]WCRF= Energy dissipated as frictional work[lb(force) ·in.]= Work done on system by external forces[lb(force) ·in.]1-11

WF, WF2,WF3 , WF4W pW pl= Weights of loaded anvil cars 1 through 4,respectively [lb(force)]= Weight of cask or package [lb(force)]= That portion of package weight concentratedat rear (far end) tiedown attachment point[lb(force)]= That portion of package weight concentrated atfront (struck end) tiedown attachment point[lb(force)]= Weight of cask-rail car [lb(force)]= Weight of front truck on cask-rail car[lb(force)]= Weight of rear truck on cask-rail car [lb(force)]= Horizontal displacement of an equivalent singledegree-of-freedom(l-DOF) representation of thepackage-railcar system, displacement of package(cask) relative to rail car (in.)XF, XF2,XF3' XF 4X pXp12' XP12Xp34, XP 34= Horizontal displacement of c9 of anvil cars 1= through 4, respectively (in.)= Horizontal displacement of cg of cask or package(in.)= Horizontal displacement of cask at rear tiedownattachment point (in.)= Horizontal displacement of cask at front tiedownattachment point (in.)= Horizontal displacement of cask-rail car at itscg (in.)= Horizontal displacement of cask-rail car atsupport point at rear truck (in.)= Horizontal displacement of cask-rail car atsupport point at front truck (in.)= Calculated and experimental relative displacementsof the cgs of two rail cars, respectively(in. )= Lower and upper limits, respectively, on travelof combined draft gears (in.)1-12

= Horizontal displacements of cgs of rear andfront trucks, respectively, on cask-rail car(in. )YCPL= Vertical displacement of coupler face oncask-rail car (in.)= Vertical displacement of an equivalent l-DOFrepresentation of package-rail car system, displacementof the package (cask) relative to railcar (in.)= Vertical displacement of cg of cask or package( in. )Yp12, YP12Yp34, YP34= Vertical displacement of cask at rear tiedownattachment point (in.)= Vertical displacement of cask at front tiedownattachment point (in.)= Vertical displacement of cg of cask-rail car( in. )YRCMAXYRC12t YRC12YRC34, YR34YRC56t YRC56YRC78t YRC78lCUGlCDGO= Maximum downward vertical displacement of railcar (the point at which suspension springsbottom out or go "so lid") (in.)= Vertical displacement of cask-rail car at reartiedown attachment point (in.)= Vertical displacement of cask-rail car at fronttiedown attachment point (in.)= Vertical displacement of cask-rail car atsupport point at rear truck (in.)= Vertical displacement of cask-rail car atsupport point at front truck (in.)= Vertical distance between line of force and cgof the rail car (in.)= Distance between centerline of draft gear andthe cg of cask-rail car (in.)= Vertical distance from horizontal centerline ofcask to its top and bottom surfaces (in.)= Vertical distance from horizontal centerline ofcask-rail car to its top and bottom surfaces(in. )1-13

U CPLu 6, u 78 CPL8 6 , 8 7epeRC~CPL= A factor to allow the damping term DWCRF to varyas a function of the absolute value of thecoupler force IFCPLI raised to the factor power= Factors that allow the suspension system dampingterm to vary as a function of the absolute valueof the velocity (YRC56, YRC78) raised to thefactor power= A multiplying factor representing the fractionof the coupler force IFCPLI actually appliedto the moving coupler faces= Multiplying factors representjng the fraction ofthe load on the respective rear ana frontsuspensions that is applied perpendicular to thesliaing surfaces of the damper= Angle of rotation of X~ and Yp axes about anaxis perpendicular to he Xp- Yp planethrough the cg of the cask or package (rad)= Angle of rotation of XRC and YRC axes aboutan axis perpendicular to the XRf - YRC planethrough the cg of the rail car rad)= The coefficient of friction for the sliding ofthe two coupler faces against each other= Multiplying factor corresponding to acoefficient of friction for the damper in adraft gear~D6. ~D7~XT= Multiplying factors corresponding tocoefficients of friction for the dampers in therear and front suspensions, respectively= Coefficients of friction for sliding contactbetween tracks and wheels of anvil cars 1through 4, respectively= A multiplying factor representing extent ofenergy dissipation (0 ~ ~XT ~ 1)~XT = ~XTC' when X T > 0 (Compaction)~XT = ~XTE' when X T ~ 0 (Recovery)1-14

~XTC~XTE~PR= Energy dissipation coefficient for cargocompaction= Energy dissipation coefficient for cargorecovery phase= Coefficient of friction for sliding of packageor cask on rail car= Multiplying factor where:$(XT) = $(XT)L, when XT ~ 5.6 in.$(XT) = $(XT), when 5.6 < XT < 6.35 in.$(XT) = $(XT)U, when XT ~ 6.35 in.= Frequency of vibration of the l-DOF EOM for therelative horizontal motion of the cask-rail carsystem (rad/s)= Frequency of vibration for the l-DOF EOM for therelative vertical motion of the cask-rail carsystem (rad/s)= Summation of horizontal forces acting on thecask or package [lb(force)]EF XkC[FypEFYkC= Summation of horizontal forces acting on rai 1car [lb(force)]= Summation of vertical forces acting on cask[lb( force)]= Summation of vertical forces acting on rail car[lb(force)]1-15

A P PEN 0 I XIIFIGURESII - 1

oHEDL 7803-106.2FIGURE 1.Spent Fuel Shipping Cask-Rail Car System Modeled.__I MTR 1 -----+ .fL-Mr.:..:....F~I _FIGURE 2.Spring-Mass Model of Cask-Rail Car System.HEDl7803-106.4II-3

--M!Ijr -,p1--lrSI5.., .y,52I- IM RC55I1 59. ~ 51~ ny5 L~ 53SCARS1 8 J{ ,{M f 1~56 57 ~ 1IIMTR I I Myf IHEDl 7803-106.3FIGURE 3. One Possible Orientation of Cask-Rail Car System After Impact .....-"1 IIIr-----"""1II: ~Xp_ ... __ .... - ---of+. IP12: X -rl r- lfr ...•...... ~-, -t Ypl2 T IIIIIIIII I .L----i- --J_ I- - t- - - - - - - - - - - - - - - -- - -r - - t--+-----,II____ L _ ....l..----L........J ---!..._+-.-- _HEDl 7803-106.5FIGURE 4.Comparison of Orientation of Cask-Rail Car System After Impactwith Initial State.II-4

VXRC1 - ,Xl rX2IHAM~:i CA' ~ STR:C~L LXRCX01CA'I"'0 0X-gLoLx O ' ~XFLEGEND(0) COUPlER SUBSYSTEM SUBMODELoo - CALCULATDll'3o - EXPER IMENTr.,LI M,C t---t e-t M, Ienoz:::>00~~lwUQ::o...... t...o...... Lx LXQ::oI RC F w(J1...J0...(b) COUPlER SUBSYSTEM SUBMODEL WITH EACH DRAFT GEAR REDUCED TO AN :::>o:0.EQUIVALENT SPRING u

.......'"00"'~ ~l:0: n-;:;h0I (\I.I LEGEND~I1 I L~GENO0- CALCULATED~.,~.jI o - EXPER I MENTALiIII IcJ Iojr" 1I I;:,.; -.1DI I tl IZ=:>Io CJ II~: ~~ ~ 0- U'l, I~ ! IWU Ia:: i I .25 t... ~ I6j ItJu a • 16.n~ .U>I •....... :~iJ i 0 1 I~ ~1O'l ~ - Iel~\'0oj1·0@@.....8 @S'SOH ;:)O'HOH()laEJ 8 g ~ ____ ooOJC'Joo - CALCULATEDo - EXPER I MENTAL·.·c....n·· ·n·· '0-··0"'0':' f----,.-------,-,---"-----".--------".-------" top I I Ii II IO.CO 0.01 0.0l;! 0.12 0.!6 0.20 0.21 0.00 O.O~ 0.08 0.12 0.\6 0.2C' 0.24TIME (SECONDS)TIME (SECONDS)FIGURE 7. Coupler Force vs Time During Impact FIGURE 8. Coupler Force vs Time During Impact ofof Two Hopper Cars Loaded with GravelTwo Hopper Cars Loaded with Gravel(Spring Constant of "Solid" Draft("Solid" Draft Gear Spring Constant aGears = 1 x 106 lbs(force)/inch). Function of Draft Gear Travel, X T ).

~.,,---------------------------'IoL'l0::00f-';"ucr:L...Ul...... Z......I""-J~ ~ I~o /• . I-'r') ,,~ /0' ///----/ .....JP-,q~(").N1 / I 8 ~~I ~ i~J // I'"00..-I ....;'* o~.o~· ,,5·00I5·25i5·50I5. 7 5 5·uuI'6·25 E·5GI5·~: 0.00 0.05RELAT!VE GISPLRCEMENT, !NCHEScSooj,..-...~UoC::c:io~Cf)qor-Z~00~c.oW oU.c.;0:::o~o0:::'"~q(;)oq0···0I0.10o -o -TIME (SECONDS)LEGENDCALCULATEDEXPER IMENTALI0.15I020FIGURE 9. Ratio of "Solid" Draft Gear Spring FIGURE 10. Coupler Force vs Time During ImpactConstant to a Base Value.of Two Hopper Cars Loaded with Gravel.

0 qa) 0~LEGEND G LEGEND0cD o - CALCULATED 0 o - CALCULATED~...Q ... e ...o.O... Q ... Q .. O..• Q •.O... e··o - EXPER IMENTALei~ o - EXPER I MENTAL-.(j)qCl[LIt'B---ElZqB~ B 00Bu eDUIIIE'I[LIZ...... 0 E'ICf)~

8 q'"q8G~f;.:]if)'2)qf/5~-........if)f;.:]o::Co~~.....""-"..... 0::..... ~Zo.....o·8~NI,...JqI.D ~ougu

o~-§LEGENDa a a = X"bq* -o a>Zq ..o-.. ~ ... ~.. =.TC!o ~ X TA '&.lU~ J··'E)·"G ..oSUoO::aio......... ·G.rnrz..rz:l' 0'0.{f)0::r: gor-U.Q•.•.;z;ZQ::J...... oq......)::'C! 0.. ~~~g...:l '0"''0'''0''-0rz:loU~ "''0'''0..'0...'0..~·G ...().~ "'0"''0'''0SIIii i0.00 0.05 OlO 0.15 0.20TIME (SECONDS) .i0::rz..g,gsg ~'0-".~;;-'.,' I." \'0.00 0.05"~I Io ,'f'I II II IIIIo, ,IIIIIț,oI,I, ,III , ,I , I , ,,,,,,,,,0.10 0.15TIME (SECONDS)LEGENDCALCULATEDEXPERIMENTAL---._--------------_.0.20FIGURE 15. Relative Velocity of Two Gravel FIGURE 16. Coupler Force vs Time During ImpactFilled Hopper Cars vs Time Duringof Two Gravel-Filled Hopper Cars.Impact.

00;'gl'-0 r,n.Cz;Jr-::r::u~C!_coE-z~o:::Elti~u............t:C!u~0...:I~o>~til>0~g...:I~oo:::g~g0.00LEGENDCALCULATED.--------- EXPERIMENTAL------------0.05 0.10 0.15 0.20TIME (SECONDS)FIGURE 17.Relative Displacement of Two Gravp.lFilled Hopper Cars vs Time DuringImpact.FIGURE 18.Relative Velocity of Two GravelFilled Hopper Cars vs Time DuringImpact.

0~0~0~c:::lZ~~...........c:::lzq~~............ enI--'...........N~§UẔ0~:~",,"- I ,~ " ,,:: , ~0 I',,~ I' ""I"\_... 'bo* LEGEND~--- CALCULATED gUoO::a:i---------. EXPERIMENTAL ~gs~Z~a:~I, ---I~oIIU.o0::I,II,III ~IIIIIIII~oc.. oo::ooio.....Jo..q~C'JoI~III\\\\\U30d,0.00 0.05g~I iii iii I I0.10 0.15 0.20 M W M M ~ M M W M MTI ME (SECONDS)RELATI VE DISPLACEMENT (INCHES)FIGURE 19. Relative Acceleration of Two Gravel FIGURE 20. Calculated Coupler Force vs CalculaFilled Hopper Cars vs Time Duringted Relative Displacement of TwoImpact.Gravel-Filled Hopper Cars DuringImpact.

-"bq* q ...FIGURE 21.oc::i 4-J...::::::---r--,--.,...-----r---,r--,...----r----,j----,10.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 9.0RELATIVE DISPLACEMENT (INCHES)Measured Coupler Force vs Measured Relative Displacement of TwoGravel-Filled Hopper Car~ During Impact.FRICTION DAMPERDRAFT GEARRAil CAR SYS TEMSUSPENSIONSUBSYSTEMSPRINGGROUP--.+TRUCKHEDl7904-32O.1FIGURE 22.Arrangement of Springs and Dampers Simulating Rail Car Couplerand Suspension Subsystems. Neg 7904699-111-13

£Rfe-- QCPL-~I IMReI ~ __ I~ - ---I : rt~ z-

-- --/~~CD.Ik l2CDkk Rj,..rI"'" l< u..--- -..........: ~3~3) "'Fl :::::::--R.........-:::::~ kR2 ---- R3 --kF3F56 57rL({ULIIIIHEDl 78().4-17.....FIGURE 27.Dynamic Model of Cask-Rail Car System with Bending Submodel.d IIMfMMf-2r

CASK-RAll CARANVil TRAINHEOl 7902-125.1FIGURE 29.Cask-RailCar and Anvil Train. Neg 7901733-1"bq..... CIl* -g-2 1234COUPLERSHammer Car - Anvil #1Anvil #1 - Anvil #2Anvil #2 - Anvil #3Anvil #3 - Anvil #4t:a::lU o~.0

2 .'.0·· .. · '''''''''0. '.LEGEND1 Hanmer Car2 Anvil Car Nl3 Anvil Car *24 Anvil Car *35 Anvil Car N4.~o'qCf)OCxJ::r::u3Zo-gjQ.''''·0· .. ·,t5" - - -fr - - - -6 - - - - -6- - - - -tl - - - - 6- - - --f!/;~I,,,o , 4, "'--'- --+-'-'-+-,, /,,/ 5/ ~~ ~ ---"---i

"0... ° ..,,;az°N0°ItI,,,"-.-=.-...::..;-- -- -------------FM-MUIIiPLEXTAPE/vr/'f0u oC:::lN GROUND SIAIION IU)I.........SAVANNAH RIVER LABS -lCl - - - - - - - - - - - - - - - W~D£~AH~ IZoC! .\~)A / VFM IAPEU ...IC:::JIIU) .'0 !-.........cr...::r:'" ./ -I[ID9]J\~C!WID£-BAHD FM-MULIIPlLXl I FM IAPE JAPE--' u \L ~~I~1..0 ._ẔV°a:iGRAPHIC I. I POPIICYBER 14I01 SPLAY IIBCSI~-0---0- CARDS Hodel Results (Full System) < >IANAlYIiCAl0 MDD£L0 ---z=:..~ CARDS Model Results (Isobted Ra11 Car)i-~-~- Experimental Results (Filtered at 100 Hz)HANFORD ENGINEERING DEVELOPMENT LAB0Ni0.00 0.05 0.10 0.15 020 025TI ME (SECONDS)FIGURE 33. Horizontal Acceleration of the Cask FIGURE 34. Shock/Vibration Data Flow for DataRail Car During Impact with FourReduction Model Verification.Hopper Cars Loaded with Ballast.(Test 3 - Instrument 12: Filteredat 100 HZ)(Case 1: MeasuredCo~pler Force).

............IIE 32010o-10-20>-MAGN ITUOE OF FFTIE 6N 1.0a- ·11 i1,\1'\I 'I ii,IIIIII, II: I: , II II IrII: iI:~I 't :I Ii llli ,riI\11,I I IHOR I ZONT AL CENTERACCELERATION -o2XRC(\ II' !\ I ~,I I' : ,I ) Ii I, : 1i f i',r'Io 0,51 1.02 1.53 2.04 2.56SECONDSIE 3I I I I-J-----I---l---I>....--l----I-- VERTI CAL STRUCK END _40 ACCELERATIONo2YR 56I20-20,Q! 1JlW..-.l-+.--+.-----J.-l..-...I--+---+-+----l. ~kl ,rr I )11 I I .1.';111 I!I! :i I !I! 11I!i. \Illlillll "hilI \ hlll~U"'II/~,lll.oi rI,; 11!-40aMAGNITUDE OF FFTIE 61.0Ii' 1\1f1'r WIll W~llf /imnrlWI'l'tfI"TI0.51 1.02 1.53SECONDS2.042.560,80.80.60.60.40.40.20,2oo 10 20 3D 40 50FIGURE 35a. Acceleration Wave Shape and CorrespondingFrequency Spectrum Obtainedby Fast Fourier Transform. (HorizontalCenter Acceleration.)HZo oFIGURE 35b.10203040 ,0HzAcceleration Wave Shape and CorrespondingFrequency Spectrum Obtainedby Fast Fourier Transform. (Vertical,Struck End Acceleration.)

1E 34020-20III:.111 Ij.l I I':; ~ I' II j ill , :~ ~ ~ ~i 1.1;". J' : II,1l,,'1 .!hllI !,;'!if!' I 1;1 1rm Hilli' 'Ill iIp .•IIVERTICAL-FAR ENDACCEl£RATIONo2YR 78 -I~\AGNI TUDE OF FFT OF 0 2YR S6-40 ~o 0.51 1.02 I.S3 2.04 2.S6 0 10 20oSECONDS-MAGNITUDE OF FFT IXI91IE3IE 6-IN 1.0--' 400.80.60.40.2o o O.SI 1.02 I.S3 2.04 2.56o 10 20 30 40 so SECONDSHZFIGURE 35c. Acceleration Wave Shape and Corre FIGURE 36a. Filtering of Acceleration Datasponding Frequency Spectrum Obtained Emp1oyi ng Inverse FFT., (Powerby Fast Fouri er Transf orm. (Vert i Spectra and Time Domain Image.)cal, Far End Acceleration.)IE 61.00.80.60.40.220-20-40o• I, 'I'!IIi,I, I,Ii 11\ JI \ i I \\rlA ) '" '\..fJlh' '~i~i'~I..~IsO"IHzpowJR SPEJTRA_oTO SO Hz7S~~IME D~AIN IIMAGE10F100" OF THE SPECTR A -o TO SO HzI UI~IAh,. ! ;'' 1"'1~ I' 'II HI'I"II I,~,,I

IE JIE 340I20oI-20ILit 'pill Id1l1;,' r 1 .!!I~IIIii'\\l' i'~lll,:11-'1i~lh II ~ll,.' .I!!hjiljjil l\/I~l'I I ITIME DOMAIN _IMAGE Of 75"OF THE SPECTRAoTO 37,5 hz -IIfI~H,15-5IIII ., I! ~Ii p,. f ~ I 1,1!Ir~, " \1 III \ h..l~IiII!i 1\1 II! 1\ 'I Ii: \1IIII \1,1'I:r IrII I ~ rII IHOR IZONTAL CENTERACCELERATION WITH _HANNING WINDOW·40 -152.56o 0,51 1.02 1.53 2.04 o 0.51 1.02 1.53 2.04 2.56I,ISECONDS.......... IE 3 IE 3INN10I !" ~" ,," I""lI"I I ITIME DOMAINIMAGEOF50'J0OF THE SPECTRAoTO 25 hzI_,~MAGNI TUOE OF FFT D2X RCSECONDSIo!V~ .- Vv ~ v v;1I y300II• ! ,200-10,I I100I;i-20o 0. 51 1.02 1.53 2.04 2.56 oSECONDS500400} !1/ ~ 1 ), ,o 10 20 30 40 50HziiFIGURE 36b.Filtering of Acceleration DataEmploying Inverse FFT. (TimeDoma i n Images.)FIGURE 37a. Hanning Window Effect on Power SpectraWhen Applied to Time Domain Data.(Horizontal, Center Accelerationwith Hanning Window.)

1E3D2YR5610 1 r I 1-'-------'VERTICAL. STRUCK END6-} I I II I I ACCELERATION WITH HANNING WINDOWt--j--+--rl+-:tt-t---I--+-4--+----4--1-2"a'~-6............ 10INW«Xl-101 ! .! ! I I I I I I Io 0.51 1.02 1.53 2.04 2.56MAGNITUDE OF FFT D2YR56SECONDS300I28 lO-'O CEllHEOl 7811229.1mOOWN CONFIGURATION .".200100Ij\~ / "-o ,o 10 20 30 40 50HZ..r-J J\FIGURE 37b. Hanning Window Effect on Power Spec FIGURE 38. Tiedown Configuration and Instrumenttra When App 1i ed to Time DOOIa in. Data.Location for Cask-Rail Car-Tiedown(Vertical, Struck End Accelerationwith Hanning Window.)Tests (Tiedown Configuration "A").

3 FORCE4 DISPLACEMENTFIaJRE 39.~ TRUCK28 LOAD CELLHEDL 7811229.2Tiedown Configuration and Instrument Location for Cask-Rail CarTiedown Tests (Tiedown Configuration "B") •1 ON CABLESHEDl 7811229.3FIaJRE 40.Tiedown Confiquration and Instrument Location for Cask-Rail CarTiedown Tests. (Tiedown Configuration "e").II-24

CABlE LOAD CELL263 FORCE/,4 DISPlACEMENTFIGURE 41.28 LOAD CElL HEDL 7811229.4Tiedown Configuration and Instrument Location for Cask-Rail CarTiedown Tests (Tiedown Configuration "Oil).."VI...100o'0> -50E.:0>'"FILE·RECORDSlE-3TESTIH.OAT33 TO 49c;o..-;:;t!!-190-150• SF • Scale Factor f~ Table 8FIGURE 42.-298o .~ .41 .614 .819 1.924.182 .307 .512 .717 .922IE 3IluIIber of Data SUlples (Thousands)(Tt_ In Seconds· No. Salllples • fl.39 MIlllsf'conds/Saoople)Horizontal or Longitudinal Acceleration of Car at Car/Cask Interfacevs Time (Instrument No. 12 - Unfiltered).II-25

... •on..zse290FILE' TESTlA.DATRECORDS 33 TOlE-349150109'0 "' 58"' .>-"' 0" 8>1:U.=c-58"' c!u.. -lee0...

lE-3• Frequency DC to ZSO Hz's1013o oOrder of IlIl"111Oillcs(Frequency· • Order of Itll"lllOnlcs x Z.S Hz/llIl'11Onlc Dhlslon)FIGURE 45.Transfer Function Magnitude vs Frequency (Vertical Energy Transferfrom Instrument No. 22 to Instrument No. 11).9s• Frequency DC. to ZSO Hz's--z~:> 70'"~Cx63READY:t210 20 40 66 70 80 90 100Order of IlIl"111nlcs(Frequency· • Order of IlIl"111nlcs x Z.S IIzllfll'1llOnlc Division)FIGURE 46.Transfer Function Magnitude vs Frequency (Vertical Energy Transferfrom Instrument No. 11 to Instrument No.9).II-27

7• Frequency DC to 250 Hz' S61READY~ . 10 40 713 80 510 100FIGURE 47.Or~er of Hannonlcs(Frequency· • Order of ilannonlcs x 2.5 Hz/llannonic Division)Transfer Function Magnitude vs Frequency (Horizontal EnergyTransfer from Instrument No. 12 to Instrument No. 10).3.3• Frequency DC to 250 Hz's32.521.51\FIGURE 48..5REAOY* ee 10 20 30 . ole 60 80 loaOrder of lIannonlcs .(Frequency· • Orde~ of Hannonlcs x 2.5 Hz/llal1loonlc/Olvlslon)Transfer Function Magnitude vs Frequency (Horizontal EnergyTransfer from Instrument No. 10 to Instrument No.8).11-28

-C!sO!0~ex?0ex?E-o 0E-0Zr...:JZr...:J..... r-u~ Uei-tz..tz..-tz..tz..~ex?r...:JOeoUo·OU> >E-olQE-o IO::3 0 ~ei...... ~ ~I g~N Z1.0 Z........... CY...,.rz:Ieil:/)C":l....:lo-rz:I::r:E-o~l:/)e')....:lei.....rz:I::r:E-ocq..., ...,000C! C!0, 00.00 0.05 0.10 0.15 0.20 0.00 0.05 0.10 0.15020TI ME (SECONDS)TIME (SECONDS)FIGURE 49. Comparison of Calculated and Mea FIGURE 50. Comparison of Calculated and Measuredsured Coupler Forces Using Theil'sRelative Displacements of Rail CarInequality Coefficient as a FigureCenters of Gravity in the Time Domainof Merit.Using Theil's Inequality Coefficientas a Figure of Merit.

9 9O!0O!0.-..-.•w0It!E-t 0Zt:il-r-Qd-r%..~CI)8°~lQ:3 0~a' ...t:z:ldẔC'J)~....::lo-t:z:l:r:E-ttlf0It!E-t 0Zt:ilu~&:r%..t:ilCl)o·C,)0>E-t 1O:3 d~a' ...t:z:ldẔ~~-t:il:r:E-ttlf0~0 aC!0,0.00 0.05TIME0.10(SECONDS)0.15,020g0.00 0.05TI ME0.10(SECONDS)0.15 0.20FIGURE 51.Comparison of Calculated and MeasuredRelative Velocities in theTime Domain Using Theil's InequalityCoefficient as a Figure of Merit.FIGURE 52.Comparison of Calculated and MeasuredRelative Accelerations in the TimeDomain Using Theil's InequalityCoefficient as a Figure of Merit.

:~e-.lX!'bq~~ZO~~ou~- Ur-- 0::r;:d0r:..r:..~ rnq°eooSUdZ> ::>e-.0-",....:l.~q U.......... a-w • Zd 0 r:..q---'0::-~.,.0::-~...:Ie?~Q..d....:lQ..qor ...eo::>q~ 0'"::>CI:lU::::So~ CARDS Model Results_____ Experimental Resultsd "~0g~I I I I d0.00 0.05 0.10 0.15 0.20 0.00 0.05 0.10 0.15 020 025Tl ME(SECONDS)Tl ME (SECONDS)FIGURE 53. Simultaneous Comparison of Calcula FIGURE 54. Coupler Force vs Time During Impactted and Measured Response Variablesof Cask-Rail Car with Four Hopperin the Time Domain Using Theil's Cars Loaded with Ballast (Test 3 Multiple Inequality Coefficient as Instrument 3) (Case 1: Measuredan Overall Figure of Merit.Coupler Force).

"0 _ co qit,I~ ",,II, ỊI •"bq _...:¢~0I

C!~l..-..ur:.::lC!~§U'" lr:.::lC/).......... 0~~UIgJ--\.IUZ, ,.....-- --II'~Z§ 0...... OM...... ~IIW ~r:.::lowrj§U.,. 1 0

0§.'"~,-...0~~...........U~oC/) ............§cn~::r:UZC!0........z...... °0......I ~§W~-~ rx;J1...:l~C!8~

'Oq*'~0~"b 0 _cd* q..-0=!..-..~Uo::q100~rnQ5~0-0..-IWU1 ~qUIO 1 0::0~q0i~Ig10.00,'. ," ()I ,> Q 'Q (,>,,0 b/ '.'PI ,\ ,\ ,\, I\\ IQ >,0'e'(SE) = Struck End(FE) " Far End---0-----0-- Struck End (SE)~ Far End.. (FE)0.05 OJO OJ5 0.20 0.25TI ME (SECONDS)..-..~~U~rnqQSZ::>~_0cD~U0::o~~0::~~0..::>q0"u\QI,I,",I' ,,,~ ,,' ,,,' ,,,' ,\,1 -6~: oq I~,' Io.~_/\\I.. 9\ , \I, ,", \a, : ~, \ I ,, I I \, I I ,r \, ~-~i;--~~---o---~- Experimental-0-0- Calculated .....I I I I0.00 0.05 0.10 0.15 0.20 0.25TI ME (SECONDS)FIGURE 61.Vertical Tiedown Forces DuringImpact with Four Hopper Cars Lo~dedwith Ballast (Test 3) (Case 1:Measured Coupler Force).FIGURE 62.Coupler Force vs Time During Impactof Cask-Rail Car with Four HopperCars Loaded with Ballast (Test 3 Instrument 3) (Case 2: CalculatedCoupler Force).

"'00;:-'cO"0 "r.: ", " I, ỊI:Q,0 ---0----0-- ExperimentalcD~ , I, ,l'.:z:JU,I~ Ioq,r:,....r, ,,(/)IClZo ,I:::::>t"i..........0 oIwIIl.,Ici,0' 0,9I0~~~eII, I,II,cj.,I"•~Calculated"'oq.... ..r*~~Uol'.:z:J 0~~(/)0-""""'N(/)1l'.:z:J::r:uZq_..r-IZooe::«cD~Il'.:z:J....Jl'.:z:Jou

0~ §"'"00...... _t')...... E-

§ 0...,.oN§ 0(')lC)..../'~'[)Clc.::J8Cf.la:J..........Uc.::J oCf.l'&t§:r:Uzo _0-Z...... °0......I~~W 0::COc.::J1....:Ic.::JCl~§

C!~g"bC!_0it ..............:;0g-rz:lU0::C!0\0ez.gszc!~o\0I;J0.. ~........I rz:lo\W u.o1,~ \0::0 0.ez. ,,,0Q :-ci~C!CD~~~~~,'q s:', /Gl., ~qz ..: " '0=>~'4Jo..qo'(f)I:III(SE) = Struck End ~I '-0 (FE) ,. far End.--

'9~*~~~tjO::qo.ra.ra-I~~oz~~.0~9~910.00IIII ", I, Io CALCULATED, II' , _~u~1~ltQ_:-__ UJ;:;:L ?J&~I I, I, IIIIIIIIIIIIIcDIII ~I, 'II,II ,II ,I, I , I ,II ~,III I, ,II19I , ,II .. G1 QI '0-' "()Q.06 OJO OJ5 020 0.25TIME (SECONDS)§•q~-q~~"u~q&f~::z::u-Zq_0Z0 0~§0::'"~Icjq~~

~l ~I0 CALCULATEDo CALCULATED o SRL T~10 - INST ltl50HZ6-u~o ~§00 00....................u§ _~__ sEt_-'tE$J'JJl_:-_)RSt_~n9PJjZ) ~~ -i.- -~ALC; -RAlt" -CA""R- o1J't"R .'rlHJ~da:.E:~ ~~,=~§f2= u~§ Z_0-j-............ z~ 0It&i. .~\t..... ~~ ~,0:::.~r'0:::'~ ~~§ ~" /~~ u_

~g* *"bC!-~~ C!...~...... E z~...... t'd o ~I~No SRL TESTll - ! NST 3£~.... ~~~ ,~C!cnro- C!~0--0cie-o~~~~.... 0~CJori08" 0..C!~~....~~....&i~~9C!0g -il----·-rj------rj------"r------r-,--I ---.-- I0.0 0.2 0.4 0.8 0.8 10RELATIVE DISPLACEMENT (INCHES)0.00 0.05 OJO OJ5 0.20TI ME (SECONDS)0.25FIGURE 75. Stiffness Coefficient of Horizontal FIGURE 76. Coupler Force vs Time During ImpactComponent of Tiedowns vs Relativeof Cask-Rail Car with Four HopperDisplacement Between Cask and Cars Loaded with Ballast (Test 11 Rail Car (Tests 10 and 11). Instrument 3).

..........I~W9~* -q:!:~g~l:t::oOedrz.l'J)°0 z·::>10~C!...~o.!.o~'.• eJ," II" ' I,,I,,, ,,,I,,¢,,,,,,,,o CALCULATED_9__ $..iji'_J:ES.TJl::_J.l·lS1_?7&~, ,a. "", , ".,\El..~&,_..(;)~~- ~l'J)......... q~~.........~5Zq.-.0-~.-.~oe3~~I~U~ o§TSI'I-6 - Ef- S-IO- -0o CALCULA;,:,T;.!;!E~D----..........---,,..,....,..,,,,,,,,""~_9__ ~~L_J:F;$J'JJ __-: __U~S1_t~(tQQR4}IIii iii f I i I I0.00 0.05 0.10 0.15 0.20 0.25 0.00 o.os 0.10 0.15 0.20 025TIME (SECONDS)TI ME (SECONDS)FIGURE 77. Horizontal Force of Interaction FIGURE 78. Horizontal Acceleration of the CaskBetween Cask and Rail Car vs TimeRail Car During Impact with FourDuring Impact with Four Hopper CarsHopper Cars Loaded with BallastLoaded with Ballast (Test 11 (Test 11 - Instrument 12: FilteredInstruments 27 and 28).at 100 Hz).

- ~CIl~1ti"§i't'i.I ..~~-IZ..... 0I~-~ ~~Ifjl~

TESTS 3 AND 18STRUCK END....4.__---- It---J~IIII L..-00I 4OTONJrI I.. 70 TON SCl .....J 1-00FAR ENDTEST J- STD DRAFT GEAR- T1EDOWNS . 6 BOLTS· P-22 RAil CARTEST 18· CUSHION UNDERFRAME- TIEDOWNS - 6 CABLES· PS-22 RAil CARHfDl IJIM-lf6.1FIGURE 81. Cask-Rail Car Configuration Used in Tests 3 and 18.TESTS 10 AND 11r91.61.In.- -~STRUCK END.. ~00- STANDARD DRAFT GEAR- TIEDOWNS • 6 BOLTS70 TON .J,~70 TON SCl P-2200I..FAR ENDHfDllJIM 166.2FIGURE 82. Cask-Rail Car Configuration Used in Tests 10 and 11.11-45

TEST 13_38.5_in.STRUCK ENDJ:=tlI 40 TON -$ IFAR END~TONUC -~.---------I000 000- EOC CUSHION DEVICE - STANDARD DRAFT GEAR- TIEDOWNS . 6 CABLESIHEDll3lM·'''.3FIGURE 83. Cask-Rail Car Configuration Used in Tests 13.TEST 1618.25 in.~---L.......-__~ l ~40 TON -Etr~S-----I-----FA-R-EN-DSTRUCK END000_~BOTON UC . 000- STANDARD DRAfT GEAR - EOC CUSHION DEVICE- TIEDOWNS . 6 CABLESFIGURE 84. Cask-Rail Car C~nfiguration Used in Test 16.HEDll3lM·' •.411-46

'bC!-~*C!::!:C!SwUO:::C!OcoI':............r.nI 0....... ~00..~ Z

'bq

§'OJ'~..-.,~§enCll"'U~eng"'-0en~::z:...... U...... ~oI~I.D'-"Z0E=§

C!_0* I()0.0..."'oC!_

O-'"'o:=>- lfl*wucc0q't'~- f£ ~lI- ~U"1~~~ II3qo... '"oSRL TEST13 - I l\iST 3o7 ii, I I I0.00 0.05 0.10 0.15 020 02"TI' 'E (~-~O':~~·'\'1 ;:::.~\... 1\1;':::-)c.;'bg- ~)*~gqli](/J 00Z;:)on. q'"ITo 8II01:10'7 I0.00\'(j) "I, : '," , , ,: • 0 CALCULATED?~,~/ \1 \, ~ dJ L, Gi, , ,CD\ CJ"\ , I\, \,: 1, _?- - $J~~. IB$:tJ.~. -=-. JK$.1 J~J\1 Q,' ,,, , .0;~•"I i I I ,005 0.10 0.15 0.:20 02.5TI N' IE (~t:'(-O';D-')~~~ _., ;:,FIGURE 93.Coupler Force vs Time During Impactof Cask-Rail Car with Four HopperCars Loaded with Ballast (Test 13 Instrument 3).FIGURE94. Horizontal Force of InteractionBetween Cask and Rail Car vs TimeDuring Impact with Four Hopper CarsLoaded with Ballast (Test 13 Instruments 27 and 28).

§1gJ ,g: 0 CALCULATED__ MUMU gJ:.9__ MSJ~C. I'tESJ'J~. ::-. JNS.T.?IB.o.8?J,,A-_. AX .__ .__ .__ .__ , IEI3 C\I I rb' : ~,'': ~\, I,~I\, I'I 1 /:;JlfJg,"I \q ", \ , \I , \?;)~-QL\ , I ...... \ I I~ I \ I ,, \u ::r: "\...... ..... 0,......I -~~l' \N\ "\J jl:il g \ , ,.....E~U~U i"J"< 'i8j I"'I1 I.__ .~i1 "1"1----.....----TI----...,-,------",.------"'000 0.05 010 0.15 0.20 0'2.;TI :ViE: (3ECO:-i03),.-...u~lfJ"U~1§wolfJ"~::c:Ub\ ,~§ \-I\,z\o~

"'-. E'~ o CALCULATED_~__ $J~1._ .IESJ'J~ _-=-_ Jt{~t _nCQ9RZ)~8~grn- 8 1ut'rn 10 (2)' ,",C:il ,~,, ,"'-.81 ..... ,. ~ "/..... ~ ~~~~', ,f,I. '(Jl :::::.°r~ ' /'...-..U C:i]8rn'""'-.~ , ~§J-..... , , " . ," 0 ::c: /.UC:ilC:il /,o CALCULATED_~__ ~ESJ'J_::i _-=-~ J~~t _~i9PJ:i?)://~,U, \ze:: I" ~ "I•I ,/~8,..... , ,, ........-C\J ,I 9I ,ILl CDZ Q :\ ,W o . ' ,,,' ' o " '"~ Ok,' ',.--, ' , ,"'~ ~1 ~iIC:ilJ•, 'J I',/ ,/0v'r\ I I I \ IC:J CD J \ I \u8II I, \1U C\Jlu8II If 1 IU ::ll

·0 q ·0 q~~q""''"_0* '"q o CALCULATEDg o SRL TEST18 - I NST 3 _'?__ ;un",_ .:r.~SJ'J~ _~_ JR~t _?J _M~UJ~ ~_~aq1

~~--- u~~Cf).........~§Cf).........~::cuz...... ...... 0......I Z00101e:~§~- ..;ll~UU

-I~l§,-.,U~C/)-........u~oC/)-........&5::r:uZ8...... ...,......... IZ

~G~oC/)d~~C/) gC!-~ _'f~~o..i 0°0.. 0~~rz..i00Z~~I.....IE--< 0(Jl-.....I&3~...JIe~oS

E'~uens~C!'I Q

-IU'1\.0g~ ~E: 1 [3 0CASE: I [3 0- ~2 G·········· ... ···OCASt::I tI--------A , , CASE: 2 G················OCASE: 1 _.--+ u ,_8 CASE: 5 )( ~ W \ CASE: 3 tI--------A(/)\ug\w .....\_.--+(/)U\ CASE: "..... We\(/)LnCASE: 5 >E ~..... N lI.t3§ o!:CC7la::ZQ::-Z;§ o0'"-~8-~a:: N~8WO -l-l .... WWUUUU oa::a:: 0 -l-ltDa::ea::ZLnu ,- "lilt0-~~§ ,. , '. ,,a::>. , , o0:::W>0 W-g >0~ ..I ""',:.,'a"-0a:: "~-l a::W -l-w Ln ~~~~::l ~-l ::l~§a::",-/,,

§.?is~o~§_I- E-§... CIJoi;fiCiP::_a: 1III ~§. CIJ1•r:z.! O~.....Z,.....O·I• -0' ~~0 ~ ~I...:l~!! LzJ~..~~Iil!~~;;;Zll!I§§0::.10~ ;:t:§....I0.00 0.02 0.04 0.06 0.08 0.10TI ME (SECONDS)..~u§ r.:::I_CIJ~~CIJoi ~~;~~0..fi;Ii. Zi~~. ~~~~• ~§~ (j.~~~!!~SIll'ISt CIlS£ 13 EI:;i 'CIlS£ 7 C3 El~§CASt 8 b 6 !..~~>...0S0.12 0.14 0.16 C0.00.0.,I ,I, , ,, al,, ,Q/ ,I, \ ,, / Q.,/,II \,I ,/I\81'151: CIISC C3 EI IG,CASt: 7 C3 El ,/I/,CASt: 8 b (I)'5," I ,I,,,I,,q{IIIIII///0I ,I/~I/I/ ~ y .''''-...-.,./--0.02 0.04 0.06 0.06 0.10 0.12 0.14 0.16TI ME (SECONDS)FIGURE 111. Horizontal Acceleration of the FIGURE 112. Vertical Acceleration of the SupportSupport for an Equivalent Singlefor an Equivalent Single-Degree-ofDegree-of-Freedom SystemFreedom System (Requested Base Case(Requested Base Case and Cases 7and Cases 7 and 8).and 8).

-0I -0' --~C'IJ...........0Usc..:l_ 15C'lJIt................. Q.;

~-- 0:::f"AR D«lBAse CASE: 0 0CASt 7 0············0~ CASt e -t-------+0.(3---__~"' ",N:~w- ,w\\ :1~~ ~§t....:;l .,V)'\'.~Cl V)'Cl,,~ 5§•,Il.. °0..•- . •• ,~~ w,I0:::~8 "Clt...E~,Z............~.I8~ °8N - w_~....88-'"~....'~§o,~~ - U0:::8gi.... ....STRUCK END°:J: ~~ eAse CASE o 0~ICASE: 7 0············0CRSC e -t-------+~ ,'i8IIo Ell .,.,..- Iii Iii I ~ I i I I I0.00 0.02 0.0'1 0.06 0.08 0.10 0.12 0.1'1 0.16 0.00 0.02 0.0'1 0.06 0.08 0.10 0.12 o. 1'1 0.16TIME (SECONDS)TIME (SECONDS)FIGURE 115. Force on the Horizontal Component FIGURE 116. Force on the Vertical Component ofof the Tiedown at the Far Endthe Tiedown at the Struck End(Requested Base Case and Cases 7 (Requested Base Case and Cases 7and 8).and 8).

-0\-I8~.,~~~ -~~0~~~CD~~~ ....W~~Zw- §~- :~ 5.~~~~,,, I,•IIII•I,I.,,,,: ,:':'f '::',:': I:..:',,I,, ~.08 ....uwrAR EtCl~§Ill'lSECASE C3 El (f)CflSE 7 0············0......ZCI'ISC II +------+Zo~§....a:::0:::W-lw~§.-l....a:::Z0N~§~ ....W:>.... a:::-l81BASE: CASE: C3 El~~ CASE 7 Cl 0CASE e 6 6Ẉ ...~-l0lfl§ a:::_Xa::::E:o • ,==:iii,~'wi j i I o I I Iii I I I I iii I0.00 0.02 0.0" 0.06 O.OB 0.10 0.12 0.1" 0.16 o 20 iO 60 BO IDO 120 140 160 1BO 200 220 2iO 260TiME (SECONDS)FREQUENCY

c8018..§~U1.......(.)wU1~§- .....~z0;::8~~w...JW(.)~~...Ja:(.)- ~§.....W ....... >IO'lW~ >~~...JW0:::Wf-C3~0U1CDa:x§~-~ " ~0., (.)I ' I\ ~ \~~(.)\ • I" IwU10' ~ ........\\ ' I\ ClI.III IIa:I,13l~~I!J\.ZI.0 'IS)I , \ O:::c\f \ ~~ ...\a: 'lll ' 'cil~ I ' \BASE CASE a EJI\' \ICASE 7 G------oCASE 8~lij\\~_.6 ~\I --.~ w\ (.) \\ (.)6ḷI.\ ...Jwa:II\ f\0IQO:::c~ _.~-\>-IIII\ f-Gl,\\ a:,I~...JW\ 0.\O:::c c",W\~,f"-- ..-'-......" ''''~~ , '- "6'0.,-a'o.-q_e_iJa: ~1:\ LI>w I!l\,.~.---~a:\Q\\I\~Gl\\\x-....~ 'G-e- 1>-e_ E)~~~'"'"1!0---6.o I , 1 Iii Iii iii I I 0o 20 40 60 80 100 120 140 160 180 200 220 240 260 0 20 40 60 80 100 120 140 160 180 200 220 240 260fRE~UENCY (RADIPl6/SECtJID> fREOUENCY (fWlliV'lS/SEaJID>FIGURE 119. Response Spectrum: Maximum AbsoluteRelative Vertical Accelerationvs Frequency (Requested Base Caseand Cases 7 and 8).FIGURE 120. Response Spectrum: Maximum AbsoluteRelative Rotational Acceleration vsFrequency (Requested Base Case andCases 7 and 8).

~§'"........~§...... CDB§(".') cocj......W(/)U........"0.W(J1zo-8~8- "z- "oo zo1-0a:: 0:::0 °~8WIDa:: o:::ID °....lWW....lUWuUcfa::!3UoL1>T .a:: °~I'.....la::Zou...... ~8......0:::0~8o~WOI>.:x:W~~~~~~~ ....lV".'1'mU1W0:::WO5~.. '.................................. o() ..... c:,.B.... ............(/)CD~§ uppeR ~IMITS 0 · ·0a:: L.OWER ~IMITS 0 ..··· ·..··0J: 8RSt: CRse'0>S~W0:::W3~gCDa::XOa:: 8J:-uppeR ~ IMITS~OWCR LIMITSBAse CAsenQ0· "0o Iii Iii Iii iii Ia 20 '10 60 80 100 120 140 160 leo 200 220 2'10 25GFREOUENCY (RADIANS/SECOND)IFIGuRE 121. Response Spectrum: Maximum Abso FIGURE 122. Response Spectrum: Maximum Absolutelute Relative Horizontal Accelerationsvs Frequency (Base Case,Frequency (Base Case, + 50% BaseRelative Vertical Accelerations vs± 50% Base Case, and Cases 1, 2, Case, and Cases 1, 2, C, 0, and 3C, 0, and 3 through 21). through 21).

8..oWlfle'-1II0'"Wlfl.......aa:~~za-~a:we~-J lQ.Woa:-JuPPCR-~~~.....a:BRSE: CRSf: 6 to.....a~I0"10"1 ~~w>-~LI /11 rs G······· .. ·······OLOW[R L1/1ITS 0················0a:-Jw~8w~::l-Jalfl~~J~~o~o 20 40 60 80 100 120 140 160 180 200 220 240 260PREOUENCY (RADIANS/SECOND)R~S~GNS[PFlRil~~jCRCPSCP2WPcPlcnKXZPCPS:P6KlLOCRCP3CP1VARIRBL[: MAXIMUM RBSOLUT[ PeAK HORIZONTRL SUPPORT RCC[L[RATIONCASCS RIINK fl8SOLUTC P(RCCNT 0 JrrCRCNCC rROM BIISC CASC0 10 20 3010 50I I III20 1 I21 II3 2 I4 I I1 I2 3 I IIC 1 IDIus 5 I17 I II5 5 I8 I11 e15 t?12 7 013 B 07•B 9II 10IB199 II10 12FIGURE 123. Response Spectrum: Maximum AbsoluteRelative Rotational AcceleraPercent Difference of Absolute PeakFIGURE 124. Ranking of Parameters by Absolutetions vs Frequency (Base Case,Horizontal Support Acceleration from~ 50% Base Case, and Cases 1, 2, Base Case Value.C, D, and 3 through 21).

;:::~P:\5~ 1"9~:A6~::: ~~Xj~u~ ~5:;·Oi..UiC PEA~ VERi!Cf1L SUPPORT ACCELERATiON ~::S~c\5:: VARIR9L£:: MAXIMUM RBSOLUiE PEAK ROTATIONAL SUPPORT ACCELERATION....IO"l'",~r:.-" .:";:,,:C Tf:RKYLOCRCP6CPICP2WI'ZJ'cpeCPSKXCP7CP1CP3CPoSES7e\IIB1913C031I211IS202112S61617109I231567e9RANK10II1213ABSOLUTE PERceNT 0 I rrERENCE rRQM BRSE CASE0 20 iO 60 BO 100 IL1I I I I IIII ~IIIbP II IE?b00IIIIIIIIP~","~:::CRCP2KYcpeCPlLeeRCPOCPlCP3WI'CPSZPKXCf'7CR~ES317e2021C0IIIB191310912121115S61617RANKI231S07e910II12131ABSOLUTE PERCENT [j) rrE~ENCE rROM BPSE CASE0 so 100 I~O 200 2Q1IIIIIIII~IIIIE?~~IIIIIIIII=:JIIIFIGURE 125.Ranking of Parameters by AbsolutePercent Difference of Absolute PeakVertical Support Acceleration fromBase Case Value.FIGURE 126.Ranking of Parameters by AbsolutePercent Difference of Absolute PeakRotational Support Acceleration fromBase Case Value.

....IO'lcoRESPONSE VRRIRBLE: MRXIMUM RBSOLUTE RrLRTlvE HORIZONTRL RCCELERnTIONPRRfYlCTER CRSl:S RRNKABSOLUTE PERCENT OIrrERCNCE rRO" BRSE10IWI'CP2CPe171KXen1PCI'5CPeLOCll171ItTCoP!»I2312021C05eIe171115121311III19107II9I2315157e910\I12120IIbEJEJEJ[JJ00~IIIIIIIII20 30IIICRSE10I50IRESPONSE VARIRBLE: MRXIMUM RBSOLUTE RELRTIVE veRTICAL RCCeLERRTIONPflRllMCTER CIlSCS RflHK0KT1715l.OCIl171172WI''U'CPBCPSKXCP7171CP37e13\IIe19c031I2111520211251511517109I2 I3156IIII7EJe I9 c=::J1010\I12t?t?0/lIl:lO..UTE PERCENT 0JrrERENCE rROM BRSI: CflSE20 10 60 eo 100 120I I I ,I!IIII IIIIIIIIII IFIGURE 127.Ranking of Parameters by AbsolutePercent Difference of Maximum AbsoluteRelative Horizontal Accelerationfrom Base Case Value.FIGURE 128.Ranking of Parameters by AbsolutePercent Difference of Maximum Absolute Relative Vertical Accelerationfrom Base Case Value.

R~SPONS~ VARIABLE: MAXIMUM AeSOLUT[ RELATIVE ROTATION~L AC:[~[RATJON P.~SPONS[ VARIABLE: MAXI~UM HORIZONTAL TICOOWN rORCE - STRUCK [NOP~~A~[TCR CASCS RANK ABSOLUTC PC~:crIT 0 I rrCR[I';CC rROM ~RSC CPSC ?ARR~cr[~ CASCS RANK ABSOLUTC PCRCCNT 0 I rrCRCNCC rROM BASC C~SCCP2CPSKTCl'10 SO 100 ISO 200 r-,):) 0 10 20 30 10 ~OI I I I I I I II,3 1 I 3 I ICP21 I 1 I20 2 I 20 2 ICPS21 I I 21 I7 3 I 1 IIf'e I I 2 3 IC 1 I 5 IKX0 I I 6 1 III 5 c ICPILOCR 18 0 1I19CP6 13 6 ~ 16 ICl'717 1 It?>--

............I-.....I0ReSPONse VARIA8Le: MAXIMUM HORIZONTAL TJeOOWN rORce - rAR eND Rc5PO~Se VARIABLe: MAXIMUM VeRTICAL TJeOOwN rORce - STRUCK eNDPARRMl:Tl:RCP2CPBWPen ...KXCPI1J'CPSCI'6LOCRI('(CASCS3i2021RANKI12 31617 156C0Ii15121311181978 ,0ABSOLUTt PCRCt:NT 0IrrCRCNCe rROM BASE: CASE:10 20 30 10I I I I2 II567B91011t?00!IIIIIIIIII ISOIPARMe:1:R1J'CP8CASE:S11152021RRNK120IIABSOLUTE:10IPI:RCt:NT 0 JrrLRCNCE: rRQM BASE: CASE:20 30 10I I ICPS 12 J I ICP2LOCR~CP6CPIKX.CP7CP131 1 ICl'3 9 127KT8 11CP1 10 13 I CP3 9 12 0II18191213C056161710567B9910IIpPE?IbI IIIIIIII III IIIso,IFIGURE 131.Ranking of Parameters by AbsolutePercent Difference of Maximum AbsoluteHorizontal Tiedown Force(Far End) from Base Case Value.FIGURE 132.Ranking of Parameters by AbsolutePercent Difference of Maximum AbsoluteVertical Tiedown Force (StruckEnd) from Base Case Value.

............-.........~c:~O~SE VRRIRSLE: MRXIMUM VERilCRL TIEOOWN rORCE - rRR ENDPf:.~q~~jCRZPcP2cPBCI'6WI"CPSl.OCRKX~7CPJnCPICP'ICRS(SI'! IIS2-20 32:RANK0!IIIJ 4 II21211181956161797eC010561B9101112lJIIIIIP8DABSOLUTE10II IIIIIIIPERCCIIT OlrrERENCE rROM BAS( CI'ISE20 JO 10 $,IIII IIIIIIIIII~~§U owif)........U~§........ enC)CI:0:::o:::§C)a:lUwBASE: CASE~§ur-.wif)........Z8=$zC) ~-----~~0:::w...Jwo_____________ ~~~~:---------2-----------u8u ..CI:i-'0:::0~~Q..:::JBRSE CElSE RNO CASES 1 AND 8if)o~oI - VERT I CAl.CI:~2 - HOR [ZONTALwQ.. J - ROTRTlONRL X 10if) 0!D8CI:_o! I I ,0.5 1 1. 5 2RATIO Of KS2 AND KS3 TO BASE CASE VALUESFIGURE 133.Ranking of Parameters by AbsolutePercent Difference of Maximum AbsoluteVertical Tiedown Force (FarEnd) from Base Case Value.FIGURE 134.Sensitivity of Absolute Peak SupportAccelerations to Changes in the StiffnessCoefficients of the Vertical Componentsof the Tiedowns (RequestedBase Case and Cases 7 and 8).

08_su8w(/"), Us,c::::l~gceQ::§@3a:>U,0 ~8u ....w(/")~§_CDBAS£: CASEz -------------------~-----------~-----------~---------- -----2§.-. li'".-. Q::IW""-JNd8U..uoce-1 0~~(/")coceox8ce'"~....BASE CASE ANO CASES 7 AND Bx1 - ·Vl:RT ICALceO~82 - HORIZONTAL3 - ROTATIONAL X 10o I I i I0.5 I 1.5 2RATIO OF KS2 AND KS3 TO BASE CASE VALUES'"'" ..Lf)x0"xwQ:: U'" •0'"t...IlIlSE CAS£:(/") ---------------------------------------6 3c::::l~ ",t- --.--.--.~.--.--.--.--.---_.--:CLwUQ::",BASE CASE AI() CASES 7 ANlJ B~'"!-W!-=:)-1'"0"':l.f)CDceo . I - Vl:RTICAL lFt:1 o 0t...'"2 - Vl:RTI CAL IS£:1-'·············0Z 3 - HORIZONTAL IFt:J b-------63:of - HORIZONTAL (S£:IoII'" o I I I I0.5 I 1.5 2RATIO OF KS2 AND KS3 TO BASE CASE VALUE~~FIGURE 135.Sensitivity of Maximax AbsoluteRelative Accelerations to Changesin the Stiffness Coefficients ofthe Vertical Components of theTiedowns (Base Case and Cases 7and 8).FIGURE 136.Sensitivity of Absolute TiedownForces to Changes in the StiffnessCoefficients of the Vertical Componentsof the Tiedowns (RequestedBase Case and Cases 7 and 8).

A P PEN 0 I XIIITABLESII 1-1

TABLE 1PARAMETERS USED IN THE CARDT MODEL FOR SIMULATIONOF IMPACT BETWEEN TWO HOPPER CARS LOADED WITH GRAVELWeight of Hammer Car [lb(force)] WRC218,000Weight of Anvil Car [lb(force)] WF211,000Upper Limit on Travel of Combined Draft Gears (in.) X TU5.6Lower Limit on Travel of Combined Draft Gears (in.) X TL-5.6Spring Constants of Draft Gears During "Active" State[lb(force)/in.]Base Spring Constants of Draft Gears During "Solid"State [lb(force)/in.] kSDG10,kSDG20 75,000Energy Dissipation Coefficient for Cargo CompactionPhase ~XTC 0.01Energy Dissipation Coefficient for Cargo RecoveryPhase ~XTE 0.95TABLE 2SUMMARY OF CONFIGURATIONS AND CONDITIONSOF COMPLETED CASK-RAIL CAR- TIEDOWN TESTSTest~ DatePIP2P312345678g1011121314151617186/86/86/871147/18711971197/207/267/267/267126712771277/318/18118/18/2813813Ra i1f!!:....IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIICouplerStdStdStdStdStdStdStdStdEOCEOCEOCEOCStdStdEOCEOCStdStdStdCushionCushionCask Wt.~42.542.542.5404040404040404040707040404040404040IlIlPactSpeed MPH55} 7.611.88.39.010.510.710.52.85.69.29.28.011.211.211.25.46.510.85.910.7StopFrequencyf n Tiedown RemarksHiHiHiLowHiAA*ABDCCCCAADDCC0DDPreliminary test no instrumentationrConcrete simulationWelded Steel StopCable Rigging to Restrain WeightNo structural damageInstrumented Coupler FaultyInstrumented Coupler FaultyInstrumented Coupler FaultyCable Load Instru~nts FaultyNo Photography - No Data on TapeNo PhotograPhy - No Data on TapeNo Photography - No Data on TapeNo Photography - No Data on TapeOne High Speed Camera OnlyOne High Speed Camera OnlyOata QuestionableReport of Test 12Some Cables Loose After Test*Support Underbeam Reinforced (i.e., stiffened)~Railcars: I 70 ton SCL • Std CouplersII 70 ton SCL - CuShion UnderframeIII 80 ton Union Carbide - Mixed CouplersTiedowns:A - 2 load cells between stop and cask b~er be&fts• 2 load bolts reproducibly snugB • Same as A. except fn lowered with bumper bea~sC - Ten I" cables at same ang Ie - No stopo - Vertical Tiedown with six cables - two instrumentedII 1-3

TABLE 3FORCE TERMS FROM THE CARDS lEST 3 SIMULATION RUNMEASURED AT THE TIME (0.116 SECOND) WHEN THE VERTICALACCELERATION OF THE RAIL CAR (SUPPORT) IS A MAXIMUMVariableValuelb(Force)DUS2 44754.6DUS3 -54094.7DWS2 17899.5DWS3 4904.6DUS6 74418.0DUS7 -51971.8DWS6 0.0DWS7 0.0DWCRF 0.0TABLE 4FORCE TERMS FROM THE CARDS TEST 3 SIMULATION RUNMEASURED AT THE TIME (0.057 SECOND) WHEN THE HORIZONTALACCELERATION OF THE RAIL CAR (SUPPORT) IS A MAXIMUMVariableValuelb(Force)DUS1 221589.0OUS4 0.0OWS1 -57230.0OWS4 -57230.0OUS5 -31802.7DUS8 -31802.7OWS5 34563.8DWS8 34563.8OUSCAR (Experimental) 1160000.0DWPI -23200.0DWP4 -23200.0111-4

TABLE 5INPUT DATA AND RESULTS FROM THE CARDS TEST 3 SIMULATION RUNRESULTS MEASURED AT THE TIME (0.116 SECOND) WHEN THE VERTICALACCELERATION OF THE RAIL CAR (SUPPORT) IS A MAXIMUMInput DataCalculated ResultsM = 207 1b(force)-s2/in . = 2.82 x 10- 3 pe RCradiank = 1 x 10~ 1b(force)/in. = -0.12993 radian/sS2 = k eS3RCC = 2 x 10 3 1b(force)-s/in. = -6.89 radians/s 2S2= C S3e RC.. . 2= 166.5 in. YRC= -353.9 1n./s2= 70.5 in. YRC78 = 1465.5 in./s= 264 in.TABLE 6INPUT DATA AND RESULTS FROM THE CARDS TEST 3 SIMULATION RUNRESULTS MEASURED AT THE TIME (0.057 SECOND) WHEN THE HORIZONTALACCELERATION OF THE RAIL CAR (SUPPORT) IS A MAXIMUMInput DataM p= 207 1b(force)-s2/in .= 1.05 x 10 6 1b(force)/in.Calculated Results=' 3.03506 x 10- 4 radiank S1= 0 1b(force)/in. = 3.84508 x 10- 5 radiank S4 ~C= = 2000 1b(force)-s/in. = 1.2836 x 10- 2 radian/sC S1C S4e RCZp = 31 in. = 2.944 radians/s 2e RCZRC = 18 in. X = -4180.5 in./s 2RC= 7.25067 x 10- 2 radian/s111-5

..................IO'lTABLE 7INSTRUMENT CONFIGURATION FOR CASK-RAIL CAR-TIEDOWN TESTSCONFIGURATIONS A AND BInstrument --------,-'---I~-s't-r~m~~l~--- ----r'-·------..·.,-- -N:.-~:~:-:J.~:~·:':::n 1.;::;:OE-_2 Bolt Holddown (Side)3 Coupler4 Struck End Of Car5 Car Structure (SE)*6 Car Structure (SE)7 Car Structure (SE)8 Ca~k (SE)9 Cask (SE)10 Cask (FE)11 Cask (FE)12 Car/Cask Interface13 Car/Cask Interface14 Car/Cask Interface15 Cask Base (SE)16 Cask Base (SE)17 Cask Base (FE)lB Cask Base (FE).19 Cask Top Center20 Cask Side Center21 Car Structure (FE)22 Car Structure (FE)23 Truck (SE)24 Truck (FE)25 I Rail Car Above TruckCen ter (SE)26 Bolted Holddown (FE)27 Base/Chock Interface (SE)2B Base/Chock Interface (SE)I..;n-s~-~~::~-~d- ~:~~._- -~h~~::s~e~~:~:,~~~- ,Instrumented BoltBridge TypeDisplacementPR AccelerometerPR AccelerometerPE AccelerometerPR AccelerometerPR AcceleraneterPR AccelerometerPR AccelerometerPR AccelerometerPR AccelerometerPR AccelerometerPE AccelerometerP£ AccelerometerPE AccelerometerPE AccelerometerPE AccelerometerPE AccelerometerPE AccelerometerPE AccelerometerPE AccelerometerPE AccelerometerPE AccelerometerInstrument BoltLoad CellLoad CellIChange in TensionForce/TimeDisplacement/TimeShockShockShockShockShockShockChange in TensionChange in CompressionChange in'Compressionca:~: t;~;';:tCouplerStruck End Of CarCar Structu,'e (SO"Car Structure (SE)Car Structure (SE)Cask (SOCask (SE)Cask (FE)Cask (FE)Car/Cask InterfaceCar/Cask InterfaceCar/Cask InterfaceCask Base.(SE)Cask Base (SE)Cask Base (FE)Cask Base (FE)Cask Top CenterCask Side ~enterCar Structure (FE)Rail Car Above TruckCenter (FE)Truck (SE)Truck (FE)Rail Car ~bove TruckCenter (SE)Cahle (FE)B~se/Chock Interface (SE)Base/Chock Interface (SE)CONFIGURATIONS C**ANO 0=-l--I~'~r~~;e~,-;----~'-------- ..·--....L~ca tJ.I-~-::-~~~~----t~~~:~'~~~~~~I: ;~;l----[Iri dge TypeDisplacementPR AccelerometerPR AccelerometerFE Accelerometerpn AccelerometerPR AccelerometerPR AccelerometerPR AccelerometerPR AccelerometerPR AccelerometerPE AccelerometerPE AccelerometerPE AccelerometerPE AccelerometerPE AccelerometerPE AccelerometerPE AccelerometerPE AccelerometerPE AccelerometerPE AccelerometerPE AccelerometerPE Acce I erometerLo"d Ce 11Load CellLoad C~llForce/TillieDi splacelllcnt/T imeShockShockShockShockShodChilt\ClC' ill 1 L'IlS i nilCh.,nge ill Compl'pss i OilCh~IHJe ill C01l1111'r,; i i l..'fl*SE = Struck End; FE = Far End.**On1y Instruments 1,3 and 26 on Configuration C.

DATACHANNELIDINSTNO.TABLE 8MEASURED AND REDUCED PARAMETER VALUES FROM RAIL CAR HUMPING TESTS(Test No.1: 40-Ton Cask, 70-Ton Seaboard Coastline Rail Car,Impact Velocity 8.3 mph)LOCATIONMEASUREDPARAMETERRAW DATASCALE FACTOR (SF)(FULL SCALE +2V)A 4 (SE) Car Displ acement Timing OnlyFILTEREDDATA(Max/Min)UNFILTEREDDATl\(Max/Min)B 1 (FE) Bolt Holddown Force 43.75 K#/V 20.21/-1. 4 20.13/_2.12C 2 (SIDE) Bolt Holddown Force 21.88 K#/V 16.58/_2.12 16.84/_2.19I-tI-tI-tI-.....JD 8 (SE) CaskL-Acc..:!:.150g/V1.5/-13.4 3.3/-13.5E 9 (SE) CaskV-Ace. .:!:.62.5g/V6/-5.46.25/_5.9F 10 (FE) Cask L-Acc. .:!:.150g/V 1.65/-10.65 3.75/_12G 11 (FE) Cask V-Ace. .:!:.62.5g/V 40/-3.69 40.63/-4.063HJ12,13Car/Cask InterfaceCar/Cask InterfaceL-Acc.T-Acc..:!:.150g/V.:!:.25g/V4.65/_9.93.5/-3.9214.55/-18.7510.75/_11.5K 14 Car /C ask Interf ace V-Ace. .:!:.62.5g/V (Impulse Noise) (Impulse Noise)L 17 (FE) Cask Base L-Acc. .:!:.100g/V 2.5/-7.9 3.5/-8.4M 22 (FE) Car Structure V-Ace. .:!:.375g/V 22.1/-58.5 76 .88 / -155. 6N 26 (FE) Bolt Holddown Force 35 K#/V43.75 K#/V10.98/_.7913.73/_.9811.73/_8.814.66/-1.1

TABLE 9THEIL'S INEQUALITY COEFFICIENTS FOR RESPONSE VARIABLESDETERMINED USING CALCULATED AND MEASURED COUPLER FORCETheil's Two-Variable Inequality Coefficients*Case 1: Measured Case 2: CalculatedResponse Variable Coupler Force Coupler ForceCoupler Force 0 0.223Longitudinal Force ofInteraction BetweenCask and Rail Car 0.158 0.194Horizontal Accelerationof Cask 0.205 0.252Horizontal Accelerationof Rail Car 0.211 0.445Vertical Accelerationof Cask at Far End 0.600 0.776Vertical Accelerationof Cask at Struck End 0.656 0.470Theil's MultipleInequality Coefficient 0.059 0.214*A value of 0 indicates the best agreement, and a value of 1 indicates thepoorest agreement.TABLE 10DEFINITIONS OF CASES USED FOR GENERATIONOF PRELIMINARY RESPONSE SPECTRACA~tCONDITION *1 2 3 4 5I. Rear Tiedowns- Loose- TightXX X X X2. Cask Pos it ion on Ra i1 Car- Centered Fore & Aft- Cask Centerline 4 ftFon-Iard of Rail CarCenterlineX X X XX3. Coupler Force Used- Calculated by CARDS- Measured During SRL Tests4. Damp i ng in CARDS Mocel- Viscous + Friction**- Viscous Only- No Damp ing5. Damp i ng in CARRS Model- Viscous + Friction**- Viscous Only- No Damp i ng*Ccnditions not sp~cified here are base case conditions in the CARDS model.**Friction opposing horizontal.motion of cask relative to the rail car.111-8X X X X XX X X X XIXXXXI,IIIXIIii,

TABLE 11CONDITIONS IMPOSED ON CASES REQUESTED FOR PARAMETRIC AND SENSITIVITY ANALYSISAND GENERATION OF RESPONSE SPECTRACASESCONDITIONBase 12C034567 A9101112131415161718192021.................I1..0LRear Tiedowns- Loose- Tight X2. Cask Position on Rail Car- Cask Centerline 4 ft. Forwardof Rail Car Centerline- Tiedown Attachment Pointon Cask at Far End LocatedAbove c9 of Rail Car- Cask Centered Fore andAft- Tledown Attachment Pointon Cask at Struck EndLocated Above cg of RailCar3. Coupl el" Force UsedXXXXXXXXX X X X X II II X X X X X X X II XXXXXXXXXXXXXX X X X- Calculated by CARDS- '-leasured During SRL Tests II X X X X II X X II X X X X X X X X X X X X X X X4. DaMping in CARDS Model- Viscous t Friction- Viscous Only- ~lo Dal'lpi n9X X X X X X X X X X X X X X X X X X X X X X X XXXXXXXXI5. Damping in CARRS I~del- Viscous t Friction- Vi~cous Only- No Dal~p ingX X X X.."X X X X II X X X X II X II X X X X X X X

TABLE 12 TABLE 13DEFINITIONS OF "PURE" PARAMETERS AND THEIR CASESDEFINITIONS OF "COMPOSITE" PARAMETERS AND THEIR CASESPARA~lETERCASEDHINITIONCOMPOS ITEPARAr1ETERCASEDEFINITION.....................I-..IaW p{K }x{k }ytOCRZp12567811181914151. CasK weight W p doubled.2. CaSK weight W p halved.1. K and K S4doubled.SI2. K and K halved.SI S41. K S2and K S3doubl~.2. K and K halved.S2 S31. t = O. This is equivalent to theCFtiedown attachment point on the caSKat the strucK end being located directlyabove the center or cg of the railcar,or t OCR = t pF '2. t = 1pF' This is equivalent to theCFcaSK being centered on the railcar,i.e.• the cg of the caSK directlyabove the cg of the railcar, or tOCR = O.3. t = O. This is equivalent to theCRtiedown attachment point on the caSKat the far end being located directlyabove the cg of the railcar, orIOCR = IpR.1. Zp increased by 50~.2. Zp reduced by 25~.CPl C 1. K Sl' K S4• K S2and k S3doubled.CP2D342.1.2.K Sl ' K S4' k S2and K S3halved.Wp ' k Sl' K S4' k S2and K S3doubled.W p ' k Sl' k S4' k S2and K S3halved.CP3 9 K halved and K changed such thctS2 S3their sum remains constant.CP4 10 k S3halved and k changed such thatS2their sum remains constant.CPS 12 t pRand t pF increased by 50% .CPS 13 t pR and t pFincreased by 50% witht CR= £CF (cask centered on rail car).CP7IS17CPS 20211.2.1.2.IOCR = 0 and K SIand K S4doubled.tOCR= 0 and k Sland k S4halved.(cask centered on rail car when 10CR = 0)Wp' K Sl ' k S2 ' k S3 ' K S4 ' K SS ' k SS ' K S7and k S8doubled.Wp' k Sl ' K S2 ' k S3 ' K S4 ' k SS ' K SS ' K S7and K S8halved.

TABLE 14PARAMETER VALUES USED IN CASES REQUESTED FOR PARAMETRIC/SENSITIVITY ANALYSIS..................I---'VARIABLEINPuTPAIlN-1UERl:t> ,~Sl (Low)f-----~C;I (High)f---'..---k~4 (Low)kS~(lligh)eASECASEa x 10 45 ~ 10 4l~oll5 x 10 4I x 10 6CASES 1. 22 ICHANGE CHANGE4 x 10 4 \.6 x 105k SZ5 x 10 62.5 x 10---6 IK S3 5 x 10 6 2. 5 ~ 10 6 ICASES C. 0CASES 3. 45 x 10 5 2 x 10 6 ·~~-1-~5- 1- 62 x 130C 4 3CIIAIIGE CHANGE CHANGE_..CIiAllroE_.--S4 x IO~ 1.6 x 102.5 x 10 4 I x 10 5 2.5 x 10 4 I x 105.~5 x 10 5 2 x 10 6 5 x 105 2 x 10 62.5 x 10 4 I x 10 5 2.5 x 10 4 I x 10 5x 10 7 Z.5 x 10 6 I x 10'x 10 7 -62. 5 ~ 10--Ix 10 7-CASES 7, :lCASES 5. 65 x 10 5 2 x 10 66 5CHANGE CHANGE2.5 x 10 4 I x 10 55 x 10 5 2 x 10 6'---42.5 x 10 1 x 105a I 7CHMGE~ r:tI~;~_E_.--_.2.5 x 10 6 7-~- f-I-.~_II)2.5 x 10 I x 1;/---"10CHANGECASES 9. 109CHANGE7.5 x 10 6 2.5 x 10 62.5 x 10 6 7.5 x 10°

TABLE 14(Cont'd)..................I--'NVARIABLEINPUTPARAMH[R8ASECASEW p 8 x 104CASES 16, 17 CASES 20. 21 CASE 18 CASES 11, 19 CASES 12, 13 CASES 14, 1517CHAIIGE16CIlAHGE21CIlANGE20CttAlIGE4 x 10 4 1.6 x 10 5k S1 (low) 5 x 10~ 2.5 x 10 4 I x 10 5 2.5 x 10 4 I x 10 5k S1(hiyh) I x 10 6 5 x 105 2 x lOb 5 x 105 2 x 10 6k S4(low) -S~ 2.5 x 10 4 I x 10 5 2.5 x 10 4 I x 10 5k S4(h i 9h)k S2 5 x 1061 x 10 6 5 x 105 2 x 10 6 5 x 105 2 x 10 62.5 x 10 6 I x 10 7k S35 x 10 6 2.5 x 10 6 I x 10 718CHANG[19CHAlIGEIICHANG[ICF 151 102 204 O. 10213CHANGEI CR 53 102 O. 204 102-I pF 102153 153-IpR 102 153 153CHANGE15CHANGE14CHAliGEZp 31 23.25 46.5._-lOCk·49 0 0 (0)" ( -102) (102) (51) (2)'\5 •• 1. 0.5 2.k .... 6.4 x 10 4 3.2 x 10 4 1.28 x 1056k 7 6.4 x 10 4 3.2 x 10 4 1.28x10 5'\11 .. I. 0.5 2." Values of IOCR derived from I pF and I CF ' i.e., IOCR' IpF - ICF '.. loIultipliers of basic spring constants from which k S5and k S8 derived.••• kS' k6, k7and kaare basic spring constants from which k S5 ' k S6 ' k S7 and kS3 are derived.

TABLE 15PARAMETRIC AND SENSITIVITY ANALYSIS - SENSITIVITY OF RESPONSE VARIABLES TO PARAMETER CHANGESRESPONSEVARIABLEBASECASECASES 1, 2 CASES C, 0 CASES 3, 4 CASES 5, 6 CASES 7, 82CHANGE1CHANGE0CHANGECCHANGE4CIIANGE3CHANGE6CHANGE5CHANGE8CHANGE7CHANGEI':(slmax 4189 4663 3843 4544 3760 4874 3256 4535 3784 4,04 4176OlFF. FROMBASF - 474 -346 355 -429 685 -933 346 -405 15 -13% Ol FF. FRor~RA~F-- 11.3% -8.3% 8.5% -10.2% 16.4% -22.3% 8.26% -9.67% 0.36% -0.31%..................,-'wIV)max 5626 6748 3883 2876 10400 3487 7302 5852 5142 2786 11369.7OlFF. FRO/·1RA~F-- 1122 -1743 -2750 4774 -2139 1676 226 -484 -?840 5743.7% 01 FF. FRor~BASE-- 19.9% -30.98% . -48.9% 84.8% -38.0% 29.8% 4.02% 8.6% -50.5% 102.1%IOslmax 306.1 181. 2 437.3 163.9 554 96.5 791.7 316.8 281.8 157.96 603.2OIFF. FROM8ASE-- -124.9 131. 2 -142.2 247.9 -209.6 485.6 10.7 -24.3 -148.14 297.1% ImF FROIIBASE- -40.8% 42.9% -46.4',1; 81.0% -68.5% 158.6% 3.5% -7.94% -48.4% 97.1%-_._-_._ ._--_.IXdIlila x 5406 4812 6662 5764 5995 4964 6158 5765 5965 5405 5399OIFF. FROI~RA~F- - -594 1256 358 589 -442 752 359 559 -1 -7% 01 FF. FRO'lRA~F- -11.0% 23_2% 6.62% 10.9% -8.2% 13.9~ 6.64% 10.34% -0.02% -0.13%Iv) ,m 4093 5009 2B72 2069 7756 2488 5308 4218 3825 1970 8301Ol FF. FROMBASE- - 916 -1221 -2024 3663 -1605 1215 125 -268 -2123 4208% OIFF. FROM- - 22.4% -29.8% -49.5% 89.5% - 39.2% 29.7% 3.05% -6.55% -51.9% 102.8%BASEltidl 143.7 89.1 197.9 71.4 279.6 43.9 387.4 138 140.4 73.5 285.1maxOIFF. FROH- -54.6 54.2 -72.3 135.9 -99.8 243.7 -5.7 -3.3 -70.2 141.4BASE% OlFF. FRatl- - -38.0% 37.7% - 50.3% 94.6% -69.5% 169.6% -3.97% -2.3% -48.9% 98.4%BASE

TABLE 15(Cont'd)RESPONSEVARIABLEBASECASECASES 9. 10---10 9CHANGE CHANGElBCIIANGECASE 1BCASES 11. 1919 11CHANGE CIIANGECASES 12. 1313 12CHANGE CHAlIGECASES 14. 1515 14CHANGE CIIANGEIXsl maxOJ H. FROl1BASE~ oIH FROMBASE41B9--4190 41951 60.024% 0.143~419230.072~417B 4175-11 -140.26~ -0.33~4139 4136-50 -53-1. 19~ -1. 27~4141 4310-4B 121-1. 15~ 2.9~IYslmax 5626 5B76 5500 62.3 11320 l11BO 52.2 4673 4B9B 7033OHF. FROMBASE~ 01 FF. FROt·,BASE--250 -1264.44% -2.24%-5564-9B.9~5694 5554101. 2~ 9B. 7~-5574 -953-99. a -16.9~-72B 1412-12.9% 25. a..................I--'~\6slmaxOIFF. FRO~'BASEl 0IF F. f RO~,BASE306.1--461.9 15B.2155.B -147.950.9% -4B.3%237.2-6B.9-22.5~36B.7 B1.662.6 -224.520.4% -73.3%107.1 194.2-199. -111.9-65.~ - 36.6%266.2 384-39.9 77.9-13.% 25.4%\" IXd maxOIFF. FROnBASE~ OIFF. FRO~lBASE5406--5392 . 5413-14 7-0.26~ 0.13%53B6-20-0.37~5465 546459 561.09% 1.07%54Bo 549980 931.48~ 1. 72~54B9 521B83 -1881.54% -3.48%I" IYd maxOIH. FROIlBASE~ OIFF. FROMBASE4093 4203 4117- 110 24- 2.69~ 0.59~73.4-4020-98.2~B081 793239B8 383997.4% 93.8~61.99 34744031 -61998.5~ -15. a3593 5052-500 959-12.2% 23.4%IOdlmaxOIFF. FROl1BASE% DI~F. fKUI-lBASE143.7--218. 75.74.3 -68.751. 7~ -47. B%Ill. 7-32.-22.3%170.3 36.826.6 -106.9lB.5~ -74.4%50.1 90.%-93.6~ -52.7-65. a - 36. 7~125.4 179.1-IB.3 35.4-12.7% 24.6:::

TABLE 15(Cont'd)RESPONSEVAnIAllLEI" I Xs maxDIFF. FROMBASE,; DIFF. FROi·\BASEBASECASE4\B9- --CASES \6. \7 CASES 20. 2\\7CHAIIGE45353468.26:\6CHANGE37B4-405-9.67:2\CHANGE5017B2B19.B:20CHANGE311B-1071-25.61:Iy Is maxDIFF. FROMBASE: 01 FF. FROllBASE5626--. "5B522264.02:5144-482-8.57:4530-1096-19.5:5350-276-4.9:..................I-'(j1loslmaxDIFF. FROIlBASE:: DIFF. FRCiMRI\

00 __-'-..-.-TABLE 15(Cont'd)CASES 1. 2 CASES C. 0 CASES 3. 4 CASES 5. 6 CASES 7. 8 CAjES 9. 10RESPONSE BASEVARIABLE CASE 2 1 0 C 4 3 6 5 8 7 \0 9CHANGE CHANGE CHAIIGE CHANGE CHANGE CHANGE CHANGE CHANGE CHANGE C1iANGE CIIANGE CIIArlGEOUSlmax328800 222900 424880 273700 369300 187900 477600 273700 368800 328000 328800328400 32830001 FF. FROr1BASE-105900 96080 -55100 40500 -140900 148800 -55100 40000 -800 O. -400. -500.%OIFF. FROIlBASE -32.2% 29.22% -16.75% 12.31% -42.9% 45.3% -16.761 12.171 -0.243% O. -0.12t -0.15~OUS4 max 298900 205000 386260 248000 335800 170000 434200 248800 335300 298200 298900 298500 298500--I-'0'\I 0 IFF. t KUflBASE -93900 87360 -50100 36900 -128100 135300 -50100 36400 -700 O.1 OIH. FROt1Bf-SE-400. -400.-31.41 29.231 -16.76% 12.351 -42.861 45.271 -16.76% 12.181 -0.23:: a.-o.nt -0.13:;DUS2 n1ax 101300 71)700 132040 94840 109500 69350 144800 86500 117700 115400 93310 97580 116600OIH. FROMRAC;F' -30600 30740 -6460 8200 -31950 43500 -14800 16400 14100 -2990-3720. 15300.1 DIH. FnonBIISE-30.211 30.35% -6.381 8.0951 -31.51 42.91 -14.611 16.191 13.92;0 -2.951 -3.67% 15.a-----DUS3 max -88500 -63920 -112000 -79260 -91060 -62680 -113500 -00700 -92500 -92300 -88880 -95120 -86120DIH. FROM24660 -24220 9320 -2430 25900 -24920 7880 -3920 - 3720 -JOO -6540 24f,OIlAc;r- .._-------,t UIFF. mOM -(7.Il':: 27.3:t -10.521 2.8t -29.2% 28.1% -8.91 4.431 4.21. O. J4'~ 7. Jilt -2. B'tB.~S~ _._-___

TABLE 15(Cont'd)CASE 18 CASES 11. 19 CASES 12. 13 CASES 14. 15 CASES 16. 17 CASES 20. 21RESPOffSEBASE18 19 11VARIABLE CASE13 12 15 14 17 16 21 20CIIANGE CIIAflGE CHAHGE CHANGE CHAilGE CHANGE CIIAHGE C1iA'IGE CIIANGE CHANGE CHANGEOUSlmax 328800 328400 329900 330100 332300 332600 331900 321500 273700 36BBoo 194300 466500DIFF. FRO~I8ASE-400. 1100. 1300. 3500. 3800. 3100. -7300. -55100 40000 -134500 1377002: 01 FF. FRO~'I1I\SE-0. 122: 0.335% 0.395% 1.06% 1.16% 0.943% -2.22% -16.8% 12.17% -40.9% 41. 9%0---40---40---4I--'-....JOUS4 298900 298500 300000 300100 302100 302300 301700 292300 248800 335300 176600 424100n1

,TABLE 16PARAMETRIC AND SENSITIVITY ANALYSIS - RANKING OF PARAMETERS BY ABSOLUTE PERCENT DIFFERENCEOF RESPONSE VARIABLES FROM BASE CASE VALUESABSOLUTERESPONSEPERCENTVARIABLES PARAMETERS CASES DIFFERENCE PARAMETER(RV)(P)FROM BASE I RANKING 8Y1% oFBI 1% oF81I IRESPONSEVARiABLES(RY)PARAHETERS{P}CASESABSOLUTEPERCENTDIFFERENCEFROII BASE1% oFB IPARAMETERRANKING BYIt oFB I.....................I~00I 'it 5 ' W p 1 8.3I\lip 2 11.3 3CPl C 10.2 4CP1 0 8.5CP2 3 22.3 2CP2 4 16.4{kxl 5 9.67 5(kxl 6 8.26{kyl 7 0.31{kyl 8 0.36 9CP3 9 0.143 11CP4 10 0.024 1210CR11 0.33I1010CR 18 0.07210CR 19 0.26CPS 12 1.27 7CP6 13 1.19 I 8Zp 14 2.9 6Zp 15 1. 15CP7 16 9.67 5IVs'maxW p 130.98 6W p 219.9CPl C 84.8 4CPl 048.9CP2 329.8CP2 438. 5(k) 58.6 10(kxl 64.02(kyl 7 102.1 1(kyl 850.5CP3 9 2.24 13CP4 10 4.44 1210CR 119a.710CR 1898.910CRCPSCP6191213101.216.999.1293Zp 1425.1 7Zp 1512.9CP7 164.02CP7 17 8.26CP8 20 2:i.6 1CP7 178.57 11CP8 204.9CP8I21 19.8CP8 2119.5 8

TABLE 16(Cont'd)RESPONSEVARIABLES PARAI1ETERS CASES(RV)(P)ABSOLUTEPERCENTDIFFERENCEFROM BASEPARAMETERRANKING BYI: OFBI I: Oro IIABSOLUTEPERCENTRES?CllSEPARAMETERS CASES DIFFERENCEPf,RAMETERI VAP.I':-3LES(P)FROM BASERANKING BY( "V)I: DFB I I: DFal15simax '

TABLE 16(Cont'd)...............INaABSOLUTERESPONSEPERCENTVARIABLES PARAJ~ETE RS CASESDIFFERENCEPARAMETER( RV) (P) FRO/l BASE RANKING BYI::: DFB 1 I::: DFB 1IYdi maxW p 1 29.8 6W p 2 22.4CPl C 89.5 4CPl D 49.5CP2 3 29.7CP2 4 39.2 5(kxl 5 6.55 10{k xi 6 3.05{kyl 7 102.8 1{k y} 8 51.9CP3 9 0.59 12I P.ES?G"'SE I I OIFFERENCEABSOLUTEPERCENTI V';RIAGLES PARAMETERS C,l,SESPARAMETER(i):; ) (P)FROM BASE RANKING BYI::: OFBI",' I. ':'d Irn3x \4p137.7lipI ,(k I 5 I 2.3 I Ix2 38. 9CPl C 94.6 4CPl D50.3I I "2 I ·CP2 3169.6 1I - 69.5I::: OFa I{kxl 63.97I12I{kyl7 98.4 3{kyl8 48.9CP3 947.8II8!CP4 10 2.69 11tI OCR I11 93.8It OCR18 98.2 3lOCR 19 97.4CP4 10 51. 7 7lOCR 11 74.4 5lOCR 18 22.3lOCR 19 18.5CPS 12 15.1 9CPS 12 36.7 10CP6 13 98.5 2Zp 14I23.4 7Zp 15 1'2.2ICP7 16 6.55 10ICP7 17 3.05CP8 20 19.6CP8 21 22.6 8IjIICP6 13 65.1 6Zp 14 24.6 11Zp15 12.7CP7 16 2.3CP7 173.97 12CP8II20 157.1 2CP8 21 63.1i

TABLE 16(Cont'd)RESPONSEVARIABLES PI\RAt1ETE RS CASES( RVI (P)A8S0LUTEPERCENT01 FFERENCE PARAl1ETERFROM BASERAllKING BYI: DFB I 1% DFBIIRESPONSEVARIABLES( RV)PARAMETERS(P)CASESABSOLUTEPERCENTDIFFERENCEFROM BASE1% DFB IPARAMETERRANKING BY1% DFBI..................IN~DUS1 W p 1 29.2maxW p 2 32.2 3CP1 C 12.31CP1 0 16.75 6CP2 3 45.3 1CP2 4 42.9{kxl 5 12.17{kxl 6 16.76 5{k yl 7 0{k y l 8 0.243 11CP3 9 0.15 12CP4 10 0.12 13ItI OCR 11 0.39510t OCR I 18 0.12t OCR 19 0.335'DUS4 maxW p 1 29.23lip 2 31.4 3CP1 C 12.35CP1 D 16.76 4CP2 3 45.27 1CP2 4 42.86{k.l 5 12.18{k.l 6 16.76 4{kyl 7 0{kyl 8 0.23 9CP3 9 0.13 10CP4 10 0.13 10t OCR 11 0.4 8t OCR 18 0.13t OCR 19 0.368IZpICP5 12 1.16 8CP6 13 1.06 9Zp 14 2.2215 0.943CP7 i 6 12.17I I IC?7 17 16.13 4CPS i 20 41.9 2I I I I/ ! CPS 21 40. I9I7HCP5 12 1.14 6CP6 13 1.07 7Zp 14I2.2I5iZpCP71516I0.93712.18ICP7 17 16.76 ~CP8 20 41. 9 2CP8 21 40.9I

TABLE 16(Cont'd)RESPONSEVARIABLES(RV)PARAMEiERS(p)CASESABSOLUTEPERCENTDIFFERENCEFROM 8ASE1% OrB IPARAMETERRANKING 8YI~ DFBIIRESPONSEVARIABLES( RV)PARAMETERS(P)CASESABSOLUTEPERCENTDIFFERENCEFRO/l BASEI: DFBIPARAr~ETERRANKING BY1% DrBI..................INNDUS2 maxW p 1 30.35 5Wp 2 30.21CP1 C 8.095 11CP1 0 6.38CP2 J 42.9 2CP2 4 31.5{k } x5 16.19 8{k } x6 14.61{k } y7 2.95{k } y8 13.92 10CP3 9 15.1 9CP4 10 3.67 12L OCR 11 20.2 7L eCR 1~ 8.82L eCR 19 10.66CPS 12 30.27 6CP6 13 37.2 4Zp 14 47.38 1Zp 15I24.6CP7 16 16.19 SCP7 17 14.6CP8 20 41.07 3CP8 21 30.9DUS3 maxW p 1 27.3Wp 2 27.8 6CP1 C 2.8CP1 0 10.52 8CP2 3 28.1CP2 4 29.2 4(k } x5 4.43(k } x6 8.9 9{k } y7 0.34{k } y8 4.2 11CP3 9 2.8 12CP4 10 7.38 10L OCR 11 27.9 5L OCR 18 6.1L eCR 19 7.25CPS 12 31.93CP6 13 26.6 7IZp 1448.6 1Zp 1524.8CP7 164.43CP7 178.9 9CP8 2036.15 2CP8 2130.2

TABLE 17PARAMETRIC AND SENSITIVITY ANALYSIS - SENSITIVITY OF RESPONSE VARIABLESIN TERMS OF PERCENT DIFFERENCE FROM BASE CASE VALUES..................INW:WIGE OF INSENSITIVE SENSITIVE, oFB _o • 20 20.01 • '0 '0.01 • 60 60.01 • 80. 80.01 • 100 UPRESPOItlOERATELY RV RV HIGHLYVAR lA8LE (RVINSENSITIVE INSENSITIVE SENSITIVE SEflSITIVE SENSITIVE'Xs !trdl w p CP8... I.y ._••CPICPIIt.)ZpCPSCP6{kyl'OCRCP3CPACP2CPB CP2 {k,/ ~CPS W p,OCRIk. ) Zp CP6CP7CPACP3CPl.J'::G< Of INSENSITIVE SENS IT IVE~ Ofa _o • 20 20.01 • 40 '0.01 • 60 60.01 • 80. 80.01 • 100 UPilESPIlNSERV RV !'OOERATEL Y Rv >tlOERATELY RV IV."IA8LE tRV ~y HfG104LYINSENSITIVE INSENSITIVE SENSITIVE SErISITIVE SENSITIVEi X d 'nwx. CP2 W pCP8iCPII k.iCPIZpCPSCP6'OCRCPAIk y }CP3IY : d . CPS CP2 (k,'(k.) W p CP6CPIZp'OCRCPA CP8 CPICP3j,s I",~u lkyl CPS CPA 'nrR CP2CP7 Zp CP3 CP6 :lt : vW pCPSCPl\I'd!.... lk.) W p CPA 'nrR CP2~PI CPS CP3 CP6 CP8Zp{K y :'CPl

TABLE 17(Cont'd).-..-..-.IN~IWIGE OfINSENSITIVESENSITIVE~ OfB - o • 20 20.01 • CO 40.01 • 60 60.0\ - 80. 80.01 • 100 UPRESPONSEVARIABLE (QVRVINSENSI TlVERV 11J00RATELTINSENSITIVERV 11J00RATEl YSENSITIVEOUS1"" CPI W p CP2!t, ICPIZpCPSCP6'OCR(t,)CPJCPCOUSC 1M'It I w• CP2CP1CPIZpCPSCP6'OCR(t,)CPJCPCCP8CPSRVSEIlS IT IVERV HIGHLYSErlSI TlVERAueE Of~ 0f'8 _RESPONSEVAR IABLE (QV[NSEIISIT 1VESENSITIVEo • 20 20.01 - 40 40.01 • 60 60.01 • 80. 80.01 • 100 UPRVINSENSITIVERV rtIOERATEl YINSENSITIVERV rtIOERATEl YSENSIT IVEDUSZn;u (t, }CP6 ZpCPI Wp CP2CPJ CPS CPS(t y )'ncRCP1CP4!JUS)""" CP1 CP8 Zp(t, ICPICPC[t,)CP3CPSCP2'OCRW pCP6RVSEr:SITIVERV HIGHLYSENSI TI VE...

TABLE 18PARAMETRIC AND SENSITIVITY ANALYSIS - RANKING OF "pURE"BY INFLUENCE COEFFICIENT AND SENSITIVITYPARAMETERSRESPOHSEVARIABLES(RV)Ix ,___PARAMETERS(PlINFLUENCECOEFFICIE/ITSttWSENSITIVITY~.(P) a PPARAMETERRANKING 5YWFLUENCECOEFFICIENTPARAMETERRANKING 6YSENSITIVITYw p -6.833 x 10- 3 -a20. 3 1(kxl • -4.768 l 10. 4 -751. 4 Z(kyl - -3.733 x 10- 6 -28. 5 42 p'OCR7.3-0.0147169.7-3.1235..IRESPONSEV.RI~6LES( RvlIIPARAMETERS(P)INFLUENCECOEFFICIENTSitWSENSITIVITY:!n l .(PlPARAMETERRANKIIIG 5TINFLUltlCECOUFICIENTPARAMETERRANKING 5TSENSITIVITYI Xd~~.J,x "p 0.015~2 1850. 2 1ok-I(: 1.2698 , 10" 200. 4 3(k ... i -8.0 x 10- i -6. 5 4Zp -11.66 -271. 1 2'OCR -0.0049 -1. 3 5I-tI-tI-tINU1Iv,I_••Wp(kxl(kylZp-'OCR (FE)-0.02388 -2865. 4 4-4.508 x 10- 4 -710. 6 6-1. 144 • 10-38580. 5 392.04 2140. 3 5109. , 1118. 2 2IVd!max W p -0.01781 -2137. 4 4lkxl .2.495 x '0- 4 .. , -393. 6 6lkyl 8.441 x iO- 4 6331. 5 3Zp 62.75 1459. 3 5'OCR (FE) 77. 7854. 2 2'oCR (SE)-110. -11220. 1 1'OCR (5E) ·78.5 ·8007. I 1le -2.222 x 10- 5 -35. 5 5(ky> 5.937 x 10. 5 445 4 ,Zp5.067 117.6 1 4l!d~m4xW p{ltx }(kylZp9.07 x 10. 4 62.821 x 10. 5Z.31109.2.4212.53.735 1354'OCR-1.407 -287. 2 2'OCR ·0.65U -133.52 2

t"::'TABLE 18(Cont'd)......IPESPllHSE \VAR IABLES( RVJPAR~TERS(P)ItIFLUENCECOEFFICIENTS**SENSITIVITYffi11 A(P)PAlW4ETERRNlKING BYINFLUENCECOEFFICIENTPARA.'lETERRNIKlrIG BYSEHS liI'IITYOUSl tMJl Wp 1.68 201600. 2 1lkJlI 0.0604 95130. 4 2'k v l 1.067 , 10. 4 dOO. 5 4lp .447.3 ·10400. 1 3'OCR 0.9804 200. 3 5ouS..... W p 0.51 61200. 2 2{k.l 0.0;49 86468. 4 1lk y ! 9.33 l10·5 700. 5 4lp -404.3 - 9400. 1 3............0.4902 100. 3 5• S~t of stiffness coefficienu of the horizontal components of th* tfedownsI'OCRSet of stHfn.55 co.fficlents of the vertical cOllPOnents of the t1edo'4ns.NenOOS2.... W p 0.5161200. 3 2'OCR dhlded Int4 two pac4lOeters. 'OCR (FE) when the c9 0' the cuk is on the lacend of the rail c.r eg.•nd tOCR (SE) when the C9 of the cuk is on the Hruck end(k,.\0.019831185. 4 4of t~e rli 1 car eg.(kyl -2.279. 10- 3 -17092. 5 5IIRES?CH5E IVARloIBLESPARAM£TE~S(P)(~V)\IHFLUENCECOEFFICIENTS**SENSITIVITY:l;j) 4(P)PAlWlETERRNlKIHG BYIHFLUENCECOEFFICIEHTOUSJr.ldX wP ·0.401 .48840. 3 2{It. t ·0.00149 _11197. 4 4(k) 4.56 • 10. 4 3420. 5 5PARAMETERRANKIHG BYSENSITIVITYlp -2196. -65007. 1 1'OCR -152.6 -31130. 2 3IIlp 3138 .72959. 1 I.'OCR .153.4 31294. 2 3

TABLE 19PARAMETRIC AND SENSITIVITY ANALYSIS - RANKING OF PARAMETERSBY PARAMETER RATIO-BASED INFLUENCE COEFFICIENT AND SENSITIVITY-- IN'-JII RESPONSEVARIABLES(RY)I X I• S "'axPAlWlETERS(P)INFlUENCE I iCOEFFICIENTS SENSITlYITY:l~l, :1:)1 ~(P)PAJWt:TERRANKING 8YINFLUENCECOEFF ICIEHT.(CPS) .1266. .1899, 1 IPAJWt:TERRA/lKING 8YSEHS IT!VITY.(CP2) -1078.7 .1618, 2 2• (lI p ) -546.7 -820 . 3.(CPI) -522.7 .784. 4.( Ik.') -500.7 -751. 5 5·(CP7) -500- 7 .751. 55.(Zp) Zl~, 3 169. 66.( Ik yl ) -18,7 -28. 77.( ·nr.) 0.72 3. 881" IY.· .... ·(CPS) 546.7 820. S 8·(CP2) 2543.3 3815, 6 5.(lI p ) -1910. -2865. 7 6.(CPI) 5016. 7524. 4 4.( (k,}) -473.3 -710. 9 9.(CP7) -472. -708. 10 10.(I p ) 2853.3 2140. 5 7.( lt }) y5722.5 8584. 1 3.['OCR (FE)] ·5341. 11118, 32• ['OCR (5E)] ~09, -11258. 2I34INFLUENCE=\ESPQNSE I O\RAM(TERSI iI OARA~£TERI COEFFICIENTSI SENSITIVITY"~RI~8LES(o)RANKING 8YP.A~t6~T[;t( RV) INFLUE~CE RA:lKING BY: ! ,(CP2)i I ,(W,)II I *fl, *Jl ,(P) SE~Srr!VITYI COEFFICIENT, I2. , i ,(CP8) 320.5463.5481.695.2I1170.7 256. 56:(CPl ) 260.1390.144,( 'k.)-23.3-35. 88I ,ICP7) -23.3-35, 88>(Z.)157.1 117,867.Uk.) ) 296.8 445.233~( 'oro)68.95287,1 75~ Xci I....·(CP8)'(CP2)594.796,891.1194.3232'(W p)1233.1850.11O(CPI)154.231.55.( (k,})133.3200.S6, (CP7)133.3 200.S6'(Zp)-361.3-271.44,( (k )y.4. -6.77.( IOCR) 0.241.88,

TABLE 19(Cont'd)..........IN0:>I,!INFLUENCE I~FLUENCE IPARAP€TERSCOEFFICIE~TS I SENS IT IVITY PAJWlETERRESPONSE I PARAM£TERS COEFFICIENTS SENSITIVITYRAHKING 8YPARA/1£TERVARI;'SLES(RV)(P)*WO(P) I (P)INFLUENCE(RV) :1~1) , :1~1) o(P):m l ,SENSITIviTY IRESPONSEPARA~1ETERVARIASLESRAAKING 8Y PAwnERRA11'1~IG BY INFLUENCE IWIKIIlG BYCOEFFICIENTCGHFICIENT SEilS ITlVlni YetI m .(CP8)1153.3 1730. I 87OUS 1m.u ,(CP8)1.815 x 10 5 2.1Z2 x 10 522I .(CP2)1880. 2820. 6 5dCP2)1.931 x 10' 2.897 x 10511.(W p )-1424. I -2137. 76.(W p )1.341 x lOS 2.0198 x 105 33.(CPl ) 3791. 5687. 3 4.(CP1 ) 6.373 • 10 4 49.56 x 104 4.( (kxl) -252. ·393.99,(fk.l) 6.34 • 10 4 49.51 x 1055o( CP7) -Z62.·393. 9 9 .(CP7)6.34 • 10 449.51 x 10 55o(Zp) 1945.3 1459. 58.(Zp).1.3867 x 10 4 4-1.04 x 10 66.( lk }) 3v4Z20.7 6331, 1 .«kyl)533.800.77'('OCR(FE)] -377S.7858. 42.( 'IVR)•48 . -200 •88• ('OCR(SE)] 3847. -8008 •21GUS4 ITIIx.(CP8)1.65 x '0552.475 x 1022\. I .(CP8) 211. 317 . 2 21. 756 x 10' 2.634 x 10'I1d maxi .ICP2)5·(CP2) Z29, 344.11.(W p ) 1.2084 x 10' 1.8126 x 1033«W p ) 72.5 108.8 56 .(CPI) 5.8 x 10 B.7 • 10'44'(CPl ) 138.8 208.2 4 4 .( Itx I) 5.71 • 104 8.65 x 104 s5'(fk x ) )1.6Z.4 I 8 8 .1 CP7) 5.71 x 10448.65 x 1055'(CP7) 1.6 Z.4 88.(Zp) ·1.253 x 10' -9400. 66'(Zp)71.6 53.7 6 I.1 (k 1)y461.700 .77• (; tyl)141.1 211.6 33t( 'nrR)·Z4.-100.8 8'(l.nr.)32.1 133.575

TABLE 19(Cont1d)............,N~V RpPOflSE RIAOLESI (RV)OUSZ.~,OUS3~xIINFLUENCEPARAMETERS COEFFICIENTS SENS IT IV1TY PAAA'IETER(P) RANKING BYPARAMETER:!W :1:» A(P) .INFLUENCE RANKING BYCOEffICIENT SelSITIVITY.(CP8) 4.859 , 10' 7.Z89 , 10' 33o(CPZ)45.03, 10 7.545 x 10 4 Z 1o(W O)• (CP1)4.089 x 10 4 6.134 x 10 4 49773. 14660• 78>«(k,l) Z08OO. 31ZOO. 55>(CP7) Z08oo.31ZOO. 5 5>(Z.) 91280. 7Z960. 1Z>( (tv» 7S17 . 21300. 86.( 'nr.)·11393. .17090. 67>(CP8) ·56987. -85480. Z.(CP2) ·33880. ·50820. 3.(W p) ·32587. -48880..(CP1) -7867. -11800. 56.( Ikxll.(CP7)• (Zp).( (kyl).( 'OCR).7867. -11800. 5 6·7840.-11760. 67-86680. -65010. 1 ZZ280. 3420.B 87478. 31140. 7 54A134

A P PEN 0 I XIVLISTING OF CARDS MODELIV-l

LISTING OF CARDSMODELI' P O('.i1A" CARD::>• r. __ C'_~'!.~.!! ~ __MuQ._~!~_M~~_E-----!!iE __.1.9_1" §!! lL['J1!A~.L ~~R_ItP~..!__ ~!il)~ _• ROTATIONAL MOTION OF A CASK-RAIL CAR SYSTEM DURINb COUPLING'OFERATIONl? IPRE1HIINARY MODEL wITH BENDING Qf---lHE RAIL C.!..~__. _••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••*•.•--.-------- --.._---------- . -_._.. _----_._-_ .._---- ._._--- _.-----~•--- ._-------_._----- --_.__._.... ---------::-----=-: ._--_._-_._----_.PPPPPPPP 111111111111111 22222222222.2222 333333333333'33'_____--:,,-P.PPPPP";'P-':P,...".,o:-::-_ __11111111) 111111 22_~22~22222222223 3'3~3~1~U3:33'T DTDTD 1111111111111 2222222222222 3333333333333'• RC~CI

on__ •__1t CONSTANT PAYR12 : +1 • 01-08 -81. _... ,.QfojS.UKLP!..'!'..E!~..:_~L.... .e••• _ •• •••• •• • __ • ._·.·.-0-l":'C-8 ~.d1CONSTA~T PAYCPL : .1.01-0S-bl_ .._._. ~S.I!h.LP..A1...c.£L.....=..=.l..L_ .. . .__.__ . . .. _fU..~.l2:'..A1'---"[lGHT~ vF SYSTEM cOHPONENTS'eON S I AN I Wp~ • It E 5. hi E -1 • 7n'. .rT R =~.1..5.O.....~1.E.-7 1 SO •• ....wl\~.2..I.£..!i _'ONSTA~T ~P=&.E!t S'itO TON CAS~' ]-03-79____-C-CliSJ'.A!iT liRe: 5.96fit .. .L...U.~.ILCO:-'STANT FRHP=n.Ci 8-28-79CONS UN..LW~I.!lES. WE 2= 1 .HE 5. WF 3=..l.... l..!I~~~.1!i.£S 7 -03-~.'---HOHE~T~ OF INE~TIA'cONS IAN T IP =5. lB~ 5. I RC=2. 5liU!, . .........8o...;-:;.,3.....C=.1.9_'---HODULUS OF ELASTICITY or BEAM (RAIL CARJ'CONSTANT E=3,E7'---0 IHENS IONS'CONS T ANT L1CC: 2bit at LP=2 37 at LCR= I.O..t.hL.t..E.:l.fl.h~.1.P.1t=..1le..._S.~l.E.f";:..l.tl~ ..0 J -If'-srCONSTAtH PI = 3.1it1b01f-1I-6(CONSTANT LtPL = 3g1.25CONSTANT ZRC= 18., ZP=~l., WDTHRC= 2.CONST ANT ZC.OGO"-'=::.J.....3....S'---aUIAI VEl OCTJIES'CONSTANT VXPl=.176.,VYPI=0.~VTHPI=0.~VXR'I=.17~.,VYRCI=0 •• , ••yTHRCI=o•• YXTRI='17p•• VXTfl=·~~Y~~._CO~STANT VXf2t=0.,VXF3I:G.,VXFIfI=0.~ ---l...!ilLil~..Jl.1~.~.u.t.r..." ... E-"N!..!'T-,,~,-' . _CONSTANT XPI=O.,YPI=C.OO,THPI:O.,XRCI=O.,YRCI=C.OC,THRCI=O.CONSTANT XTRI:O ••XTFI=O •• XfI:O.CONSTA~T Xf2I=O.,Xf3I=0.,XfIfI=0.CONS IAl1 LXI..lll.U =-. a . ._.. 0 Z_7.c.1.:-.bL'·---INITIAL VALUES OF INFLUENCE COEfFICIENT~ ANo OERIVATIVES ·D5-1S-6~____..JC~O_~.l~IU_U~.bI.l.CU ...~Jh . ... .. e' .3.:=_1L=L'i..CONSTANT IC9I=0.,OIC91=0. 14-12-79___~C~O~T.!lH ICl;;I=CuJU..u'..llI=p. ._________ 1j-12-79CONSTANT IC111=0.,0IC11I=0, 14-12-79__-----'C'-"O....,r....."S'-'TANT I C12 1=0 •• Q.H.l..il.:.Q.L.-. ._ _ !I-12-H._CONSTANT IC13I=0.,OIC131=0. 14-12-79___~C~O..!!!N.s.I.!.~LH_t~l~n......tiIli..l.1fI :C..L-_ _ • :-.1.~.7JLCONSTANT IC1~I=C.,DIC1SI=0. 14-12-79CONSTANT IC1bI=p.,OIC16I=O.'-12-7~CONSTANT IC171=0.,OIC17I=0. 14-12-79CONS rANT I !;.18 1=0,. DIC 181 =0 ,..3.=12.~LCONSTANT IC1~I=O.,OIC191=0. 14-12-79__.....J

CONSTANT IC261=0.,DIC26I=0. ~-12-79CONSTA~T IC271=C.,OIC27I=0. ~-12-79------cok"s TAiiTTc2'b1=C .,oic-Z-H=o. ---.----.----.--.-..--------.----... q-1Z-=-79'---LIMITS ON DISPLACEMENTS'----.- CON sTANTXRPL 0 ~ - •0 b'::'2~S-,'::"X"::"R-:::P7.'-;I-:::=:-.'""'O:-:6-::Z="'S;:-O-HCONSTANT YRCHAX = -1.125 9 -08-79---~C07-N~S=-=-T""AN~T XTU= S.t. ,XTl2U: S.6,XT23U= S.6,XT3I1U: 5.6CONS TANT XTL = -5.6 ,XT 12L=-S. b,X T23L=-S.6, Xl 3~L.=--S~__.. . __CONSTANT XTU1 = 2.8,XTU2 = 5.6 8-6-79CONSTANT XTLI =-Z.8,XTL2 =-5.6--:-.------A,-,O"..J.:.,U::,...S TH'ENT FAC TOR S FOR RE LA TI VE VELOC IT r'ES • 8-15-79___--;:CD;.N;:.;S;.T=-'A;;tiT AQRCF=- 10 • 8 -29-79CONS TANT A012 =0. 9-07-79CONSTANT A023=0. 9 -07-79CONSTANT AD3~=0.'-97Cj:"f9''---OAHPIN~ COEFFICIENT~S~'~~~~-:::-~~-:::-~~~~ ~CO NSTAN T CS 1::2.E3, CS2=2.E3, CS 3 =2. E3,.CSq= Z.. E3 ,CS s""=2.[ 3~ CS 6=2. E3 8-28-79CONSTANT CS7=Z.E3,CS8=2.E3,CSCARS=2.E3 8-28-79CONSTANT C56=000.,CS7=OOC. o1-07-& ~CONSTANT C512=.0 ,CSRI =.0~_~,CSF1 =.0 ,C531: .0CONSTANT C523= .C ,C5R3 -.0 ,CSf3 =.0 ,C5R2 :.0CONSTANT CSF2= O.~=:"SPR:iNG c'oNSfAN TSCS T:~I'-"F'""'F'7N:-;E;-::5:-:S;-;E;-::S:-:)-::''---'----SPRING CO~STANTS CNON-BENDING)'CO~STANTK5CARS=1.0115E7,KSl=1.E7,K52=I.E7,K53=1.~7,KSq=I.E7CONSTA~T KSZ=I.0ES,KS3=1.0E5-----CONSTANT KSS=1.E6,KS6=6.29[q,K57=6;Z9EII,KSS=1.E601-11-acCONSTANT KSS=1.E6,KS8=1.E6--~c~o~NsfANt K56I=b.29EII,KS7I=6.29EII,KS6INf=Z.l7,KS7INf=2.E70.1-2q-8C'CONSTANT KS61NF= 1.E6,KS7INF= 1.E6 9-09-79CONSTANT KSILO:S.EII,KSIHI=1.E6,K5qLO=S.EII,K5qHI=1.E68J -z~ -oCCONSTANT K2FF2=QS666.-----~'~O~N~S~T~ANT Kl=48666.,K2;-=~1I"::"8~6~6~6-.-,~K:-:l-::F"r"2~=~1I:-8~6-b""6-.-,7.K"::"1~F~2~F~3:-:=:-~=8666.CONS TANT K2 FZF3 =118666 '.LKJ F3F ~=" ~_666!,. K2F3F~ =-~.866 6.:..-=:-:----'-_CONSTANT K5DG1=.SE6,KSDG2=.SE6,KSFF21=.SE6,KSFF22=.SE6CONS TAIH KSF 2 31 =.SE6, KSF232= .SE 6 ,K SF3 Q1=. SE 6 L~~F 3c_II.:.:2=-=~.~S:;...:E::..;:6=-- -:CONSTANT K6=a.OEII,K7=8.0ll101-17-erCONSTANT KSDGI0=.7S~S,KSOG20=.7SES·-----CO"'S TAN TKSDG1 0 =0.iE·6----------·----..CCNSTANT KSF21G=.7SES,KSF220=.7SE5------CCNS TANTK~iTIo=~75E:S ,K S2320 =.-=7-=S-=E-=S--_._--_._-_._--CONSTANl KS3410=.75[S,KS31120=.7S[~S~ _CONSTANT~HRCFU=4.~K"RCFL=1 •.CONSTANT KMFF2L=1.,KHFF2U=Q. -_._-----_._--CONST AN--rKHF 2 3L=1. ,K-HF2 3U=~.CONSTANT KHF3QL=1.,KHF3I1U=Q.--·----CONS TANT RCOR =1. ,FOR=ti:----·-·--·..,------------------~-----CHANGE REOUIRED DUE TO SLACK IN TO-S ·05-27-8('tCNSTANT RCoR = ).05-27-bCCONSTA~T LOO~E = .TRUE. S·LOGICAL VALUE~' _ 07-02_-80CONSTANT F'20R=G.CONSTANT F30R =0.-----coN-StA"FrT F 4 0 R=0 •'---MULTIPLI(R A~D S.1TCH TO GOVERN ~ENDI~G·-·------ccNS-TANT BEN u Sw =o. S • N0 BE N0 I N~G;.:.:.;W~H';:'E:-:'N~O-.-::·-------------------'----$PRING CONSTANTS CBENDING OF RAIL CAf)··----coNsTAi;T·--ifi2=.0 ~-KRI =.0 ,KFI = .C! , K31=--;O·--------·IV-5

CONSTANT K~3~ .0 ,KR3 = .0 ,kf3 = .0 ,KRZ = .0CONSTANT KfZ~O.----OEf-INIY·io"N-OfOPAf=-=-T-G=-E=-A--:R CHARA CfE-R-iSTIcs..------- - -------.----.----..----.- ------~PRING CONSTANTS (DRAfT GEAR)'.- -··---CO~~sTAI~-i"·-Krfc=2:09E-7.KF= 2."09[7---··-------------------------------·---___...__l:.QN$ TAN T I(.•CR C1~1.3 bE 5, KCRC2= 5.36 Ell, KC RC3 =?'-",C!!:2~8""'E.::5_CONSTANT KCfl=Z.36E5,~Cf2=5,36EIl,KCf3=2.28E5.__.__.~O.~~~.To. KCR_l!'l!:=?_!.9!.1..t~CfINf=Z.U_ .__.__ . .. .. ...-----POINTS WHERE I( VALUES CHANGE'. __.__fQ..NSJ..Al\IT.. J(UR-'-Q=_.Q~_-,XUR_U= Q..981l.,_XUR~2-=~'!..t!UR~~=~8 . . _CONSTANT XUfO=0.,XUfl=.98",XUf2=3.,XUf3=3.768_ ---TJLHELAG ~EfO~E 06 ACTIVE STATE' J -.J..L':1.LCONSTANT TLAGCf= .0380 -------------12-06-79__._CONS ~~.!iLJ~.!.t?!:f.= .0380 __. t2 -0b.=.7!!_---COEffICIENTS Of fRICTION'__-'C~.lAJiL_"-UC.;:_JLl1!JS-=='"" ... ..... S'-"8'-_CONSTANT HUPR=.5S__",-,cONSTANT MU=.S8. 1.1.-1-77CONSTANT MUCPL=.CS.HUTR= .5,MUTf= .5,HUf= .S8,HUFZ=.S8,"Uf3=.S8CONSTANT HUfll=.S8-- CONSTANT-HUf=~3C;HUf2=:30."Uf3=.30.MUF.. =.3D ----··-·--·--·---i::C3=i"9·__ • _. _. .~_~!!~.1~_~.L.HU~.!'_~~~ . . __._ ..__._. 0 •• 0 _ •• ••.5CONSTANT MUD= .5,MUDb= .5.MUD7=____C.Q.N~_U!'U_"LU.Q.~.E=!.?J HU C~C =.5 ._ . ._._ •••• _9 -J Q.::U._CONSTAhT MUD7E=.2.HU07C=.S 9-10-79_12-1~-7S_._._.__ C~~..l~ll.!_~~.! ..,L2C=Q.!Q.!H..!J_!.2~::.95 .._. __..._.__. _~~~~ ..CONSTANT MXT23C=0.O,HXT23E=.95 8-22-79___.,....:CONSTANT MXT3C1C=C.O,HX13 ..E::._!L 8-22-7...2..______.l;ONS_~_A.~! ~~~fE!.~.,..!'.Y~f1 :=_'!..~~~L2 H=. S.t.!1Jf.Z 3_2-=.• ~,.", Uf3.. !.=.5_.~uf_.3_~_2_~.!..LCONSTANT MXRCfC=0.O,HXRCFE=0.8---fRICTION fORCES ONCOUPLERS'___ CONSJ.A!!.I...£.~t..~~-=-~.EIl_•.f SCf=S &Il ... -------------- --- --.---fRICTION fORCES ON SUSPENSION SPRINGS__._._.-£.ONUANT__ .L~~J~T~.!50 "fR~.CTt9h OLLO~.£L_~~-1...B_~~ . . .-~-FRONT AND REAR BRAKE SWITCHES. 1. WHEN_____~O NU..!'iL.BR AKEf....':'-!l• .a....!.~AK~.. _._._BRAkES ON, O. OTHERWISE' 12-1-77. _---OTHER TRAII'4 BRAKE SET SWITCH, 1. WHEN BRAKES, O. OTHERWI~E'. CQ~_~H~~Rli~C :: 1. _S~~.U_U.Q.~.BRAKER ANO__BR~!-_~.L...lliOULJ?_ ~LJl.a._'_. __ .. _._CONSTANT BRKfZ::l.Z.BRKF3=1.2,8RKF.. ::l.Z8-2Z-79___._. __ ....t.o.~ IAN T.....8Rl

CO~STANT DTMIN=1.E30,DTHAX=-I.E30 OQ-30-6f_"'_~_-_:L_0.AD.:P~F.L.U..!.;l_O~_~.'='.i.~E_. F: QR_P-R!LT__ GE~R:-D I~PL, __ \L~L-'~9.!.Q~. ... . .__ ._. ....__TABLE XOG,I,~/0.,.98~,3.,3.7b8,0 •• 2.32ES.3._ES,S.J5ESI._. _ ._!~B'=LK_HfR~G_J.J~/5~!"S.8~!..h_~~~...L.ll.!..,.l·_'l...~_3..t..h!__. . l,L-U:..I5TABLE KHFf2f,I,_/S.b,S.8S,b.l,b.~S,I •• I.S,2.S,\.1_.. TA&LE KHf 2 3f d_!..~J5 • b. 5.65,b • 1 , (,.·35 ! 1. , 1..!~t.?-=•..::S:..J'L\.:.:.:..:/:..-__. _TAaLE KHf3_f,I,_/S.b,S.8S,6.1,6.3••1.,I.S,2.S,\.1'---COUPLER FORCE-SRL EXPERIHEhT-!!..~..L:.!7-l?_.---- iN ST 3 .------- ~ 1-29-7 9TABLE DUSf,I,2l/0.,.0_8,.OS,.DS_,.07,.07S,.076,.08,.Q8S•• 095, ••• 11-29-79----------------:D, .136, .1_ 5, • iSs, .206,. 21t2 ;:26-,~27; • 28.;·~~·-i~i9':'-791.,... 11-29-790.,0.,2.E_.0.,I.E5,9.E_,2.9ES,II.[\,S.E5,... 11-29-791.16[6,3.£5,2.E5 !S.2ES.,I.E5,S~_E.!.!..?E~..!.ES, !..!...!.....__ !-.1~~.-7~1.ES,6.E_,0.,0.1·---~_O_NGITUDIN~L~..BCE-SRL EK PERI"E~l-lESI.~ ._. .11-29-79_TABLE OUSLFF,I,21/D.,.03,.05,.08,.09,.11,.I'.~IS,.161t,.176,... 11-29-79.185...19l.J..4!.uL~-,.26, .liu271t ,.~283 ,..!h~91 we .. 11-?9-7~1•••• ·• 11-29-79._.__O....!...'~_.E\,0.,2.• 8EIt,1 .1.t.~.!..'!...!.6_~_5!!..~E!...~!~_~.c.~'! I) -2!..~79_.8E5,1.8_E_,1.6E_,-I.ItE_._._EIt,-2.EIt,-2.E_, ••• 11-29-79___. -=1. 2~.'!.J..~J~.,-2.E II ,!L._~.!I LP.. H.Q~.L_· .. . _ .... ll=29_~.19'---HORIZONTAL ACCELERATION OF CASK-SRL EXP-TEST 3-INSl NO.8' 12-11-79• [)LTEREO AT ~~C_~2~JNG FfT'_ ~~18-8QTABLE D2XPF,I,S_/0.,.0096•• 01Itb ••D2C8,.0266,.0316.~0366,.O'2,••• 03-18-dO_ .. . • 1l'!l..u_D.S2.'lLlil.b...2.s...Jl.1Z.h ~.Q]j «l..u.QJl..2Il, !!l.9.M.J _•..l..:U.1~! '!!..Q~ =..U -:ilP.1356,.I__ 8,.16S_,.1898,~1968,.20\•• 2J06,... e3-18-Sf______-=.... 2'-"1'-'2'-"8J....2198 •• 2236,~?..1..Q..U_~2_~U_H_~-'.l1_?uof:s.~~_H .•O_~..::lll.":H.262,.2692,.2756,.282_,.2S98,~2958,.3026.... 03-18-80_____________.....'":3~1...P""'6.........."'!3~1~6.... 8u.u,~3~2~3!"8 .....-3..~3~3~n •• 3lf28 n ..ll,lh.....3S68. u • Q 3-18~D.3626,.3708 •• 3798,.3S9,.397,.It,.lf07,.1t09".~I,•••e3-18-8(.5,... 03-18-6f-83.IIS, It. 722, -3.15,19.15 ,~9:-7-j9;8~ 70~'-;'12.9-"-,-~~-~-(i3 -18~ir____1 7. 1 5 • -13_!~, r 8 .2~.!OL!J.::li9..,! ~...I.':' Z.t!.~,."_ ,...._•• .Q.~.=.U-:.~ ~-,_9.5,--103.,-625.1,-718.6,177.7.-2781.. ••• 03-18-b[___If..Q.~h -22.!hJJ..1.1-'..!..1lQ.LL.!...li. £J~"'.O..~l..L._'...t!.! 03 - U.":..H-3.38&,-101.5,102.1,-121 ••-63.02,-116.5, ••• 03-18-EO________________ :~..J_!l»~,'-1110 .3.J 9.5!.J..:..~.[!0_!~J-5.P ....~!.t.= ... 2.2~,__ ._._. 0 3~tlt::8J'30.79,~139.7,1t0.7l,-282.3,-19~._,-252.1f, ••• 03-18-80... . ::-I.J~6_5J.:U~h 1.2J...!.h...:n.!.71 '_U_~'!..!.J..-'3~~19.L·_·_·_ __ _ _Q.;3~..t~:~9-21.~1.-113.1,-87.29,0.,0.1 03-18-~0~=---VtRTl~~L ACCELERATI9_~ OF C~~.!L.M SlRUCK~D-SR~_ txP-1ll.T 3-.INli..~~_~.J.1:,79• FILTERED AT 50 HZ USING FFT' 0"-23-S0_. ._ TAB ~~Jl_?.e! _F. L 1_, .~~~~[JJ~~ J_._021..t_~_0_lf..~L,~P$.1,_~_06~ J_~ !991.u_t21"_'-~~~ o-. -~~-8.~.151t,.18118,.201.. ,.216,.237,.2606,.2682,... 8"-23-60____.__ ..... ._. .. _.2.!Q.2_,~3.1."',_,'3~~_, ~ll1_•. '39~~~_'~Q,~.,'!~.P~5 t .•,.! p!::n-:flO.5, •• ~ 0"-23-&0________________ 109...!h-2!!..~9.-13.6_ .-72 .'~h=2.D~_•.~Q.8.U~_L __-l.!.:l.~=-8.Q.1157.,-1&61.,1986.,-1t31.6,-203.5,-S31.'.... 0"-23-&0____... ?JU...~.J..::2.U_•..IL::..23tt~l....1..::.lQ07 ...IJ5'U.?....L~Q9 • .J~~ ._.Jl.'_:'.~~::9..c-8.9.,8.-275.8,109.9,0••0.1e"-23-ao_~.::::_::,:!O,!.!ZO.~.!~L...~_t.UJ,E:~A!.I_QJLq~_~A.SI(~ ..~_~IL: __ S_~.L~.n_:-__J.U.J _.3__ ."': ... INS1....J.2 ~ __Ll.~2..?_-J!• FILTERED AT 100 HZ USING FFT' 03-18-8e__.__ TABLE 02XR.~~.1-, !1(Q.~._0.!.~6-.1..&.C..l~~ulLZJ.!.L • .Qn2.J_!.-QH6, :O'-UI...._." e 3-18-8[1.• ) 52, .0568,.0616, ,0672, .(j731t,. 09'38, .0\92, ••• 82-08-&0_____.__._. ~_Q9.1!,E!.J_.!09~'.!.H)~2_, ~_l..1JI2 ~ .• !?D~ t.~ 12!»2.,_~ 1~.~_~_,-!_!_! Q?_::,pa-_& ~.1~_S,.1661t,.1712,.172,.1736,.17\1t,.1762, ••• 02-08-80IV-}

.179,.18,.18Q8,.1822,.1832,.181t,.1&52, •••02-08-6C________. ._. ti..§..(l~_l-.J.8a.l~J.jJi61_• .1.9~.L.•_a_lf.z.._.n_~2. LlCl7 "-__•. , ,. 1l2.=n.8.=.H.1971t,.1988,.1998,.2,.S, ••• 03-18-80) 77.2 , -9«t.._~1.. 2.6S--l.~6..l..a.J8-1 -2 B• 2, ~.2..l.OJ..-. •. .!l2.~OA..=bO100.8,11.52,-231.7,-lZ9.,-269.~,-52.97, ••• 02-08-6r__________________________=-~!~8~O~9~.~.~-~'uS~I~9LA.~~.-'778••1226••-758.2, ••A- 02-C8_SC-631.2,-80Z.8,-398.S,-2817.,15S7~.lZ5.2,••• 02-08-&C_________~1 J .9,-79 3a..J..a.::2.1..D.....9..=.lJl.U••-S 92 .2,.=Jl2.9.....s......a..-"--__ a 2 -DS~j)C.-795.7,-769.4,-761.4,-749.7,-705.8,-618.1,... OZ-08-60____________...::--"'g.... 3""SL-I.'-"2'-l.L:-~9r-7..... !lL...l.02.d....a.ZD.L i>. 251. 1.11~.L_J:ll~--. 02 -08 -&.ll366.9,370.7,~.,D.103-18-fiC·---VERTICAI ACCflfRATIO~ Of CASk AI fAR END_SRL ElP-TEST 3-1NSI IJ· J1-29-79• FILTEREO AT SO HZ USING HI" 041-23-IH'TABLE D2P12fll,27IQ•••OJ2'•• Q222 ••~332,.041!••QS~~~~732•••• 04-2~~.0978,.1178,.1534,.1888,.Z018,.2102,.2336,... 04-23-80•.n12••267lt2896•• 3Q"_,.'31..U~!...-".JUz..... JlIi-23-&r.3714,.3932,.4094,.4095,.S,~..04-23-8C-165••,52.8.-30.1'.57.33.79.59.90.17.9.973 •••• 09-2 3 -SO68.97,-!27.",Z"65.,-2051.,601.8,370.3,427.1, ••• 04-23-8C_____________- .....1Zk.... 1 :L.L..L.3....7L.L.l!.L...::.~9." ._8..§_t.J...z.J.l..•.-L._U2....L1.a..=J!~L..t..L.--O.4 -U--=!U;72.97,38.8,Z9D ... ,~165.7,O.,0.1Oq-2~-60~SPRItY......£O NS T~ ~ TS-H OUll NT AL SP ~.lJ!!i..s-=-~.I.Q... TRUC KS_·l.1..~a.=J..!lTABLE KS58f,1,7/-1.,-.11,-.1,0.,.1,.11,1.,.ZE6,.2E6,.ZE6,.ZE6, ••• 02-01-8C.2E6..2Eb..2E6102-01-o.£:..·---NON-LINE.AR STIffNESS COEfFICIENT fOR VERTICAL TIEDOWN AT fAR 'OS-lS-8r___---,O-::-"E...,N'-'

.ZO~7,.21,1., ••• 01-0S-SI19b.b,-337.7,lb3.~.-b~5.8,99.1Z,-53.3S, 01-CS-bl--7.~:"'::3:7b-.9. -~blj;I, 3 9S .b. -fliTZ. ;b67-:-&. -1 ~ 5l ;;-iSO-.6"~~·:01"="G8-81-lb97. ,Z5b.b, Zl1.5, C·.,O .1 . D.!..:OS:8)·-·-~-~vnTlrAi.ACCET[lfAflON OF CAR STpUCTURE AT 'SE-SRL EXP-T£.ST 3-INST b' flJ-DS-blFILTEREO AT 50HZ USING FFT' 01-0S-8~SOMEWHERE BETWEEN D2YCPL AND DZYR7S' 01-0S-81_____~T~A~DL~E OZtPLF,1,18/u.,.00~l,.01~Z,.02S~ •• 052,.Ob~1.071_~L0899L-~~~-1-Q~~~)_.1066~.1203•• 1Z72~.1~~9,.1652,.1823,.197, ••• e1-0S-&1.ZO~7,.Zl. 1., II..-Ol-0S-8.t-171.3,-zi9.,-89.S1,-3S8~,l~~.7,-198._,-11~ •••••Ol-0S-&1~3181.,~Q5.~,-983.,-791.J,-2951.,1026~.••• OJ-OS-S1-912.2,113.6,-168.,O.,D.1el-08-81FILTERED AT Z5 HZ USING FfT' 01-12-81TABLE OZCPLG.1.1C/0.,.0109,.0_52,.08~S •• 11~6 •• 1_2~,.IS~2••20~7 ••••01-12-81__________.::;.;2:;.:..1......::;..1..:.. .......~.-=-•...:.o--::,.".-__Q.1 -12 - 01-37Z.,-611 •• 326.,-1_2~•• -8~5•• -1539 ••296., ••• 01-12-81-369•• 0 •• 0.1 tJ.1-12-sL••••••••••••••••••••••••••••••••••• ---D ASE-----cA"SEPA··R;-;;A.....H..E...T"'E..R"'S:------'""l·.-------------------------------- 83 -1 ~ -80·----WEIGHTS Of SYSTEM COMPONENTS' 93-1~-8~CONSTANT Wf =1.75E5 S'(REF;-[NSC0Jl83-i,,=acCONSTANT WfZ= 1.75E5S·(REF. ENSCOJ' 03-1~-8J-------C~ONSTANT Wf3= 1.75~E~5~-----------------------------~S~·~(~RlF.ENSCOJ' 03-1_-&0CONSTANT WF~= 1.75E5 S·(R£.F. ENSCOP 03-Jq-bC-------CONS TAhYWP=8 .E~ S'~O TON CASK' ··------_··-----ff3-11i-ocCONSTANT WR:: 5.b9E~ S'I_NCLUO~S Z BULKHEADS (REF. ENSCOJ' 03-1~-8(--------.,C:-;o:-:N;-:s~fANT WTF: 1.3SE~---i"i&REF.ENSCOJ' 03-1~-8CCONSTANT WTR= 1.35E~S·,REF. ENSCOJ' 93-1~-8r·----MOMENTS Of INERTIA'D3-H-SCCONSTANT IP : 8.57E5 s·(REF. ENSCO.J· 03-1~-8Q.CONSTANT IRC: Z.8~95E6 S·,RE-F.-ENSCOP 03-1~-80'---rHODULUS OF ELASTICITY OF BEAM 'RAIL CARJ' 63-1_-8('CONSTANT E = 3.E7 S·'REF. ENSCOI' o3-f_-8-n·----OIMENSIONS·O~~~CONSTANT LCPL: 3~1.25S·'REF. ENSCOI' B3-1~-80___ CONSTANT LCF: 185.125-S·l.~EF'._E~SC_Q"J~-.9}~_~!t.~~J)'CONS rANT LCR: 95.125s" REF. ENSCO J' B3-H-8C'______CONS T ANT LPF: Z07. .-!~ ._!tE.~~!(~CJll_·_.9~:._t~~_QC·O"ijSfANT LPR: 37.25S·'REF'. ENSCOP 03-1~-8rCONSTANl LRC: Z59.5S·'Rf.F. ENSCOJ' 93-H-8CCONSTANT ZCDGO = 6.15 S'-IREF'. Et-lSCOJO e:!- ~-8(CONSTANT ZP = 31. 03-1~-8rCONSTANT ZRC : Z5.2 S'(REF;""ENSC-OP-03-1_-8Co----LI"ITS ON DISPLACE~ENTS~-----CONsr-ANTXn :-~S.25 -93- ~-ar.So"iR"EF .--ENs-coYi-03-1~=-i;rCOt-lSHNT XTll : -Z.625 S·'REF'. ENSCOJ' 03-n-Sf:lCONSTANT XTL2 : -5.25 S·'REF'. ENSCOJ' e3-1~-80CONSTANT XTU : 5.25 s·'REF. ENSCOI' 93- "'-8('CONsTANT XTUI : 2.625 S·(REF'. ENSCO)' 03-1~-brCONSTANT XTU2 : 5.25 s·(REF. ENSCOJ' 03-Jlt-SQ"·-----soTRU.--ENS·t-O-)"i-li"3-:i..-~6r---C-ON"STA-NT xTl2l : -5.Z5CONSTANT X112U : 5.25 S·,REF. ENSCOI' 03-1~-8C------~C~ONSTANT XT23L = -5.Z5 s·(REF. ENSCOI' 03-1~-80CONSTANT XTZ3U = 5.Z5s·'REF. ENSCD.I" 03-n-aO--- __---CONsfi"N"T---iffIt L=-:'~~-is---- -_'_-0- --- S • ( RH -: -EN SC O~J'-o3"':i.. ="8cIV-9

CCNSTA~T XT3~U = S.ZSS·'RLF. ENSCOJ· 03-1~-8r.._·-:.---s prtNG.S() ~~!..A--!!.!§~__. . . . "_.__JJ..~~ -sotONSTA~T KSDG10 = S.ES S·LOWER LIMIT (REF. ENSCOJ· 03-1~-SrCO~STANT KSFZ10 = 5.ES S·LOWER LIMIT (REF. ENSCO •• 03-1~-~C- ---CONS TAN·f-i(sfizo-::-S:-fS- S-iOWERLIHIT -- iR£:F:--ENSC·0-f..--03-1..-:&·r-·____C~O~~IANT KSZ310 :: 5.E5 S·LOW~R LIMIT (REF. ENSCO!· 03-1~-8CCO~STANT KSZ320 :: 5.E5 S·LOWER LIMIT (REF. ENSCOJ· D3-1~-&C_______~ONS~ANT KS3 :: S.Eb S·LOwER LIMp ._!...~~.!.-._~~~.3-1~-SOCONSTANT KS3~lC :: S.E5 S·LOWER LIMIT (REF. ENSCOJ· B3-1.-S0____ cON_S T AN!_IL~H20 :: 5'!li-...!~.Qd..R_u..M.11 ..'~~I..!....-E_~SCOJ.~J':'I~-6o..CONSTANT KS5 =5.ES S·LOWER LIMIT 'REF. ENSCOJ· 03-1~-SC____C01!.STANT KS6INF = 3.E7s·,REF. ENSCOP B3-1~-SOCONSTANT KS7INf = 3.E7S·(REF. ENSCO.J· B3-IIl-Se:'____ CONST.~~L~S8 ='5.E5 S·LOilER LIMIT 'REJ:..!.._Efj~j;.!U"~_.9._~-1~-6JLCONSTANT Kl = I.S2E5S·,REF. ENSCO.P B3-1~-SO____..£01llSTA~.L_K2 = 1.S2[5 ,.~!.!t~__~NS~Clt~_.J!~~~lLCONSTANT KIFf2 =1.62E5 S·CREF. ENSCOJ· 03-1~-6C___.....l:oC~O~ANT K1F2F3 = .1.82E5 S·CRj:,F. ENSCO.P 0.3-U-6Q..cONSTANT KIF3F~ :: 1.62E5 S.,REf. ENSCOP B3-11t-80tONSTANT K2F2r3 :: I.S2E5S·CREf. ENSCOJ· D3-14-S0----CONS TANT·KiF3r~-·= -1.82L5-,-i·e-REf. ENS·CClJo -B3-1,i,;,a"o_._ .. £Q.N..u~~.!....!

'O~STA~T CS6 = ,coo., CS7 = 2000. OS-0~-8~.. c:Qt! S_!~!'Il_K _S_L_~_.~ .!f.L-..!._·_EQ.!LA~ l~_ ~.3_~ _. . __ __ . ~1.:-~ ~.-_8 r._CO"'STA~T DLTY = 0.11 OS-01-8e_.fQN.E.!!~.L DL T ~:: J. 22 __ . .__.. Q_~_':Q..~~jll:'CO"STANT KS2LO = 2.E5OS-Cl-ar___...:C_Q.N2TA~T KS2L.02 = 3.5E5 oS-ol-~_CONSTANT KS2HI = 5.ESnS-02-oCCONSTANT cS2L=0.-- -----CO~STANTCSZ-H-=l 5 00.. -.__ .__._.. . ..__._. __~.~-~':~.LOS-l"-EICCONSTANT KS2L=O.9~-1~-8.Q--- --c.()NSfiN"Ti

LONS T ANT CASE = 11.___~ Q_t'!.ll.AijL~~_S t,__ -=-.J..£a.CONS T ANT CASE = 13.__ --.J:_Q.tt.U.A..~J~UL __=_..l..1f •CONSTANT CASE = 15.CO",STANT CASE _ 16.CONSTANT CASE17.__ CON..llA.lti-4J.ll- = 18.CONSTANT CASE. = 19.---'.QH.S...UNT CAS E _ 2 1 •.cOtllSTANT CASE = l::l.--i:.0NSTANT CASE = 21 ACONS T ANT CASE = 1.CONSTANT CASE = 2.CONSTANT CASE = 0.1_~ONSTANTCONSTANTCONsTANTCONSTANTCASL-= 0.2CASE = 3.CASE : It.CASE : S.CONSTANT._CASE : b.CONSTANT CASE = 7._ CO~SJ ANJ CASE: 8.CONSTANT CASE = 9.CCNSIANT Ct.SE : 1.1CONSTANT eCASE : O.__CON.il.~NT CASP = 1.CONS T ANT CASE B 2.---'-0111 S T ANL.J:.A.S.LC = 3.CONSTANTCONSTANTCONSHNTCONSTANTCONSTANTCONSJAIHCONSTANTCONS JAinCONSTANT~_1iST AN TCONS T ANT_~°to STAN TCCNS T ANT.~NS TANTCONSTANT__C.Q_~_S~ANT.cONSTANT__C.~NTCONSTANTCONSTANTCONS IANTCASED = II.CASES: S.CASE6: b.C"S£7= 7.CASE8= 8.CASE 9 ; 9.CASEI0 = 10.CA S f II = 11.CASEl~ = 1Z.CAS E 13 : 13.CASE III = 111.CAS E 1515 •CASE 10 = 16.CASEl7 = 17.CASE.I8 : 18.CAS E. 19 = 19.CASEZO = 20.CASL.il. ; 4 I...!.__CASlCC : 0.1CAS1..DD = 0.2PCAS[l ; !al--.£Qt!.s...I..!!iI--k~_.: •. FALSE.CONSTANT MUPR= O. S'ELIMINATE FRICTIONAL DAMPING'--f..Q!!S- T!

IFfCAS[.EC.cCASE)bO TO 1& 07-30-80IFfCASE.E~.CAS(5)GO TO 17 08-0~-bO-·-----rr((; ASLEQ-;CAsr6TG-O--ro18 --- -.-..---------------..-Ej 8 -O~ -anIF(CASE.E~.CASE7)GO TO 19 08-0~-8C·-----rF"i"CA·SE.El,;-;(ASE&'TGOTOTi"::"o------'--08-=O~';80-IF(CASE.E~.CASE9)GO TO 111 09-11-801 F (C ASE • E " .e AS~E:..:1:...:0~)~G:..0-:...;T::..0...:.:I;..;1;.,Z~------------------~0=-9~-.:..18:..--:..:.:8[;IF(CASE.Ew.eAsE11)60 TO 113 e9-19-s r---IrfCASE:Ew.eASEIZ)GO TO I1~------- --159--22::-80IF (CASE.EQ.eASE13)GO TO 115 09:?.1.-8£t---fF (CASE .EQ .CASE717-~-7-)-:'G-:'0-=T-:'0---=I-7176------- 89-23-80~F(eASE.EQ.eASE1s)GO TO 117 ~9-2~-8rIF(CASE.EQ.eAS£lb)60 TO 118 09-2~-SC__--,;I;.:F;-(CASE.E Q.eASE,17 )60 TO I 19 _Q9-2~-80IFeCASE.EQ.eASE18)GO TO 12069-2~-orIf (CASE.EQ.CAS£19)GO TO 121 09-2~-SO_IF(CASE.EQ.CASE20)GO TO I2i ~0-17-snIF(CASE.EQ.eASE2UGO TO 123 1!l-17-S(lIf (CA sE .E Q.eA SECC ) GO TO I 2~ 1.0 -23-80If(CASE.EQ.OSEDD)GO TO 125 10-23-80---rnCAst.Ew.PCASE})GO TO I2& 11-19-~0GO TO IS 07-20-Sf:-'I~l~.-.~C~ONTINUE S'CASEA=CASE 1 ~ ITEH 3eA) I~ SAFER BRIEf' 09-23-8CWP 2.*WP e7-31-erKSILO = KSILO 07-20-SCKSIHI = KS1HI 07-20-~0--'KS 2T ==-K~S;:,2·T.::----------------------------=0-=7~-20-S0eS2T CS2T 07-20-S0KS 3 KS3 07-20-S0KS'ILO = KS~LO 07-20-SCKS~HI KSAHI 07-20-&e60 TO 15 07-20-tic~I~Z;-.-.~C~O~N~TINUE "CASE B = CASE Z - ITEH 3(B) IN SAFER BRIE.F' 09-23-80WP .~~P 07-31-SCKS1LO KSILO 07-20-8[1__~K;.:S:....:l_HI = KS1Hl 07-20-&eKS2T - KSZ 07-20-S(CS2T = CSZ 87-20-&0Ks3 = KS3 C17-Z0-acKS~LOKS4HI KS~LO= KS4HI --------------------07-Z0-8e07-20-8eGO TO 1'5 07-20-S0I3 •• CONTINU[ ~'CASE C = CASE 3 - ITEM 3(C) IN SAFER BRIEF' 0~-23-srWP = 2.*WP 07-31-S0KSILO = KS1LO.Z. 07-20-srK51HI KSlHl.Z. 07-20-S[----jfszr- I'. S2 T*2. ----------------------07-20-S rCS2T = cS2T 07-20-S0KS3 = KS3*~. 07-20-SCKS~LO = KS4LO.Z. 87-20-dP--""K.r.S~4;;-:'riI = I'. S~H i.;. • .;.Z.:...=O------------------------;:0:-,:7:---;2~0:....--7'&OGO TO IS 07-20-S0----.,I'7.4-.-.~C--ONTI~TjrT'-cASrO-= cTs"["- ~ - IT E M 3(0) IN -SAFER BR 1 EF ' -[i'9 -23".:a-fWP .s.wp 07-31-SC_---KSILO = I\SllO.O.Se7-20-bOKS IHI = KSlHho. 5 . ~7-20-bJ:J.---1

CS2Y :: CS2Y 01-20-erK53 :: I\S3*0.5 01-20-81)_~'-Ks-ifLO"-:-KS~LO*O:S-- __._-_.--_·__~_----------_·_--_·-o7-2ci·.:e~A _ ••_. K5lftiI :: KSIfHhO.S 01-20-~_Q_-- --G"o ro--I5-------------'------------'-- 08-12-EC_~!.._£..Q.NTINU~CASE :: B~~·--------------~--------~FORORIGINAL BASr CASE, REMOVE All BUT09-23-8C'01-30-80___________________..!G_O~9___IS*' _ D_!~b('_~p = WP 01-31-Sr.____~_S}!_..Q____=__~~.!_l.Q..._ __. _ _._o.1-1O=§.PKSIHI :: KSIHI 01-30-60__~2T = KS2T_ 01-30-8(1CS2T = CS2T 01-30-lSC__,---:K S 3__ ---=-._K S~___a 7~3O=MLKSIfLO :: KSlflO 97-30-8('____KS~.tiL--=--.1'.~&!~tL . ~1.-3.D.=.!!.LGO TO IS 07-30-&~-lli~QNT.1..~.Y!-J.'CASE S ~ ITEM-JJ_GJ IN S.HR BRIEF' 08-D"~WP :: wP OS-Olf-SP.KS lLO = KSIlO*Z. ._ _ JL~_-Olf-S[----K5i"H-C =-Ks-iHI*2.OS-Olf-SCIKS2T :: KS2T _ JtS-OIf-SQ..-----C52-Y--:- CS;;T£l8-01f-Sf_______~~} :: iLS..I Q..8-01f-be.KSlfLO = KSlflO*2. oe-Olf-beKSlfHI :: KSlfHh2. O~Q~=i>O_---- ---GO--TOI-S-- -- ------------------.- --. oe-olf-soIb•• CONTINUE S·CASE 6 ~ ITEM 3(HJ IN SA£!B __ ~R.Uf" ~kO .. -ltO.-w·p--- =-W-P----------- ------08-01f-SOKSILO ::. KSll.O*Il.S D8_~01f-8rKSIHI = KSIHho.5 oe-olf-soKS2T :: KS2T 08-011-8~_C~2T = CS2T 08-011-60_____KS..l...--=_ KS308-011-8_~KSlfLO = KSIflO*O.S 08-01f-SO___KS If HI _~.SlfHhO.Sa9-01f-or_GO TO IS 08-olf-Be__I_~~CO~hUE S'CASE 1 - lTE~_-1..!ll~_t!.2.!.li'i.~EF' 08-01f-SCwP :: loP £lS-OIf-se______~_S_lLO __~~.i.U__O a~_~~ILKsIHI = KSIHI OS-Olf-&('__---"-'-K ~ 2T = K':;..ll.!Z.. ~~CS2T = CS2T OB-Oll-br____K_S_3 ==- KS-3*.1.. .___________ 08 -0 If ~KSlfLO = KSlllO OP-01f-60_____~_~~ ::__ .Jl~1t.1:f .1.. . .______________ _--.-.D~=-~_c.GO TO IS 08-01f-8CllCJ..CONTI,.,UE ,'CAS[ 8 - 111!LJ.!fJ IN S..All.Ii...BB1u' 08-01l-fl!l.wp = wP 98 -01f-80K.S_IlO =-ll!l..Q.____ .Q.S-Olf-:-.!i._r.--~KSIHI :: KS1Hl 08-01l-bO_K..~_?L ; KS21$.5 . .__.._. ~_~-olf_:Ji.r_Cs 2T = CS2 T 08 -Olf -i> 0__---..:K.:.:S=.."L__ -=...!-~~*.508-04t-8CKSlfLO = KSIflO D8-01f-80____ . __K~_If-'tI_._:: _li~~JiI ._ _ rn_~01f-80_GO TO IS 08-01f-&OIV-14

111 •• CONTlhU( S·CAS( 9 - IT(M 3(11 IN SAf(R BRIEF' U9-1l-bO-·---~{llO·· ~ i~ii.o .-------.-.-- ---- ..--_._-_._.-. .-.--.------~~:+~-=~{-I

LOCR = - CASK CG FORWARc OF CAR CG '09-19-o~. .. ~_9__ TJ1 ..1J' ~.__._. ... _. . ... ._ .-O.9_~2.J_=_IH.115 •• CONTI~UE !'CAS( 13 - ITEM 3(P) OF SAFER BRIEf· 09-Zz-eC__JiP.__: ...wpQ9-22-OC.KSILO = KSILO D9-ZZ-&CKSIHI r l\SlHI 09-72-80KSZT KSZT 69-Z2-SCC S 2T = C S2 T -ll.9-=22~KS3 = I\S3 09-ZZ-&OKSliLO = KSIILO 09-22-aCKSIIHI - KSIIHI 69-22-SCLPR r LpR.],5 ,,9-22-QCLPF LPF'leS 09-2Z-80SUHLC LCR • LCf 09-22-8C.SUMLP LPR • LPf 09-Z2-8CLC F = SUHLCI2. 09-22 -cOLCR LCf 89-22-80LOCR = y. ,'SAME AS LCR=LCf, IE,CASK CEtiJERfD '89-73-80'fORE AND AFT ON THE RAI L CAR '£19 -2Z-8(1GO TO IbA D~~Ilb•• CONTlhU[ "CASE III - ITEM3(Q) IN SAFER BRIEf' 09-23-&0.__--.J P III P ~_~.=.lll'KS lLO KSlLO 09-Z3-S(1._---

GO TO IS 09-Z"-6f"lIZl •• CO~lI~UE J'CASE 19 - ITE~ !lNJ or SAFER BRIEF' 09:~~-S(l--'';-':~'';-;-':-'=~------------t.ASECAsT~xcfpT-CCR = c.--=·----- 09-Z.. -8C• REAR TO ATTACHHENT POINT O~ CAR LOCATED" 09-ZII-SC--,- OVER CAR CG AND DIRECTLY UNDER REAR' (J9-Z11-8CATTACHHENT P01NT ON CASK." 09 -ZII -j)eCASK LOCATED FOR~ARD Of CAR CG." 1'9-Z"-bOLCTOT = LCF • LCR ll!...-ZII-80-.--a:.CR - = [j. ..=...::..:..:------------------------'09-Z" -0('LCF = LCTOT - LCR 09 -ZII-8060 TO IS 09-Z11-8£'-l1..Z-,.·CONTINUE '"CASE ZO - POSSIBLE All ITEM 3IC)" 10-17-S0wp = ~P.Z. 10-17-S0KSILO : KSILO • Z. ID-17-S0KSIHI : KSIHI • Z. 10-17-S0KSZT = KSZT • Z. 10-17-S0_CSZT : CSZT 1~-17-&[.Z.KS3 KS3 1C-17-eoKSIILO = KSIILO • Z. 10-17-SCKSIIHI : KSIIHI • Z. 10-17-sr-----"":-:-K:7P-S--==-"H I< 5 • z.1 0 -17 - HHK8 = HK8 • Z. 10-17-S0-----·Kb-·~---;-K;-:6c-=--,.,...-:;;Z,..:.:...:.....--------------------- -------;1--;0:'Ti-=af·K7 = 1\ 7 • ~Z~.=--- ___..:l;;O=_-~1=-7_-:::.80~-----=-GO TO IS 10-17-0('IZ'3..CONTi,.,Ul "CASE ZI - POSSIBLE. All I:...:T..=E:...."--=3....:1..=0....:J_·______ lO-17-BrWP 11115*.5 ---- ---10=17-eo-KSILO = KSILe ••5 10-17-erKSIHI = ... SIHI ••5 10-17-&0KSZT = KSZT ••5 10-17-S0CSZT = CSZT .1D-17-S0KS 3 ;:--_==--K~S;:.,3,....,:-.,:".7-5__-::---:;1;-::{]:;.---i'1 7 -& C----:iK"iSIiCO : KSlilO ••S lC-17-orKSIIHI : KSIIHI ••5 1('-17-8(1_HKS = HI

KS4HI = KS4HI*.5 1{l-23-c:GO TO IS 1(J-23-8(---I2-t.-;~·cON1Tt.U[-"S"iPCA5El=PJfEIT"It,'-AR"1-C-As[1OP- TRAllIc------.--------l~i9=8C-LOO~E = .TRUE. '-SLACK IN PEAR TIEOOWhS- 11-19-&C----'------fx PFRC=--: TRUE. '·-07-3"0-8 i.---- ---- ------..--CABLES = .rALSE.'-06-30-8PWTF = 1.35E4 '-07-08-81_. .~ ~_R ~~3 5 [It .~ ~_91.:08_~..!.~ .. .. . _XRPLO = -0.0t.25 11-19-8"____X_RPHI._ = O.Ob-ZE__ . .__ 11.:..l.?-8_().MUPR - 0.58 11-19-8C_____ - --~-------~---"'--- .. WP THRU. kS4HI THE Sf.•.::H!..l:E~A~S~B.~C~A:.::S~E=_-~__..__~1:.::1~-19-liGO TO 15 1.1-19-80IS•• CONTINUE '-END OF CASE SELECTION- 97-20-80LOCR = LPF - LCF ----------09-19-6016A •• CONTINUE '-END _'J.LCASE SE~llQ.r:e_________ Q~_::~:t-d_L----·-:.:-.:==-~.=-~::~---EN[j OF CASE SELECTIOt... 07-23-80_____.2.0 TO ITT 0'3-10-81IT 10..CONTINUE03-10 -8 JGO TO ITT . ~3-10-81--- IT iT~_:c-ON-iI NUE-----GO TO ITT---IYi3~:C'ONT I NUE·------··---'---G5---~2---8-1------.--_GO TO ITT _ITT•• CONTI~UE 03-10-61HRCP =ZRC+ZP ,-DISTANCE BETwHN CASK AND ICC.--- '-P1p~---~-.;pi"i;-------'---------------,CGS- 0.3-?8~_~O.--MRC = WRC/G'--'---MTR----=--w'iR I G._-------HTFIII Tf IGHFWff GHF2 = wF2/G-----:c:.:: M F,...::3:--WXTw = _TR+.RC/2.+(LRC+LOCR)*WP/(2••lRC~.__~W X..!L..-=: WTF + loR C12 • + ( LRC-LO CR )*Ii P~. *lRC-")RR = (LRC*WRC+1LRC+LOCR)*WP)/(2.*LRC)'='- ~ r31 G-____~.~__ = WF4/G _ _ __.. ~r.. ::. _1 LR c *w RC+ ( L R_C -!".Q~R) *wP ).L!..2 • *LM.L _YRC56I = o._._. ..._YR...CL~l =.Q..L _YRCI = (YRC56I+YRC76I)/2.______L~RCI_:-J~R~561-yRCI1,~/~L~R~C _YRC121 = YRtI.lCR*THRCI__. .---X.f.1_~_L__~_J H~ !.ll.- --,----------YRC341 = yRCI - lCF*THRCI----- '------'----- -------------______.... _y_P-.I!lL._:::_. YR.C....3 .....4:LX"-_ ---------------_._._--------_.THPl= THRC IYP I = YRC I i~::..lQII.lC::.!R:!.:*~Tl..:H~R~C=.:I!....._._----:- - =_:_~_:_ _:_:""'="=_::_--------I~ITIAllZE FOR MODEL WALIOATION USING THEIlS INEQwALITY COEFFS- 11-29-79N = O. 11-~:-79-.-----sT3-----=. o. 11-29-79S14 = o. U-29-74l_-. ------S53-----=.--6. 12-11-79SS4 = O. 11-29-79S55 = G. 11-29-79____. ~~G. = o. lJ-29-79S to 1 = o. 11-11 -79_IV-18

S13X = u. ~1-29-79SlllX = O. 11-29-79--.----S53~--=·u-~-.------------------ -.------.-.---------...-. ------,i-Z-=-11---i9S 511 X = u. .__J1. -29_=-I~- ---- S55X -=--0;--'--' 11-29-79_____ Sf. OX = G. 11-29-7'!.Sb1X = u. 12-11-79SOB = O. ._ 1.1-29-?~------·-sDi~-=- O. 11-29-79So 53 = O. __~_?-=:l.1.:-_I~S05.. = c. ~1-29-79SO 55 = 0'. 11-29-79SL 6J = u. 11-29-79S061 = O. 12-11-79--=-SR~1-:3 --:-0. -----0 If -111-& 0SRH : G. 04+-11f-8f).01f-11f-5(1--SR53-:-C.SRS/f = [). 01f-1/f-8::;-----SR6C : O. 04+-1/f-SOSRb 1 : c. a.q -1/f - 8 C- - ---·_--sR 13X--·=-O·.----·- '----'----------- -Oil-16':'ic----------s~-si"x-:; ·C-.------·----------·------_. --- ----SR1ljX : O. JLIf-:.!.6-!ln01l-16-8n_____ ~~.L_=__O~. 0 II -16 - 8 [ISR60X : C. Olf-16-8e______ ._~_~6.!.~_.__=...Q._Q/f-~..b-~i'SVR.l3 : 0:. lJ"-CIf-SC'SVR111 = O. O-lf-O/f-8C--SV-RS"3---=c.----.-------...--.--------------a.q -O/f--SCSV R5./f O. Olf-O/f-80.SVRoO = O. Olf-0/f-8"SVRbl : O. alf-O/f-SO------·-svRl3x =-b:--·-------- --------.----------- o-it-':lb=-ifSVR111X = 0. . .__.__!l~:.!_6-!i!'S-VR53X : 0--:-------------- lJ"-lb-80___.. SVR5/fX: U. O"-.lP..=J!..Q...SVR60X = C.fl4-16-Sr:SVRblX : o. .0.1f:16:.H.(j" -II-SO------NN ---:-ci----- -. --- ---_.- -------___ .----e.~_~f.N Q.~_jjIf_b!.fTJ.9.!!..S_iD'_AR;..A -".0." ~~J_~O R_J_AC1U!.~~_S__ ~.!:'f~l.~D __9NE; ~.!~ •• _A TIME'I = O.ol.WuTHRC.ZRC••3B81 : LRC-LOCR-::[P---eel = lRC+LOCR+LP----.----L Ll-·-----=2":.lRC·...:.....=:..:...-.--· ----- - -----.----- --------- _ .. - ----X21 : L~e-LoeR+LP.. -····_--··X-3··j--- "::"--l'RC-"--'--- - ..----. -----------.--.---,..-------.....----------_____0~1_:_1--"'-: CCC~.l!tlB l.! L L 1 J.!.!.?.l.U~.~,=_I.:.J-:- ' _021 = 8Bl*clLl-X2IJ.CCC1*CLL1+&elJ- •••_._ C..I.1....1~2J_~ *_'!.V.{J~_._*f:_! ~*LLl_J . _- ..---- 031 : bPl.CLl1-X3IJ*CCCI.CLL1·BBll-ClLl-X31J**2J/______.. . "J~.• *E.!_~..h,_~.U __.______ _ .. _. __._. . ._. _Bb2 = lPC-LOCR+LP______.c.c.l_._=_.l~..!.L.Q.~=1..'-p _------,----_._---------LL2 = Z .*LRC_____ X.t?,_., ';'__ L,.PC-'!"_QC-'-~-:l_~ . . . .. ._. _X32 : LRCIV-19

0~2 = CCZ*X1Z*(BB2*ClLZ+CCZI-XI2**ZI/(b.*E*I.ll21_________0n =-..H CC_'-~~_4..lil..2.L._•..21L.J.J ._..r.....lL. ..._032 = (CC2.XJ2.(BB2.(Ll2+CC21-X3Z•• ~II/(b ••E.I.LL21_____ .__.8..b.3....__-=-.L..R.L_CC3= l P.CLL3 - Z.*LRCX13 = lPC-lOCR-LP______a.X.. 7..;t3__ ~.Lo.C.=-.L.L.IoLO.Lo.C.u.R~+.L.LJ::P_013 (CC3.XI3.(BB3.(Ll3+CC31-Xl~•• Z~J/(b••E.I.LL31OZ 3 = bB3. lLLZ-X23I.!_lCC3* (Ll3+B.B..3J-CLl3-XZ..J3J.1~.~ ... 2.L1.L/-A.""."". . _(b••E.I.LL3J033 «CO.BB3/LUI"V/ (3••['UDIU = 031.01Z·0Z3+0Z1*03Z·013+011·0Z2*033-011*03Z*OZ3- •••Q12.pZl.033-p31.p2Z*OI3'----CALCN Of SPRING CO~STANTS FOR BENOING Of RAIL CAR'Kl1 = (022*033-03Z.023)/OHAK12 = C032.013-01Z*033)/OHAKZl = KIZ S'By MAxwELL RECIPROCAL tHEOREM'K31(021*032-02Z*0311/0HAK13 K31 S'BY MAXWELL RECIPRli~llH E..... OxR... E...

~:Acr;:,~GNFIR,A)PRO CEO URALIR=A)- --- -TnX:-n:-cT:- )-if=---1.----------.--..---IFIA.E~.O.) R= -1.S-15-79-------·mA-~-GT•c:TR = •i:-::.-----------------------·----- - .. -------._--:E:.:.I';;.:D;..!'OF PROCEDURAL'hACRO ENCJ,------~---~---PRCCEDURAL TO SELECT TEST DATA' 03-10~a1~P~R~O~C=E=DU~ALIDUSLFX,DUSX~ID2XRCXIDZXPXID2P-1~~ZX~,D~2~P~3~~~X-I~02~R-1-Z7.X-.U~·~2~R~1~Z~T-,-.-.-.- 03-10-S10~R56XICJ2CPLXIOZCPLT=TXLF,TXCF)__Q~~O-SLIFITEST.E~.3.)GO TO A 03-10-81IFITEST.Ew.10.)GO TO 8 03-10-S1IFITEST.E~.11.JGO TO CIFITEST.Ew.13.JGO TO 0-----=-GO-to TFIN03-10-S1A••CONTINUE0 "-10-Sl--~ 0 USLF X = DUSL F""'F=-"I""""'T=-"X-L""""'F=-"J,--------------- -------- .=.OUSX~ OUSFITXCFJ "Q~-07-S1'OlXRCX lJ2XPCFITxCF) S'Q~-07-81'OZXPXD2XPFITXCF) "Oq-07-81~D2P12X DlP12F (TXCF )-=-=-S~,~0-~-=--~0-=7-=--78-=-1-;-'-------------------02P3qx = OZP3~FITXCFJ*POL6102RIZX = DZR1ZF ITXCFT.PA·~YO:-R7-12=----------02R12T = D2R1ZGITXCF)*PAYR1ZOZRS6X OZR56FITXCFJ*PAYR56o3-10-S1OlCPLX = D2CPLFCTXCFJ*PAYCPL03 -10-ti1-----02CPLT - lJ2tPLGCTXCF J*PAYCPL -. 03-10-61 .GO TO TFIN 03-10-1: 1b ••CONT INUEo3-10-S1OUSLFX = T10IZ7ITXLF)*PIOI27 + T10I28ITXLF)*P10I28OUSXq T10I3ITXCF)*P1013 S'O~-07-81' 03-10-8JOZXRCX T10I1ZITXCFJ*PIOIl~Z~~S~·~0~-07-81' 03-10-81OZXPX TIOISITXCF)*P10I8 S'O~-07-81' 03-10-51OZP12X T1GI11ITXCFJ*P10I11 S'~_-07-S1'02P3QX T10I9ITXCF)*P10I9OJ-JO-ti1_______~O=2R12X TOIJ~F(TXCF)*PAYR1Z [)3-10-81OZR12T = TOI1QGITXCF)*PAYR12___,O.Z R56X = r 1Q.U2CTXCT J$P10IZ2_OlCPLX = T10I6FITXCFJ*PAYCPLOlCPLT = T10I6GITXCFJ*PAYCP~L~__GO TO TfIN~ ..CONlINUEOUSLFX = T11IZ7ITXLFJ*P11I27 • T11IZ8ITXLFJ*P11128OUSXQ = T11I3ITXCFJ*P11I3 S'O~-09-81'------- 02XRCX = TllI12Cn,CF)$PllI12 '-'0"-09-81'02XPX = T11161TXCfJ*P11I6 S·OQ-D9-81'--·-----O-ZP12X--=liIT11 I T-)(-m*P 1fTIT---s '-C~-':()9-:'-8I"'------- .------.---- ----GO TO TFINb •• CONTINUEOUSLfX = T13I27(TXLFJ*P13127------=O=-"U:,..,sXi+-:: T13I31 TXCf J*P13I 3 ---OZXRCX = TJ3I7ITXCF)*P13I7-----------D2XRCI~Ti3fmTXCF}*1>-i3 IiZ-------------------- ---'. ---02XPXT13ItITXCFJ*P13I6Dl P12 X = T13 111 I TXCF:-::-:)*:-:P~1~3=-I~1:-1----------------------D,P3~X = T13I9ITXCF)*P13I9---------GO--TOTFTN--------_·---_··----------------._------ ---- -·----0 ----IV-21

Tflt.•• Cor-;TIt~U[ 03-10-81[NO ,'Cf PROCELURAL TO SELECT TE~T OA!~__. Q3-1o..=.i!l.-----·-:::.=-=:.:.-.:.-:=::----=--~PROCEOURALTO CALCULATE KSIHITO tlSUO' 03-25-81_.P..B_l?~f.0 URA!:..I. tiS !!!.u.~~~H..l..,~l.h.9...L! ._GE.O 'J..B~ T A6E.,..@.ETA&C)__ .__..__. ._.__JlJ.-07-~.r:K~6 = ~6.(I.-HUD6.&ETA6.SGNFIDYRC56)1 OJ-07-BO_____ YRC56GO TO 03___...:O:...:~:...:.:...:.:...:C:..;O:..N:.:..T.:...I::.N:.:.U=[= YRC+LRC.THRC~S'_'...:I;.;,F--.,;T:...:.~L~E=-.~O=.-' _.::"~_--:_~~HUD6 = RS~(OYRC56.GE.0.,~UD6E,~UD6C) V-I0-79____ ._..;B~E:-T.:...:A::.:6=---= R S.w (OYRC56 .GE.O. ,9E TA6E~8=-E-=-T,=A-,,-6-=-C-7J_______ ._jl_l_-07-:8.£.K~6 = K6*(I.-HU06*BETA~*~GhF(OY~CS6J) 0~-C7-&OHU07 RS~ ([)YRC78. GE.O. ,~U07E ,MU 07C) ~.:.!0-7L_---.-.- BE TAl R slJi ([)YRC78. GE .0-:-;iEfA7E;i·rTA7C) e1-07-8C____-.:.:K ~ 7 = K7* ( 1. -'1UOL!i.t TA 7. ~ &.hfJ.Q.tRC....7uS"-J:..J:..- -O..!:.07 -8...c...YRC56 C.YRC78 = C.----- ···GoT()oit·_-- '·GO 10 ENO-·--____P2..... :.QNTI~.U.L_ .._. ._. .__ ._..__ ..__.. . . . ._.IF(YRC78.LE.YRCHAX) GO TO 02·--------------~---------yRC78.G~~~~~~~~~£zO 'eS-Ol-tQHUQ7 = RSlJiIDYRC78.GE.0.,HU07E,MUD7C) 9-10-79__---'B~[~TA7_= R.SW jDj'RC7JhJ&.&•• BE TA 7E.I.8..El.!.7C)__QJ.=.OJ~.Q.K~7 = K7.11.-HU07*SETA7.SGNFIDYRC78J) 01-07-80____. J.B..P8 =.!P.C:..::L.l~~!f~_.GO TO O~ s' 0 TO END'1RCS6 .LE. !RCMA X.BOJJ:O~"L.r....KS6 = KS6INFo I ..CONTIhU[ s' I IF D.LJ_' •_YR C56 .~_YE~~c;~THR~ .__. .__. _GO TO D302..CONTINUE -----------_._._._._---- ----_._.__ ..·----··-1(51"- = K S7INf-____yt...rR C76 XRS;; -L~llTL!H!l!R!l.C~ ~ _=GO TO Dq.. J1.~.!..!.~ .Q..NI!t.J1..F; . ----_._------_._-_._--ENu i'OF PROCEOUnAL'IV-22

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AND.DXRPI\C.L l.u .,HKSltF"·,O.) "00-25-81'____ .111< Slt_ = RS. I D~.fB..~..L.LhO..u.!.~~~!IU.~MKS_II£..L.O.• L._.~ ~.fL:Z 9:-!ll-~__._.__KSII = KSllll1. + MKSIIlSGNFIDXRPRt:n $'00-25-81'_. C ~_~--'-.S.Ii....-. _ _ __-Ll9---=-ll.d1l.HP = ~Plll.-FRMPJ/G 8-28-79Mee = 'WRC+WPtfRMpI,G 8 -78-79GO TO 50 8-01-79__liu.c..oJilIt"UE '"CASK MOVES TOMARO fRONT Of CAR' _'_' 09-U.-~KS1 = KSILO "CABLES TAUT, RUT NO CONTACT WITH CHOCKS' 09-1~-6 C___-----'---"1'---LK....S.....l._---':::~n.R S.....LC..dXRfR.C. GT. xRp._wt~~XJif.H.L.a.A ....._AND,DXRPRC,LT.O.,HKS1F~0.J$~0~-25-81'"1KS1 = RSIM COXRPRC.I T.O •• AND.CAm rS.MKslf.O. I $ '..Q.Q.=.Z..9~-=-8~1-=-' _KSI = KSllC1. + "KS1.SG~F(DXRPRcJJ 5'00-25-81'(S1 = CS1 09-17-8CIFITEST.EQ.10 •• 0R.TEST.EQ.11.JGO TO A10A S'03-30-81'K S II ::: O. , 'CA ~..sLA.CK. AN 0 NO COtLIA.C._L.w..IIJL.~HQtll '---.il..9-=lldt.MI

= ~S.IXRPRC.GT.XRPLO.AhD.XRPRC.LT.XRPHl ••••AN 0 • DxRPRC• L _T • 0 • ,_~~~ Ii F,-~_ ~~_~_2~_- 8 1 ~-- -- ----irKS.. = RS\illlXRPRc.LT.O ••AND.CABLES,HKSliF,O.) "06-29-81'KSIi = KS4.ll ... HKSIi.SGNFIOXRPRCU "00-25-81'CS If = CS&f -....;;;..------·--09--1-7--8-0HP = .P/G 8-,8-79MRC = WRC/G 8-26-79GO TO SO 8-CI-79----"Ii--.,C:-.-.~CONTINUE '-'CASK H6v~s TOWARO REAR OF CA--po----------09-16-ar-IFITEST.EQ.I0 •• 0R.TEsT.EO.II.)GO TO AliOA "03-30-81'KSI O. S'CArsUS SLACK, BuTtiOcONTAC·T WITH CHOCKS' 09-16-0[HKS1 = RSWIXRPRC.GT.XRPLO.A~O.XRPRC.LT.XRPHI ••••ANO.OXRPRC.LT.0 ••MKS1f.0.) "06-25-81'"I

L CR.LTHRC) -0 YP) -CS 3 .LPfH lOYRC-LCF.O THRC) -OYP») IIP06 -26 -llC'____._~ .::':-.:'::.:--:--:'-=--:-.::=.~==-=.~-=fRE 9Y!..~.C .!I-S__. . '.~L~:.l~~ b Q.0"1 X = SCRT(US1+i(SII)/MP) 0,6-26-80OMY = SORT UKSZ+KS3J/MP) __.__O~-Z~~_~_-. -·------·O~ T·;.----=·-s·o'RTicIK·sl+K SII) .TP"••Z+KSi-.LPR.;2+KSH-LPF** 2 j / IP) 0 6-Z6-b~__ .__'.::----_n ::-.:- --- --------CO':1J'..!'il§.O~~_. ..Q.L..!£~~R AT 1 OtiL-O.LB.!.lL.£.A R~6 -26 -6 (, TO RHS fUNCIONS '66-26-60___. I!..':!.~XA-.._:::._f

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O.SF3= -CSf3 *OTHRC*LRC**2_________~~S_R_?_:__ -CS.Jl..L!..Ql.!:fB~~_U.R.~~L~.!2...O.SFZ= -CSf2 *OTHRC*ILRC-LCF)**Z,------------------------ ----____ ~S-]5-OC'------~-------INTEGRATEDVELOCITIES AND DISPLACEMENTSDXRC - INTfG'Q7XRC.VXRCI!'05-15-8 CXRC = INTEGIO(RC,XRCI)_____.D.E...L.l!HJ...YB C,0 YRC =YR CI ,Q2YR C, VI BC I ,I p~Ct:.A.U_l... o... o.a. ...... J_DBLINTITHRC,DTHRC=THRCI,DZTHRC,VTHRcI,THRCLO,THRCHI)_____IJiBJ:.tU = lYR C-=1B. CMAX» I LRC----------------THRCLO = -THRCHI,---------R[AR TRUCKS ON RaIL CAR OR IRANSPORTER'------~-------EQUATION OF HOTION IHORIZONTAL ACCELERATION)_____pZXTR = IDusS-DwS5+DwCTRJ/MTR'65-15-80D"CTR = FXTRF XTR= - ~_\,!la.!..w..nR~G Nf ( 0 XI R.1.!.a..R!Jif..R'------~-------PROCEDURAL TO CALCULATE KSS' 10-17-SCPROCEDURALIKSS=MKS) 1 0 -]7-80KSS = KSSeFIXRCTR) ll-Z8-H_---:-:-::--,------,--------=-----'K~S"'-=-S-: = KSS8FIXRCTR)*MK5 j.ll=il~ a.c~ND S'OF pROCEDURAL TO CALCULATE IFFli..-=_ R S"lE9Ji~LQ.ti •...I..lLS.f..z..l...aJ.K_Hf..-Zl_L8-15-19KSFFZ2 = ~SwIFZOR,E~,1"KsrZ20,KSFFZZ)IV-28

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·------~-------RHS rORCINij fUNCTIONS fOR RESPONSE SPECTRA CALCNS 'D6-26-eOACS.2lMoj) = CS2 .____ 01:01-8Jl.----·----AI\.r:.XlNt~) = R-,.::H~S~X--06-26-arARHS\,lNN) = RHS)'06-26-~r--------ARHSTHlt-.N) = RHST~H;-:-----------------'--- - 06-26-&0ATHlNN) = T 06-26-00AOU~1CNh) = OUSI 09-11-80ADUS2lNN) OUS2 89-11-8('A0 US 3 INt.) = O~U~S~3:--------------------------:0=-9~-7'11:-_"':8~CAOUS'HNN) = OUS" D9-11-80--------:..:X-=.H:7 X ;=-;...:AMA Xl-=I-=.X7. I1 ""'X,.-•....,.X:"':P:-•....,X':":R::-:C=-.-:X""'T=-R=-.:7 X -=T-=f-.""'Xc:: f '"")---- ---------=--=- --XHN = A~INlIX~N.XP.XRC.XTR,XTf.XfJYHX = AHAXlIYHX.YP.YRCJYHNAHINlIYI1N.YP.YRCJTHHXAHAXlITHHX.THP.THRCJTHHNAHINllTHHN.THP.THRCJ-----~D~XHX = A~AXlI0XHX.DXP.DXRC~OXTR.DXTf.OXfJDXHNA~INlI0XHN.DXP.DXRC.OXTR.OXTf.pXFJDYHXAHAXlI0YI1X.OYP.DYRCJDYHN = A~INlI0YHN.DYP.OYRCJDTHHXAHAXlI0THHX~OTHP.DTHRCJDTHHN = A~INlI0THHN.OTHP.DTHRCJD2XHX = AHAXlI0ZXHX.DZXP.OZXRC.OZXTR.OZXTF.02XF •••• OJ-25-80OZXRCX.D2XPXJo J -25-~')D2XHN = AMINll0ZXHN.DZXP.DZXRt.OZXTR.O~XTf.02XF •••• 01-Z5,..~r._____~-=-=-,.......,.,- 0 ZXRC X• 0ZXPX J ____01-Z5-8CDZYHXAHAXlI0ZyHX.OZYP.OZYRCJDZYHN = A~INlI0ZYHN.OZYP.DZYRCJD2THHX A~AXlI0ZTHHX.DZTHP.OZTHRC~D2THHN AHINIIDZTHHN.DZTHP,OZTHRCJXRHX = A~AXIIXRHX.XRpRC.XRRCF.XR~TR.XRCTFJXRHN = AHINIIXRHN.XRPRC.XRRCF,XRtTR.XRCTFJYHX2 = AMAXIIYHXZ.YP12.YPIZX.YP3~,-7.Y~P~3~~~X~.~Y7.R~C~17Z-.:7YR~C-=3~4-.~Y-=R-=C:"':5-:6"-.-.-.-.-:a=-5=---=OS-8rYRC78.YCPLX.YCPL.YR12X,YRS6XJ01-OS-81------Y....,.H~N-2--=--:A....,.~:-:_1....,.N:-l-I-:Y~~~N~'Z=.YPlZ.YP12X.YP3~.YP3~X.YRCIZ.YRC31f.VRC56 ••••05-0S-8C1\,RC 78. YCPLX, YCPL ,YR 12X, YRS6X J0 1-0S-& LOYHX2 = AMAXIIOYHX2.DYPIZ.0YP12X.OYP31f.OYP3lfX.OYRClZ.... 85-0S-80__-=....,.,...,':":":":,.--_-,-~,..,........,.[JYRC31f.OYHS-6. OYRC7 8 JQ_S-O@.":.!LDYHNZ = AMINll[JYHXZ.OYPlZ.DYP12X.OYP31f.OYP3"X.OYRCJ2.... 05-0S-60._ OYRC3~Y_!L~5b.JOYRCH! J ._.~~-DS-8..i..02YHXZ = A~AXIlOZYHXZ.02YP12.DZYP3",02YR12~OZYR31f,02YRS6, •••_______________________-P.ZYR78.D2P12X,OZP3~X.D2CPLX.02YCPL.... 01-08-01OZRI2X.OZR56XJ81-0S-&1____~OZ YHNZ = AMI.N 1l OZYHNZ .OZYP1Z! OZYP3 If .OZ YRl~.!..o.~.Y~-'" 02YR56.L•.....::. • ..:.. • ..:...~=

SCALEtTH~~,THMX=THMN,THMX)SCALEtDXMN,DXMX=OXMN,OXHX) .-- --.--scALEIOyMr;-;oyMx=OYKN,oyMxT-----.----.---------.----._----_-::S:..:Co.::A.LE tQTHMN,.QTHHX=OTHHN ,OTH" x). .._.SCALElD2XHN,02XKX=D2X"N,OZX"X)________~S~C~A~L~E~l~D~Z~YHN,D2Y"X=DZY"N,OZYHX)SCALElD2THMN,CZTHHX =OZTH"N,D2THMX)_____ SCALE lXRI'!N ,XRHX=XR"~,XRHX)_SCALElYHNZ,YHXZ=Y"NZ,YHX2)_____.~~.Ll..D_l!.NZ, 0 YH XZ =O!."-N~.!J YIII X Z:-')'------="":--_SCALElD~YHN2,DZ~HXZ=DZYMNZ,D2yHXZ). ~S CALE l 0 UU N, 0 T" AX-==-=O..:.T...;,H~I:.:.;N:.J't.!:D=--,T:..;.".:.:A:..:X~. ..:0:...11.:..-....;3:::..:0:::,.-_&;:.[1::...'SCA~ElFCPLH~ ,FCPLHX=FCPL"N,FCPLHX''-------,--CALCULA TIO~ OF ,PROBA8ILIT.Irr.____ _~~:~o-SP_'--------------CALCULATION or VARIANCE'04-30-80_____liN = 0 _. ....D.!::.~..£.T2 •• cONTINU[04-1S-SCNN = NN.! 1 ~SVR13 = SVR13 • lXRI3lNN)-EPI3)**Z 04-15-60____S.~B!_It__ = ~VIU_~. !~.!U~J_~-E_Rl~'!.!.?__ _. . .__Q"-.:..IS-SC._.SVR53 = SVRS3 • lXRS3lNN)-ERS3)**Z 04-15-80.~y~It_ ___=___SJ'R~~_._ .P~_~. ~ltl!'!'!) -~~.511·t** ?_. 04 -15 -8 CSvR61 = SVR61 • (XR61lNN)-ERbU"Z ·--·-----·--..---·-04-15=~·O·SVR13X = SVR13X • eXR13XlNN)-ERl'3X."12 04-16-sr-------·svk14"x = S'VR litX • UR 1IfX"fN04 i'-=ER 1iix-;)-.*z---------------------8 4 -16':SO----. ~~~~+-- ~ ~~~-~~--:. ~~:}~·H~~+:~:;·;~ l:~}---- -----.- ..---%::~:::g-.SVR60X = SVR60X • eXR60XeNN)-ER60X).*Z _.Jl4-1~-80.---.......=SVR61 X =SVR61x. (XR61XfNN) -ER6'lX;J-**2- £]11-16-80·------,----T~_VARIANCE IS THE SQUARt OF THE SID DEVIATION, 5I6HA..Z' 04l-15-SL·----------VRXX = S16I1A**2'01l-15-8eIR13 =.RSliirS_VRI3.EQ.O.,EPSR,SVPI3/NN) 04-16-tlO.VR lit R SW eSVR 14.EO.O. ,EPSR ,S \/Rl4l/NN J --0-;;-:-16-:'8-ryRS3 = ~~J.SVRS3.EO.• D.tEPS~SVRS3/NN1_ . ._....9..~-16-&.~..~R54 Ks.rSVRS4.EO.O.,EPSR,SVRSll/N~) 6~-16-8rVRbO = R_SW CSVRbO .EO.O. ,EP_S-Btl!..~bC'N~) __. .D"~Jb.-h G_VP.bl = Rs~eSVR61.EO.o •• EPSR,SVRbl/NNJ ~1I-16-8(______~R13X = fiS~~~l~)(~Q.O •• Ef>SR.S~.u~~.~_. . . ..P.'L-:}6-&(l.VR1qX Rs~esVRlqX.Ew.C ••EPSR,SVRlItX/NN. 6~-16-6C___....Y!!.?.J..JL = h~~.J§..Y.B5~_~~;~~!U.J.~!'~I~..Y!t~~.UJHiJ .. . 011 =l6-i>O.VR5Qx = ks.eSVRS4x.Ew.o.,EPSR,SVRS4X/NN) 04-16-80~R60 X = JiS~.~.x..!.E Q. o•• EP S!U.~_~ ~X!J!lh.L . O_"_:-.16.=li.C.VRblX = RsweSVR61X.tQ.O.,[PSK,5VR61X/NNJ D4-16-o~IF, NN .L T, ~!~1:U"§L!LI.L- .. . -l)~.=1~=:_~o_NN = 0 0~-1l-80_____.AB.u = __.Lod~~RTC2 .*PI*VRI3) . . .__~-IS_:...l?.L.ARlit = 1./SQRTlZ.*PI*VR14) OQ-15-8CARS3 = 1./SQRT.J1.*Pl*YRS}1 641-15-80_ARSQ = 1./SQRTrZ.*PI*VRSQ) Oil-IS-SO_____-'A;:.:R~b-O----_---=-.l..~-'SQR TJZ ••PI *VR~.O_).D.~~I~~JLc...AR~l = 1./SQRTlz.*PI*VR61) Oil-IS-SOAR13X---'-i.R1Q )(= 1,/SQRTl Z.*PhVR13X).=i-.I s·clHc--i:*pI'-v 'Ri..Xi-----._.----------_._ 04l-1~-80- 0II -16 - 8~AP. 5 3 X = I ,/}Jt!U..L..Z.,~P 1*VB.5..J.!L ll~fl..=b...r.AR5ltX = l~/SQRT( Z.*PI*VRSllX) 04l-16-80JL!:li..::..B .r:_ARblX = 1./SCRT( Z.*P1*VRb1X) 04-16-sr___ ARb Q!....__7...J..dS QR..!..L1...•. *P I ~V ~.b °!lIV-34

Q_-:l~_-_$~Ll~ESC 7) ,'INfORMS SYSTE~ ABOUT TO PRINT 7 LIN[S' 0_-17-80_---:.P....:.R:...::I ~~ 8_~ Rl3 • E; ~J~j: ~~.l .. ~ B~~RJ) ('_J.!....R.~.1 ,~t_V-'U.!l,_~~a, ~ ~ fJ. ~.:.J S_- 8.9vRS-,VR60,VR61,ARI3,AR1_,ARS3,ARS_,AR60,AR61,... 0--16-bry___..__. ~_~.1.I~, E~ I_X, ER S 3X 'E.R S~.X ,E R60X ,ER~.1!.!~_. .. O~-16 -0"':VI:'13X,VRl_X,VRS3X,VRS_X,VR60X,VR61X, •••f)-4!-16-110ARl}X, AR 14 X, ARS 3X, AR ~~!.!..~ P60X • AR61 X.__.Jl9..:li=.a.r9& •• FORMATC3X,·ER13=·,£IZ.4,3X,·ER14=',E12.4,3X,'ERS3= ·,£lZ.4, ••• 04-17-80____3~~~54=·,E1 Z._, 3X, 'ER60=', E1~~3X,·[~61~..u;H_.li!.!.!-~_~_:u.,:~r;.3X,'VR13=',EIZ.4,3X,'VR1Q=',E1Z.-,3x,'VRS3=',EI2.4'3X,...D~-17-8r'VRS4=',E1Z.4,3X,'VR60=',EIZ.4,3X,'VR61=',E1Z.4/...04-17-8C----;;3,..."X,..., 'H13=' ,E 12.4, 3X, 'AR lit =', E1Z. 4, '3~'iRS3='-;Ei2·~",3X , : -:-:- -··elll-17-ao·'ARS4=',E12._,3X,'AR6C;~E12._,3X,'AR61='IEIZ.-'...~~~!7-&~.3X,'ER13X='~E12.q,3X,'ER1qX=',E12,1t,3X,'ERS3X=',E1Z ...,3X,... 04-17-80'[RS-X=',l12._,3X,'ER60X=',EJ2.-,3X~'ER61X=~,EI2._ I,..OQ-17-8C------3X~·VR13X=';[12~q, 3X I 'VRITX=' ,El2. II 13X;eVRS3X = ~f12 .,,;3X,. ~-Qll:i7-8T______~V RS_X.~_, E 12 .~t..5~ 'VR6Cl..=_" E1 2. -, 3X.I~VR~~~'• E:l2 ......~~ .__ ..Jl...I1..~-o_r_3 X , 'A f.-8J'fXRl_XCNN) - AR14X*EXPtC-1.*CXRlqXCNN)-ERl_xJ*.2)/t2••VRlIIX)) Oq-16-Sr______~f~X=RS3XtNN) = ARS3X.EXPli-l.*CXRS3XCNN)-£RS3~).*2)/CZ.*VRS3X)) 0_-1~~~.fXRS_XCNt.) = JRS-X*EXPcc-l.*CXRSltXCNN)-ERS_X)**Z)/(2 •• VRsqX))rXR60XCNN) = AR60X*EXPCC-l.*CXR60XCNN)-ER6Qxh.Z)1&2.*VR60X))0_-16-oC0_-16_tiC-----=fxRbfiiN~-)-=-Aif61x.[XPC ( -1.*'ix-R6IxHiN )-[R 6J. X~••i17n~-.-:iIR·6Tx-))--- 0 _ -16 '~s'C1(13 = XR13CNN) ._.P~__1.!.~.g'_R11+ = XP1_ CNN) Oq-ll-B(l___...:.:RS3 =-)(RS_3 CNN) o--u_-~RS4 XPS4 C~N) e_ -11-80R6C = XR60CNN) DQ-11-&C---~.-----=-xR61-ci.!N'--- --.---.---------.-._--...-. ---·---oii-li=-ao·R13X = XRI3XCN~) 01l-16-o~----:.:.R=-14=.:X------ = XRTiix-c'~N )--._-_... _------- .---- ..- ----. --. ------ ---"o-ei=l6'':s CRS3X = XRS3XCNN) 01l-16.:i 8_RS4X = xRS-XCNNJ 0--16-50R60X = XPbOXCNN)_. .__. . O~l..c.§qR61X"-- ---=xP61xiNN)0--16-00__ .__f.P13 --=-..£.XRJ ~.J...N~) ._._ . .~ . _. ._..__ _... o_~_-:.H_-@'~fR1_ = rXR1_CNNJ ell-11-80___....:..f':u...- = rxR~3JNN J ._ _ -.Q.!!-=U_=_~fPS_ = rXRS4CNN) OIl-11-oCfRbO = rXR6GCNN) e~-11-80---fP.61-- -~ rX~61cNN)----------·------··_-----·------- ---D-.~ii:&(-___ ..__f.R!1..x ....:-Y~B.!l_X_CNNL__. .__. .._u .. ._...~~_-l6.:'8CfR1_X = fXRIQX(Nh) 011-16-50___--:..f~R.:S3X = f lCR_53X CNN) . ._. Clll-J.~-§.Q..fRS-X = rXR5QXcN~) 01l-16-S0_____ £.!?~Q! -=-E.~~~_C~JNN....L. .__ ._.. . !J_!',,:,H-oQfR61X = fXR61XC~h) 0_-16-liOIV-35

'--------------~--------~PRINT fINAL INFO O~ PROSAelLIT1E5__ . L. t~~~J1l....._~~~f O~..~L.H.~.lf.!LllQ .•,U__TILPJUNt __~.LI NL.S.' . .. __ .'D~-30-6:__ ._.. _D.1t -1.1_~il ':._____..FPINT 99.Nh.RI3.fR13.P.13X.FRI3X.....__._..__Ji.J~ ,FR 11l •.RllL.fJU..~~ .Oq-lb-o[...__.nq=~El=..aLRS3.FRS3,RS3X,FRS3X,...H5~,ER5~.R59X,ER5gX,...Oq-16-oro9-16-bc.R60,FRbO.RbOX,FRbuX,...Oq-16-&~B...b..4£R0 1. ROB.fRO! X . .-B..!l=ll=.8D._99 •• fORHAT(SX,'NN=',lq,Sx,·R13=·,E1Z.q,SX,·FR13=·,E1Z.q,SX~·RI3X=·, •••eq-16-6C. E.... l--'2......c.=IqL.l.~5ll>X~.B 13 X=••f 12." I • u______ _'f;1")(=' ,ElZ.If/...ag-IEl-oC_17X.·R53=·.EIZ.",SX,·FR53=',E12.".5X,·RS3X=·,E1~.~,SX •••• Oq-16-8r• FRS 3 X=' , E12. " I • • • . _ll..!l:li_~.17X.'RSq=·,ElZ''',SX,·FRS''=',E1Z.q ,SX,'RS''X:·,EIZ.q,5X, ••• O~-16-80•••~..::lA.=.H.17X,·Rlq=·.E1Z.q,SX,·FR1q=·,ElZ.q.SX,·Rl"X=·~EI2.q.SX, ••• Oq-16-~Q______~~ X='~."I.••17X,·R6C=·,E12.",SX,·FQ60=·,E12.",5X,'R60X=~,E12.",SX'a~~...l~Jic..O"-16-8C• FRbO X=•• El2." I. • • 09 ~.l..6.=.a.c.....17X,'R61=·,EIZ.q,SX.·FRbJ=',E12''',5X.·Rb1X=·,EJ2.Q,SX, ••• Olt-lb-Sf___ '.£RU X=' ,E12." II ) .____09~.l~_- tH:._'---------FCRCING FUNCTIONS FOR RESPONSE SPECTRA CALChS '86-26-80. .c.s...Z ~Ji.C.S..z..JttN ) . . .D..l=.Ql..=.il£RHSX = ARHSXI~N) O~-Z6-8r.R..!:!..H = ARHSY INN) _[lb-20-O C ..RHSTH = ARHSTHINN) D6-2b-&QT = ~..ll1.11t1i...l- __...__._ _ .__0..6.=26.=:..8.llDUSl = ADUSHNN) 09-11-8,:_____........, 0.... I....lS... 2~--=-=~US l ( NN )09..=.1.1-.&ILOUS3 = AOUS3(NN) 09-11-bfPUS' ; ADUSM(NNI 09-1l-60LINlS(Z) S'INFOR~S SYSTEM A80UT TO WRITE 2 LINES' e6-26-dCWRITE CZb. 1 OQ) T. RHS X.RHsy .R HS TH. CS l.puS 1.0USZ""'O'U'u....D..u.s"0 9~1=-lU!....100.,I'"OR'UHSEI2.Q/"E12.Q)O~-l1-o~____J.LLNJ't..!..I...L.NhH I GO TO Tl -ll..!L.=..l.!t..~.c.GO TO T998 03-11-b 1T99~ •• CONTINU[ 03~1n=aL.LINLSCl) ,'PRINT 1 LINE'O~-11-81____...W'-"R......UE (b , 1 G1)_--fl3=.ll..~.aL101 .. I'"ORt'\ATlIX,2bHINDICHED TEST NOT ON LIST) 0'3-11-bl__..:...T~9~9",-cIIC CI.N TI NU_E. _ __..ll3 ~...l.1 -:.1;_1LND "01'" TERHI~AL'~ >' vI'" P ~ O~_'_IV-36

SET TITLE = 'PRELIMINARy DYNAMIC MODEL OF CASK-RAILCAR SYSTE.H·SET RRR = 98-;"SETUP FerR -0 EB Li:.."G,....-L...;I;..;S;.,T::--:O=-:F=--A""'L,...,L;--.,.,\/-:'A'=R--I..."A--B-,-l-=E,..,S:--W.,-;H-;-;£:-:N~T;;-==c-.'=0"""2' ----oe"=-o~ -8-~ACTION ·VAP·=0.Q2,·VAL·=I.·LOC·=NDBUG 08-011-80OUTPUT T, •••ADXT,...i-lS-7~--....;A:=-;D~X::..;T;.I.;2..:,..:.-.-.--·_---------------·--~-----8-=-1S-"79__---:..e.::.-_ ADXTZ3,... -=,_,. _ 8-1S-79-------------.....".. • .,-.••• ---------------------------'f',., SET OF VARIABLES TO BE PRINTED OUT'YRPRt, •••YRIZT 9.. ,OJ -IZ-81yRIZX. ••• 01-08-61-------------,Y;,..R:-S;.;.6.;X.......!:,---=.:....:.::..:.~-----------------------0~1-08 -81·__________----..."..;l~T:..:.A..:..T.:..;H--=,-=.:....:.:....:.~-----------------------=.0.;06_-2&-8e!ZENDPREPAR T, ••'.AUXT, ••• 8-17-79________~ADXTIZ,••• 8-17-79AD)(T23, ••• a:r7-79 .AUXT311, ••• 8-17-79DT H" N, •••,.••••,.• SET OF VARIABLES TO BE PLOTTEO'••••lTATH t· •• 06-2&-8 ~. ....;K.=,S.;oI.....-=.-=•....:•....; . _KS ll, •••OXRPRC, •••"----zNCCRDSTARTRANGE XP.XRC.XTR,XTF,XF,YP,YRC,THP.THRCRANG~ XRPRC,XRRCF XRCTR,XRCTF.YRPR~,THPPRCDXP,OXRC,oxfR,DXTF,OXF,DYP;OYRC9DTHP~DTHRC----------_. ---.._-------~R-:'A·NGERANGE OZXP,D2XRC,DZXTR,D,XTF,DZXF,D2YP,OZYRC,D2THP,D2THRC,... Dj-2S-bP----- D2XRCX ,OZXPX ---------OI-ZS-afRANGE YPIZ,YP311,YRCI2,YRC311,YRCS6,YRC78RANGE YCPL 9-02-79RANuE D2XRCH,OLTYI2CS-OS-8QRAHuE OZD Yl2 ,=D-:Z'=07:Y~3":;:1l---:"-------------------------:e6 -02-6CRANGE OHY12,:>MY3/f06-D2-8C---'---RANGrYP1~ , Yl5lz X, YP'3 II, YP 3 IIXOS -os -8(iRAN~E DYP12,DYP311,OYRCl"DYRC311.DYRCS6,OYRC78RANGE DZYPI2,uZyP3Q,OZYRIZ,DZYRS6,D2YR78,DZPIZX,DZP3I1X,DZYR3II Ol-ZS-bCRANGE. D2X),D~YD,D2THD 07 -OZ ~lH'-··RANGE XF2~-i;::f~XF;Il, x T, XTt2. XTz 3 ,XT 311IV-37

kA~GE~A~GEDXF2,OXF3,D7f4,~XT,DXTI2,DXT23,DXT31fC2.F~,~2XF3,D2XF4--------- ifAtIIGE- DU Sc\ R,DUFF 2, ou-i:' 2F j;DUF3Tti_________Ii~~..~_~liLQUSIi1 Q-23-lK-RANGE OUS2,OUS3 9-03-79RANG[ RHS X, RhS~H=-:S~T:.:H::-:-~~~_~.....;Ol

P l.. 0 T lIU S 1 I (lu S" I_. ._p..~...Q!..9US2.,.PUS 3• SA,., E •. _PLOT 'XAXIs' : T,'XLO' =O.,·XHI· = TSTOP. .~.b2}__~.1...~..L...P.:.::!.'!!!.1..' HI' ;.Y,.,X ,.~c;.!!AR~=·_~tlR~_'-~.fJ!~R· =_~.~.~~~E.~ . _PLOT THP,'LO'=TH~N,'HI';'TH~X,'CHAR'='A'~THRC,'CHAR';"6','SAHE'PLOT OXP, 'LO ';OXMN , 'HI'=OXMX, 'CHAR ·;.·A ',OXRC, 'CHAk '='8', •••oXTR,'CHAR'='C',OXTF,'CHAR'='O',DXF,'CHAR'='E','SAHE'PLOT [lYP,'LO'=OYHIII,'HI':OY"1X,'CHAR'='A',OYRC,'CHAR' ='B','SAHE' __.. __ .. _ ..-------PL"OTDTHP, 'U)';'OTHHN, 'HI' ;.·DT HHi~'iCHA~'''='A' ,OT HRC","CHA-If'=-' B'-,-~-:-:'SAME •-----..---PL OTCi'2XR C,'L O' =02XMN, 'Hi '=0 2X,.,'X;' CHA·R'·=-·A·, 0 2xP~. CHAR .='S.-;'~ ~:------ ._.___.. ('2!!.~~~CHAR· =' ~TF, 'CH..AP· ='0' ,D2XF,' CHA!~=·E· .. 'SAM E' _P LOT 02 YP, •La'=0 2 YHN , • HI' =0 2 YHX, 'C HAR • =' A', 0 2 YRC , • CHAR • = • B', • I •----.-.- FOLOT'SAME •02 THP ,""'·=-:L,....O-=-=-·-=02 THHN, 'H I' =0 2TH~x-;-'CHAR' =;eA";DiTtiR-C--; '-~-.-----..-- --·CHAk.·=·b',·SAHE'----·--P·COT-XRp·Rc;-°LO· =XRHN, 'HI' =XR HX, ·CHAR'~i·A'i·;XRR-CF-;'C.HAR' ='8-' ~~-:-:-. ---._--XRCT~,'CHAR'='C',XR~TF,'CHAR'='O','SAHE' . _PL aT DXRPH__. P!-.2J~.~R..!-J~.CH~.~~~~ TH.!!..PR...~~HA~?~~· ... .. _.._ ...PLOT YP12x,·LO·=YHIII2,·HI'=YHX2,YP3~,YRC12,YRC3q,YP12,... OS-Ob-er_ . .__.... ._~3. ~ _~.,.~~.A~; .~ .. . ..__ ... ._. '_... . _. __._ .Q.5 - Cib.-lgPLOT TIC13,'LC'=O,,'Hl'=1.,'CHAR'='.·.....fJ...Q1....JJ.il~.J..~ =0 •..L.tIJ...!...;l_h.~ ~.tiA R'= '.'PLOT T1CS3,'LC'=0.,'HI·=1.,'CHAR'='.'05-0b-tCa 5 -O~~Q..r.05-Cb-80______... ~QJ __U.~~_'!.Lk9~=_h.1 ~.tl~::.t~~_Ii~:::~~ ... .__._ 02...-..0.~:-~QPLOT TICbu,'LO'=O,,'HI'=l.,'CHAR'='.'OS-Cb-8~_____...--?L 01...-!..I..l;_f> 1, • Lc' =O.!..L' HI ';'1., , CHA R': '.'.__.__._..__---fl~ =-Db_-J'.rPLOT TMIC ,'LO'=O.,'HI'=l.,'cHAR':'.' OS-Db-foO______-"P~L..::O""T:.._.:.Y.:.:.R.::C:..:5:...::o~'=Y~N2,'HI' :YH Xl. 'CH AR':' A' I YRC 7!l~l!AR' ='e~. '"YRCIZ,·CHAR'='C·',YRC3Q,'CHAR':'O','SAME'e9-12-80._--,Pc...::cL...::OT OYP J.£I.~~_O' =OYMh ?_L~ ..L~..=.D:!!.'.~.?...t! CHAR' :~_~~'.l.p_.rP3_~~ . ._ ...• CHAR ':'8', OYRC12, 'CHAR '='C' ,DYRC3.. , 'CH' R'='O ',. a. 0"-22-l:.c__ .. .._..!t..!.E.l

A P PEN 0 I XVLISTING OF CARRS MODELV-l

LISTING OF CARRE MODEL- P~OGI\ a"': c.~s- ------------- ---·----06--3C-80'--(CAI~tt IRIAIl CAR (P.IESPO~SE (SIPECTRA '07-01-80----~~ i"O[;~C I u CA CCULJlTE ACCELE!'A TION Vl~ SPONS~ SP~-CT"R""'-US1~ ---+0 75"!)1--1l 0, RESUl TS Tf.ANSFERREO FPO" THE .CARQS. "OOEL VIA FILE .TRAN---•• '07-01-80, - -C'" C( K Ll 5 T • 09-U-ltO, 11) SET PI\f911 '09-12-8QI,) (HEC'" (O~I ROL (Al:;US·U9..-rz"'8~(2,11 ASSIGNINf FILE FPO" .CAROS. '09-1&-80IZ,ZI USING FILE FRO," .CAFlUS. vIA O~VI(E 26 'U9-1b40INTEGER ~ON[,NN,NNH,N06-3u-80INiCEER NCASE09 ~~-8U.I~TEGEl< "'HOP 09-Z5-80LOGICAL PREUl fl., l-z-ao06-Z&-80!~IT!'LAKKI t tI "ON E" (~) ,AR RSX 1I2 0) t lRA$' I 12C) ,.WAS I AI 1Z0" A'''' IlZU),... G7----m-.;8tJAC~~(12Q),~OUS1(120),AOUSZ(120I,AOUS3(1201,AOUSq(120) C9-1Z-80ARRlly Cd:OH1l2Cj,02tD"'U2UJ,02IAOI'!(1,CJ, 0"'1120)09-?S-"'8'C'--SYSTE" INPUT P~RA"ETERS'06-2&-80CORSIAN' CIlONE - 0.01,0.001;0.01 06-3cr-suCONSTAhT CSI = 2.E3 07-01-8C-----rCU1'f!TJIiO I csn - 1'·OQ. -------ljT-Cl--8(lCONSTANT CS3 = 1500. (;7-01-60CONsTANt Csq - ,.E' 07-~1·80CONSTANT OTHPI = C. 06-:!J-80CONStllNI OIARCI - C. '--lJ6--:!Q-80COhS1ANT OYPI = O. 0~-30-80CCNSlANl uncI -- o. flf,-~-o--80CONSTANT 02THO! = u. 09-25-8~CONstANY OZxOI a O. 09-2S-~t1CO~STANT OZYOI : O. 09-25-80CONSHNT EPS 1.~a6 ~-3t}-!lOCO~STANT G = 3~6.q 06-30-&0CONSTAN T IP - 8.S7E~ 06~~8tlCONSTANT LPF = 1aZ. 06-30-80CONSIIINY (pI; - HZ. 06~"'80~~XTfKVAl MAXT:J.OOI 06-26-80CONS I AN I MOFR - U .5 ~ ---------m-·:30-aoCONSTAhT NCASE' : 1 09-25-80----Cl"'"n'OKrN~STTI"N1 NS tOP _ 2 I ._u . ~-- ..1J9-25-ecCONSTANT NN~; = lIb ''INTEGEr VALUE" 06-30-80CONs IIlN' OR IH - Zl'U- "'6--~(j-8~CChSTANT OMX = 5C. 06-3G-80CONSTANT O"t - lOCo 06--3~OCONSTANT PRE911 = .TRUE. 09-12-80-----,C..."Ow-s'AN' PRE911 .FAtS~. ---.--.----- 09-1Z-80CON~TANT RHS1Hl = a.0~-3(j-80CONSIANY RASXI _ y. 06~~nCONSTANT RHSVr = O. 06-30-80' a_.aa.a••• ---SWITC"~S CO~T"CLLI"G 0 A"PI "b. lEI«)----vl'ftw-"1t1-17-·SQUNDAMPED. ONE WHEN OA~PED. '07-17-80-----,CMO~NI

--- -TO~Tl\NT TAPI - oj. ..-.--------Ll6.--~O-!OCU~STA~T THFCI = ~. 06-30-80-_._- ~~1-"'1'rt-'fte - G.0 3 ---_.-._-- ----""0f.-30--8 0CCNS~ANT TSTOP = 0.15 06-30-eC--~C~j-'tJ;Nr

---NN ::. :-

E ""(1·~6COC Tr CO"'PtITf S lC,,< fUNCTIO~··" _.---._...--.-.07-Cl-80!"ACRO sc~.'rlp,AJr>;OCFCllf\ 6L If< =A JYFIA.lT.C.J R=-1.I F I A • £C • G. J P =-1 • - - - -- •. - -.-----------06-2b-800E:-26- 8 006 -26-8006 -2b -80I F I A • b T• l.. J P =+ 1 •06-2b-60£ NO ~ • OF PRO C£ OUP II L- of' O~,.._eRO-~-NN-FF-4O----0E:-26-80Io1AC"O ENe06-26-8e-0 ----~I,.,GLE DEGREE OF -FRE:-Eeo-!'l--H~t1Al~5-"*--MOTI ON07-01-80ARkAhGED TO yIELD RfLATIVE ACCELERATIONS07-01-80WITH TwO I"'TE6RATIONS--T06-1Y-E-\lH.-~C-HJ-E-S AND ['ISPLACEI4(NTS 07-01-80D2XD = RHSX-XO*0~X**?-1 Cs1+CsQJ*DxD*SwOxO/HP •• o 07-1il-80. -·--·.~UJ'R*-rwI-""'P1I , * s ~NF I El XEl, *~WDXD F IMP -- --OXOINTfGlu2XO,DXDIJXO INH"G101fD-t~01t- -- -----..---.OZYORHSY-YD*0~Y**2-ICS2+CS3'.DYO.SWOYO/MPOYD HIT fG f OZYO,oyor-r-- ----------- ---YO = I~TEGIOYO,YOIJU2 Tl-H:' --. --= -m'fSiH-Tf'm -O"'im~ Anh0 T HO't'Slltn"MD --~THOI~TEGI02THO,OTHOI'THO = INTEEfOTHO,THOIJ----···-----·--- -..!i 'oF DERI VAll vE··------------------------"'ax·--A~O_!'II1'i--VALUEsfOR PLOTXM~ = A~AX1IXMX ,XO JX~N =··A"INr-t X~N" ·--,"'lrr---'l'c---------------- .-.YMX = AMA~lIY,"X ,YO JYMN = M'IN11yflN- ,-yo ---,------------ ..THIo1X = A~AX1ITHMX ,THO JTH"'t\ =A"IN1 I TH!'t!'l --·-.fHD---·.,..-----------·OXMX = A~AX110XHX ,DXP J~Y~XA~AX1IUYHX ,OYD JOyHNA"INIIDYl'IPt -,-nVo---,----------·---·-·DTHH)( = A"AX110TH"X ,OTHO JOTHHN =-A"llo'ltoTH"'N- ,"OT-Ho--"1------OZXMX = A!"AX1102X04X ,02)('0 ,RHS)( J02'O"~! -..= A,..IP;1·10~X ... N"-,"1)2"Kt)--"""S~-.,..··O,YHX AMAX1(u2v~x ,02yO .RHSV )OZytH' = A"IN1fD?Y'1"'- ,02VD-·-..,--RH·S-V _·-t--------.- -·u~",,,, ----=-J1'!"1?-l 1 (0 x"'~ ,:1IIT)Xr Orr--...,,------D2TH~X = A~A~1102THMX,OZTHO ,RH~TH I02TH~~ = A~I~1IU2TH~~,DZTHO,RH~TH 1IFIP~£911JGO TO !:'1. OUSX '" X--=--A"ljl.XI f DUS X1"IX i~~Jtf)rt11:l""5ca:q""'J--·DUSXu~A~I~110USXMN~DUS1,DUSQJOUSY,..X A"'AX1(0t1s"",X.OUS-Z-,·1)~~"1----;---· - ..OUSp· ... = A"H-'110IJSYHN,OUS2,OUS3J-Ol •• CO!'HINU[ .--.-----JFIT.['T.~oJGO TO OY1--------. _..----------1-r-..,....~~-.-------------D2XO~= AA~(D2X['IJD2Y[.rP =ABSfD2fflI-f~2THOP = A~~1[2THOJ)GO TO eVluY1 •• CO~TI ... U[ "If T.Gr.o.DZxO .. tHCASf t -_-A"""'1(i;*e~~_ilbrflP'it-D2Vo~·INCt.SEl = bMAXI IABsIDZvOJ,OZyOPJ02TH0t'1INCASE: J = bl'!hXt IASSlfl2THoJ·,t)2TlID-P1---..-.- ·'---"-07-18-8006 -26-8006 - 26 -8007-02-8006-26-8006-26-8007-02-8006-2b-8006-2&-&006-2&-80SCALES 07-11-8007-11-8007-11-8007-11-8007 -11-8007-11-8007-11-8007-11-8007-11-80U7-11-8007-11-8007-11-8007-11-8007-11-8007-11-8007-11-8007-11-8007-11-8007-11-8009-12-fOQQ-12-8009-12-8009-12-8009-12-8009-1Z-8009-25-800 9 -25-8009-25-8009-25-8009-25-8009-25-8009-25-8009-2:»-800 9 -25 - 8 009-25-80V-6

n__----C9-25-80---- -----------mqlil.lrSt:, _ ,,1'1 X -- _.. _u__ o_·__ ··_·_ --_. - 09-15·80~2XuP A~S(92X[M(NCASE)) 09-25-80---------- ~lY[)!> = Af'S eEZ fE'I'IINeA~t,) ----- ----PZTH~P = ~~S(02THOM(~CASE)) 09-25-60tIN E ! t 1 )-09--2rBODRI~T~Qu, CM(NCASE),02XO~(NCASE),OZYOH(NCASEJ,02THOH(NCASE)G9-Z5-80fER,..! ll.GE.ISiOPI 06~END S'OF" OYNA~lC' 06-16-80TFRM!NAtfH-H~{l'----------------- RClUNOING OFF" MAX AND MIN VALUES FOR USE '07-11-&0ON PLOTS SC-L~S 'O~~OSCAlElXH~ ,XHX = XHN ,XMX 07-11-80SCAlr,f"K ,f~X - IAN ,iMA 0' 11 BeSCAlECTH~N ,THHX = THHN ,THHX ) 07-11-80SCAlECDXP.K ,tXl'll( DXMN ,0)(")( J OT-11-80SCAlf(OYMN ,OYHX = OYHN ,OYHX ) 07-11-80SCALE" (DIAI'IN ,DTA"'X - oT""1I1 ,0TRI'Il J 07-11--"8"0SCAl flO2 XHN ,[,Z XliX = OZXHN ,OZXMX ) 07-11-80SCAltluZfRN ,U~T~A - U~T"N ,DZYPX OT-11-80SCAlEl02THMN,OZTHHX = 02T~MN,OZTHHX) 07-11-80IftPK[91lJGO 10 11 09-1T-1roSCA LE lDUSXHN ,CUSl':HX:OUSXMN,DUSXHX)09-12-&0~C At r cDU Sf ''IN ,DtI S '1'1 X-UtlS f 1'1111 ,DU~ I 1'1 XI -----o-J~tl-80Tl •• CONTI~UL 09-12-80IF(IIOCASE.EU.fClSIOPIGO 10 iZ09-Zs---snG0 TO T~09-ZS-~CIZ •• C01IINOE S'NCAS!.tQ.NSTOP' ---~·~S-80NCASE = 0 09-Z5-80T3 •• CONTI~OE S'NCASE.tT.NSTOP' 09-25-80NCASE = NCASE + 1 09-Z5-80LINt.SUI 09-25""80WRITECZ7,300) OH(NCASE),02XOM(NCASEI,OZYOM(NCASEI,DZTHOHfNCAS[)09-15-80.5"C..FOl{I'IIiI(4EIZ.4J09-!5--1l0PRI~T3CO,OHfNCASEI,D2~DM(NCASE),OZYOH(NCASEJ,02THOHfNCASE)09-Z5-80• IF(NCASE.C T.I'ISIOPIGO 10 13 0 9 -25-80T~ •• CONTlhUE ,·NCASE.NE.NSTOP· 09-Z5-80trw $'oF TtHI'11r.AL"Ol-II-lJOEND "or PROG~AH' 06-1&-80V-7

--~UrP't'l -f---·-----,.~......-••---------------------- -----{)6-?6-80C52 •••• 07-01-80---tOt-'Tf1H'!10~----=-.• -=-..,..• ..,...-------------------------A06"-Z-~O_ _____""1Di1Ur."S~I-"':".":"."':"._:.------------------------..;0--9-, 12 -80oG$ .: • • • • 09rt7...."8t)DUS3 •••• Q9-12-80-------OUSq •••• 09 12-60DxD •••• 06-26-80-------flOr'ltrfOr---=-.:;-.-• ..,...--------------------------if}t~--80D2THD ,... 06-26-80-------wr":·..:-1Xt10n---:-,"':' • ..,...~.~--------------------------6~"....,6--?tr_&tlo 7y 0 •• • • 06 -26-80N •••• 06-30..80RHS TH •••• 06-26-80R~SX •••• 06 26 80RHS Y •••• 06-26-80I AD ,.. • 06-2b-80X D •••• 06-26-80------"'Yt'-fOt---=-,.....-=-.-=.--------------------------iElFt,6--z-6--8-DZTATH ,... 07-01-80ZE N D --0-6- 2-6-110PREP~R T ,.. • 06-26-80-------rD'r"T1~FI1'tfl--=,-=.~.:-:.:---------------------------i'lO.,.6-?to-80DUSl ,... 09-12-80DeS? •••• 0' 1~0DUS3 •••• 09-12-80---------jO:'l'"Utts

0L (\ T CU s:" • L O· =ut'S-y"!~;-·HT-. =DUSYl'IT,u(;ST'-· SA PE • 09-12-80F NO ! 'OF P:

S[ T f; CAS ( = t 2 ..-- 0~-:?5-8C!S~T C'r-.)( - loa. 07-11-80

_._-_. -- ---s E""-~rr-'=-77"'C-.--------------------·-'-'------ -- ..- '0""'" 1S-80SeT CMTH = '2~. 07-15-80--""'r,-"'C----- -----------u-1- t 5 - 8DSET ~CASE = 2~ 09-25-80----srT' t'P,X - 2 :50. ---07-1S'"'1l0SET CMY = 23C. 07-15-8 0SC:T Cii',TI'l - 23U. G1 !!'J 8UGO 07-15-80--~T ";CASf: - '0; 09 !5-80SET NIX = 2~O. 07-15-8GSO eM, - 2 qc. --or-i7-froSET OMTH = 2QC. 07-15-80bG01· !~·!l0SET NeASE = 2bG9-25-80SE:t NIX 2~J. 07-15-80SET OMY = 250. 07-15-80---So:1E~TT-"""C'''''F.'Tl'''H-_---'2'''~'''or.-------------------------"'10.,..7,...-~OGO 07-15-80SE INCASE - Z I 09-25-80S£T OMX = 260. 07-15-80SET (1M' 260. 07-1S-atlSET OMTH = 260. 07-15-80"1:GCt'Or------------------------·----------10'7~15-_eCSTOPC7-Q2-8CV-ll

A P PEN 0 I XVILISTING OF FFT PROGRAMVI-l

LISTING OF FFT PROGRAMSU~qOUTJNE giFTfXC.~H.NHN.IFlJGJC • * .. SUB P C IJ T IP4 ( R r r T • r TN •••C" • • SlJ !H~ 0 UTI N[.T " TAI( l 1 H( 0 FlOf A Q. [ AlCe •• ~~N:NU"8t~ OF ~EAl POINT~=2.eMMCO~PlfX xCC J02bJ"m:NNII/;'H: r1M - IN VZ :NI' / ZCCl:3.141~9265·/FlO'TC~NJSO: SPI cr~ A •C(l:CO~COA'5:0.0c: 1.0JF CIFlAG.NE .eJ GOCALL rfTlXc.r..OJTOlc~aTJ P'1 E F' Ufl C T JON * ...5: CONTI"U(tCIN",olJ:xtclJ00 100 J=I,t:V2yP(:Rf AL Ilf( C1 J J .P(ll C"C lIlN-I .'], JY~O:RlllCJCCr,,-p(~LIXCI~N-T'2"Yl(:'I~'GCXCfl'J'AIMArcXCCN~-!'~"YIO:AJMAGCXCfI'J-AIHAt-lX(lNN-I'?"AJ:Y~C·C·YI(-S.YROAl=Y10-C·Y~O-S·YI(JCCI':t.5·C~PlXfAlt'2J11=lnE-C*YIE·S·YRO'2:-YIO-C·Y~O-S·YI[XCCNh-lo:' : 1.5 • (HPlXfAI. A21l=C·CO-S.~(IS=S.CfIoC.SD( =T100 CONTI~U(XCCNV~'IJ='ONJGfXCCNV2'JI'Rf. Tug",1000 00 lloe l:l,NVZAl:RUUHCI))'2: A J H 1GCXCfltJ.3:R[AlCXCf NN-I·2IJA·:'1~AGCXC(NN-J·2JIY''':=''1'13YPO=-SeAI-C*4Z·S·'3-C·'~YJE:C*AI-S.Al-C·,3-S·'QYIO:'2-'"XCC~"-1·21=CHPlXfcyq(·YROJ.fYIE·YIOJl/f2.t·NHJX(" C, I =CHPlX f fYR ( -Y R0 J • CVI E-Y 1 0 J JIf 2 • Q.H~ JT =C *CO -So ~DS=S"'CO·C.~O(=TVI-3

1100 CO'I TJ NUr)CC~V2·11=CONJGIXC(NV2·I",FLnATCNN'CALL f"fTfXC,I'1,J,RETURN(NOirTN,Isro rJLTP.ffT~UBPOUTJN[ rFT(X,H,IFLGJC••• SUPPOUTIN( FFT.rTN •••c••• SU!t~OUTINE CC"'PUTE~ OFT •••C~H~LEXCOMPLEx )(11':'2~1N=;"·"'INV~=N'2,..~I=N-l..1=10=-).U,W,T,THPIr(!fLG.[U.~' GO 10 ~50:1.00 51') J=I,N)( f ! J ='I I 1 J ,,..~O C(HlTJ~Ur~5 on 7 l~I,~HJIrlY.GE.J' GO 10 ~T=XIJ''IfJ':,xfl'II I I I : t5 K=tIV;b Irn.r.(.J' GO TO 7J=J-M":"'/~GO TO 67 "=,, ....PJ=J.lq)592~~~6~97900 Zl' l:I, ...l~=Z··LU'l=L(/zU=fl.0,O.OIW=C~PlXICOSIPI/fLOATIlEl",O·SJNCPI/rlOATClElll'[)O 2r. J= 1 ,tf 1(\0 10 J=J,N,lEl"=l·UlT:).fJr,·uXUPJ:x" '-110 XCI.:Xf!'.T20 U=U.W61 fO~HAT(IHl ,·X ARRAY rR[QUENCY OO~~IN DATA APDIL 10 TEST.,62 fC~~AT(JX. JUr,IZ.5,R(TUPNENDVI-4

DISTRIBUTIONNUREG/CR-2146, Vol. 3HEDL-TME 83-18RTRTDOE-RL/Office of Asst Managerfor Advanced Reactor ProgramsP.O. Box 550Richland, WA 99352EC Norman, Director, TechnologyDevelopment DivisionJJ Keating, Director, BreederTechnology DivisionDOE/Chicago Patent Group9800 South Cass AvenueArgonne, IL 60439AA ChurmDOE-HQ/Office of Operational SafetyEP-32Washington, DC 20545J. CountsE. I. Du Pont DeNemours and CompanySavannah River LaboratoryAiken, SC 29801RH TowellLos Alamos National LaboratoryP.O. Box 1663Los Alamos, NM 87545TO ButlerBattellePacific Northwest LaboratoryP.O. Box 999Richland, WA 99352LD Wi 11 i amsSandia LaboratoriesP.O. Box 5800Albuquerque, NM 87185CF MagnusonHJ AndersonW/C-28JD BergerW/E-12HA CarlsonW/C-28MCJ CarlsonW/C-28RE DahlW/C-22SR Fi e1ds (l4 ) W/C-28SJ MechW/A-132LH RiceW/C-5Central Files (3) W/C-110Publ Services (2) W/C-1l5Microfilm Services W/C-123Distr-l

NRC FORM 335(7-77)1. REPORT NUMBER (Assigned by DDCIU.S. NUCLEAR REGULATORY COMMISSIONNUREG/CR-2146, Vol. 3BIBLIOGRAPHIC DATA SHEET HEDL-TME 83-184. TITLE AND SUBTITLE (Add Volume No., if ."prOt'rilllf11DYNAMIC ANALYSIS TO ESTABLISH NORMAL SHOCK AND VIBRATIONOF RADIOACTIVE MATERIAL SHIPPING PACKAGESFINAL SUMMARY REPORT2. (Leave billflkl3. RECIPIENT'S ACCESSION NO.7. AUTHOR IS) S. DATE REPORT COMPLETEDMONTH I YEAR1983S. R. Fields August9. P!RFORMING ORGANIZATION NAME AND MAILING ADDRESS (Include Zip Codel DATE REPORT ISSUEDHanford Engineering Development LaboratoryP.O. Box 1970Richland, WA 99352MONTH· I YEAROctober19836. (Leave blanklB. (Leave blankl12. SPONSORING ORGANIZATION NAME AND MAl LING ADDRESS (Include Z,p CodelDivision of Engineering TechnologyOffice of Nuclear Regulatory ResearchU.S. Nuclear Regulatory CommissionWashington, DC 2055510. PROJECT/TASK/WORK UNIT NO.11. CONTRACT NO.FIN B228313. TYPE OF REPORT IPERIOD COVERED (InclusIve dareslFINAL SUMMARY REPORT15. SUPPLEMENTARY NOTES 14. (Leave blilflkl16. ABSTRACT (200 words' or lesslA model to simulate the dynamic behavior of shipping packages (casks) and their rail cartransporters during normal transport conditions was developed. This model, CARDS (Cask-Rail Car Qynamic iimulator), was used to simulate the cask-rail car systems used in-rests3, 10, 11, 13, 16 and 18 of the series of rail car coupling tests conducted at the SavannahRiver Laboratories in 1978. On the basis of good agreement between calculated andmeasured results for these tests, it was concluded that the model has been validated asan acceptable tool for the simulation of similar systems.A companion model, CARRS (Cask-~ail Car ~esponse ~ectrum Generator), consisting of singledegree-of-freedomrepresentations of the equations of motion in CARDS, was developed togenerate frequency response spectra.A parametric and sensitivity analysis was conducted that identified the most influentialof a selected set of parameters and the response variables that are the most sens iti veto changes in the parameters.17. KEY WORDS AND DOCUMENT ANALYSIS 17a. DESCRIPTORS17b. IDENTIFIERS/OPEN·ENDED TERMS18. AVAILABILITY STATEMENTNRC FORM 335 (7·77)19. SECURITY CLASS (ThIS reportl 21. NO. OF PAGESlin,. 1 ~ c: cd T; onUnlimited20. SECURITY CLASS (Th,spagel 22. PRICES

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