january 31, 2018 docket no. 52-048 u.s. nuclear regulatory ... · the software can perform the...

RAIO-0118-58472

NuScale Power, LLC1100 NE Circle Blvd., Suite 200 Corvalis, Oregon 97330, Office: 541.360.0500, Fax: 541.207.3928

www.nuscalepower.com

January 31, 2018 Docket No. 52-048

U.S. Nuclear Regulatory CommissionATTN: Document Control DeskOne White Flint North11555 Rockville PikeRockville, MD 20852-2738

SUBJECT: NuScale Power, LLC Response to NRC Request for Additional Information No.133 (eRAI No. 8936) on the NuScale Design Certification Application

REFERENCES: 1. U.S. Nuclear Regulatory Commission, "Request for Additional InformationNo. 133 (eRAI No. 8936)," dated August 05, 2017

The purpose of this letter is to provide the NuScale Power, LLC (NuScale) response to thereferenced NRC Request for Additional Information (RAI).

The Enclosure to this letter contains NuScale's response to the following RAI Question fromNRC eRAI No. 8936:

03.07.02-7

The response to RAI Question 03.07.02-12 was previously provided in Reference 2. Theresponse to RAI Questions 03.07.02-8, 03.07.02-9 and 03.07.02-11 were previously provided inReference 3. The response to question 03.07.02-10 will be provided by April 20, 2018.

This letter and the enclosed response make no new regulatory commitments and no revisions toany existing regulatory commitments.

If you have any questions on this response, please contact Marty Bryan at 541-452-7172 or [email protected].

Sincerely,

Zackary W. RadDirector, Regulatory AffairsNuScale Power, LLC

y

Zackary W. RadDirector Regulatory Affairs

RAIO-0118-58472



Distribution: Gregory Cranston, NRC, OWFN-8G9ASamuel Lee, NRC, OWFN-8G9AMarieliz Vera, NRC, OWFN-8G9A

Enclosure 1: NuScale Response to NRC Request for Additional Information eRAI No. 8936

RAIO-0118-58472



Enclosure 1:

NuScale Response to NRC Request for Additional Information eRAI No. 8936

NuScale Nonproprietary

Response to Request for Additional InformationDocket No. 52-048

eRAI No.: 8936Date of RAI Issue: 08/05/2017

NRC Question No.: 03.07.02-7

10 CFR 50 Appendix S requires that the safety functions of structures, systems, andcomponents (SSCs) must be assured during and after the vibratory ground motion associatedwith the Safe Shutdown Earthquake (SSE) through design, testing, or qualification methods.

In FSAR Section 3.7.5, the applicant provided a brief description of the computer programsused in the analysis and design of the site-independent seismic Category I and Category IIstructures. However, it did not provide sufficient information regarding the verification &validation (V&V) of these programs. The applicant is requested to provide in the DCAinformation summarizing the V&V of the computer programs used to determine design-basisseismic demands for NuScale seismic Category I and II structures. The demonstration shouldtest those characteristics of the software that mimic the physical conditions, material properties,and physical processes that represent the NuScale design in numerical analysis. The V&Vshould cover the full range of parameters used in NuScale design-basis seismic demand calculations including the discretization and aspect ratio of finite elements, Poisson’s ratio,frequencies of analysis, and other parameters pertinent to seismic system analyses.

NuScale Response:

A summary report of the verification and validation (V&V) of the computer programs, used in theanalysis and design of the NuScale Category I and Category II structures, is described in thisresponse.

ANSYS is a commercial, general use finite element analysis (FEA) software. ANSYS is used todetermine demand loads and stresses in structures, supports, equipment andcomponents/assemblies. ANSYS Mechanical software offers a comprehensive product solutionfor structural linear, nonlinear, and dynamic analysis. The product provides a complete set ofelement behavior, material models, and equation solvers for a wide range of engineeringproblems. Table 1 summarizes all ANSYS verification problems for elements used in theNuScale models.


SAP2000 is a general-purpose, three-dimensional static and dynamic finite-element computerprogram. Analyses, up to and including calculation of deflections, forces, and stresses, may bedone on structures constructed of any material or combination of materials.

It features a powerful graphical interface which is used to create/modify finite element models.This same interface is used to execute the analysis and for checking the optimization of thedesign. Graphical displays of the results, including real-time animations of time-historydisplacements are produced. SAP2000 provides automated generation of loads for designbased on a number of National Standards.

The software can perform the following types of analyses: static linear analysis, static nonlinearanalysis, modal analysis, dynamic response spectrum analysis, dynamic linear and nonlineartime history analysis, bridge analysis, moving load analysis, and buckling analysis. Tables 2through 7 summarize all of the SAP2000 verification problems. The problems are categorizedinto groups based on the structural elements used or design type of the example.

SASSI, a System for Analysis of Soil-Structure Interaction, consists of a number of interrelatedcomputer program modules which can be used to solve a wide range of dynamic soil-structureinteraction (SSI) problems in two or three dimensions.

The verification problems for SASSI2010 are shown in Tables 8 through 16. The SASSI2010V&V includes 30 test cases developed from nine different problems to verify the capabilities ofSASSI2010. These test cases were developed using published literature and/or handcalculations. The problems are designed to check the program’s capabilities under variousconditions, in addition to showing accurate performance of the SASSI2010 methodologies.These problems provide reasonable assurance that a certified user (i.e., qualified engineer whopossesses an understanding of soil-structure interaction) can apply SASSI2010 over theintended range of use. Other than the nine verification problems, an additional problem,Problem No. 10, was used to verify the overall validity of the SASSI2010 program to calculatecorrect static and dynamic responses for complex structures by comparing the results fromSASSI2010 with the results from the independently verified SAP2000 program. Table 17 showsthe descriptions and verification results of two analysis cases for Problem 10. In each case, theSASSI2010 program calculates the static and dynamic responses of a surface-founded, fixed-base complex structure. The total static reactions and the structural frequencies calculated bySASSI2010 are compared with the corresponding reactions and frequencies calculated by theverified SAP2000

The computer program SHAKE2000 computes the free-field response of a semi-infinite,horizontally layered soil column overlying a uniform half-space subjected to an input motionprescribed as the object motion in the form of vertically propagating shear waves. SHAKE2000is used for the analysis of site-specific response and for the evaluation of earthquake effects onsoil deposits. It provides an approximation of the dynamic response of a site. SHAKE2000computes the response in a system of homogeneous, viscoelastic layers of infinite horizontalextent subjected to vertically traveling shear waves. Verification problems, summarized in Table


18, were designed to test SHAKE2000 major analytical capabilities.

The RspMatchEDT Module for SHAKE2000 is a pre- and post-processor for the RspMatch2009program, which is part of SHAKE2000. The RspMatch2009 program performs a time-domainmodification of an acceleration time history to make it compatible with a user-specified targetspectrum. Table 19 provides a description of the RspMatch verification problems.

This software V&V summary tests those characteristics of the software that mimic the physicalconditions, material properties, and physical processes that represent the NuScale design innumerical analysis. It also covers the full range of parameters used in NuScale design-basis,seismic demand calculations, including the discretization and aspect ratio of finite elements,Poisson’s ratio, frequencies of analysis, and other parameters pertinent to seismic systemanalyses.

FSAR Tier 2, Section 3.7.5 is revised to include the above information.


Table 1: ANSYS Verification Problems

ProblemNo. Problem Title ANSYS Verification Problem

DescriptionMethod of IndependentVerification

vm2Beam Stresses andDeflectionsBeam188

A standard 30" WF beam, withcross-sectional area A, issupported and loaded on theoverhangs by a uniformlydistributed load w. Determine themaximum bending stress σ in themiddle portion of the beam and thedeflection δ at the middle of thebeam.

S. Timoshenko, Strengthof Material, Part I,Elementary Theory andProblems, 3rd Edition, D.Van Nostrand Co., Inc.,New York, NY, 1955, p.98, problem 4.

vm6 Pinched CylinderShell181

A thin-walled cylinder is pinched byforce F at the middle of the cylinderlength. Determine the radialdisplacement δ at the point whereF is applied. The ends of thecylinder are free edges.

R. D. Cook, Concepts andApplications of FiniteElement Analysis, 2ndEdition, John Wiley andSons, Inc., New York, NY,1981, pp. 284-287.

vm7Plastic Compressionof a Pipe AssemblyShell181

Two coaxial tubes, the inner one of1020 CR steel and cross-sectionalarea As, and the outer one of2024-T4 aluminum alloy and ofarea Aa, are compressed betweenheavy, flat end plates. Determinethe load-deflection curve of theassembly as it is compressed intothe plastic region by an axialdisplacement. Assume that the endplates are so stiff that both tubesare shortened by exactly the sameamount.

H. Takemoto, R. D. Cook,"Some Modifications of anIsoparametric ShellElement", InternationalJournal for NumericalMethods in Engineering,Vol. 7 No. 3, 1973.

vm9

Large LateralDeflection of UnequalStiffness SpringsCombin14Combin40

A two-spring system is subjected toa force F. Determine the strainenergy of the system and thedisplacements δx and δy.

G. N. Vanderplaats,Numerical OptimizationTechniques forEngineering Design withApplications, McGraw-HillBook Co., Inc., New York,NY, 1984, pp. 72-73, ex.3-1.

vm10Bending of a Tee-Shaped BeamBeam188

Find the maximum tensile andcompressive bending stresses inan unsymmetrical T beamsubjected to uniform bending Mz,with dimensions and geometricproperties.

S. H. Crandall, N. C. Dahl,An Introduction to theMechanics of Solids,McGraw-Hill Book Co.,Inc., New York, NY, 1959,pg. 294, ex. 7.2.


vm17

Snap-ThroughBuckling of a HingedShell63Shell181Shell281

A hinged cylindrical shell issubjected to a vertical point load(P) at its center. Find the verticaldisplacement (UY) at points A andB for the load of 1000 N.

C. C. Chang, “PeriodicallyRestarted Quasi-NewtonUpdates in Constant Arc-Length Method”,Computers andStructures, Vol. 41 No. 5,1991, pp. 963-972.

vm19

Random VibrationAnalysis of a DeepSimply-SupportedBeamBeam188

A deep, simply-supported squarebeam of length l, thickness t, andmass density m, is subjected torandom uniform force powerspectral density. Determine thepeak response PSD value.

NAFEMS, SelectedBenchmarks for ForcedVibration, Report preparedby W. S. AtkinsEngineering Sciences,April 1989, Test 5R.

vm21 Tie Rod with LateralLoading Beam188

A tie rod is subjected to the actionof a tensile force F and a uniformlateral load p. Determine themaximum deflection zmax, theslope Θ at the left-hand end, andthe maximum bending momentMmax. In addition, determine thesame three quantities for theunstiffened tie rod (F = 0).

S. Timoshenko, Strengthof Material, Part II,Elementary Theory andProblems, 3rd Edition, D.Van Nostrand Co., Inc.,New York, NY, 1956, pg.42, article 6.

vm26 Large Deflection of aCantilever SHELL181

A cantilevered plate of length l,width b, and thickness t is fixed atone end and subjected to a purebending moment M at the free end.Determine the true (largedeflection) free-end displacementsand rotation, and the top surfacestress at the fixed end, using shellelements.

K. J. Bathe, E. N. Dvorkin,"A Formulation of GeneralShell Elements - The Useof Mixed Interpolation ofTensorial Components”,Int. Journal for NumericalMethods in Engineering,Vol. 22 No. 3, 1986, pg.720.

vm27

Thermal Expansion toClose a GapLINK180CONTA178

An aluminum-alloy bar is fixed atone end and has a gap δ betweenits other end and a rigid wall whenat ambient temperature Ta.Calculate the stress σ, and thethermal strain εThermal in the barafter it has been heated totemperature T.

C. O. Harris, Introductionto Stress Analysis, TheMacmillan Co., New York,NY, 1959, pg. 58, problem8.

vm34

Bending of a TaperedPlate (Beam)SHELL63BEAM188SHELL181 SHELL281

A tapered cantilever plate ofrectangular cross-section issubjected to a load F at its tip. Findthe maximum deflection δ and themaximum principal stress σ1 in theplate.

C. O. Harris, Introductionto Stress Analysis, TheMacmillan Co., New York,NY, 1959, pg. 114,problem 61.


vm36Limit Moment AnalysisBeam188COMBIN40

A symmetric cross-section beam ofbending stiffness EIy, and height h,totally fixed at C, simply-supportedat A, is subjected to a concentratedload P at point B. Verify that a loadP which is slightly smaller than thetheoretical load limit PL will causeelastic deformation and that a loadwhich is slightly larger than PL willcause plastic deformation. Alsodetermine the maximum deflectionδ, the reaction force at the left endRA, and the reaction moment atthe right end Mc just prior to thedevelopment of a plastic hinge.

S. H. Crandall, N. C. Dahl,An Introduction to theMechanics of Solids,McGraw-Hill Book Co.,Inc., New York, NY, 1959,pg. 389, ex. 8.9.

vm37

Elongation of a SolidBarSolid 145Solid185Solid45SOLSH190

A tapered aluminum alloy bar ofsquare cross-section and length Lis suspended from a ceiling. Anaxial load F is applied to the freeend of the bar. Determine themaximum axial deflection δ in thebar and the axial stress σy at mid-length (Y = L/2).

C. O. Harris, Introductionto Stress Analysis, TheMacmillan Co., New York,NY, 1959, pg. 237,problem 4.

vm38

Internal PressureLoading of a Thick-Walled CylinderPlane182Solid185Surf153Surf154

A long, thick-walled cylinder issubjected to an internal pressure p(with no end cap load). Determinethe radial stress, σr, and thetangential (hoop) stress, σt, atlocations near the inner and outersurfaces of the cylinder for apressure, pel, just below the yieldstrength of the material, a fullyelastic material condition.



vm39

Bending of a CircularPlate with a CenterHoleShell63Shell181

A circular plate of thickness t with acenter hole is rigidly attached alongthe inner edge and unsupportedalong the outer edge. The plate issubjected to bending by a momentMa applied uniformly along theouter edge. Determine themaximum deflection δ and themaximum slope Φ of the plate. Inaddition, determine the moment Mand stress σx at the top centroidallocations of element 1 (near inneredge) and element 6 (near outeredge).

S. Timoshenko, Strengthof Material, Part II,Elementary Theory andProblems, 3rd Edition, D.Van Nostrand Co., Inc.,New York, NY, 1956, pg.111, eq. E and F.

vm40

Large Deflection andRotation of a BeamPinned at One EndBeam188

A massless beam of length L isinitially at position AB on ahorizontal frictionless table. Point Ais pinned to the table and given alarge rotation Θz through a fullrevolution at speed ωz. Determinethe position of the beam in terms ofδ, and Θ at various angularlocations. Show that the beam hasno axial stress σ at any position.

Any basic mathematicsbook

vm41

Small Deflection of aRigid BeamMATRIX27BEAM188

A very stiff beam of length L,subjected to a lateral load F, isinitially at position AB on ahorizontal table. Point A is pinnedto the table and restrained fromrotation by a relatively weak torsionspring. Determine the final positionof the beam in terms of δx, δy, andΘ. Show that the bending stress inthe beam σbend is negligible.

Any basic Statics andStrength of Materials Book

vm42

Barrel Vault RoofUnder Self WeightShell181Shell281

A cylindrical shell roof of density ρis subjected to a loading of its ownweight. The roof is supported bywalls at each end and is free alongthe sides. Find the x and ydisplacements at point A and thetop and bottom stresses at points Aand B. Express stresses in thecylindrical coordinate system.

R. D. Cook, Concepts andApplications of FiniteElement Analysis, 2ndEdition, John Wiley andSons, Inc., New York, NY,1981, pp. 284-287.


vm45

Natural Frequency ofa Spring-MassSystemCombin14Mass21

An instrument of weight W is set ona rubber mount system having astiffness k. Determine its naturalfrequency of vibration f.

W. T. Thomson, VibrationTheory and Applications,2nd Printing, Prentice-Hall, Inc., EnglewoodCliffs, NJ, 1965, pg. 6, ex.1.2-2.

vm47

Torsional Frequencyof a Suspended DiskCombin14Mass21

A disk of mass m which has a polarmoment of inertia J is suspended atthe end of a slender wire. Thetorsional stiffness of the wire is kθ.Determine the natural frequency fof the disk in torsion.

W. T. Thomson, VibrationTheory and Applications,2nd Printing, Prentice-Hall, Inc., EnglewoodCliffs, NJ, 1965, pg. 10,ex. 1.3-2

vm48

Natural Frequency ofa Motor-GeneratorBEAM188Mass21

A small generator of mass m isdriven off a main engine through asolid steel shaft of diameter d. Ifthe polar moment of inertia of thegenerator rotor is J, determine thenatural frequency f in torsion.Assume that the engine is largecompared to the rotor so that theengine end of the shaft may beassumed to be fixed. Neglect themass of the shaft also.


vm51

Electrostatic ForcesBetween ChargedSpheresSOLID123 SOLID122INFIN111 PLANE121MESH200

Two spheres with radii = 1 m,separated by a distance of 3 m, aresubjected to a surface charge. Findthe resultant electrostatic forcebetween the spheres.

Any General PhysicsTextbook

vm52

AutomobileSuspension SystemVibration BEAM188COMBIN14 MASS21

An automobile suspension systemis simplified to consider only twomajor motions of the system:· up and down linear motion of thebody· pitching angular motion of thebodyIf the body is idealized as a lumpedmass with weight W and radius ofgyration r, determine thecorresponding coupled frequenciesf1 and f2.



vm54

Vibration of a RotatingCantilever BladeSHELL63 SOLSH190SHELL181 SHELL281

A blade is cantilevered from a rigidrotating cylinder. Determine thefundamental frequency of vibrationof the blade, f, when the cylinder isspinning at a rate of Ω.

W. Carnegie, "Vibrationsof Rotating CantileverBlading", JournalMechanical EngineeringScience, Vol. 1 No. 3,1959, pg. 239

vm56

Hyperelastic ThickCylinder UnderInternal PressurePLANE183 SOLID185SOLID186

An infinitely long cylinder is madeof Mooney-Rivlin type material. Aninternal pressure of Pi is applied.Find the radial displacement at theinner radius and the radial stress atradius R = 8.16 in (center of 1stelement).

J. T. Oden, FiniteElements of NonlinearContinua, McGraw-HillBook Co., Inc., New York,NY, 1972, pp. 325-331.

vm57

Torsional Frequenciesof a Drill PipePIPE16 MASS21PIPE288 PIPE289BEAM188 BEAM189

Determine the first two naturalfrequencies f1 and f2 of an oil-welldrill pipe of length l and polarmoment of inertia lp fixed at theupper end and terminating at thelower end to a drill collar withtorsional mass inertia Jo. The drillcollar length is small compared tothe pipe length.

W. T. Thomson, VibrationTheory and Applications,2nd Printing, Prentice-Hall, Inc., EnglewoodCliffs, NJ, 1965, pg. 272,ex. 8.4-5.

vm59Lateral Vibration of anAxially-loaded BarBEAM188

A square cross-sectioned bar oflength l and weight per unit lengthγA is pinned at its ends andsubjected to an axial compressiveforce F. Determine the stress σ andthe axial displacement δ of the barunder these conditions. Determinethe first three natural frequencies fiof lateral vibration of the bar.

S. Timoshenko, D. H.Young, VibrationProblems in Engineering,3rd Edition, D. VanNostrand Co., Inc., NewYork, NY, 1955, pg. 374,article 59.

vm61Longitudinal Vibrationof a Free-free RodBEAM188

Determine the first three naturalfrequencies fi of a free-free rod (arod with both ends free) having alength 800 in.


vm62Vibration of a WedgeSHELL63 SHELL181SHELL281

Determine the fundamentalfrequency of out-of-plane vibration fof a wedge-shaped plate of uniformthickness t, base 2b, and length16in.



vm63

Static Hertz ContactProblem PLANE82PLANE183CONTA178

A sphere of radius r is pressedagainst a rigid flat plane. Determinethe contact radius, a, for a givenload F.

S. Timoshenko, J. N.Goodier, Theory ofElasticity, 3rd Edition,McGraw-Hill Book Co.,Inc., New York, NY, 1970,pg. 409-413, article 140.

vm65

Transient Responseof a Ball Impacting aFlexible SurfaceMASS21 CONTA175

A rigid ball of mass m is droppedthrough a height h onto a flexiblesurface of stiffness k. Determinethe velocity, kinetic energy, anddisplacement y of the ball at impactand the maximum displacement ofthe ball.


vm66

Vibration of a FlatPlateSHELL63SOLSH190SHELL181SHELL281

Determine the fundamental naturalfrequency of lateral vibration f of aflat rectangular plate. The plate isof uniform thickness t, width 2b,and length 16 in.


vm77

Transient Responseto a Constant ForceBEAM188MASS21

A steel beam of length andgeometric properties is supportinga concentrated mass, m. The beamis subjected to a dynamic load F(t)with a rise time tr and a maximumvalue F1. If the weight of the beamis considered negligible, determinethe time of maximum displacementresponse tmax and the maximumdisplacement response ymax.Additionally, determine themaximum bending stress σbend inthe beam.

J. M. Biggs, Introduction toStructural Dynamics,McGraw-Hill Book Co.,Inc., New York, NY, 1964,pg. 50, ex. E.

vm80

Plastic Response to aSuddenly AppliedConstant ForceLINK180MASS21

A mass m supported on a thin rodof area A and length 100in issubjected to the action of asuddenly applied constant forceF1. Determine the maximumdeflection ymax and minimumdeflection ymin of the mass,neglecting the mass of the rod.

J. M. Biggs, Introduction toStructural Dynamics,McGraw-Hill Book Co.,Inc., New York, NY, 1964,pg. 69, article 2.7.


vm81

Transient Responseof a DroppedContainerCOMBIN40MASS21

A mass m is packaged in a rigidbox, and dropped through a heighth. Determine the velocity anddisplacement y of the mass atimpact and the maximumdisplacement of the mass. Assumethat the mass of the box is largecompared to that of the enclosedmass m and that the box remainsin contact with the floor after impact


vm82

Simply SupportedLaminated PlateUnder PressureSOLSH190SOLID186SHELL181SHELL281SOLID185

A simply-supported, square, cross-ply laminated plate is subjected toa uniform pressure po. Thestacking sequence of the plies issymmetric about the middle plane.Determine the center deflection δ(Z-direction) of the plate due to thepressure load.

J. N. Reddy, "ExactSolutions of ModeratelyThick Laminated Shells",ASCE JournalEngineering Mechanics,Vol. 110 No. 5, 1984, pp.794�809.

vm89

Natural Frequenciesof a Two-mass-springSystemCOMBIN14MASS21

Determine the normal modes andnatural frequencies of the systemfor the values of the masses andspring stiffnesses given.


vm90

Harmonic Responseof a Two-Mass-SpringSystemCOMBIN14MASS21

Determine the response amplitude(Xi) and phase angle (Φi) for eachmass (mi) when excited by aharmonic force (F1sin ωt) acting onmass m1.


vm91

Large Rotation of aSwinging PendulumLINK180MASS21

A pendulum consists of a mass msupported by a rod of length 100 inand cross-sectional area A.Determine the motion of thependulum in terms of thedisplacement of the mass from itsinitial position Θo in the x and ydirections, δx and δy, respectively.The pendulum starts with zeroinitial velocity.



vm127

Buckling of a Bar withHinged Ends (LineElements)BEAM188

Determine the critical buckling loadof an axially loaded long slenderbar of length 200in with hingedends. The bar has a square cross-section with width and height set to0.5 inches.


vm131Acceleration of aRotating Crane BoomMASS21

Determine the acceleration at thetip P of a crane boom that has aconstant angular velocity cabrotation (Ω) while being raised witha constant angular velocity (ω).

F. P. Beer, E. R.Johnston, Jr., VectorMechanics for Engineers,Statics and Dynamics, 5thEdition, McGraw-Hill BookCo., Inc., New York, NY,1962, pg. 616, problem15.13.

vm133

Motion of a Rod Dueto Irradiation InducedCreepBEAM188

A rod of length 1 in. and squarecross-sectional area A is held at aconstant stress σo at atemperature To. The rod is alsosubjected to a constant neutronflux Φ. The rod material has anirradiation-induced creep strain rategiven by the relationship dεcr / dt =k1σΦe - (Φt / k2). Determine theamount of creep strain εcraccumulated up to 5 hours.

Any basic calculus book

vm134Plastic Bending of aClamped I-BeamBEAM188

A wide-flanged I-beam of length144in, with clamped ends, isuniformly loaded. Investigate thebehavior of the beam at load w1when yielding just begins at theends, at load w2, when themidpoint begins to yield, and atload w3, when pronounced plasticyielding has occurred.

N. J. Hoff, The Analysis ofStructures, John Wileyand Sons, Inc., New York,NY, 1956, pg. 388, article4.5.

vm136

Large Deflection of aBuckled Bar (theElastica)BEAM188

A slender square cross-sectionalbar of length l, and area A, fixed atthe base and free at the upper end,is loaded with a value larger thanthe critical buckling load. Determinethe displacement (ΔX, ΔY, Θ) ofthe free end and display thedeformed shape of the bar atvarious loadings.

S. Timoshenko, J. M.Gere, Theory of ElasticStability, 2nd Edition,McGraw-Hill Book Co.Inc., New York, NY, 1961,pg. 78, article 2.7.


vm141

DiametralCompression of aDiskPLANE82PLANE183MATRIX50SHELL181SHELL281

Two equal and opposite forces actalong the vertical diameter of adisk. Determine the compressivestress at the center of the disk andon the major horizontal diameter at0.1 in. from the center.

S. Timoshenko, J. N.Goodier, Theory ofElasticity, 2nd Edition,McGraw-Hill Book Co.,Inc., New York, NY, 1951,pg. 107, article 37.

vm143

Fracture MechanicsStress for a Crack in aPlateSOLID95SOLID45PLANE183SOLID186SOLID185

A long plate with a center crack issubjected to an end tensile stressσo. Determine the fracturemechanics stress intensity factorKI.

W. F. Brown, Jr., J. E.Srawley, "Plane StrainCrack Toughness Testingof High Strength MetallicMaterials", ASTMSTP-410, 1966.

vm144

Bending of aComposite BeamSOLID185SOLID186SOLSH190SHELL281

A beam of length l and width w,made up of two layers of differentmaterials, is subjected to a uniformrise in temperature from Tref to Toand a bending moment My at thefree-end. Determine the free-enddisplacement δ (in the Z-direction)and the X-direction stresses at thetop and bottom surfaces of thelayered beam. Ei and αicorrespond to the Young's modulusand thermal coefficient ofexpansion for layer i, respectively.

R. J. Roark, W. C. Young,Formulas for Stress andStrain, McGraw-Hill BookCo., Inc., New York, NY,1975, pg. 112-114, article7.2.

vm145Stretching of anOrthotropic SolidSOLID185

A unit cube of side 1 in, havingorthotropic material properties, issubjected to forces FX and FY.Three orthogonal faces aresupported and the opposite threefaces are free. Determine thetranslational displacements (ΔX,ΔY, and ΔZ) of the free faces.

S. H. Crandall, N. C. Dahl,An Introduction to theMechanics of Solids,McGraw-Hill Book Co.,Inc., New York, NY, 1959,pg. 225.


vm149

Residual Vector inMode-SuperpositionHarmonic AnalysisCOMBIN14MASS21

A mode-superposition harmonicanalysis is performed on a spring-mass model for two cases:Case 1: Extracting all availablemodesCase 2: Extracting one mode andresidual vector (RESVEC)

J.M.Dickens, J.M.Nakagawa, M.J.Wittbrodt,“ A Critique ofMode Acceleration andModal TruncationAugmentation Methods forModal ResponseAnalysis”. Computers &Structures, Vol.62,pp.985-998, 1997.

vm150From

Version14

Acceleration of a Tankof FluidFLUID80

A large rectangular tank is partiallyfilled with an incompressible liquid.The tank has a constantacceleration a to the right.Determine the elevation of theliquid surface relative to the zeroacceleration elevation along the Y-axis. Also determine the slope ofthe free surface and the pressure pin the fluid near the bottom leftcorner of the tank.

K. Brenkert, Jr.,Elementary TheoreticalFluid Mechanics, JohnWiley and Sons, Inc., NewYork, NY, 1960, pg. 50,article 17.

vm153

3-D Non-axisymmetricVibration of aStretched MembraneSHELL181

A circular membrane under auniform tension S is allowed tovibrate freely. The edge of themembrane is simply supported.Determine the natural frequenciesfi,j for the first two modes ofvibration (j = 1, 2 = no. of nodalcircles, including the boundary) forthe first two harmonics (i = 0, 1 =no. of harmonic indices).


vm154

Vibration of a FluidCouplingFLUID38COMBIN14

A long cylinder is immersed in acircular hole. The cylinder isseparated from the containmentsurface by a frictionless,incompressible liquid annulus. Aspring restraint is attached to thecylinder from ground. Determinethe natural frequency f of thesystem based upon thehydrodynamic mass of the liquidannulus.

R. J. Fritz, "The Effect ofLiquids on the DynamicMotions of ImmersedSolids", ASME, J. of Engr.for Industry, Vol. 94, Feb.1972, pp. 167-173.


vm156

Natural Frequency ofa Nonlinear Spring-Mass SystemCOMBIN39MASS21

A mass is supported from a springhaving nonlinear characteristics.The mass is displaced an amount δfrom its equilibrium position andreleased (with no initial velocity).Find the corresponding period ofvibration τ.

S. Timoshenko, D. H.Young, VibrationProblems in Engineering,3rd Edition, D. VanNostrand Co., Inc., NewYork, NY, 1955, pg. 141.

vm171

Permanent MagnetCircuit With an ElasticKeeperPLANE13COMBIN14

A permanent magnet circuitconsisting of a highly-permeablecore and a permanent magnet isused to model a relay switch. Anelastic keeper is modeled with ahighly permeable iron and twosprings. Assuming no flux leakage,determine the equilibriumdisplacements, δ, of the keeperand the operating point (fluxdensity) in the permanent magnet.

F. C. Moon, Magneto-Solid Mechanics, JohnWiley and Sons, Inc., NewYork, NY, 1984, pg. 275.

vm177

Natural Frequency ofa Submerged RingFLUID30SHELL63FLUID29BEAM188SHELL181SHELL281FLUID221

A steel ring is submerged in acompressible fluid (water).Determine the lowest naturalfrequency for x-y plane bendingmodes of the fluid-structuresystem.

E. A. Schroeder, M. S.Marcus, "Finite ElementSolution of Fluid StructureInteraction Problems",Shock and VibrationSymposium, San Diego,CA, 1975.

vm179

Dynamic DoubleRotation of a JointedBeamMPC184MASS21BEAM188

A torque M1 is applied at thepinned end of an aluminum beamto cause a 90° rotation. A secondtorque M2 is then applied at arevolute joint in the beam to createan out-of-plane rotation. The jointhas a rotational stiffness k, inertialmass J, frictional torque Tf, andlocks when a 5° rotation occurs.Structural mass elements withrotational mass are added at thejoint notes. Determine the positionof the beam at the end of eachrotation.

Any basic mechanics text


vm180

Bending of a CurvedBeamPLANE183BEAM188

A curved beam spans a 90° arc.The bottom end is supported whilethe top end is free. For a bendingmoment M applied at the top end,determine the maximum tensilestress σt and the maximumcompressive stress σc in the beam.

S. Timoshenko, J. N.Goodier, Theory ofElasticity, 3rd Edition,McGraw-Hill Book Co.Inc., New York, NY, 1970,pg. 73, article 29.

vm189Stress Relaxation of aChloroprene RubberSOLID185

A uniaxial compression test withintermittent relaxation time isperformed on a block modeled withChloroprene rubber. The block issubjected to true strain rates of έ =

-0.002s-1and

έ = -0.1s-1 with 120s relaxationtime at έ = -0.3 and έ = -0.6,respectively.

Dal, H. et al. "Bergstrom-Boyce model for nonlinearfinite rubberviscoelasticity: theoreticalaspects and algorithmictreatment for the FEmethod”. ComputationalMechanics. 2009, 44:809-823

vm191

Hertz ContactBetween TwoCylindersCONTA175PLANE182SOLID185

Two long cylinders of radii R1 andR2, in frictionless contact with theiraxes parallel to each other arepressed together with a force perunit length, F. Determine the semi-contact length b and the approachdistance d.

N. Chandrasekaran, W. E.Haisler, R. E. Goforth,"Finite Element Analysisof Hertz Contact Problemwith Friction", FiniteElements in Analysis andDesign, Vol. 3, 1987, pp.39-56.

vm195

Toggle MechanismMPC184BEAM188COMBIN14LINK11

Determine the maximum force(Fmax) of a toggle mechanismacting upon a resisting spring.

G. H. Martin, Kinematicsand Dynamics ofMachines, 2nd Edition,McGraw-Hill Book Co.,Inc., New York, NY, 1982,pp. 55-56, fig. 3-22.

vm196

Counter-BalancedLoads on a BlockSOLID45SOLID185MATRIX50

Determine the free-body moments(MX, MY, MZ) about the origin andthe rotational accelerations (ωx,ωy, ωz) at the center of mass of analuminum block due to the forcesFX and FY.

Any basic mechanics text

vm198

Large Strain In-planeTorsion TestPLANE182PLANE183SOLID185

A hollow, thick-walled, long cylindermade of an elastoplastic material isunder an in-plane torsional loadingwhich causes the inner surface ofthe cylinder to undergo a rotation of60°. Find the maximum shearstress (τmax) developed at theinner surface at the end of loading.

J. C. Nagtegaal, J. E.DeJong, "SomeComputational Aspects ofElastic-Plastic StrainAnalysis", Intl J. ofNumerical Methods inEngineering, Vol. 17,1981, pp. 15�41.


vm199

Viscoplastic Analysisof a Body (ShearDeformation)PLANE182PLANE183SOLID185

A cubic shaped body made up of aviscoplastic material obeyingAnand's law undergoes uniaxialshear deformation at a constantrate of 0.01 cm/s. The temperatureof the body is maintained at 400°C.Find the shear load (Fx) required tomaintain the deformation rate of0.01 cm/sec at time equal to 20seconds.

B. Lwo, G. M. Eggert, "AnImplicit Stress UpdateAlgorithm Using a PlasticPredictor", Submitted toComputer Methods inApplied Mechanics andEngineering, January1991.

vm201

Rubber CylinderPressed Between TwoPlatesPLANE182SOLID185TARGE169TARGE170CONTA175MESH200

A long rubber cylinder is pressedbetween two rigid plates using amaximum imposed displacement ofδmax. Determine the force-deflection response.

T. Tussman, K-J Bathe, "AFinite ElementFormulation for NonlinearIncompressible Elasticand Inelastic Analysis",Computers andStructures, Vol. 26 Nos1/2, 1987, pp. 357-409.

vm211

Rubber CylinderPressed Between TwoPlatesPLANE182PLANE183SOLID185CONTA171CONTA172CONTA173CONTA174TARGE169TARGE170

A long rubber cylinder is pressedbetween two rigid plates using amaximum imposed displacement ofδmax. Determine the force-deflection response.

T. Tussman, K-J Bathe, "AFinite ElementFormulation for NonlinearIncompressible Elasticand Inelastic Analysis",Computers andStructures, Vol. 26 Nos1/2, 1987, pp. 357-409.


vm212

DDAM Analysis ofFoundation System(2-DOF System)MASS21COMBIN40BEAM188

A simple equipment-foundationsystem is modeled using a spring-damper element (COMBIN40)representing the foundation, abeam element (BEAM188)representing the equipment, and amass element (MASS21)representing the equipment mass.Shock loading is applied at thefixed base of the foundation systemalong the athwart ship direction.The shock spectrum is based onthe ship type, mounting location,direction of shock, and type ofdesign (elastic or elastic-plastic).DDAM analysis is performed onthis system to determine naturalfrequency, deflection, and shockdesign value.

O’Hara, G.J., Cunniff, P.F., “Interim Design Valuesfor Shock Design ofShipboard Equipment”,NRL Memorandum Report1396, 1963, p. 10.

vm216

Lateral Buckling of aRight Angle FrameBEAM188BEAM189

A 0.6in thick plate that is 30in wideis fashioned into a cantilever rightangle frame, and is subjected to anin-plane fixed end load (Fx). Theframe is driven to buckling mode bya perturbation load (Fz) applied atthe free end, normal to the plane ofthe frame. This perturbation isremoved close to the buckling load.Determine the critical load.

J. C. Simo, L. Vu-Quoc,"Three-DimensionalFinite-Strain Rod Model,Part II", ComputerMethods in AppliedMechanical Engineering,Vol. 58, 1986, pp. 79-116.

vm217

Portal Frame UnderSymmetric LoadingBEAM188BEAM189

A rigid rectangular frame issubjected to a uniform distributedload ω across the span. Determinethe maximum rotation, andmaximum bending moment. Themoment of inertia for the span,Ispan is five times the moment ofinertia for the columns, Icol.

N. J. Hoff, The Analysis ofStructures, John Wileyand Sons, Inc., New York,NY, 1956, pp. 115-119.

vm218

Hyperelastic CircularPlateSHELL181SHELL208SHELL209SHELL281

A flat, circular membrane made ofa rubber material is subjected touniform water pressure. The edgesof the membrane are fixed.Determine the response aspressure is increased to 50 psi.

J. T. Oden, FiniteElements of NonlinearContinua, McGraw-HillBook Co., Inc., New York,NY, 1972, pp. 318-321.


vm219

Frequency Responseof a PrestressedBeam using APDLMATH CommandsBEAM188TRANS126

A beam is in series with anelectromechanical transducer. Witha voltage applied to the beam,determine the prestressed naturalfrequencies of the beam.

R. D. Blevins, Formulasfor Natural Frequency andMode Shape, VanNostrand Reinhold Co.,pg. 144, equation 8-20.

vm221Simulation of ShapeMemory Alloy EffectSOLID185

A block is composed of shapememory alloy material. The block,which has an initial temperature of253.15K, is loaded up to 70 MPA toobtain detwinned martensiticstructure, and then unloaded until itis stress free to obtain a martensiticstructure in which residual strainremains. The temperature is thenincreased to 259.15K to recoverresidual strain and regain theaustenitic structure. The final stressand strain is obtained andcompared against the referencesolution.

A. Souza, et al. "Three-dimensional model forsolids undergoing stress-induced phasetransformation”. Eur. J.Mech. A/Solids. 1998, 17:789-806.

vm222Warping Torsion BarBEAM188BEAM189

A cantilever I-beam is fixed at bothends and a uniform moment, Mx, isapplied along its length

C-N Chen, "The WarpingTorsion Bar Model of theDifferential QuadratureMethod", Computers andStructures, Vol. 66 No.2-3, 1998, pp. 249-257.

vm225

Rectangular Cross-Section Bar withPreloadSOLID185PRETS179SOLID186

A compressive preload is applied toa rectangular cross-section bar.Determine the resulting stress anddisplacement.

Engineering Statics Text

vm232

Stress Intensity Factorfor a Single EdgeCrack with PressureLoad Using UMMMethodSOLID185SOLID186SOLID187

A solid block with width W = 1 m,height H = 5 m, and thickness t =0.1 m is modeled with a singleedge crack of length a = 0.1 m. Thecrack is subjected to a pressureload P and the stress intensityfactor is determined using the UMMmethod (CINT,UMM,ON). Theresults are compared to theanalytical solution given in thereference (point b in Table 6.1, p.130).

Stephens, R.I., Fatemi, A.,Stephens, R.R., Fuchs,H.O., Metal Fatigue inEngineering, 2nd Edition,2006, pg. 130.


vm234Cyclic Loading of aRubber BlockSOLID185

A cube of rubber is subjected to asinusoidal displacement controlledload with a mean value of zero(completely reversed). The loadamplitude is constant within a fullcycle (4 seconds) and increaseswith each successive cycle. For thefirst period A = 0.01 and itincreases by 0.01 each cycle untilthe fourth when A = 0.04. At t = 16seconds the load is removed andthe residual stresses are permittedto relax.

G. A. Holzapfel, "On LargeStrain Viscoelasticity:Continuum Formulationand Finite ElementApplications toElastomeric Structures",International Journal forNumerical Methods inEngineering, Vol. 39,1996, pp. 3903-3926.

vm235

Frequency Responseof a PrestressedBeamBEAM188TRANS126

A beam is in series with anelectromechanical transducer. Witha voltage applied to the beam,determine the prestressed naturalfrequencies of the beam.

R. D. Blevins, Formulasfor Natural Frequency andMode Shape, VanNostrand Reinhold Co.,pg. 144, equation 8-20.

vm236

Hysteresis Calculationof a Beam UnderElectrostatic LoadPLANE223PLANE182CONTA178

A beam of length L = 80 μm at aheight T = 0.5 μm is suspended 0.7μm above a ground plane and isclamped at either end. Using thisbeam, model the hysteresis (pull-inand release behaviors) when it isplaced under electrostatic load.

J. R. Gilbert, G. K.Ananthasuresh, S. D.Senturia, "3D Modeling ofContact Problems andHysteresis in CoupledElectro-Mechanics",MEMS, 1996, pp.127-132.

vm239

Mechanics of theRevolute andUniversal JointsBEAM188MPC184TARGE170

A double universal joint drive shaftdrives a simple slider-crankmechanism. Compare the rotationsat different points in the drive shaftwith the applied rotation. Also,show the linear motion caused bythe slider-crank satisfied theappropriate equation.

J. E. Shigley, J. J. Uicker,Jr., Theory of Machinesand Mechanisms, 2ndEdition, McGraw-Hill, Inc.,1995, p.115.

vm240

Thermal Expansion ofRigid Beams in aComposite BarSOLID185MPC184

A composite bar consists of twobase materials with 25 rigid beamsembedded along its length. Acoefficient of thermal expansion isdefined for only the rigid beams.Compare the stresses resulting inboth solid composite materialswhen a temperature is applied.

J.M. Gere, S.P.Timoshenko, Mechanicsof Materials, 2nd Edition,PWS Publishers, 1984, p.20-21,71


vm241

Static ForceComputation of a 3-DSolenoid ActuatorSOLID231(SOLID232SOLID236SOLID237MESH200

For the given solenoid actuator withan applied total coil current of 5000A-turns, find the magnetic fluxdensity (BZ) of the Pole, themagnetic flux density (BZ) of theArm, and the Magnetic Force in theZ-direction. The center pole andyoke are made of steelcharacterized by the B-H curve

N.Takahashi, T. Nakata,and H. Morishige,“Summary of Results forProblem 20 (3-D StaticForce Problem)”,COMPEL, Vol.14 (1995),pp. 57-75.

vm244

Modal Analysis of aCyclic SymmetricAnnular PlateSOLID185SOLID186SOLID187SHELL181SOLSH190SHELL281

The fundamental natural frequencyof an annular plate is determinedusing a mode-frequency analysis.The lower bound is calculated fromthe natural frequency of theannular plates, which are free onthe inner radius and fixed on theouter. The bounds for the platefrequency are compared to thetheoretical results.

R. D. Blevins, Formulasfor Natural Frequency andMode Shape, New York,NY, VanNostrandReinhold Publishing Inc.,1979, pp. 246-247,286-287.

vm247

Campbell Diagramsand Critical SpeedsUsing SymmetricBearingsBEAM188MASS21COMBIN14

A rotor-bearing system is analyzedto determine the whirl speeds. Thedistributed rotor was modeled as aconfiguration of six elements witheach element composed ofsubelements. Two undampedlinear bearings were located atpositions four and six. Modalanalysis is performed on rotorbearing system with multiple loadsteps to determine the criticalspeeds and Campbell values forthe system.

Nelson andMcVaugh,"The Dynamicsof Rotor-Bearing SystemsUsing Finite Elements",Journal of Engineering forIndustry, May 1976.

vm248

Delamination Analysisof Double CantileverBeamPLANE182INTER202CONTA171PLANE183INTER203CONTA172SOLID185INTER205CONTA173TARGE169TARGE170

A double cantilever beam of lengthl, width w and height h with aninitial crack of length a at the freeend is subjected to a maximumvertical displacement Umax at topand bottom free end nodes.Determine the vertical reaction atpoint P based on the verticaldisplacement for the interfacemodel.

G. Alfano and M. A.CrisfieldFinite ElementInterface Models for theDelamination Analysis ofLaminated Composites:Mechanical andComputational Issues,International Journal forNumerical Methods inEngineering, Vol. 50, pp.1701-1736 (2001).


vm250

Gasket Material UnderUniaxial CompressionLoading - 3-DAnalysisSOLID185SOLID186INTER195INTER194

A thin interface layer of thickness tis defined between two blocks oflength l, width W, and height Hplaced on top of each other. Theblocks are constrained on the left,bottom, and back faces and loadedwith pressure P on the top face.Determine the pressure-closureresponse for gasket elements.

Any Nonlinear MaterialVerification Text

vm251

Shape Memory AlloyUnder UniaxialTension LoadPLANE182PLANE183SOLID185

A square block of length, heightand width L is constrained in the X-direction on the left face,constrained in the Y-direction rearon the bottom face and constrainedin the Z-direction on the rear face(3-D case only). It is uniaxiallyloaded with tensile stress of s andunloaded on the top face.Determine the stress-strainresponse for a Ni-Ti alloy.

Ferdinando Auricchio,Robert L. Taylor, andJacob Lubliner, Shape-memory alloys:macromodelling andnumerical simulations ofthe superelastic behavior,Comput. Methods Appl.Mech. Engrg., Vol. 146,pp. 281-312 (1997).

vm253

Gurson HydrostaticTension Benchmark -3-D AnalysisSOLID185SOLID186

The model is a three dimensionalbin with all sides equal to unity. Anapplied displacement of 0.15” isapplied at the nodes correspondingto x = 1, y =1, and z =1. To preventrigid body motion, the model isconstrained in the x direction at x =0, y-direction at y = 0, and z-direction at z = 0.

N. Aravas, "On theNumerical Integration of aClass of PressureDependent PlasticityModels", InternationalJournal for NumericalMethods in Engineering,Vol. 24, pp. 1395-1416,Section 5.2, Figure 7(1987).

vm254

Campbell Diagramsand Critical SpeedsUsing SymmetricOrthotropic BearingsPIPE16PIPE288MASS21COMBI214

A rotor-bearing system is analyzedto determine the forward andbackward whirl speeds. Thedistributed rotor was modeled as aconfiguration of six elements witheach element composed ofsubelements. Two symmetricorthotropic bearings were locatedat positions four and six. Modalanalysis is performed on rotorbearing system with multiple loadsteps to determine the whirl speedsand Campbell values for thesystem.

Nelson, H.D., McVaugh,J.M., “The Dynamics ofRotor-Bearing SystemsUsing Finite Elements”,Journal of Engineering forIndustry, Vol 98, pp.593-600, 1976


vm256

Fracture MechanicsStress for a Crack in aPlate using CINTCommandPLANE183SOLID185SOLID186

A long plate with a center crack issubjected to an end tensile stressσ. Symmetry boundary conditionsare considered and the fracturemechanics stress intensity factor KIis determined using CINTcommand.

W.F.Brown, Jr.,J.E.Srawley, Plane straincrack toughness testing ofhigh strength metallicmaterials, ASTMSTP-410, (1966).

vm257

Transient Analysis ofa Swing with TwoRigid Links and BeamBEAM188MPC184TARGE170

The swing consists of a longaluminum beam of rectangularcross-section (width = 1mm, depth= 5 mm) and a mid-span mass(mass = 0.5 kg). The mass is rigidlyconnected to the beam at its mid-span position. The beam issuspended at each end by two rigidlinks, and is initially at rest. Therigid links impose a kinematicconstraint corresponding to fixeddistance between points O1 and A,and O2 and E of 0.36 and 0.72,respectively. The points B and Dindicate the quarter and threequarter span points of the beam,respectively. The loading of thesystem consists of a triangularpulse in the direction applied at themid-span mass. This pulse starts attime t = 0 s, reaches a peak valueof 2N at t =0.128 s and goes backto zero at t = 0.256 s.

O.A. Bauchau, G.Damilano, and N.J.Theron NumericalIntegration of Non-LinearElastic Multi-BodySystems, InternationalJournal for NumericalMethods in Engineering,Vol. 38, 2727-2751(1995).


vm259

Missing Mass withRigid ResponsesEffects in SpectrumAnalysis for BM3Piping ModelPIPE16PIPE18COMBIN14

The BM3 piping model is meshedwith PIPE16 and PIPE18 elements.The model is supported by elasticspring-damper elements(COMBIN14). Lumped mass matrixformulation is used in the modalanalysis. Single point responsespectrum analysis is thenperformed with an accelerationinput spectra defined by 75 points(FREQ and SV). The first 14modes are included in thespectrum analysis. The model isexcited in X direction and themodal responses are combinedusing SRSS mode combinationmethod with displacement solutionoutput. The analysis is performedfor three cases:With missing mass effect(ZPA=0.54g).With missing mass (ZPA=0.54g)and rigid responses effect (LindleyMethod).With missing mass (ZPA=0.54g)and rigid responses effect (GuptaMethod, F1=2.8Hz and F2=6.0Hz).

R. Morante, Y.Wang,Reevaluation ofregulatory guidance onmodal responsecombination methods forseismic responsespectrum analysis(NUREG/CR-6645),Brookhaven NationalLaboratory, Dec 1999.

vm261

Rotating Beam withInternal ViscousDampingBEAM188COMBI214

A beam with internal viscousdamping is simply supported bymeans of two isotropic undampedbearings. Modal analysis isperformed with multiple load stepsto determine the critical speeds andlogarithmic decrement of thesystem.

E.S. Zorzi, H.D. Nelson,“Finite element simulationof rotor-bearing systemswith internal damping”,ASME Journal ofEngineering for Power,Vol. 99, 1976, pg. 71-76.


vm265

Elastic Rod Impactinga Rigid WallSHELL181CONTA177TARGE170

A linear elastic prismatic rod ismoving with an initial velocity and isimpacting a rigid wall. The shockwave created from impact travelsas a compression wave through therod. During this time, the rodremains in contact with the rigidwall. The compression wave is thenreflected as a dilatational waveupon reaching the free end of therod and travels back to the contactsurface. The rod gets separatedfrom the rigid wall once thedilatational wave reaches thecontact surface. The time at impactand at separation is determinedfrom the analysis along withcorresponding displacements,velocities and normal contactforces at the contact surface andcompared to the solutions given inthe reference. The time historyplots are also compared to thereference plots.

N.J.Carpenter, R.L. Taylorand M.G. Katona,"Lagrange Constraints ForTransient Finite ElementSurface Contact",International Journal forNumerical Methods inEngineering, vol.32, 1991.Pg. 103-128.

vm266

3-D Crossing Beamsin Contact withFrictionBEAM188CONTA176TARGE170

Two orthogonal beams with similarcross section and with an initial out-of-plane displacement are broughtinto contact by undergoing largedisplacements in 3-D space.Normal and frictional contact forcesare calculated at 0.5, 0.66, 0.83,and 1 second, and then comparedagainst reference values.

G. Zavarise and P.Wriggers, “Contact withfriction between beams in3-D space", InternationalJournal for NumericalMethods in Engineering,2000, vol.49, pp.977-1006.

vm272

2-D and 3-D FrictionalHertz ContactPLANE182CONTA171TARGE169SURF153SOLID185CONTA173TARGE170SURF154

Two parallel linear elastic halfcylinders of radius R are pressedby a small distributed pressure p. Atangential pressure, q, is thenapplied to cause friction at thecontact interface. The bottom of thelower cylinder is fixed in alldirections. Determine the contactpressure and friction results acrossthe contact interface.

Two Dimensional MortarContact Methods for LargeDeformation FrictionalSliding, InternationalJournal for NumericalMethods in EngineeringVol.62, pp 1183-1225.


vm273

Shape Memory AlloyWith Thermal EffectUnder UniaxialLoadingSOLID185

A block is made of shape memoryalloy material. One cycle of uniaxialdisplacement loading is applied invertical direction. The wholeprocess includes tension, unload,compression, and unload. Thewhole loading history repeats withbody temperature 285.15K and253.15K, respectively. The stresshistory is obtained and comparedagainst the reference solution.

Auricchio, F. et al."Improvements andalgorithmeicalconsiderations on a recentthree-dimensional modeldescrbing stress-inducedsolid phasetransformation”.International Journal forNumerical Methods inEngineering, 55.1225-1284. 2002

vm274

Stabilizing SquealDampingSOLID185CONTA173TARGE170COMBIN14MASS21

A rigid block (Young’s modulus E,Poisson ratio ν, density ρ, length ofedge a, area A) is elasticallysupported by a spring-damperelement and guided by a rail with avelocity υ. The whole assembly issliding on the rough ex-ey-plane(coefficient of friction μ, normalpressure p). Linear perturbationmodal analysis is performed usingthe DAMP eigensolver to determinethe damped frequency and modaldamping ratio, which is thencompared against analyticalresults.

Any Dynamics Textbook

vm277

Hall Plate in a UniformMagnetic FieldSOLID236CIRCU124MESH200

A series of static electromagneticanalyses is performed on a platewith length 2a, height 2b, andthickness c to determine the Hallvoltage produced by a uniformmagnetic field B perpendicular tothe plate surfaces

Meijer, G. Smart SensorSystems. John Wiley &Sons, Ltd. 2008, p. 252.

vm279

T-Stress for a Crack ina Plate Using theCINT CommandPLANE183SOLID185SOLID186

A rectangular plate with a centercrack is subjected to an end tensilestress σ Symmetry boundaryconditions are considered and T-Stress is determined using theCINT command.

Fett, T., Stress IntensityFactors, T-Stresses,Weight Functions, Instituteof Ceramics in MechanicalEngineering, University ofKarlsruhe, 2008, pp.151-152


vm281

Effect of StressStiffening and SpinSoftening on aRotating PlateSHELL181SOLID185

A steel plate, clamped on one edgeand free on the other edges, isrotating about an offset axis. Thefirst bending frequency isdetermined as a function of therotational velocity. The analysis isdone for two cases: rotation aboutthe Z-axis and about the X-axis.

Lawrence, C., Aiello, R.A., Ernst, M. A., McGee,O. G., “A NASTRANPrimer for the Analysis ofRotating Flexible Blades”,NASA TechnicalMemorandum 89861,1987, p. 14

vm282

Mode-SuperpositionResponse Analysis ofa Piston-Fluid SystemFLUID30MASS21COMBIN14CONTA174TARGE170

A simple piston-fluid system ismodeled using a spring damperelement (COMBIN14) for thepiston, fluid elements (FLUID30) forthe fluid column, and a masselement (MASS21) for the mass ofthe piston,. The contact betweenthe piston and the fluid column isestablished using the surface-to-surface contact element(CONTA174).

Axisa, F., Antunes, J.,Modelling MechanicalSystems: Fluid-StructureInteraction, 2006, p. 486

vm284

Acceleration Solutionin ResponseSpectrum AnalysisUsing Missing MassMethodBEAM188MASS21

Single point acceleration responsespectrum analysis is performed ona vertical tank model that is 200inches tall and 35 inches indiameter by exciting the structure inthe global Z-direction. The tank issupported by a braced leg supportand is filled with a fluid with aspecific gravity of 1.57. Thespectrum analysis is performedwith the first four modes andmissing mass to account for thehigher modes. The modes arecombined using the SRSS modecombination method and theabsolute acceleration at differentelevation points of the structure isobtained by summing the SRSSmodal response with the absolutemissing mass response. Theaccelerations are comparedagainst the reference values shownin Column 9 of Table 1 in thereference document.

Biswas, J.K, Duff, C.G.,“Response SpectrumMethod with ResidualTerms”, ASMEPublications, April 1978.


vm286

Wear of a BlockUnder UniformCompressionPLANE182CONTA171TARGE169SOLID185CONTA173TARGE170

Wear analysis is performed on ablock with length L in contact with arigid plate using a frictionlessstandard contact pair. In the firstload step, a displacement load isapplied on one face of the block tocompress the block onto the rigidplate. In the second load step,displacement is applied on the rigidplate to make it slide, resulting inwear of the block. The contactpressure and amount of wear onthe block is computed andcompared against the analyticalsolution.

Any standard engineeringtextbook.

vm292

Interference FitBetween TwoCylindersSOLID185CONTA173TARGE170

Two cylinders connected by meansof standard frictionless contact aremodeled with an interference fitbetween them. Static analysis isperformed to predict the contactpressure between the twocylinders.

Budynas, R.G., Nisbett,J.K., Shigley's MechanicalEngineering Design, 9thedition, pg. 116, 2011.


Table 2: SAP2000 Summary of Group 1 (FRAME) Verification Problems

ProblemNo.

ProblemTitle

SAP2000Frame ElementFeatures Tested

Method of IndependentVerification

1-001 General Loading

· Calculation and applicationof self load· Projected, uniformlydistributed load· Application of uniformlydistributed load in globalcoordinates· Uniformly distributed loadin frame object localcoordinates· Trapezoidal and triangulardistributed load on frames· Joint moments and forces· Static analysis of framesunder all of these loadingtypes

Hand calculation using the unitload method described on page244 in Cook and Young 1985.

1-002 Temperature Loading

· The specification of jointpatterns· The application oftemperature increase· Transverse temperaturegradient· The calculation ofdisplacements in freeexpansion· Reaction forces inrestrained case caused bytemperature loads

Hand calculation using standardthermal expansion formulas andusing Table 3 items 6a and 6con page 107 in Roark andYoung 1975.

1-003Distributed andConcentratedMoments

The application of:· Distributed moments(uniform, trapezoidal,triangular) to frame objects· Concentrated moments toframe objects

Hand calculation using equation8.1.3 on page 284 in Cook andYoung 1985.

1-004 Rotated Local AxesFrame local axes rotatedfrom global axes.Use of AISC sections.

Hand calculation using thebeam deflection formulas inTable 3 item 1a and Table 3item 2a on pages 96 and 98,respectively, in Table 3 in Roarkand Young 1975.


1-005 Displacement Loading

· Settlement of support inframe structures· Rotation of support inframe structures· Settlement of support withlinear (translational) spring· Rotation of support withrotational spring· Skewed supports· Skewed support settlement


1-006

Non-PrismaticSections andAutomatic FrameSubdivision

· Structural behavior of anon-prismatic frame section· Self-weight calculations· Linear variation of sectionarea· Linear, parabolic and cubicvariation of moment of inertia· Linear variation of sectiontorsional constant· Automatic framesubdivision


1-007 End Releases

The end releases in a frameelement, includingAxial releaseShear releaseBending releaseThe related frame staticanalysis

Hand calculation using basicstatics.

1-008 Partial Fixity EndReleases

The partial fixity endreleases in a frame element,includingShear partial fixityBending partial fixityThe application of gravityload to a frame object


1-009 Prestress Applied ToFrame Objects

· Prestress tendon withparabolic tendon profile anddifferent eccentricities at thetwo ends· Prestress tendon modeledusing loads· Prestress tendon modeledas elements· Prestress losses

Hand calculation using basicprinciples and the unit loadmethod described on page 244in Cook and Young 1985.


1-010 End Offsets

The use of end offsets inframes, includingNon-rigid offsetsPartially rigid offsetsFully rigid offsetsThe effect of end offsets onthe frame static analysisresults


1-011 Insertion Point Cardinal pointJoint offsets Hand calculation using statics.

1-012No Tension and NoCompression FrameObjects

Tension and compressionlimits for frame objectsEnd releases

Hand calculation using the unitload method described on page244 in Cook and Young 1985together with statics.

1-013Simply SupportedBeam on ElasticFoundation

Frame line springassignmentsStatic analysis of beam onelastic foundationAutomatic frame subdivision

Hand calculated using formulaspresented in Problem 3 on page23 of Timoshenko 1956.

1-014 Eigenvalue Problem

Eigenvalue analysis of aframe with unequal momentof inertia values (I22 ≠ I33)for bending modesAutomatic frame subdivision

Hand calculation based onformulas presented on page313 of Clough and Penzien1975.

1-015 Steady StateHarmonic Loads

Steady state analysis offrame systemsTime history analysis offrame systems with periodicloadingLine mass assignment toframe objectsAutomatic frame subdivision

Comparison with illustrativeexample 20.2 on page 434 ofPaz 1985.

1-016Tension StiffeningUsing P-DeltaAnalysis

P-Delta force assignment toframe objectsNonlinear static analysisusing the P-Delta optionAutomatic frame subdivision

Hand calculation using equation23 on page 28 and equations43 and 45 on page 43 ofTimoshenko 1956.

1-017 Vibration of a StringUnder Tension

Static nonlinear analysisusing the P-Delta option toprovide tension stiffeningModal analysis of frame foreigenvalues

Hand calculation using vibrationtheory presented on pages 506through 510 of Kreyszig 1983.


1-018Bending, Shear andAxial Deformations ina Rigid Frame

Calculation of bending,shear and axial deformationsin a rigid frameFrame property modificationfactors


1-019 Buckling of a RigidFrame

Buckling analysis of a rigidframeAutomatic frame subdivision

Hand calculation using formulaspresented in Article 2.4 onpages 62 through 66 ofTimoshenko and Gere 1961.

1-020

Response SpectrumAnalysis of a Two-Dimensional RigidFrame

Modal analysis of frame foreigenvalues and timeperiodsResponse spectrum analysisJoint masses

Comparison with example 13.11on page 521 of Chopra 1995.

1-021 Bathe and WilsonEigenvalue Problem

Modal analysis foreigenvaluesLine mass assignment toframe objects

Comparison with resultspublished in Bathe and Wilson1972 and comparison withresults from another computerprogram published in Peterson1981.

1-022

Two-DimensionalMoment Frame withStatic and DynamicLoads

· Diaphragm constraint· Joint force assignments· Joint mass assignments· Modal analysis foreigenvalues· Response spectrumanalysis· Modal time history analysisfor base excitation· Direct integration timehistory analysis for baseexcitation

Comparison with results fromanother computer programpublished byEngineering/Analysis andComputers/ StructuresInternational.

1-023 ASMEEigenvalue Problem

Three-dimensional frameanalysisModal analysis usingeigenvectorsJoint mass assignments

Comparison with results fromanother computer programpublished in Peterson 1981 andin DeSalvo and Swanson 1977.

1-024

Response SpectrumAnalysis of a Three-Dimensional MomentFrame

· Three-dimensional frameanalysis· Modal analysis usingeigenvectors· Rigid diaphragm constraint· Joint mass assignments· Response spectrumanalysis

Comparison with results fromanother computer programpublished in Peterson 1981.


1-025

Response SpectrumAnalysis of a Three-Dimensional BracedFrame

· Three-dimensional frameanalysis· Modal analysis usingeigenvectors· Rigid diaphragm constraint· Joint mass assignments· Response spectrumanalysis

Comparison with results fromanother computer programpublished inPeterson 1981.

1-026 Moment and ShearHinges

Static nonlinear analysis of aframe structure usingmoment and shear hinges

Hand calculation using the unitload method described on page244 in Cook and Young 1985together with basic deflectionformulas and superposition.

1-027 ConstructionSequence Loading

Nonlinear static analysisusing the constructionsequence loading optionFrame end releases

Hand calculation using the unitload method described on page244 in Cook and Young 1985together with basic deflectionformulas.

1-028 Large AxialDisplacements

Static nonlinear analysis offrame structure with largeaxial displacements usingthe SAP2000 P-Delta pluslarge displacements optionFrame end releases

Hand calculation using basicstatics.

1-029 Large BendingDisplacements

Static nonlinear analysis offrame structure with largebending displacements usingthe SAP2000 P-Delta pluslarge displacements option

Hand calculation and Equation4 in Article 7.1 of Chapter 7 onpage 91 of Roark and Young1975.

1-030 Moving LoadsMoving load caseMulti-step static load casefor vehicles

Comparison with resultspublished in Appendix A ofAASHTO 1990 and handcalculation.


Table 3: SAP2000 Summary of Group 2 (SHELL) Verification Problems

ProblemNo. Problem Title SAP2000 Shell Element Features Tested

Method ofIndependentVerification

2-001

Patch TestWithPrescribedDisplacements

· Membrane analysis using shell elements· Plate bending analysis using shell elements· Thin-plate option· Thick-plate option· Joint displacement loading

Hand calculationbased theory inTimoshenko andGoodier 1951 andTimoshenko andWoinowsky-Krieger1959. Results alsopublished inMacNeal andHarder 1985.

2-002Straight Beamwith StaticLoads

· Membrane analysis using shell elements· Plate bending analysis using shell elements· Effect of shell element aspect ratio· Effect of geometrical distortion of shell element fromrectangular· Joint force loading

Hand calculationusing the unit loadmethod describedon page 244 inCook and Young1985 and usingformulas fromRoark and Young1975. Results alsopublished inMacNeal andHarder 1985.

2-003Curved Beamwith StaticLoads

· Membrane analysis using shell elements· Plate bending analysis using shell elements· Joint force loading

Hand calculationusing the unit loadmethod describedon page 244 inCook and Young1985.Results alsopublished inMacNeal andHarder 1985.


2-004Twisted Beamwith StaticLoads

· Membrane analysis using shell elements· Plate bending analysis using shell elements· Joint force loading


2-005RectangularPlate withStatic Loads

· Plate bending analysis using shell elements· Uniform load applied to shell elements· Joint force loading

Hand calculationbased theory inTimoshenko andWoinowsky-Krieger1959. Results alsopublished inMacNeal andHarder 1985.

2-006Scordelis -LoRoof withStatic Loads

· Three-dimensional analysis using shell elements· Self-weight applied to shell elements· Gravity load applied to shell elements· Uniform load applied to shell elements

Some resultspublished inMacNeal andHarder 1985.Other resultsscaled from plottedresults inZienkiewicz1977that werecalculated usingtheory presented inScordelis and Lo1964.

2-007

HemisphericalShell Structurewith StaticLoads

· Three-dimensional analysis using shell elements· Joint local axes· Joint force loads

Result published inM a c N e a l a n dHarder 1985.

2-008

CantileverPlateEigenvalueProblem

· Eigenvalue analysis using shell elements· Area object mass assignment· Area object automatic mesh· Area object stiffness modifiers

Hand calculationusing Table 7.7 onpage 7-30 of Harrisand Crede 1976.

2-009Plate onElasticFoundation

· Plate bending analysis using shell elements· Area object spring assignment· Joint force loads

Hand calculationusing equation 185on page 275 ofTimoshenko andWoinowsky-Krieger1959.

2-010Cylinder withInternalPressure

· Three-dimensional analysis using shell elements· Surface pressure load applied to shell elements· Joint local axes

Hand calculationusing item 1b inTable 29 on page448 of Roark andYoung 1975.


2-011

ASMECooling TowerProblem withStatic WindPressure

· Three-dimensional analysis using shell elements· Joint patterns· Shell element surface pressure load using joint pattern

Results scaledfrom plottedresults inZienkiewicz1977that werecalculated usingtheory presented inAlbasiny andMartin 1967.

2-012

Plate Bendingwhen ShearDeformationsAre Significant

· Plate bending analysis of shell elements when sheardeformations are significant· Area object stiffness modifiers· Frame distributed loads

Results publishedin example shownon page 376 ofRoark and Young1975.

2-013

TemperatureLoad that IsConstantThrough ShellThickness

· Temperature loading for shell elements

Hand calculationusing equation1.3.4 on page 9 ofCook and Young1985.

2-014

TemperatureGradientThrough ShellThickness

· Temperature gradient loading for shell elements· Area object local axes· Joint local axes

Hand calculationusing formulaspresented in item8e of Table 24 onpage 361 of Roarkand Young 1975.

2-015 OrthotropicPlate

· Plate bending analysis of shells· Orthotropic material properties· Area object stiffness modifiers

Hand calculatedusing theorypresented inChapter 6 ofUgural 1981.

2-016 Out-of-PlaneBuckling

· Buckling analysis of shells· Automatic area meshing (N x N) with added restraints· Joint springs· Frame property modifiers· Frame distributed load· Frame automatic subdivide at intermediate joints

Hand calculatedusing theorypresented inTimoshenko andGere 1961.

2-017 In-PlaneBuckling

· Buckling analysis of shells· Joint force loads· Active degrees of freedom

Hand calculatedusing equation 2-4on page 48 ofTimoshenko andGere 1961.

2-018 Large AxialDisplacements

· Static nonlinear analysis of shell structure with large axialdisplacements using the SAP2000 P-Delta plus largedisplacements option· Joint constraints

Hand calculationusing basic statics.

2-019 Large BendingDisplacements

· Static nonlinear analysis of shell structure with largebending displacements using the SAP2000 P-Delta pluslarge displacements option· Automatic area meshing

Hand calculationand Equation 4 inArticle 7.1 ofChapter 7 on page91 of Roark andYoung 1975.


2-020PrestressApplied toArea Objects

· Prestress tendon with parabolic tendon profile and differenteccentricities at the two ends· Prestress tendon modeled using loads and applied to areaobjects· Prestress tendon modeled as elements and applied to areaobjects· Prestress losses

Hand calculationusing basicprinciples and theunit load methoddescribed on page244 in Cook andYoung 1985.


Table 4: SAP2000 Summary of Group 3 (PLANE) Verification Problems

ProblemNo. Problem Title SAP2000 Plane Element Features Tested


3-001


· Membrane analysis using plane stress elements· Incompatible bending mode option for plane elements· Joint displacement loading

Hand calculationbased theory inTimoshenko andGoodier 1951.Results alsopublished inMacNeal andHarder 1985.


· Membrane analysis using plane elements· Effect of plane element aspect ratio· Effect of geometrical distortion of plane element from rectangular· Joint force loading

Hand calculationusing the unitload methoddescribed onpage 244 inCook and Young1985 and usingformulas fromRoark andYoung 1975.Results alsopublished inMacNeal andHarder 1985.


· Membrane analysis using plane stress elements· Joint force loading

Hand calculationusing the unitload methoddescribed onPage 244 inCook and Young1985.Results alsopublished inMacNeal andHarder 1985.


3-004 Thick-WalledCylinder

· Analysis using plane stress elements· Analysis using plane strain elements· Plane surface pressure load

Hand calculationbased on theoryin Timoshenko1956 and basedon formulas inRoark andYoung 1975.Results alsopublished inMacNeal andHarder 1985.

3-005 Pore Pressure · Pore pressure loading for planes· Joint pattern

Hand calculationusing basicprinciples.

Table 5: SAP2000 Summary of Group 4 (ASOLID) Verification Problems

ProblemNo. Problem Title SAP2000 ASOLID Element

FeaturesTestedMethod of IndependentVerification

4-001Soil SupportingUniformly LoadedCircular Footing

Analysis using asolidelements

Asolid surface pressure load

Incompatible bending modesfor asolid objects

Hand calculation based on datapresented in Poulos and Davis1974.



Asolid surface pressure load

Hand calculation based ontheory in Timoshenko 1956.Results also published inMacNeal and Harder 1985.

4-003 Rotating AnnularDisk


Asolid rotation load

Hand calculation based onequations presented in Item 8on page 567 of Roark andYoung 1975.

4-004 Pore Pressure

Pore pressure loading forasolids

Joint pattern

Hand calculation using basicprinciples.


Table 6: SAP2000 Summary of Group 5 (SOLID) Verification Problems

ProblemNo.

ProblemTitle SAP2000 Solid Element Features Tested


5-001


· Patch test using solid elements· Joint displacement loading

Results alsopublished inMacNeal andHarder 1985.


· Solid object bending with and without the incompatible modesoption· Effect of solid object aspect ratio· Effect of geometrical distortion of solid object from a cube· Joint force loading



· Solid object bending with the incompatible bending modesoption· Joint force loading


5-004Twisted Beamwith StaticLoads

· Solid object bending and twist with the incompatible bendingmodes option· Joint force loading



5-005RectangularPlate withStatic Loads

· Plate bending analysis using solid elements· Surface pressure load applied to solid objects· Joint force loading

Hand calculationbased theory inTimoshenko andWoinowsky-Krieger1959. Results alsopublished inMacNeal andHarder 1985.

5-006Scordelis -LoRoof withStatic Loads

· Three-dimensional analysis using solid objects· Self-weight applied to solid objects· Gravity load applied to shell objects

Some resultspublished inMacNeal andHarder 1985.Other resultsscaled from plottedresults inZienkiewicz1977that werecalculated usingtheory presented inScordelis and Lo1964.

5-007

HemisphericalDomeStructure withStatic Loads

· Three-dimensional analysis using solid elements· Joint force loads

Results publishedin MacNeal andHarder 1985.


· Analysis using solid elements· Solid surface pressure load· Joint local axes

Hand calculationbased on theory inTimoshenko 1956.Results alsopublished inMacNeal andHarder 1985.

5-009PrestressApplied toSolid Objects

· Prestress tendon with parabolic tendon profile and differenteccentricities at the two ends· Prestress tendon modeled using loads and applied to solidobjects· Prestress tendon modeled as elements and applied to solidobjects· Prestress losses

Hand calculationusing basicprinciples and theunit load methoddescribed on page244 in Cook andYoung 1985.

5-010 Buckling· Buckling analysis of solids· Joint force loads· Active degrees of freedom

Hand calculationusing equation 2-4on page 48 ofTimoshenko andGere 1961.

5-011 TemperatureLoad · Temperature loading for solid elements

Hand calculationusing equation1.3.4 on page 9 ofCook and Young1985.


5-012Plate onElasticFoundation

· Plate bending analysis using solid elements· Solid object surface spring assignment· Solid object automatic mesh· Joint force loads

Hand calculationusing equation 185on page 275 ofTimoshenko andWoinowsky-Krieger1959.

5-013 Pore Pressure· Pore pressure loading for solids· Solid local axis assignments· Joint pattern

Hand calculationusing basicprinciples.


Table 7: SAP2000 Summary of Group 6 (LINK) Verification Problems

ProblemNo. Problem Title SAP2000 Link Element

Features TestedMethod of IndependentVerification

6-001 Linear Link with RampLoading

· Linear links· Modal load case foreigenvectors· Modal time history load case· Direct integration timehistory load case· Ramp loading

Hand calculation usingtheory presented in section4.5 on Pages 126 through129 of Chopra 1995.

6-002 Multi-linear Elastic Link· Multi-linear links· Displacement-controllednonlinear static analysis

Comparison with definedlink force- deformationcharacteristics.

6-003 Gap Element

· Gap element links· Force-controlled nonlinearstatic analysis· Nonlinear modal time historyanalysis· Nonlinear direct time historyanalysis· Frame point loads· Joint force loads· Joint mass assignments· Ramp loading for timehistories

Hand calculation using theunit load method describedon page 244 in Cook andYoung 1985.

6-004 Hook Element

· Hook element links· Force-controlled nonlinearstatic analysis· Frame temperature loads

Hand calculation usingstandard thermal expansionformulas.

6-005 Damper Element UnderHarmonic Loading

· Damper element links· Linear link elements· Nonlinear modal time historyanalysis· Nonlinear direct integrationtime history analysis· Joint force loads

Hand calculation usingequation 3.2.6 on page 7 inChopra 1995.


6-006 SUNY Buffalo Damper withLinear Velocity Exponent

· Damper links with linearvelocity exponents· Frame end length offsets· Joint mass assignments· Modal analysis for Ritzvectors· Linear modal time historyanalysis· Nonlinear modal time historyanalysis· Linear direct integration timehistory analysis· Nonlinear direct integrationtime history analysis· Generalized displacements

Comparison withexperimental results fromshake table tests publishedin Section 5, pages 61through 73, of Scheller andConstantinou 1999.

6-007SUNY Buffalo Damper withNonlinear VelocityExponent

· Damper links with nonlinearvelocity exponents· Frame end length offsets· Joint mass assignments· Modal analysis for Ritzvectors· Nonlinear modal time historyanalysis· Nonlinear direct integrationtime history analysis· Generalized displacements


6-008 Plastic Wen Link

· Plastic Wen links· Displacement-controllednonlinear static analysis· Link local axis assignments· Link gravity load


6-009 Plastic Kinematic Link

· Plastic kinematic links· Displacement-controllednonlinear static analysis· Link gravity load


6-010SUNY Buffalo Eight-StoryBuilding with RubberIsolators

· Rubber isolator links· Linear links· Zero-length, two-joint linkelements· Diaphragm constraints· Modal analysis for Ritzvectors· Nonlinear modal time historyanalysis· Nonlinear direct integrationtime history analysis· Generalized displacements

Comparison with resultsfrom the computer program3D-BASIS-ME (seeTsopelas, Constantinou andReinhorn 1994) publishedin Section 2, pages 5through 23, of Scheller andConstantinou 1999.


6-011SUNY Buffalo Seven-StoryBuilding with FrictionPendulum Isolators

· Friction pendulum linkelements· Damper link elements· Zero-length, two-joint linkelements· Diaphragm constraints· Frame end length offsets· Modal analysis for Ritzvectors· Nonlinear modal time historyanalysis· Nonlinear direct integrationtime history analysis· Joint masses


6-012 Frequency-DependentLinks

· Frequency-dependent links· Steady state analysis

Hand calculation usingformulas and theorypresented in section 3.2 onpages 68 through 69 ofChopra 1995.


Table 8: SASSI2010 Verification Problem No. 1 Analysis Cases

SASSICaseNo.

ElementType

Verified

SASSI ModelDescription

Method ofForming

ImpedanceExcitation

1

(a) 3D Brick

Determine horizontal androcking impedance of arigid massless circularfoundation.

Direct (FlexibleVolume)

Horizontal androcking harmonicforce excitation.

(b) 3D Brick,3D Beam

Determine SSI responseof a surface foundedpressurized water reactor(PWR) containmentbuilding.

Direct (FlexibleVolume)

Horizontal groundmotion excitationprescribed in the formof verticallypropagating SVwave.



SASSICaseNo.

ElementTypeVerified


Method ofFormingImpedance

Excitation

1

(a) 3D Brick

Scattering responseof embedded rigidcylinder, H=0.5,uniform soil profile.

· Direct· ExtendedSubtraction· Subtraction

Horizontal ground motionexcitation prescribed in theform of horizontallypropagating SH wave.

(b) Same asCase 1(a) Same as Case 1(a).

Horizontal ground motionexcitation prescribed in theform of vertically propagatingSV wave.

2

(a) 3D Brick






3

(a) 3D Brick






4 - 3D Brick

Scattering responseof embedded rigidcylinder, H=1.0,inverted soil profile.



5 - 3D Brick

Scattering responseof embedded rigidcylinder, H=2.0,inverted soil profile.



6 - 3D Brick

Scattering responseof embedded rigidcylinder, H=1.0,increasing soil profile.



7 - 3D Brick

Scattering responseof embedded rigidcylinder, H=2.0,increasing soil profile.





SASSICaseNo.

Element TypeVerified


Method ofForming

ImpedanceExcitation

13D Brick, 3D

Plate/Shell, 3DBeam

SSI Response ofLotung ¼ ScaleContainment Model.

· Direct (FlexibleVolume)· ExtendedSubtraction· Subtraction

Horizontal groundmotion excitationprescribed in theform of verticallypropagating SVwave.



SASSICaseNo.

ElementType Verified SASSI Model Description

Method ofForming

ImpedanceExcitation

13D Brick, 3DInter-Pile, 3DBeam

Horizontal and verticalresponse at the pile head of asingle pile in a homogeneoushalfspace using inter-pileelements.

Subtraction

Horizontal andvertical harmonicloading applied atcenter of pilecap.


Horizontal and verticalresponse at the pile head of a2×2 pile group with S/D=2 ina homogeneous halfspaceusing inter-pile elements.

Subtraction




Subtraction




Subtraction




SASSIProblem

5Case No.

ElementType

VerifiedSASSI Model Description

Method ofForming

ImpedanceExcitation

1 3D Brick,3D Beam

Horizontal and verticalresponse at the pile head of2×2 pile groups with S/D=2, 5,and 10 in a homogeneoushalfspace using the pileimpedance method.

Direct


2 3D Brick,3D Beam


Direct


3 3D Brick,3D Beam


Direct




SASSIProblem

6Case No.

ElementType

Verified


Method ofForming

ImpedanceExcitation

13D ThickShell, 3D

Beam

Determine SSI responseof a surface-foundedpressurized water reactor(PWR) containmentbuilding.

Direct

Horizontal groundmotion excitationprescribed in the form ofhorizontally propagatingSV wave. Coherentground motion (30 timehistories)

23D ThickShell, 3D

Beam


Direct

Horizontal groundmotion excitationprescribed in the form ofhorizontally propagatingSV wave. Coherentground motion (RandomVibration Theory)

33D ThickShell, 3D

Beam


Direct

Horizontal groundmotion excitationprescribed in the form ofhorizontally propagatingSV wave. Incoherentground motion (30 timehistories)

43D ThickShell, 3D

Beam


Direct

Horizontal groundmotion excitationprescribed in the form ofhorizontally propagatingSV wave. Incoherentground motion (RandomVibration Theory)



SASSIProble

m 7CaseNo.

Element TypeVerified SASSI Model Description Excitation

1(a) Rectangular Brick

Two elements form a column of 1'x1' incross section and 4' in heightsupported on the surface of a rigidhalfspace.

Vertical harmonicforce excitation

(b) Triangular Brick Four elements form the same columnas in Case 1(a)

Vertical harmonicforce excitation

2

(a) 3D BeamFive elements were used to form acantilever beam supported on thesurface of a rigid halfspace.

Harmonic lateralforce excitationsapplied at the tip ofthe beam.

(b) 3D Beam Same as Case 2(a)

Horizontal groundmotion excitationprescribed in theform of verticallypropagating SVwave.

(c) 3D Beam Same as Case 2(a). Test COMBINmodule. Same as Case 2(b)

3

(a) 3D Plate/Shell

A 100'×100' ×10' vertical square platesupported on horizontal plate of thesame size supported on a rigidhalfspace.

Out-of-planehorizontal harmonicline-load excitations

(b) same as 3(a) Same as 3(a) except thickness=20'In-plane horizontalharmonic line-loadexcitation

4(a) 2D Plane Strain

Two elements form a vertical wall of aunit width supported on the surface of arigid halfspace.

Harmonic axial loadexcitation applied attop of the wall

(b) 2D Plane Strain Same as Case 4(a).Test COMBIN module. Same as Case 4(a)

5 - 3D SpringTwo elements form two single-degree-of-freedom (SDOF) systems supportedon the surface of a rigid halfspace.

Vertical harmonicforce excitations

6 -3D GeneralizedStiffness/Mass

Matrix(Same as for 3D Springs) Vertical harmonic

force excitations

7 - 3D Thick ShellElement

A 100'×100' ×10' vertical square platesupported on horizontal plate of thesame size supported on a rigidhalfspace.

Horizontal andvertical harmonicline-load excitations



SASSIProble

m 8CaseNo.

Element TypeVerified SASSI Model Description Excitation

1

(a) 2D PlaneStrain

A rigid massless strip foundation on the surfaceof a uniform viscoelastic soil overlaying rigidrock. The strip foundation was modeled in 2Dusing a one-half model consisting of 5 plane-strain elements and 12 node points.

Verticalharmonic forceexcitation

(b) 3D Plate/Shell

A rigid massless strip foundation on the surfaceof a uniform viscoelastic soil overlaying rigidrock. The strip foundation was modeled in 3Das an elongated rectangular foundation using aone-quarter model consisting of 250 3D flatplate/shell elements and 306 node points.

Verticalharmonic forceexcitation



SASSIProblem 9Case No.

ElementType

VerifiedModel Description Excitation

1 3D Brick,3D Beam

A rigid circular disk resting on auniform elastic half spacesubjected to seismic groundmotion including the effects ofincoherency.

· Horizontal ground motionexcitation prescribed in theform of verticallypropagating SV wave.· Vertical ground motionexcitation prescribed in theform of verticallypropagating P wave.



SASSIProblem10 CaseNo.

ElementTypeVerified

Model Description Methods and Results ofVerification

1Brick,Beam,Shell, Link

A surface-founded, fixed-base nuclear reactor buildingSASSI model described inReference 14 of ER-F010-6084, Rev. 0.The model has a total weightof 859,078 kips and consistsof:32,378 nodes12,075 solid elements

6,453 beamelements

18,818 shell (plate)elements

3,306 link (spring)elements

· Comparing total base reactionsdue to gravity in the three globaldirections calculated by SASSI2010with those verified by SAP2000.The differences in reactions are lessthan 0.00015%.· Comparing the structuralfrequencies calculated bySASSI2010 with those by verifiedSAP2000.The major structural frequenciesobtained at the amplification peaksin the transfer functions calculatedby SASSI2010 are compared withthe corresponding modalfrequencies by SAP2000.The differences in structuralfrequencies between SASSI2010and SAP2000 are less than 8%.The frequency differences aredeemed acceptable. Thedifferences can be attributed mostlytoa. SASSI2010 cannot completelysimulate the fixed-base condition byseating the reactor building on avery stiff free-field half space.b. Different methods in assigningmaterial damping betweenSASSI2010 (complex damping) andSAP2000 (Rayleigh damping).c. Two different numerical solutionprocedures between SASSI2010(frequency domain) and SAP2000(time domain).


2Brick,Beam,Shell, Link

A surface-founded, fixed-base nuclear control buildingSASSI model.The model has a total weightof 127,750 kips and consistsof:9,279 nodes3,966 solid elements1,393 beam elements

4,069 shell (plate)elements

864 link (spring)elements

· Comparing total base reactionsdue to gravity in the three globaldirections calculated by SASSI2010with those verified by SAP2000.The differences in reactions are lessthan 0.0025%.· Comparing the structuralfrequencies calculated bySASSI2010 with those by verifiedSAP2000.The major structural frequenciesobtained at the amplification peaksin the transfer functions calculatedby SASSI2010 are compared withthe corresponding modalfrequencies by SAP2000.The differences in structuralfrequencies between SASSI2010and SAP2000 are less than 4%.The frequency differences aredeemed acceptable. Thedifferences can be attributed mostlytoa. SASSI2010 cannot completelysimulate the fixed-base condition byseating the reactor building on avery stiff free-field half space.b. Different methods in assigningmaterial damping betweenSASSI2010 (complex damping) andSAP2000 (Rayleigh damping).c. Two different numerical solutionprocedures between SASSI2010(frequency domain) and SAP2000(time domain).


Table 18: SHAKE2000 Verification Problems

SHAKE2000Problem

No.

SHAKE2000VerificationProblemDescription

ExcitationInput

SHAKE2000Capabilities to beVerified

Methodology

1

Uniform undampedelastic half �spacesubjected to aharmonic groundmotion at the soilsurface, i.e., free-field input motion

Free-fieldhorizontalharmonicacceleration

· AmplificationSpectrum, i.e., ratioof accelerationamplitudes betweenany two layers.· Shear strain/stresstime historyresponse calculation· Calculation ofmaximum shearstrain/stress vs.depth· Calculation ofmaximumacceleration vs.depth

Closed-formsolution

2

Two-layered soilsubjected to aharmonic groundmotion at the soilsurface, i.e., free-field input motion

Free-fieldhorizontalharmonicacceleration

· AmplificationSpectrum at anytypical layer· Amplification vs.depth

Closed-formsolution

3

Multi-layered soilsubjected to aharmonic groundmotion at thebedrock.

Harmonichorizontalexcitation attop of bedrock

AmplificationSpectrum

Closed-formsolution

4

Multi-layered soilsubjected to aseismic groundmotion at theGround Surface.

Horizontalseismicexcitation atGroundSurface

· AmplificationSpectrum· Calculation oftransientaccelerationresponse timehistory

Resultscalculated by avalidatedSHAKEProgram


5

Multi-layered soilsubjected to aseismic groundmotion at thebedrock.

Horizontalseismicexcitation attop of bedrock

· Calculation ofstrain-compatible soilshear modulus anddamping ratios forsoil layers throughiteration· Calculation ofaccelerationresponse spectrumof accelerationresponse timehistory of any soillayer

· Manualiteration· ResponseSpectrumcalculated bythe validatedSAP2000Program

6

Uniform undampedelastic half -spacemodeled by 200soil layerssubjected to aharmonic groundmotion at the soilsurface, i.e., free-field input motion

Free-fieldhorizontalsinusoidalacceleration

Verify the limitationon the maximumnumber of layers of200.

Closed-formsolution


Table 19: RSPMATCH Verification Problems

RspMatchEDTTest Case No.

RspMatch2009 Capability toVerify Methodology

1

Modify a seed acceleration timehistory so that the responsespectrum of the modified timehistory closely resembles atarget spectrum.

The target spectrum used is from anARES calculation. The seedacceleration time history used is frompublished data of an actual recordedearthquake.

2 Accurately generate a responsespectrum.

The response spectrum calculated bythe program for an arbitrary selectedacceleration time history is comparedwith one calculated by the validatedprogram SAP2000.

Impact on DCA:

FSAR Tier 2, Section 3.7.5 has been revised as described in the response above and as shownin the markup provided in this response.

NuScale Final Safety Analysis Report Seismic Design

Tier 2 3.7-377 Draft Revision 1

3.7.5 Computer Programs Used in Section 3.7 Seismic Design

Only commercially available software packages were used for the analysis and design of the site-independent Seismic Category I and Seismic Category II structures. The primary software packages used are SAP2000 and SASSI2010.

RAI 03.07.02-7

The software validation and verification summary tests those characteristics of the software that mimic the physical conditions, material properties, and physical processes that represent the NuScale design in numerical analysis. It covers the full range of parameters used in NuScale design-basis seismic demand calculations including the discretization and aspect ratio of finite elements, Poisson’s ratio, frequencies of analysis, and other parameters pertinent to seismic system analyses.

3.7.5.1 ANSYS

3.7.5.1.1 Description

RAI 03.07.02-7

ANSYS is a commercial, general use finite element analysis (FEA) software. ANSYS is used to determine demand loads and stresses in structures, supports, equipment, and components/assemblies. ANSYS Mechanical software offers a comprehensive product solution for structural linear and nonlinear and dynamic analysis. The product provides a complete set of element behavior, material models, and equation solvers for a wide range of engineering problems.ANSYS is a finite element program for a broad range of structural and mechanical analyses.

3.7.5.1.2 Version Used

ANSYS Computer Program, Release 14, 15, and 16.0, January 2015. ANSYS Incorporated, Canonsburg, Pennsylvania.

RAI 03.07.02-7

3.7.5.1.3 Validation and Verification

RAI 03.07.02-7

Software validation and verification was performed in accordance with the NuScale Quality Assurance program. This included confirmation that the software was capable of addressing the NuScale design conditions and performance of the ANSYS- provided verification testing package.

3.7.5.1.4 Extent of Use

ANSYS is used for fluid structure interaction applying input motions from SASSI2010 and using fluid elements to assess the fluid pressures on walls and sloshing heights. Factors are applied to SASSI2010 results to adjust for these effects.



3.7.5.2 SAP2000


RAI 03.07.02-7

SAP2000 is a general-purpose, three-dimensional, static and dynamic finite-element computer program. Analyses, including calculation of deflections, forces, and stresses, may be done on structures constructed of any material or combination of materials.

RAI 03.07.02-7

It features a powerful graphical interface which is used to create/modify finite element models. This same interface is used to execute the analysis and for checking the optimization of the design. Graphical displays of results, including real-time animations of time-history displacements, are produced. SAP2000 provides automated generation of loads for design based on a number of National Standards.

RAI 03.07.02-7

The software can perform the following types of analyses: static linear analysis, static nonlinear analysis, modal analysis, dynamic response spectrum analysis, dynamic linear and nonlinear time history analysis, bridge analysis, moving load analysis, and buckling analysis.SAP2000 is a finite element program for analysis and design of structures. It performs both static and dynamic analysis.


SAP2000, Version 18.1.1, Computers and Structures, Inc., Berkeley.

RAI 03.07.02-7


Software validation and verification was performed in accordance with NuScale Quality Assurance program. This included confirmation that the software was capable of addressing the NuScale design conditions and performance of the Computer and Structures Inc. verification problems.


SAP2000 is used to develop the finite element models of the RXB and CRB and to perform general structural analysis of the building.

3.7.5.3 SASSI2010


RAI 03.07.02-7



SASSI, a System for Analysis of Soil-Structure Interaction, consists of a number of interrelated computer program modules which can be used to solve a wide range of dynamic soil-structure interaction (SSI) problems in two or three dimensions.SASSI2010 is used to solve a wide range of dynamic soil-structure interaction (SSI) problems, including layered soil conditions and embedment conditions, in two or three dimensions.


SASSI2010 Version 1.0, Berkeley, California

RAI 03.07.02-7


RAI 03.07.02-7

Software validation and verification was performed in accordance with NuScale Quality Assurance program. This included confirmation that SSASS2010SASSI2010 was capable of analyzing a model as large and complex as planned for the RXB, the CRB, and the RWB, and capable of using the earthquake profiles with the accelerations and frequency range of the CSDRS and CSDRS-HF. In addition, test problems were evaluated to confirm the adequacy of the program.


SASSI2010 is used to obtain seismic design loads and in-structure floor response spectra for the Seismic Category I buildings accounting for the effects of SSI.

3.7.5.4 SHAKE2000


RAI 03.07.02-7

The computer program SHAKE2000 computes the free-field response of a semi-infinite, horizontally layered soil column overlying a uniform half-space subjected to an input motion prescribed as the object motion in the form of vertically propagating shear waves. SHAKE2000 is used for the analysis of site-specific response and for the evaluation of earthquake effects on soil deposits. It provides an approximation of the dynamic response of a site. SHAKE2000 computes the response in a system of homogeneous, viscoelastic layers of infinite horizontal extent subjected to vertically traveling shear waves.SHAKE2000 is used to perform the free-field site response analysis to generate the design- earthquake-induced strain-compatible free-field soil properties and site response motions required in the seismic SSI analysis.


SHAKE2000, a module of GeoMotions Suite, Version 9.98.0, Gustavo A. Ordonez.



RAI 03.07.02-7


RAI 03.07.02-7

Software validation and verification was performed in accordance with the NuScale Quality Assurance program. Sample problems were designed to test SHAKE2000 major analytical capabilities.


RAI 03.07.02-7

SHAKE2000 is used to generate strain- compatible soil properties and free-field site response motions for use in seismic SSI analysis of the site-independent Seismic Category I and Seismic Category II structures.

3.7.5.5 RspMatch2009


RAI 03.07.02-7

RspMatch2009 is used to generate spectrum- compatible acceleration time historiesy by modifying a recorded seismic accelerogram. The RspMatch2009 program performs a time domain modification of an acceleration time history to make it compatible with a user-specified target spectrum.


RspMatch2009, Version 2009

RAI 03.07.02-7


RAI 03.07.02-7

Software validation and verification was performed in accordance with the NuScale Quality Assurance program. The program was validated by comparing the response spectrum calculated by RspMatch 2009 for an arbitrarily selected acceleration time history with one calculated by SAP2000 for the same acceleration time history.


RAI 03.07.02-7

RspMatch2009 is used to generate the five CSDRS- compatible acceleration time historiesy by modifying the recorded seismic accelerograms of five different



earthquakes and to generate the CSDRS-HF- compatible acceleration time history by modifying the recording of the time histories of a sixth earthquake.

3.7.5.6 RspMatchEDT


RAI 03.07.02-7

RspMatchEDT is used to generate spectrum- compatible acceleration time historiesy by modifying a recorded seismic accelerogram. The RspMatchEDT Module for SHAKE2000 is a pre- and post-processor for the RspMatch2009 program, which is part of SHAKE2000.


RspMatchEDT, a module of GeoMotions Suite, Version 9.98.0, Gustavo A. Ordonez.

RAI 03.07.02-7


RAI 03.07.02-7

Software validation and verification was performed in accordance with the NuScale Quality Assurance program. The program was validated by comparing the response spectrum calculated by RspMatchEDT with the spectrum calculated by RspMatch2009.


RspMatchEDT is used to confirm the adequacy of the CSDRS and CSDRS-HF compatible time histories produced with RspMatch2009.

.

january 31, 2018 docket no. 52-048 u.s. nuclear regulatory ... · the software can perform the...

Documents