ML18031B204

LLC Response to NRC Request for Additional Information No. 133 (Erai No. 8936) on the NuScale Design Certification Application

ML18031B204
Person / Time
Site:	NuScale
Issue date:	01/31/2018
From:	Rad Z NuScale
To:	Document Control Desk, Office of New Reactors
References
RAIO-0118-58472
Download: ML18031B204 (67)

Text

RAIO-0118-58472 January 31, 2018 Docket No.52-048 U.S. Nuclear Regulatory Commission ATTN: Document Control Desk One White Flint North 11555 Rockville Pike Rockville, 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 Information No. 133 (eRAI No. 8936)," dated August 05, 2017

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

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

03.07.02-7 The response to RAI Question 03.07.02-12 was previously provided in Reference 2. The response to RAI Questions 03.07.02-8, 03.07.02-9 and 03.07.02-11 were previously provided in Reference 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 to any existing regulatory commitments.

If you have any questions on this response, please contact Marty Bryan at 541-452-7172 or at mbryan@nuscalepower.com.

y Sincerely, Zackary W. Rad Director Regulatory Affairs

Director, NuScale Power, LLC NuScale Power, LLC 1100 NE Circle Blvd., Suite 200 Corvalis, Oregon 97330, Office: 541.360.0500, Fax: 541.207.3928 www.nuscalepower.com

RAIO-0118-58472 Distribution: Gregory Cranston, NRC, OWFN-8G9A Samuel Lee, NRC, OWFN-8G9A Marieliz Vera, NRC, OWFN-8G9A : NuScale Response to NRC Request for Additional Information eRAI No. 8936 NuScale Power, LLC 1100 NE Circle Blvd., Suite 200 Corvalis, Oregon 97330, Office: 541.360.0500, Fax: 541.207.3928 www.nuscalepower.com

RAIO-0118-58472 :

NuScale Response to NRC Request for Additional Information eRAI No. 8936 NuScale Power, LLC 1100 NE Circle Blvd., Suite 200 Corvalis, Oregon 97330, Office: 541.360.0500, Fax: 541.207.3928 www.nuscalepower.com

Response to Request for Additional Information Docket No.52-048 eRAI No.: 8936 Date 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, and components (SSCs) must be assured during and after the vibratory ground motion associated with 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 programs used in the analysis and design of the site-independent seismic Category I and Category II structures. However, it did not provide sufficient information regarding the verification &

validation (V&V) of these programs. The applicant is requested to provide in the DCA information summarizing the V&V of the computer programs used to determine design-basis seismic demands for NuScale seismic Category I and II structures. The demonstration should test 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&V should cover the full range of parameters used in NuScale design-basis seismic demand calculations including the discretization and aspect ratio of finite elements, Poissons 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 the analysis and design of the NuScale Category I and Category II structures, is described in this response.

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, 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. Table 1 summarizes all ANSYS verification problems for elements used in the NuScale models.

NuScale Nonproprietary

SAP2000 is a general-purpose, three-dimensional static and dynamic finite-element computer program. Analyses, up to and including calculation of deflections, forces, and stresses, may be done 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 the design. Graphical displays of the 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.

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. Tables 2 through 7 summarize all of the SAP2000 verification problems. The problems are categorized into 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 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.

The verification problems for SASSI2010 are shown in Tables 8 through 16. The SASSI2010 V&V includes 30 test cases developed from nine different problems to verify the capabilities of SASSI2010. These test cases were developed using published literature and/or hand calculations. The problems are designed to check the programs capabilities under various conditions, in addition to showing accurate performance of the SASSI2010 methodologies.

These problems provide reasonable assurance that a certified user (i.e., qualified engineer who possesses an understanding of soil-structure interaction) can apply SASSI2010 over the intended 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 calculate correct static and dynamic responses for complex structures by comparing the results from SASSI2010 with the results from the independently verified SAP2000 program. Table 17 shows the descriptions and verification results of two analysis cases for Problem 10. In each case, the SASSI2010 program calculates the static and dynamic responses of a surface-founded, fixed-base complex structure. The total static reactions and the structural frequencies calculated by SASSI2010 are compared with the corresponding reactions and frequencies calculated by the verified 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 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. Verification problems, summarized in Table NuScale Nonproprietary

18, were designed to test SHAKE2000 major analytical capabilities.

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

This software V&V 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 also covers the full range of parameters used in NuScale design-basis, seismic demand calculations, including the discretization and aspect ratio of finite elements, Poissons ratio, frequencies of analysis, and other parameters pertinent to seismic system analyses.

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

NuScale Nonproprietary

Table 1: ANSYS Verification Problems Problem ANSYS Verification Problem Method of Independent Problem Title No. Description Verification A standard 30" WF beam, with cross-sectional area A, is S. Timoshenko, Strength supported and loaded on the of Material, Part I, Beam Stresses and overhangs by a uniformly Elementary Theory and vm2 Deflections distributed load w. Determine the Problems, 3rd Edition, D.

Beam188 maximum bending stress in the Van Nostrand Co., Inc.,

middle portion of the beam and the New York, NY, 1955, p.

deflection at the middle of the 98, problem 4.

beam.

A thin-walled cylinder is pinched by R. D. Cook, Concepts and force F at the middle of the cylinder Applications of Finite Pinched Cylinder length. Determine the radial Element Analysis, 2nd vm6 Shell181 displacement at the point where Edition, John Wiley and F is applied. The ends of the Sons, Inc., New York, NY, cylinder are free edges. 1981, pp. 284-287.

Two coaxial tubes, the inner one of 1020 CR steel and cross-sectional area As, and the outer one of 2024-T4 aluminum alloy and of H. Takemoto, R. D. Cook, area Aa, are compressed between "Some Modifications of an Plastic Compression heavy, flat end plates. Determine Isoparametric Shell vm7 of a Pipe Assembly the load-deflection curve of the Element", International Shell181 assembly as it is compressed into Journal for Numerical the plastic region by an axial Methods in Engineering, displacement. Assume that the end Vol. 7 No. 3, 1973.

plates are so stiff that both tubes are shortened by exactly the same amount.

G. N. Vanderplaats, Numerical Optimization Large Lateral A two-spring system is subjected to Techniques for Deflection of Unequal a force F. Determine the strain Engineering Design with vm9 Stiffness Springs energy of the system and the Applications, McGraw-Hill Combin14 displacements x and y. Book Co., Inc., New York, Combin40 NY, 1984, pp. 72-73, ex.

3-1.

Find the maximum tensile and S. H. Crandall, N. C. Dahl, compressive bending stresses in An Introduction to the Bending of a Tee- an unsymmetrical T beam Mechanics of Solids, vm10 Shaped Beam subjected to uniform bending Mz, McGraw-Hill Book Co.,

Beam188 with dimensions and geometric Inc., New York, NY, 1959, properties. pg. 294, ex. 7.2.

NuScale Nonproprietary

C. C. Chang, Periodically Snap-Through A hinged cylindrical shell is Restarted Quasi-Newton Buckling of a Hinged subjected to a vertical point load Updates in Constant Arc-vm17 Shell63 (P) at its center. Find the vertical Length Method, Shell181 displacement (UY) at points A and Computers and Shell281 B for the load of 1000 N. Structures, Vol. 41 No. 5, 1991, pp. 963-972.

A deep, simply-supported square NAFEMS, Selected Random Vibration beam of length l, thickness t, and Benchmarks for Forced Analysis of a Deep mass density m, is subjected to Vibration, Report prepared vm19 Simply-Supported random uniform force power by W. S. Atkins Beam spectral density. Determine the Engineering Sciences, Beam188 peak response PSD value. April 1989, Test 5R.

A tie rod is subjected to the action of a tensile force F and a uniform S. Timoshenko, Strength lateral load p. Determine the of Material, Part II, maximum deflection zmax, the Elementary Theory and Tie Rod with Lateral vm21 slope at the left-hand end, and Problems, 3rd Edition, D.

Loading Beam188 the maximum bending moment Van Nostrand Co., Inc.,

Mmax. In addition, determine the New York, NY, 1956, pg.

same three quantities for the 42, article 6.

unstiffened tie rod (F = 0).

A cantilevered plate of length l, K. J. Bathe, E. N. Dvorkin, width b, and thickness t is fixed at "A Formulation of General one end and subjected to a pure Shell Elements - The Use bending moment M at the free end. of Mixed Interpolation of Large Deflection of a vm26 Determine the true (large Tensorial Components, Cantilever SHELL181 deflection) free-end displacements Int. Journal for Numerical and rotation, and the top surface Methods in Engineering, stress at the fixed end, using shell Vol. 22 No. 3, 1986, pg.

elements. 720.

An aluminum-alloy bar is fixed at one end and has a gap between its other end and a rigid wall when C. O. Harris, Introduction Thermal Expansion to at ambient temperature Ta. to Stress Analysis, The Close a Gap vm27 Calculate the stress , and the Macmillan Co., New York, LINK180 thermal strain Thermal in the bar NY, 1959, pg. 58, problem CONTA178 8.

after it has been heated to temperature T.

A tapered cantilever plate of Bending of a Tapered C. O. Harris, Introduction rectangular cross-section is Plate (Beam) to Stress Analysis, The subjected to a load F at its tip. Find vm34 SHELL63 Macmillan Co., New York, the maximum deflection and the BEAM188 NY, 1959, pg. 114, maximum principal stress 1 in the SHELL181 SHELL281 problem 61.

plate.

NuScale Nonproprietary

A symmetric cross-section beam of bending stiffness EIy, and height h, totally fixed at C, simply-supported at A, is subjected to a concentrated load P at point B. Verify that a load P which is slightly smaller than the S. H. Crandall, N. C. Dahl, An Introduction to the Limit Moment Analysis theoretical load limit PL will cause Mechanics of Solids, vm36 Beam188 elastic deformation and that a load McGraw-Hill Book Co.,

COMBIN40 which is slightly larger than PL will Inc., New York, NY, 1959, cause plastic deformation. Also pg. 389, ex. 8.9.

determine the maximum deflection

, the reaction force at the left end RA, and the reaction moment at the right end Mc just prior to the development of a plastic hinge.

A tapered aluminum alloy bar of Elongation of a Solid square cross-section and length L C. O. Harris, Introduction Bar is suspended from a ceiling. An to Stress Analysis, The Solid 145 axial load F is applied to the free vm37 Macmillan Co., New York, Solid185 end of the bar. Determine the NY, 1959, pg. 237, Solid45 maximum axial deflection in the problem 4.

SOLSH190 bar and the axial stress y at mid-length (Y = L/2).

A long, thick-walled cylinder is subjected to an internal pressure p Internal Pressure (with no end cap load). Determine S. Timoshenko, Strength Loading of a Thick- the radial stress, r, and the of Material, Part II, Walled Cylinder Elementary Theory and tangential (hoop) stress, t, at vm38 Plane182 Problems, 3rd Edition, D.

Solid185 locations near the inner and outer Van Nostrand Co., Inc.,

Surf153 surfaces of the cylinder for a New York, NY, 1956, pg.

Surf154 pressure, pel, just below the yield 388, article 70.

strength of the material, a fully elastic material condition.

NuScale Nonproprietary

A circular plate of thickness t with a center hole is rigidly attached along the inner edge and unsupported along the outer edge. The plate is subjected to bending by a moment S. Timoshenko, Strength Bending of a Circular of Material, Part II, Ma applied uniformly along the Plate with a Center Elementary Theory and outer edge. Determine the vm39 Hole Problems, 3rd Edition, D.

maximum deflection and the Shell63 Van Nostrand Co., Inc.,

maximum slope of the plate. In Shell181 New York, NY, 1956, pg.

addition, determine the moment M 111, eq. E and F.

and stress x at the top centroidal locations of element 1 (near inner edge) and element 6 (near outer edge).

A massless beam of length L is initially at position AB on a horizontal frictionless table. Point A Large Deflection and is pinned to the table and given a Rotation of a Beam large rotation z through a full Any basic mathematics vm40 Pinned at One End revolution at speed z. Determine book Beam188 the position of the beam in terms of

, and at various angular locations. Show that the beam has no axial stress at any position.

A very stiff beam of length L, subjected to a lateral load F, is initially at position AB on a Small Deflection of a horizontal table. Point A is pinned Rigid Beam to the table and restrained from Any basic Statics and vm41 rotation by a relatively weak torsion MATRIX27 Strength of Materials Book BEAM188 spring. Determine the final position of the beam in terms of x, y, and

. Show that the bending stress in the beam bend is negligible.

A cylindrical shell roof of density is subjected to a loading of its own R. D. Cook, Concepts and weight. The roof is supported by Barrel Vault Roof Applications of Finite walls at each end and is free along Under Self Weight Element Analysis, 2nd vm42 the sides. Find the x and y Shell181 Edition, John Wiley and displacements at point A and the Shell281 Sons, Inc., New York, NY, top and bottom stresses at points A 1981, pp. 284-287.

and B. Express stresses in the cylindrical coordinate system.

NuScale Nonproprietary

W. T. Thomson, Vibration Natural Frequency of An instrument of weight W is set on Theory and Applications, a Spring-Mass a rubber mount system having a 2nd Printing, Prentice-vm45 System stiffness k. Determine its natural Hall, Inc., Englewood Combin14 frequency of vibration f. Cliffs, NJ, 1965, pg. 6, ex.

Mass21 1.2-2.

A disk of mass m which has a polar W. T. Thomson, Vibration Torsional Frequency moment of inertia J is suspended at Theory and Applications, of a Suspended Disk the end of a slender wire. The 2nd Printing, Prentice-vm47 torsional stiffness of the wire is k. Hall, Inc., Englewood Combin14 Mass21 Determine the natural frequency f Cliffs, NJ, 1965, pg. 10, of the disk in torsion. ex. 1.3-2 A small generator of mass m is driven off a main engine through a solid steel shaft of diameter d. If W. T. Thomson, Vibration the polar moment of inertia of the Natural Frequency of Theory and Applications, generator rotor is J, determine the a Motor-Generator 2nd Printing, Prentice-vm48 natural frequency f in torsion.

BEAM188 Hall, Inc., Englewood Assume that the engine is large Mass21 Cliffs, NJ, 1965, pg. 10, compared to the rotor so that the ex. 1.3-3 engine end of the shaft may be assumed to be fixed. Neglect the mass of the shaft also.

Electrostatic Forces Two spheres with radii = 1 m, Between Charged separated by a distance of 3 m, are Spheres Any General Physics vm51 subjected to a surface charge. Find SOLID123 SOLID122 Textbook the resultant electrostatic force INFIN111 PLANE121 between the spheres.

MESH200 An automobile suspension system is simplified to consider only two major motions of the system:

• up and down linear motion of the W. T. Thomson, Vibration Automobile body Theory and Applications, Suspension System

• pitching angular motion of the 2nd Printing, Prentice-vm52 Vibration BEAM188 body Hall, Inc., Englewood COMBIN14 MASS21 If the body is idealized as a lumped Cliffs, NJ, 1965, pg. 181, mass with weight W and radius of ex. 6.7-1 gyration r, determine the corresponding coupled frequencies f1 and f2.

NuScale Nonproprietary

W. Carnegie, "Vibrations A blade is cantilevered from a rigid Vibration of a Rotating of Rotating Cantilever rotating cylinder. Determine the Cantilever Blade Blading", Journal vm54 fundamental frequency of vibration SHELL63 SOLSH190 Mechanical Engineering of the blade, f, when the cylinder is SHELL181 SHELL281 Science, Vol. 1 No. 3, spinning at a rate of .

1959, pg. 239 An infinitely long cylinder is made Hyperelastic Thick of Mooney-Rivlin type material. An J. T. Oden, Finite Cylinder Under internal pressure of Pi is applied. Elements of Nonlinear vm56 Internal Pressure Find the radial displacement at the Continua, McGraw-Hill PLANE183 SOLID185 inner radius and the radial stress at Book Co., Inc., New York, SOLID186 radius R = 8.16 in (center of 1st NY, 1972, pp. 325-331.

element).

Determine the first two natural frequencies f1 and f2 of an oil-well W. T. Thomson, Vibration Torsional Frequencies drill pipe of length l and polar Theory and Applications, of a Drill Pipe moment of inertia lp fixed at the 2nd Printing, Prentice-vm57 PIPE16 MASS21 upper end and terminating at the Hall, Inc., Englewood PIPE288 PIPE289 lower end to a drill collar with Cliffs, NJ, 1965, pg. 272, BEAM188 BEAM189 torsional mass inertia Jo. The drill ex. 8.4-5.

collar length is small compared to the pipe length.

A square cross-sectioned bar of length l and weight per unit length S. Timoshenko, D. H.

A is pinned at its ends and Young, Vibration Lateral Vibration of an subjected to an axial compressive Problems in Engineering, vm59 Axially-loaded Bar force F. Determine the stress and 3rd Edition, D. Van BEAM188 the axial displacement of the bar Nostrand Co., Inc., New under these conditions. Determine York, NY, 1955, pg. 374, the first three natural frequencies fi article 59.

of lateral vibration of the bar.

W. T. Thomson, Vibration Determine the first three natural Theory and Applications, Longitudinal Vibration frequencies fi of a free-free rod (a 2nd Printing, Prentice-vm61 of a Free-free Rod BEAM188 rod with both ends free) having a Hall, Inc., Englewood length 800 in. Cliffs, NJ, 1965, pg. 269, ex. 8.3-1.

S. Timoshenko, D. H.

Determine the fundamental Young, Vibration Vibration of a Wedge frequency of out-of-plane vibration f Problems in Engineering, vm62 SHELL63 SHELL181 of a wedge-shaped plate of uniform 3rd Edition, D. Van SHELL281 thickness t, base 2b, and length Nostrand Co., Inc., New 16in. York, NY, 1955, pg. 392, article 62.

NuScale Nonproprietary

S. Timoshenko, J. N.

Static Hertz Contact A sphere of radius r is pressed Goodier, Theory of Problem PLANE82 against a rigid flat plane. Determine Elasticity, 3rd Edition, vm63 PLANE183 the contact radius, a, for a given McGraw-Hill Book Co.,

CONTA178 load F. Inc., New York, NY, 1970, pg. 409-413, article 140.

A rigid ball of mass m is dropped W. T. Thomson, Vibration through a height h onto a flexible Transient Response Theory and Applications, surface of stiffness k. Determine of a Ball Impacting a 2nd Printing, Prentice-vm65 the velocity, kinetic energy, and Flexible Surface Hall, Inc., Englewood displacement y of the ball at impact MASS21 CONTA175 Cliffs, NJ, 1965, pg. 110, and the maximum displacement of ex. 4.6-1.

the ball.

S. Timoshenko, D. H.

Vibration of a Flat Determine the fundamental natural Young, Vibration Plate frequency of lateral vibration f of a Problems in Engineering, SHELL63 vm66 flat rectangular plate. The plate is 3rd Edition, D. Van SOLSH190 of uniform thickness t, width 2b, Nostrand Co., Inc., New SHELL181 and length 16 in. York, NY, 1955, pg. 338, SHELL281 article 53.

A steel beam of length and geometric properties is supporting a concentrated mass, m. The beam is subjected to a dynamic load F(t) with a rise time tr and a maximum J. M. Biggs, Introduction to Transient Response value F1. If the weight of the beam Structural Dynamics, to a Constant Force is considered negligible, determine vm77 McGraw-Hill Book Co.,

BEAM188 the time of maximum displacement Inc., New York, NY, 1964, MASS21 response tmax and the maximum pg. 50, ex. E.

displacement response ymax.

Additionally, determine the maximum bending stress bend in the beam.

A mass m supported on a thin rod of area A and length 100in is Plastic Response to a subjected to the action of a J. M. Biggs, Introduction to Suddenly Applied suddenly applied constant force Structural Dynamics, vm80 Constant Force F1. Determine the maximum McGraw-Hill Book Co.,

LINK180 Inc., New York, NY, 1964, deflection ymax and minimum MASS21 pg. 69, article 2.7.

deflection ymin of the mass, neglecting the mass of the rod.

NuScale Nonproprietary

A mass m is packaged in a rigid box, and dropped through a height

h. Determine the velocity and W. T. Thomson, Vibration Transient Response displacement y of the mass at Theory and Applications, of a Dropped impact and the maximum 2nd Printing, Prentice-vm81 Container displacement of the mass. Assume Hall, Inc., Englewood COMBIN40 that the mass of the box is large Cliffs, NJ, 1965, pg. 110, MASS21 compared to that of the enclosed ex. 4.6-1.

mass m and that the box remains in contact with the floor after impact Simply Supported A simply-supported, square, cross-Laminated Plate ply laminated plate is subjected to J. N. Reddy, "Exact a uniform pressure po. The Solutions of Moderately Under Pressure Thick Laminated Shells",

SOLSH190 stacking sequence of the plies is vm82 ASCE Journal SOLID186 symmetric about the middle plane.

Engineering Mechanics, SHELL181 Determine the center deflection Vol. 110 No. 5, 1984, pp.

SHELL281 (Z-direction) of the plate due to the 794 809.

SOLID185 pressure load.

W. T. Thomson, Vibration Natural Frequencies Determine the normal modes and Theory and Applications, of a Two-mass-spring natural frequencies of the system 2nd Printing, Prentice-vm89 System for the values of the masses and Hall, Inc., Englewood COMBIN14 spring stiffnesses given. Cliffs, NJ, 1965, pg. 163, MASS21 ex. 6.2-2.

W. T. Thomson, Vibration Harmonic Response Determine the response amplitude Theory and Applications, of a Two-Mass-Spring (Xi) and phase angle (i) for each 2nd Printing, Prentice-vm90 System mass (mi) when excited by a Hall, Inc., Englewood COMBIN14 harmonic force (F1sin t) acting on Cliffs, NJ, 1965, pg. 178, MASS21 mass m1. ex. 6.6-1.

A pendulum consists of a mass m supported by a rod of length 100 in and cross-sectional area A. W. T. Thomson, Vibration Large Rotation of a Determine the motion of the Theory and Applications, Swinging Pendulum pendulum in terms of the 2nd Printing, Prentice-vm91 displacement of the mass from its LINK180 Hall, Inc., Englewood MASS21 initial position o in the x and y Cliffs, NJ, 1965, pg. 138, directions, x and y, respectively. ex. 5.4-1.

The pendulum starts with zero initial velocity.

NuScale Nonproprietary

S. Timoshenko, Strength Determine the critical buckling load of Material, Part II, Buckling of a Bar with of an axially loaded long slender Elementary Theory and Hinged Ends (Line bar of length 200in with hinged vm127 Problems, 3rd Edition, D.

Elements) ends. The bar has a square cross-Van Nostrand Co., Inc.,

BEAM188 section with width and height set to New York, NY, 1956, pg.

0.5 inches.

148, article 29.

F. P. Beer, E. R.

Johnston, Jr., Vector Determine the acceleration at the Mechanics for Engineers, Acceleration of a tip P of a crane boom that has a Statics and Dynamics, 5th vm131 Rotating Crane Boom constant angular velocity cab Edition, McGraw-Hill Book MASS21 rotation () while being raised with Co., Inc., New York, NY, a constant angular velocity ().

1962, pg. 616, problem 15.13.

A rod of length 1 in. and square cross-sectional area A is held at a constant stress o at a temperature To. The rod is also Motion of a Rod Due subjected to a constant neutron to Irradiation Induced flux . The rod material has an vm133 Any basic calculus book Creep irradiation-induced creep strain rate BEAM188 given by the relationship dcr / dt =

k1e - (t / k2). Determine the amount of creep strain cr accumulated up to 5 hours5.787037e-5 days <br />0.00139 hours <br />8.267196e-6 weeks <br />1.9025e-6 months <br />.

A wide-flanged I-beam of length 144in, with clamped ends, is uniformly loaded. Investigate the N. J. Hoff, The Analysis of Plastic Bending of a behavior of the beam at load w 1 Structures, John Wiley vm134 Clamped I-Beam when yielding just begins at the and Sons, Inc., New York, BEAM188 ends, at load w2, when the NY, 1956, pg. 388, article midpoint begins to yield, and at 4.5.

load w3, when pronounced plastic yielding has occurred.

A slender square cross-sectional bar of length l, and area A, fixed at S. Timoshenko, J. M.

the base and free at the upper end, Large Deflection of a Gere, Theory of Elastic is loaded with a value larger than Buckled Bar (the Stability, 2nd Edition, vm136 the critical buckling load. Determine Elastica) McGraw-Hill Book Co.

the displacement (X, Y, ) of BEAM188 Inc., New York, NY, 1961, the free end and display the pg. 78, article 2.7.

deformed shape of the bar at various loadings.

NuScale Nonproprietary

Diametral Compression of a Two equal and opposite forces act S. Timoshenko, J. N.

Disk along the vertical diameter of a Goodier, Theory of PLANE82 disk. Determine the compressive Elasticity, 2nd Edition, vm141 PLANE183 stress at the center of the disk and McGraw-Hill Book Co.,

MATRIX50 on the major horizontal diameter at Inc., New York, NY, 1951, SHELL181 0.1 in. from the center. pg. 107, article 37.

SHELL281 Fracture Mechanics Stress for a Crack in a W. F. Brown, Jr., J. E.

A long plate with a center crack is Plate Srawley, "Plane Strain subjected to an end tensile stress SOLID95 Crack Toughness Testing vm143 o. Determine the fracture SOLID45 mechanics stress intensity factor of High Strength Metallic PLANE183 KI. Materials", ASTM SOLID186 STP-410, 1966.

SOLID185 A beam of length l and width w, made up of two layers of different materials, is subjected to a uniform rise in temperature from Tref to To Bending of a R. J. Roark, W. C. Young, and a bending moment My at the Composite Beam Formulas for Stress and free-end. Determine the free-end SOLID185 Strain, McGraw-Hill Book vm144 displacement (in the Z-direction)

SOLID186 Co., Inc., New York, NY, and the X-direction stresses at the SOLSH190 1975, pg. 112-114, article top and bottom surfaces of the SHELL281 7.2.

layered beam. Ei and i correspond to the Young's modulus and thermal coefficient of expansion for layer i, respectively.

A unit cube of side 1 in, having orthotropic material properties, is S. H. Crandall, N. C. Dahl, subjected to forces FX and FY. An Introduction to the Stretching of an Three orthogonal faces are Mechanics of Solids, vm145 Orthotropic Solid supported and the opposite three McGraw-Hill Book Co.,

SOLID185 faces are free. Determine the Inc., New York, NY, 1959, translational displacements (X, pg. 225.

Y, and Z) of the free faces.

NuScale Nonproprietary

J.M.Dickens, J.M.

Nakagawa, M.J.

A mode-superposition harmonic Wittbrodt, A Critique of Residual Vector in analysis is performed on a spring-Mode Acceleration and Mode-Superposition mass model for two cases:

Modal Truncation vm149 Harmonic Analysis Case 1: Extracting all available Augmentation Methods for COMBIN14 modes Modal Response MASS21 Case 2: Extracting one mode and Analysis. Computers &

residual vector (RESVEC)

Structures, Vol.62, pp.985-998, 1997.

A large rectangular tank is partially filled with an incompressible liquid.

The tank has a constant K. Brenkert, Jr.,

acceleration a to the right.

vm150 Elementary Theoretical Acceleration of a Tank Determine the elevation of the From Fluid Mechanics, John of Fluid liquid surface relative to the zero Version Wiley and Sons, Inc., New FLUID80 acceleration elevation along the Y-14 York, NY, 1960, pg. 50, axis. Also determine the slope of article 17.

the free surface and the pressure p in the fluid near the bottom left corner of the tank.

A circular membrane under a uniform tension S is allowed to vibrate freely. The edge of the S. Timoshenko, D. H.

Young, Vibration 3-D Non-axisymmetric membrane is simply supported.

Vibration of a Determine the natural frequencies Problems in Engineering, vm153 3rd Edition, D. Van Stretched Membrane fi,j for the first two modes of Nostrand Co., Inc., New SHELL181 vibration (j = 1, 2 = no. of nodal York, NY, 1955, pg. 439, circles, including the boundary) for article 69.

the first two harmonics (i = 0, 1 =

no. of harmonic indices).

A long cylinder is immersed in a circular hole. The cylinder is separated from the containment R. J. Fritz, "The Effect of surface by a frictionless, Vibration of a Fluid Liquids on the Dynamic incompressible liquid annulus. A Coupling Motions of Immersed vm154 spring restraint is attached to the FLUID38 Solids", ASME, J. of Engr.

cylinder from ground. Determine COMBIN14 for Industry, Vol. 94, Feb.

the natural frequency f of the 1972, pp. 167-173.

system based upon the hydrodynamic mass of the liquid annulus.

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A mass is supported from a spring S. Timoshenko, D. H.

Natural Frequency of having nonlinear characteristics.

Young, Vibration a Nonlinear Spring- The mass is displaced an amount Problems in Engineering, vm156 Mass System from its equilibrium position and 3rd Edition, D. Van COMBIN39 released (with no initial velocity).

Nostrand Co., Inc., New MASS21 Find the corresponding period of York, NY, 1955, pg. 141.

vibration .

A permanent magnet circuit consisting of a highly-permeable core and a permanent magnet is Permanent Magnet used to model a relay switch. An F. C. Moon, Magneto-Circuit With an Elastic elastic keeper is modeled with a Solid Mechanics, John vm171 Keeper highly permeable iron and two Wiley and Sons, Inc., New PLANE13 springs. Assuming no flux leakage, York, NY, 1984, pg. 275.

COMBIN14 determine the equilibrium displacements, , of the keeper and the operating point (flux density) in the permanent magnet.

Natural Frequency of a Submerged Ring E. A. Schroeder, M. S.

A steel ring is submerged in a FLUID30 Marcus, "Finite Element compressible fluid (water).

SHELL63 Solution of Fluid Structure Determine the lowest natural vm177 FLUID29 Interaction Problems",

frequency for x-y plane bending BEAM188 Shock and Vibration modes of the fluid-structure SHELL181 Symposium, San Diego, system.

SHELL281 CA, 1975.

FLUID221 A torque M1 is applied at the pinned end of an aluminum beam to cause a 90° rotation. A second torque M2 is then applied at a Dynamic Double revolute joint in the beam to create Rotation of a Jointed an out-of-plane rotation. The joint Beam has a rotational stiffness k, inertial vm179 Any basic mechanics text MPC184 mass J, frictional torque Tf, and MASS21 locks when a 5° rotation occurs.

BEAM188 Structural mass elements with rotational mass are added at the joint notes. Determine the position of the beam at the end of each rotation.

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A curved beam spans a 90° arc.

The bottom end is supported while S. Timoshenko, J. N.

Bending of a Curved the top end is free. For a bending Goodier, Theory of Beam moment M applied at the top end, Elasticity, 3rd Edition, vm180 PLANE183 determine the maximum tensile McGraw-Hill Book Co.

BEAM188 stress t and the maximum Inc., New York, NY, 1970, pg. 73, article 29.

compressive stress c in the beam.

A uniaxial compression test with Dal, H. et al. "Bergstrom-intermittent relaxation time is Boyce model for nonlinear performed on a block modeled with finite rubber Stress Relaxation of a Chloroprene rubber. The block is viscoelasticity: theoretical vm189 Chloroprene Rubber subjected to true strain rates of = aspects and algorithmic SOLID185 -0.002s-1and treatment for the FE method. Computational

= -0.1s-1 with 120s relaxation Mechanics. 2009, 44:

time at = -0.3 and = -0.6, 809-823 respectively.

Two long cylinders of radii R1 and N. Chandrasekaran, W. E.

Hertz Contact Haisler, R. E. Goforth, R2, in frictionless contact with their Between Two "Finite Element Analysis Cylinders axes parallel to each other are of Hertz Contact Problem vm191 pressed together with a force per CONTA175 with Friction", Finite PLANE182 unit length, F. Determine the semi- Elements in Analysis and SOLID185 contact length b and the approach Design, Vol. 3, 1987, pp.

distance d. 39-56.

G. H. Martin, Kinematics Toggle Mechanism and Dynamics of MPC184 Determine the maximum force Machines, 2nd Edition, vm195 BEAM188 (Fmax) of a toggle mechanism McGraw-Hill Book Co.,

COMBIN14 acting upon a resisting spring. Inc., New York, NY, 1982, LINK11 pp. 55-56, fig. 3-22.

Determine the free-body moments Counter-Balanced (MX, MY, MZ) about the origin and Loads on a Block the rotational accelerations (x, vm196 SOLID45 Any basic mechanics text y, z) at the center of mass of an SOLID185 MATRIX50 aluminum block due to the forces FX and FY.

A hollow, thick-walled, long cylinder J. C. Nagtegaal, J. E.

made of an elastoplastic material is DeJong, "Some Large Strain In-plane under an in-plane torsional loading Computational Aspects of Torsion Test which causes the inner surface of Elastic-Plastic Strain vm198 PLANE182 the cylinder to undergo a rotation of Analysis", Intl J. of PLANE183 60°. Find the maximum shear Numerical Methods in SOLID185 stress (max) developed at the Engineering, Vol. 17, inner surface at the end of loading. 1981, pp. 15 41.

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A cubic shaped body made up of a viscoplastic material obeying B. Lwo, G. M. Eggert, "An Viscoplastic Analysis Anand's law undergoes uniaxial Implicit Stress Update of a Body (Shear shear deformation at a constant Algorithm Using a Plastic Deformation) rate of 0.01 cm/s. The temperature Predictor", Submitted to vm199 of the body is maintained at 400°C. Computer Methods in PLANE182 PLANE183 Find the shear load (Fx) required to Applied Mechanics and SOLID185 maintain the deformation rate of Engineering, January 0.01 cm/sec at time equal to 20 1991.

seconds.

Rubber Cylinder T. Tussman, K-J Bathe, "A Pressed Between Two Plates A long rubber cylinder is pressed Finite Element between two rigid plates using a Formulation for Nonlinear PLANE182 vm201 SOLID185 maximum imposed displacement of Incompressible Elastic max. Determine the force- and Inelastic Analysis",

TARGE169 Computers and TARGE170 deflection response.

Structures, Vol. 26 Nos CONTA175 1/2, 1987, pp. 357-409.

MESH200 Rubber Cylinder Pressed Between Two Plates T. Tussman, K-J Bathe, "A PLANE182 Finite Element A long rubber cylinder is pressed PLANE183 Formulation for Nonlinear between two rigid plates using a SOLID185 Incompressible Elastic vm211 maximum imposed displacement of CONTA171 and Inelastic Analysis",

max. Determine the force-CONTA172 Computers and deflection response. Structures, Vol. 26 Nos CONTA173 CONTA174 1/2, 1987, pp. 357-409.

TARGE169 TARGE170 NuScale Nonproprietary

A simple equipment-foundation system is modeled using a spring-damper element (COMBIN40) representing the foundation, a beam element (BEAM188) representing the equipment, and a mass element (MASS21)

DDAM Analysis of OHara, G.J., Cunniff, P.

representing the equipment mass.

Foundation System F., Interim Design Values Shock loading is applied at the (2-DOF System) for Shock Design of vm212 fixed base of the foundation system MASS21 Shipboard Equipment, along the athwart ship direction.

COMBIN40 NRL Memorandum Report The shock spectrum is based on BEAM188 1396, 1963, p. 10.

the ship type, mounting location, direction of shock, and type of design (elastic or elastic-plastic).

DDAM analysis is performed on this system to determine natural frequency, deflection, and shock design value.

A 0.6in thick plate that is 30in wide is fashioned into a cantilever right angle frame, and is subjected to an J. C. Simo, L. Vu-Quoc, "Three-Dimensional Lateral Buckling of a in-plane fixed end load (Fx). The Finite-Strain Rod Model, Right Angle Frame frame is driven to buckling mode by vm216 Part II", Computer BEAM188 a perturbation load (Fz) applied at Methods in Applied BEAM189 the free end, normal to the plane of Mechanical Engineering, the frame. This perturbation is Vol. 58, 1986, pp.79-116.

removed close to the buckling load.

Determine the critical load.

A rigid rectangular frame is subjected to a uniform distributed Portal Frame Under load across the span. Determine N. J. Hoff, The Analysis of Symmetric Loading the maximum rotation, and Structures, John Wiley vm217 maximum bending moment. The BEAM188 and Sons, Inc., New York, BEAM189 moment of inertia for the span, NY, 1956, pp. 115-119.

Ispan is five times the moment of inertia for the columns, Icol.

Hyperelastic Circular A flat, circular membrane made of J. T. Oden, Finite Plate a rubber material is subjected to Elements of Nonlinear SHELL181 uniform water pressure. The edges vm218 Continua, McGraw-Hill SHELL208 of the membrane are fixed.

Book Co., Inc., New York, SHELL209 Determine the response as NY, 1972, pp. 318-321.

SHELL281 pressure is increased to 50 psi.

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Frequency Response A beam is in series with an R. D. Blevins, Formulas of a Prestressed electromechanical transducer. With for Natural Frequency and Beam using APDL vm219 a voltage applied to the beam, Mode Shape, Van MATH Commands determine the prestressed natural Nostrand Reinhold Co.,

BEAM188 frequencies of the beam. pg. 144, equation 8-20.

TRANS126 A block is composed of shape memory alloy material. The block, which has an initial temperature of 253.15K, is loaded up to 70 MPA to obtain detwinned martensitic A. Souza, et al. "Three-structure, and then unloaded until it dimensional model for Simulation of Shape is stress free to obtain a martensitic solids undergoing stress-vm221 Memory Alloy Effect structure in which residual strain induced phase SOLID185 remains. The temperature is then transformation. Eur. J.

increased to 259.15K to recover Mech. A/Solids. 1998, 17:

residual strain and regain the 789-806.

austenitic structure. The final stress and strain is obtained and compared against the reference solution.

C-N Chen, "The Warping Torsion Bar Model of the Warping Torsion Bar A cantilever I-beam is fixed at both Differential Quadrature vm222 BEAM188 ends and a uniform moment, Mx, is Method", Computers and BEAM189 applied along its length Structures, Vol. 66 No.

2-3, 1998, pp. 249-257.

Rectangular Cross-Section Bar with A compressive preload is applied to Preload a rectangular cross-section bar.

vm225 Engineering Statics Text SOLID185 Determine the resulting stress and PRETS179 displacement.

SOLID186 A solid block with width W = 1 m, height H = 5 m, and thickness t =

Stress Intensity Factor 0.1 m is modeled with a single for a Single Edge edge crack of length a = 0.1 m. The Stephens, R.I., Fatemi, A.,

Crack with Pressure crack is subjected to a pressure Stephens, R.R., Fuchs, Load Using UMM load P and the stress intensity vm232 H.O., Metal Fatigue in Method factor is determined using the UMM Engineering, 2nd Edition, SOLID185 method (CINT,UMM,ON). The 2006, pg. 130.

SOLID186 results are compared to the SOLID187 analytical solution given in the reference (point b in Table 6.1, p.

130).

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A cube of rubber is subjected to a sinusoidal displacement controlled G. A. Holzapfel, "On Large load with a mean value of zero Strain Viscoelasticity:

(completely reversed). The load Continuum Formulation amplitude is constant within a full and Finite Element Cyclic Loading of a cycle (4 seconds) and increases Applications to vm234 Rubber Block with each successive cycle. For the Elastomeric Structures",

SOLID185 first period A = 0.01 and it International Journal for increases by 0.01 each cycle until Numerical Methods in the fourth when A = 0.04. At t = 16 Engineering, Vol. 39, seconds the load is removed and 1996, pp. 3903-3926.

the residual stresses are permitted to relax.

Frequency Response A beam is in series with an R. D. Blevins, Formulas of a Prestressed electromechanical transducer. With for Natural Frequency and vm235 Beam a voltage applied to the beam, Mode Shape, Van BEAM188 determine the prestressed natural Nostrand Reinhold Co.,

TRANS126 frequencies of the beam. pg. 144, equation 8-20.

J. R. Gilbert, G. K.

A beam of length L = 80 m at a Hysteresis Calculation Ananthasuresh, S. D.

height T = 0.5 m is suspended 0.7 of a Beam Under Senturia, "3D Modeling of m above a ground plane and is Electrostatic Load Contact Problems and vm236 clamped at either end. Using this PLANE223 Hysteresis in Coupled beam, model the hysteresis (pull-in PLANE182 Electro-Mechanics",

and release behaviors) when it is CONTA178 MEMS, 1996, pp.

placed under electrostatic load.

127-132.

A double universal joint drive shaft Mechanics of the drives a simple slider-crank J. E. Shigley, J. J. Uicker, Revolute and mechanism. Compare the rotations Jr., Theory of Machines Universal Joints at different points in the drive shaft vm239 and Mechanisms, 2nd BEAM188 with the applied rotation. Also, Edition, McGraw-Hill, Inc.,

MPC184 show the linear motion caused by 1995, p.115.

TARGE170 the slider-crank satisfied the appropriate equation.

A composite bar consists of two base materials with 25 rigid beams Thermal Expansion of J.M. Gere, S.P.

embedded along its length. A Rigid Beams in a Timoshenko, Mechanics coefficient of thermal expansion is vm240 Composite Bar of Materials, 2nd Edition, defined for only the rigid beams.

SOLID185 PWS Publishers, 1984, p.

Compare the stresses resulting in MPC184 20-21,71 both solid composite materials when a temperature is applied.

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For the given solenoid actuator with Static Force an applied total coil current of 5000 N.Takahashi, T. Nakata, Computation of a 3-D A-turns, find the magnetic flux and H. Morishige, Solenoid Actuator density (BZ) of the Pole, the Summary of Results for SOLID231 vm241 magnetic flux density (BZ) of the Problem 20 (3-D Static (SOLID232 SOLID236 Arm, and the Magnetic Force in the Force Problem),

Z-direction. The center pole and COMPEL, Vol.14 (1995),

SOLID237 yoke are made of steel pp. 57-75.

MESH200 characterized by the B-H curve The fundamental natural frequency Modal Analysis of a of an annular plate is determined Cyclic Symmetric R. D. Blevins, Formulas using a mode-frequency analysis.

Annular Plate for Natural Frequency and The lower bound is calculated from SOLID185 Mode Shape, New York, the natural frequency of the vm244 SOLID186 NY, VanNostrand annular plates, which are free on SOLID187 Reinhold Publishing Inc.,

the inner radius and fixed on the SHELL181 1979, pp. 246-247, outer. The bounds for the plate SOLSH190 286-287.

frequency are compared to the SHELL281 theoretical results.

A rotor-bearing system is analyzed to determine the whirl speeds. The distributed rotor was modeled as a Campbell Diagrams configuration of six elements with Nelson and and Critical Speeds each element composed of McVaugh,"The Dynamics Using Symmetric subelements. Two undamped of Rotor-Bearing Systems vm247 Bearings linear bearings were located at Using Finite Elements",

BEAM188 positions four and six. Modal Journal of Engineering for MASS21 analysis is performed on rotor Industry, May 1976.

COMBIN14 bearing system with multiple load steps to determine the critical speeds and Campbell values for the system.

Delamination Analysis of Double Cantilever G. Alfano and M. A.

Beam A double cantilever beam of length CrisfieldFinite Element PLANE182 l, width w and height h with an Interface Models for the INTER202 initial crack of length a at the free Delamination Analysis of CONTA171 end is subjected to a maximum Laminated Composites:

PLANE183 vertical displacement Umax at top vm248 Mechanical and INTER203 and bottom free end nodes. Computational Issues, CONTA172 Determine the vertical reaction at International Journal for SOLID185 point P based on the vertical Numerical Methods in INTER205 displacement for the interface Engineering, Vol. 50, pp.

CONTA173 model. 1701-1736 (2001).

TARGE169 TARGE170 NuScale Nonproprietary

A thin interface layer of thickness t Gasket Material Under is defined between two blocks of Uniaxial Compression length l, width W, and height H Loading D placed on top of each other. The Analysis Any Nonlinear Material vm250 blocks are constrained on the left, SOLID185 Verification Text bottom, and back faces and loaded SOLID186 with pressure P on the top face.

INTER195 Determine the pressure-closure INTER194 response for gasket elements.

A square block of length, height Ferdinando Auricchio, and width L is constrained in the X-Robert L. Taylor, and direction on the left face, Shape Memory Alloy Jacob Lubliner, Shape-constrained in the Y-direction rear Under Uniaxial memory alloys:

on the bottom face and constrained Tension Load macromodelling and vm251 in the Z-direction on the rear face PLANE182 numerical simulations of (3-D case only). It is uniaxially PLANE183 the superelastic behavior, loaded with tensile stress of s and SOLID185 Comput. Methods Appl.

unloaded on the top face.

Mech. Engrg., Vol. 146, Determine the stress-strain pp. 281-312 (1997).

response for a Ni-Ti alloy.

N. Aravas, "On the The model is a three dimensional Numerical Integration of a bin with all sides equal to unity. An Class of Pressure Gurson Hydrostatic applied displacement of 0.15 is Dependent Plasticity Tension Benchmark - applied at the nodes corresponding Models", International vm253 3-D Analysis to x = 1, y =1, and z =1. To prevent Journal for Numerical SOLID185 rigid body motion, the model is Methods in Engineering, SOLID186 constrained in the x direction at x =

Vol. 24, pp. 1395-1416, 0, y-direction at y = 0, and z-Section 5.2, Figure 7 direction at z = 0.

(1987).

A rotor-bearing system is analyzed to determine the forward and backward whirl speeds. The Campbell Diagrams distributed rotor was modeled as a Nelson, H.D., McVaugh, and Critical Speeds configuration of six elements with J.M., The Dynamics of Using Symmetric each element composed of Rotor-Bearing Systems Orthotropic Bearings subelements. Two symmetric vm254 Using Finite Elements, PIPE16 orthotropic bearings were located Journal of Engineering for PIPE288 at positions four and six. Modal Industry, Vol 98, pp.

MASS21 analysis is performed on rotor 593-600, 1976 COMBI214 bearing system with multiple load steps to determine the whirl speeds and Campbell values for the system.

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Fracture Mechanics A long plate with a center crack is W.F.Brown, Jr.,

Stress for a Crack in a subjected to an end tensile stress J.E.Srawley, Plane strain Plate using CINT . Symmetry boundary conditions crack toughness testing of vm256 Command are considered and the fracture high strength metallic PLANE183 mechanics stress intensity factor KI materials, ASTM SOLID185 is determined using CINT STP-410, (1966).

SOLID186 command.

The swing consists of a long aluminum beam of rectangular cross-section (width = 1mm, depth

= 5 mm) and a mid-span mass (mass = 0.5 kg). The mass is rigidly connected to the beam at its mid-span position. The beam is suspended at each end by two rigid O.A. Bauchau, G.

links, and is initially at rest. The Damilano, and N.J.

Transient Analysis of rigid links impose a kinematic Theron Numerical a Swing with Two constraint corresponding to fixed Integration of Non-Linear Rigid Links and Beam distance between points O and A, Elastic Multi-Body vm257 1 BEAM188 Systems, International and O2 and E of 0.36 and 0.72, MPC184 Journal for Numerical TARGE170 respectively. The points B and D Methods in Engineering, indicate the quarter and three Vol. 38, 2727-2751 quarter span points of the beam, (1995).

respectively. The loading of the system consists of a triangular pulse in the direction applied at the mid-span mass. This pulse starts at time t = 0 s, reaches a peak value of 2N at t =0.128 s and goes back to zero at t = 0.256 s.

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The BM3 piping model is meshed with PIPE16 and PIPE18 elements.

The model is supported by elastic spring-damper elements (COMBIN14). Lumped mass matrix formulation is used in the modal analysis. Single point response spectrum analysis is then performed with an acceleration R. Morante, Y.

input spectra defined by 75 points Missing Mass with Wang,Reevaluation of (FREQ and SV). The first 14 Rigid Responses regulatory guidance on modes are included in the Effects in Spectrum modal response spectrum analysis. The model is Analysis for BM3 combination methods for vm259 excited in X direction and the Piping Model seismic response modal responses are combined PIPE16 spectrum analysis using SRSS mode combination PIPE18 (NUREG/CR-6645),

method with displacement solution COMBIN14 Brookhaven National output. The analysis is performed Laboratory, Dec 1999.

for three cases:

With missing mass effect (ZPA=0.54g).

With missing mass (ZPA=0.54g) and rigid responses effect (Lindley Method).

With missing mass (ZPA=0.54g) and rigid responses effect (Gupta Method, F1=2.8Hz and F2=6.0Hz).

A beam with internal viscous E.S. Zorzi, H.D. Nelson, damping is simply supported by Rotating Beam with Finite element simulation means of two isotropic undamped Internal Viscous of rotor-bearing systems bearings. Modal analysis is vm261 Damping with internal damping, performed with multiple load steps BEAM188 ASME Journal of to determine the critical speeds and COMBI214 Engineering for Power, logarithmic decrement of the Vol. 99, 1976, pg. 71-76.

system.

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A linear elastic prismatic rod is moving with an initial velocity and is impacting a rigid wall. The shock wave created from impact travels as a compression wave through the rod. During this time, the rod remains in contact with the rigid wall. The compression wave is then N.J.Carpenter, R.L. Taylor reflected as a dilatational wave and M.G. Katona, upon reaching the free end of the Elastic Rod Impacting "Lagrange Constraints For rod and travels back to the contact a Rigid Wall Transient Finite Element surface. The rod gets separated vm265 SHELL181 Surface Contact",

from the rigid wall once the CONTA177 International Journal for dilatational wave reaches the TARGE170 Numerical Methods in contact surface. The time at impact Engineering, vol.32, 1991.

and at separation is determined Pg. 103-128.

from the analysis along with corresponding displacements, velocities and normal contact forces at the contact surface and compared to the solutions given in the reference. The time history plots are also compared to the reference plots.

Two orthogonal beams with similar G. Zavarise and P.

cross section and with an initial out-3-D Crossing Beams Wriggers, Contact with of-plane displacement are brought in Contact with friction between beams in into contact by undergoing large Friction 3-D space", International vm266 displacements in 3-D space.

BEAM188 Journal for Numerical Normal and frictional contact forces CONTA176 Methods in Engineering, are calculated at 0.5, 0.66, 0.83, TARGE170 2000, vol.49, pp.

and 1 second, and then compared 977-1006.

against reference values.

2-D and 3-D Frictional Two parallel linear elastic half Hertz Contact cylinders of radius R are pressed Two Dimensional Mortar PLANE182 by a small distributed pressure p. A Contact Methods for Large CONTA171 tangential pressure, q, is then Deformation Frictional TARGE169 applied to cause friction at the vm272 Sliding, International SURF153 contact interface. The bottom of the Journal for Numerical SOLID185 lower cylinder is fixed in all Methods in Engineering CONTA173 directions. Determine the contact Vol.62, pp 1183-1225.

TARGE170 pressure and friction results across SURF154 the contact interface.

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Auricchio, F. et al.

A block is made of shape memory "Improvements and alloy material. One cycle of uniaxial algorithmeical displacement loading is applied in considerations on a recent Shape Memory Alloy vertical direction. The whole three-dimensional model With Thermal Effect process includes tension, unload, descrbing stress-induced vm273 Under Uniaxial compression, and unload. The solid phase Loading whole loading history repeats with transformation.

SOLID185 body temperature 285.15K and International Journal for 253.15K, respectively. The stress Numerical Methods in history is obtained and compared Engineering, 55.

against the reference solution.

1225-1284. 2002 A rigid block (Youngs modulus E, Poisson ratio , density , length of edge a, area A) is elastically supported by a spring-damper Stabilizing Squeal element and guided by a rail with a Damping velocity . The whole assembly is SOLID185 sliding on the rough ex-ey-plane vm274 CONTA173 (coefficient of friction , normal Any Dynamics Textbook TARGE170 pressure p). Linear perturbation COMBIN14 modal analysis is performed using MASS21 the DAMP eigensolver to determine the damped frequency and modal damping ratio, which is then compared against analytical results.

A series of static electromagnetic Hall Plate in a Uniform analyses is performed on a plate Magnetic Field with length 2a, height 2b, and Meijer, G. Smart Sensor vm277 SOLID236 thickness c to determine the Hall Systems. John Wiley &

CIRCU124 voltage produced by a uniform Sons, Ltd. 2008, p. 252.

MESH200 magnetic field B perpendicular to the plate surfaces Fett, T., Stress Intensity T-Stress for a Crack in A rectangular plate with a center Factors, T-Stresses, a Plate Using the crack is subjected to an end tensile Weight Functions, Institute CINT Command stress Symmetry boundary vm279 of Ceramics in Mechanical PLANE183 conditions are considered and T-Engineering, University of SOLID185 Stress is determined using the Karlsruhe, 2008, pp.

SOLID186 CINT command.

151-152 NuScale Nonproprietary

A steel plate, clamped on one edge Lawrence, C., Aiello, R.

Effect of Stress and free on the other edges, is A., Ernst, M. A., McGee, Stiffening and Spin rotating about an offset axis. The O. G., A NASTRAN Softening on a first bending frequency is Primer for the Analysis of vm281 Rotating Plate determined as a function of the Rotating Flexible Blades, SHELL181 rotational velocity. The analysis is NASA Technical SOLID185 done for two cases: rotation about Memorandum 89861, the Z-axis and about the X-axis. 1987, p. 14 A simple piston-fluid system is modeled using a spring damper Mode-Superposition element (COMBIN14) for the Response Analysis of piston, fluid elements (FLUID30) for a Piston-Fluid System Axisa, F., Antunes, J.,

the fluid column, and a mass FLUID30 Modelling Mechanical vm282 element (MASS21) for the mass of MASS21 Systems: Fluid-Structure the piston,. The contact between COMBIN14 Interaction, 2006, p. 486 the piston and the fluid column is CONTA174 established using the surface-to-TARGE170 surface contact element (CONTA174).

Single point acceleration response spectrum analysis is performed on a vertical tank model that is 200 inches tall and 35 inches in diameter by exciting the structure in the global Z-direction. The tank is supported by a braced leg support and is filled with a fluid with a specific gravity of 1.57. The Acceleration Solution spectrum analysis is performed in Response Biswas, J.K, Duff, C.G.,

with the first four modes and Spectrum Analysis Response Spectrum missing mass to account for the vm284 Using Missing Mass Method with Residual higher modes. The modes are Method Terms, ASME combined using the SRSS mode BEAM188 Publications, April 1978.

combination method and the MASS21 absolute acceleration at different elevation points of the structure is obtained by summing the SRSS modal response with the absolute missing mass response. The accelerations are compared against the reference values shown in Column 9 of Table 1 in the reference document.

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Wear analysis is performed on a block with length L in contact with a rigid plate using a frictionless Wear of a Block standard contact pair. In the first Under Uniform load step, a displacement load is Compression applied on one face of the block to PLANE182 compress the block onto the rigid Any standard engineering vm286 CONTA171 plate. In the second load step, textbook.

TARGE169 displacement is applied on the rigid SOLID185 plate to make it slide, resulting in CONTA173 wear of the block. The contact TARGE170 pressure and amount of wear on the block is computed and compared against the analytical solution.

Two cylinders connected by means Interference Fit of standard frictionless contact are Between Two Budynas, R.G., Nisbett, modeled with an interference fit Cylinders J.K., Shigley's Mechanical vm292 between them. Static analysis is SOLID185 Engineering Design, 9th performed to predict the contact CONTA173 edition, pg. 116, 2011.

pressure between the two TARGE170 cylinders.

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Table 2: SAP2000 Summary of Group 1 (FRAME) Verification Problems Problem Problem SAP2000Frame Element Method of Independent No. Title Features Tested Verification

• Calculation and application of self load

• Projected, uniformly distributed load

• Application of uniformly distributed load in global coordinates Hand calculation using the unit

• Uniformly distributed load 1-001 General Loading load method described on page in frame object local 244 in Cook and Young 1985.

coordinates

• Trapezoidal and triangular distributed load on frames

• Joint moments and forces

• Static analysis of frames under all of these loading types

• The specification of joint patterns

• The application of temperature increase Hand calculation using standard

• Transverse temperature thermal expansion formulas and gradient 1-002 Temperature Loading using Table 3 items 6a and 6c

• The calculation of on page 107 in Roark and displacements in free Young 1975.

expansion

• Reaction forces in restrained case caused by temperature loads The application of:

• Distributed moments Distributed and Hand calculation using equation (uniform, trapezoidal, 1-003 Concentrated 8.1.3 on page 284 in Cook and triangular) to frame objects Moments Young 1985.

• Concentrated moments to frame objects Hand calculation using the beam deflection formulas in Frame local axes rotated Table 3 item 1a and Table 3 1-004 Rotated Local Axes from global axes.

item 2a on pages 96 and 98, Use of AISC sections.

respectively, in Table 3 in Roark and Young 1975.

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• Settlement of support in frame structures

• Rotation of support in frame structures Hand calculation using the unit

• Settlement of support with 1-005 Displacement Loading load method described on page linear (translational) spring 244 in Cook and Young 1985.

• Rotation of support with rotational spring

• Skewed supports

• Skewed support settlement

• Structural behavior of a non-prismatic frame section

• Self-weight calculations

• Linear variation of section Non-Prismatic area Hand calculation using the unit Sections and 1-006

• Linear, parabolic and cubic load method described on page Automatic Frame variation of moment of inertia 244 in Cook and Young 1985.

Subdivision

• Linear variation of section torsional constant

• Automatic frame subdivision The end releases in a frame element, including Axial release Hand calculation using basic 1-007 End Releases Shear release statics.

Bending release The related frame static analysis The partial fixity end releases in a frame element, including Hand calculation using the unit Partial Fixity End 1-008 Shear partial fixity load method described on page Releases Bending partial fixity 244 in Cook and Young 1985.

The application of gravity load to a frame object

• Prestress tendon with parabolic tendon profile and different eccentricities at the Hand calculation using basic two ends Prestress Applied To principles and the unit load 1-009

• Prestress tendon modeled Frame Objects method described on page 244 using loads in Cook and Young 1985.

• Prestress tendon modeled as elements

• Prestress losses NuScale Nonproprietary

The use of end offsets in frames, including Non-rigid offsets Hand calculation using the unit Partially rigid offsets 1-010 End Offsets load method described on page Fully rigid offsets 244 in Cook and Young 1985.

The effect of end offsets on the frame static analysis results Cardinal point 1-011 Insertion Point Hand calculation using statics.

Joint offsets Hand calculation using the unit No Tension and No Tension and compression load method described on page 1-012 Compression Frame limits for frame objects 244 in Cook and Young 1985 Objects End releases together with statics.

Frame line spring Simply Supported assignments Hand calculated using formulas 1-013 Beam on Elastic Static analysis of beam on presented in Problem 3 on page Foundation elastic foundation 23 of Timoshenko 1956.

Automatic frame subdivision Eigenvalue analysis of a Hand calculation based on frame with unequal moment formulas presented on page 1-014 Eigenvalue Problem of inertia values (I22 I33) 313 of Clough and Penzien for bending modes 1975.

Automatic frame subdivision Steady state analysis of frame systems Time history analysis of Comparison with illustrative Steady State frame systems with periodic 1-015 example 20.2 on page 434 of Harmonic Loads loading Paz 1985.

Line mass assignment to frame objects Automatic frame subdivision P-Delta force assignment to Hand calculation using equation Tension Stiffening frame objects 23 on page 28 and equations 1-016 Using P-Delta Nonlinear static analysis 43 and 45 on page 43 of Analysis using the P-Delta option Timoshenko 1956.

Automatic frame subdivision Static nonlinear analysis using the P-Delta option to Hand calculation using vibration Vibration of a String 1-017 provide tension stiffening theory presented on pages 506 Under Tension Modal analysis of frame for through 510 of Kreyszig 1983.

eigenvalues NuScale Nonproprietary

Calculation of bending, Bending, Shear and shear and axial deformations Hand calculation using the unit 1-018 Axial Deformations in in a rigid frame load method described on page a Rigid Frame Frame property modification 244 in Cook and Young 1985.

factors Hand calculation using formulas Buckling analysis of a rigid Buckling of a Rigid presented in Article 2.4 on 1-019 frame Frame pages 62 through 66 of Automatic frame subdivision Timoshenko and Gere 1961.

Modal analysis of frame for Response Spectrum eigenvalues and time Analysis of a Two- Comparison with example 13.11 1-020 periods Dimensional Rigid on page 521 of Chopra 1995.

Response spectrum analysis Frame Joint masses Comparison with results Modal analysis for published in Bathe and Wilson Bathe and Wilson eigenvalues 1972 and comparison with 1-021 Eigenvalue Problem Line mass assignment to results from another computer frame objects program published in Peterson 1981.

• Diaphragm constraint

• Joint force assignments

• Joint mass assignments

• Modal analysis for Comparison with results from Two-Dimensional eigenvalues another computer program Moment Frame with

• Response spectrum published by 1-022 Static and Dynamic analysis Engineering/Analysis and Loads

• Modal time history analysis Computers/ Structures for base excitation International.

• Direct integration time history analysis for base excitation Three-dimensional frame Comparison with results from analysis ASME another computer program 1-023 Modal analysis using Eigenvalue Problem published in Peterson 1981 and eigenvectors in DeSalvo and Swanson 1977.

Joint mass assignments

• Three-dimensional frame analysis Response Spectrum

• Modal analysis using Comparison with results from Analysis of a Three- eigenvectors 1-024 another computer program Dimensional Moment

• Rigid diaphragm constraint published in Peterson 1981.

Frame

• Joint mass assignments

• Response spectrum analysis NuScale Nonproprietary

• Three-dimensional frame analysis Response Spectrum

• Modal analysis using Comparison with results from Analysis of a Three- eigenvectors another computer program 1-025 Dimensional Braced

• Rigid diaphragm constraint published in Frame

• Joint mass assignments Peterson 1981.

• Response spectrum analysis Hand calculation using the unit Static nonlinear analysis of a load method described on page Moment and Shear 1-026 frame structure using 244 in Cook and Young 1985 Hinges moment and shear hinges together with basic deflection formulas and superposition.

Hand calculation using the unit Nonlinear static analysis load method described on page Construction using the construction 1-027 244 in Cook and Young 1985 Sequence Loading sequence loading option together with basic deflection Frame end releases formulas.

Static nonlinear analysis of frame structure with large Large Axial axial displacements using Hand calculation using basic 1-028 Displacements the SAP2000 P-Delta plus statics.

large displacements option Frame end releases Static nonlinear analysis of Hand calculation and Equation frame structure with large Large Bending 4 in Article 7.1 of Chapter 7 on 1-029 bending displacements using Displacements page 91 of Roark and Young the SAP2000 P-Delta plus 1975.

large displacements option Comparison with results Moving load case published in Appendix A of 1-030 Moving Loads Multi-step static load case AASHTO 1990 and hand for vehicles calculation.

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Table 3: SAP2000 Summary of Group 2 (SHELL) Verification Problems Method of Problem Problem Title SAP2000 Shell Element Features Tested Independent No.

Verification Hand calculation based theory in Timoshenko and

• Membrane analysis using shell elements Patch Test Goodier 1951 and

• Plate bending analysis using shell elements With Timoshenko and 2-001

• Thin-plate option Prescribed Woinowsky-Krieger

• Thick-plate option Displacements 1959. Results also

• Joint displacement loading published in MacNeal and Harder 1985.

Hand calculation using the unit load method described

• Membrane analysis using shell elements on page 244 in

• Plate bending analysis using shell elements Cook and Young Straight Beam

• Effect of shell element aspect ratio 1985 and using 2-002 with Static

• Effect of geometrical distortion of shell element from formulas from Loads rectangular Roark and Young

• Joint force loading 1975. Results also published in MacNeal and Harder 1985.

• Membrane analysis using shell elements

• Plate bending analysis using shell elements

• Joint force loading Hand calculation using the unit load method described on page 244 in Curved Beam Cook and Young 2-003 with Static 1985.

Loads Results also published in MacNeal and Harder 1985.

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Hand calculation using the unit load method described on page 244 in Twisted Beam

• Membrane analysis using shell elements Cook and Young 2-004 with Static

• Plate bending analysis using shell elements 1985.

Loads

• Joint force loading Results also published in MacNeal and Harder 1985.

Hand calculation based theory in Timoshenko and Rectangular

• Plate bending analysis using shell elements Woinowsky-Krieger 2-005 Plate with

• Uniform load applied to shell elements 1959. Results also Static Loads

• Joint force loading published in MacNeal and Harder 1985.

Some results published in MacNeal and Harder 1985.

Other results

• Three-dimensional analysis using shell elements Scordelis -Lo scaled from plotted

• Self-weight applied to shell elements 2-006 Roof with results in

• Gravity load applied to shell elements Static Loads Zienkiewicz1977

• Uniform load applied to shell elements that were calculated using theory presented in Scordelis and Lo 1964.

Hemispherical

• Three-dimensional analysis using shell elements Result published in Shell Structure 2-007

• Joint local axes MacNeal and with Static

• Joint force loads Harder 1985.

Loads Cantilever

• Eigenvalue analysis using shell elements Hand calculation Plate

• Area object mass assignment using Table 7.7 on 2-008 Eigenvalue

• Area object automatic mesh page 7-30 of Harris Problem

• Area object stiffness modifiers and Crede 1976.

Hand calculation using equation 185 Plate on

• Plate bending analysis using shell elements on page 275 of 2-009 Elastic

• Area object spring assignment Timoshenko and Foundation

• Joint force loads Woinowsky-Krieger 1959.

Hand calculation Cylinder with

• Three-dimensional analysis using shell elements using item 1b in 2-010 Internal

• Surface pressure load applied to shell elements Table 29 on page Pressure

• Joint local axes 448 of Roark and Young 1975.

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Results scaled from plotted ASME results in Cooling Tower

• Three-dimensional analysis using shell elements Zienkiewicz1977 2-011 Problem with

• Joint patterns that were Static Wind

• Shell element surface pressure load using joint pattern calculated using Pressure theory presented in Albasiny and Martin 1967.

Results published Plate Bending

• Plate bending analysis of shell elements when shear in example shown when Shear deformations are significant 2-012 on page 376 of Deformations

• Area object stiffness modifiers Roark and Young Are Significant

• Frame distributed loads 1975.

Temperature Hand calculation Load that Is using equation 2-013 Constant

• Temperature loading for shell elements 1.3.4 on page 9 of Through Shell Cook and Young Thickness 1985.

Hand calculation Temperature using formulas

• Temperature gradient loading for shell elements Gradient presented in item 2-014

• Area object local axes Through Shell 8e of Table 24 on

• Joint local axes Thickness page 361 of Roark and Young 1975.

Hand calculated

• Plate bending analysis of shells using theory Orthotropic 2-015

• Orthotropic material properties presented in Plate

• Area object stiffness modifiers Chapter 6 of Ugural 1981.

• Buckling analysis of shells Hand calculated

• Automatic area meshing (N x N) with added restraints using theory Out-of-Plane

• Joint springs 2-016 presented in Buckling

• Frame property modifiers Timoshenko and

• Frame distributed load Gere 1961.

• Frame automatic subdivide at intermediate joints Hand calculated

• Buckling analysis of shells using equation 2-4 In-Plane 2-017

• Joint force loads on page 48 of Buckling

• Active degrees of freedom Timoshenko and Gere 1961.

• Static nonlinear analysis of shell structure with large axial Large Axial displacements using the SAP2000 P-Delta plus large Hand calculation 2-018 Displacements displacements option using basic statics.

• Joint constraints Hand calculation

• Static nonlinear analysis of shell structure with large and Equation 4 in Large Bending bending displacements using the SAP2000 P-Delta plus Article 7.1 of 2-019 Displacements large displacements option Chapter 7 on page

• Automatic area meshing 91 of Roark and Young 1975.

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• Prestress tendon with parabolic tendon profile and different Hand calculation eccentricities at the two ends using basic Prestress

• Prestress tendon modeled using loads and applied to area principles and the 2-020 Applied to objects unit load method Area Objects

• Prestress tendon modeled as elements and applied to area described on page objects 244 in Cook and

• Prestress losses Young 1985.

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Table 4: SAP2000 Summary of Group 3 (PLANE) Verification Problems Method of Problem Problem Title SAP2000 Plane Element Features Tested Independent No.

Verification Hand calculation based theory in Patch Test Timoshenko and

• Membrane analysis using plane stress elements With Goodier 1951.

3-001

• Incompatible bending mode option for plane elements Prescribed Results also

• Joint displacement loading Displacements published in MacNeal and Harder 1985.

Hand calculation using the unit load method described on page 244 in

• Membrane analysis using plane elements Cook and Young Straight Beam

• Effect of plane element aspect ratio 1985 and using 3-002 with Static

• Effect of geometrical distortion of plane element from rectangular formulas from Loads

• Joint force loading Roark and Young 1975.

Results also published in MacNeal and Harder 1985.

• Membrane analysis using plane stress elements

• Joint force loading Hand calculation using the unit load method described on Curved Beam Page 244 in 3-003 with Static Cook and Young Loads 1985.

Results also published in MacNeal and Harder 1985.

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Hand calculation based on theory in Timoshenko 1956 and based

• Analysis using plane stress elements on formulas in Thick-Walled 3-004

• Analysis using plane strain elements Roark and Cylinder

• Plane surface pressure load Young 1975.

Results also published in MacNeal and Harder 1985.

Hand calculation

• Pore pressure loading for planes 3-005 Pore Pressure using basic

• Joint pattern principles.

Table 5: SAP2000 Summary of Group 4 (ASOLID) Verification Problems Problem SAP2000 ASOLID Element Method of Independent Problem Title No. FeaturesTested Verification Analysis using asolid elements Soil Supporting Hand calculation based on data 4-001 Uniformly Loaded Asolid surface pressure load presented in Poulos and Davis Circular Footing 1974.

Incompatible bending modes for asolid objects Analysis using asolid Hand calculation based on Thick-Walled elements theory in Timoshenko 1956.

4-002 Cylinder Results also published in Asolid surface pressure load MacNeal and Harder 1985.

Analysis using asolid Hand calculation based on Rotating Annular elements equations presented in Item 8 4-003 Disk on page 567 of Roark and Asolid rotation load Young 1975.

Pore pressure loading for asolids Hand calculation using basic 4-004 Pore Pressure principles.

Joint pattern NuScale Nonproprietary

Table 6: SAP2000 Summary of Group 5 (SOLID) Verification Problems Method of Problem Problem SAP2000 Solid Element Features Tested Independent No. Title Verification Patch Test Results also With

• Patch test using solid elements published in 5-001 Prescribed

• Joint displacement loading MacNeal and Displacements Harder 1985.

Hand calculation using the unit load method described

• Solid object bending with and without the incompatible modes on page 244 in Straight Beam option Cook and Young 5-002 with Static

• Effect of solid object aspect ratio 1985.

Loads

• Effect of geometrical distortion of solid object from a cube Results also

• Joint force loading published in MacNeal and Harder 1985.

• Solid object bending with the incompatible bending modes option

• Joint force loading Hand calculation using the unit load method described on page 244 in Curved Beam Cook and Young 5-003 with Static 1985.

Loads Results also published in MacNeal and Harder 1985.

Hand calculation using the unit load method described on page 244 in Twisted Beam

• Solid object bending and twist with the incompatible bending Cook and Young 5-004 with Static modes option 1985.

Loads

• Joint force loading Results also published in MacNeal and Harder 1985.

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Hand calculation based theory in Timoshenko and Rectangular

• Plate bending analysis using solid elements Woinowsky-Krieger 5-005 Plate with

• Surface pressure load applied to solid objects 1959. Results also Static Loads

• Joint force loading published in MacNeal and Harder 1985.

Some results published in MacNeal and Harder 1985.

Other results Scordelis -Lo

• Three-dimensional analysis using solid objects scaled from plotted 5-006 Roof with

• Self-weight applied to solid objects results in Static Loads

• Gravity load applied to shell objects Zienkiewicz1977 that were calculated using theory presented in Scordelis and Lo 1964.

Hemispherical Results published Dome

• Three-dimensional analysis using solid elements 5-007 in MacNeal and Structure with

• Joint force loads Harder 1985.

Static Loads Hand calculation based on theory in

• Analysis using solid elements Timoshenko 1956.

Thick-Walled 5-008

• Solid surface pressure load Results also Cylinder

• Joint local axes published in MacNeal and Harder 1985.

• Prestress tendon with parabolic tendon profile and different Hand calculation eccentricities at the two ends using basic Prestress

• Prestress tendon modeled using loads and applied to solid principles and the 5-009 Applied to objects unit load method Solid Objects

• Prestress tendon modeled as elements and applied to solid described on page objects 244 in Cook and

• Prestress losses Young 1985.

Hand calculation

• Buckling analysis of solids using equation 2-4 5-010 Buckling

• Joint force loads on page 48 of

• Active degrees of freedom Timoshenko and Gere 1961.

Hand calculation using equation Temperature 5-011

• Temperature loading for solid elements 1.3.4 on page 9 of Load Cook and Young 1985.

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Hand calculation

• Plate bending analysis using solid elements using equation 185 Plate on

• Solid object surface spring assignment on page 275 of 5-012 Elastic

• Solid object automatic mesh Timoshenko and Foundation

• Joint force loads Woinowsky-Krieger 1959.

• Pore pressure loading for solids Hand calculation 5-013 Pore Pressure

• Solid local axis assignments using basic

• Joint pattern principles.

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Table 7: SAP2000 Summary of Group 6 (LINK) Verification Problems Problem SAP2000 Link Element Method of Independent Problem Title No. Features Tested Verification

• Linear links

• Modal load case for Hand calculation using eigenvectors Linear Link with Ramp theory presented in section 6-001

• Modal time history load case Loading 4.5 on Pages 126 through

• Direct integration time 129 of Chopra 1995.

history load case

• Ramp loading

• Multi-linear links Comparison with defined 6-002 Multi-linear Elastic Link

• Displacement-controlled link force- deformation nonlinear static analysis characteristics.

• Gap element links

• Force-controlled nonlinear static analysis

• Nonlinear modal time history analysis Hand calculation using the

• Nonlinear direct time history unit load method described 6-003 Gap Element analysis on page 244 in Cook and

• Frame point loads Young 1985.

• Joint force loads

• Joint mass assignments

• Ramp loading for time histories

• Hook element links Hand calculation using

• Force-controlled nonlinear 6-004 Hook Element standard thermal expansion static analysis formulas.

• Frame temperature loads

• Damper element links

• Linear link elements

• Nonlinear modal time history Hand calculation using Damper Element Under 6-005 analysis equation 3.2.6 on page 7 in Harmonic Loading

• Nonlinear direct integration Chopra 1995.

time history analysis

• Joint force loads NuScale Nonproprietary

• Damper links with linear velocity exponents

• Frame end length offsets

• Joint mass assignments

• Modal analysis for Ritz Comparison with vectors experimental results from

• Linear modal time history SUNY Buffalo Damper with shake table tests published 6-006 analysis Linear Velocity Exponent in Section 5, pages 61

• Nonlinear modal time history through 73, of Scheller and analysis Constantinou 1999.

• Linear direct integration time history analysis

• Nonlinear direct integration time history analysis

• Generalized displacements

• Damper links with nonlinear velocity exponents

• Frame end length offsets Comparison with

• Joint mass assignments experimental results from SUNY Buffalo Damper with

• Modal analysis for Ritz shake table tests published 6-007 Nonlinear Velocity vectors in Section 5, pages 61 Exponent

• Nonlinear modal time history through 73, of Scheller and analysis Constantinou 1999.

• Nonlinear direct integration time history analysis

• Generalized displacements

• Plastic Wen links

• Displacement-controlled Comparison with defined 6-008 Plastic Wen Link nonlinear static analysis link force- deformation

• Link local axis assignments characteristics.

• Link gravity load

• Plastic kinematic links Comparison with defined

• Displacement-controlled 6-009 Plastic Kinematic Link link force- deformation nonlinear static analysis characteristics.

• Link gravity load

• Rubber isolator links

• Linear links

• Zero-length, two-joint link Comparison with results elements from the computer program

• Diaphragm constraints 3D-BASIS-ME (see SUNY Buffalo Eight-Story

• Modal analysis for Ritz Tsopelas, Constantinou and 6-010 Building with Rubber vectors Reinhorn 1994) published Isolators

• Nonlinear modal time history in Section 2, pages 5 analysis through 23, of Scheller and

• Nonlinear direct integration Constantinou 1999.

time history analysis

• Generalized displacements NuScale Nonproprietary

• Friction pendulum link elements

• Damper link elements

• Zero-length, two-joint link elements Comparison with

• Diaphragm constraints experimental results from SUNY Buffalo Seven-Story

• Frame end length offsets shake table tests published 6-011 Building with Friction

• Modal analysis for Ritz in Section 4, pages 43 Pendulum Isolators vectors through 59, of Scheller and

• Nonlinear modal time history Constantinou 1999.

analysis

• Nonlinear direct integration time history analysis

• Joint masses Hand calculation using formulas and theory Frequency- Dependent

• Frequency-dependent links 6-012 presented in section 3.2 on Links

• Steady state analysis pages 68 through 69 of Chopra 1995.

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Table 8: SASSI2010 Verification Problem No. 1 Analysis Cases SASSI Element Method of SASSI Model Case Type Forming Excitation Description No. Verified Impedance Determine horizontal and Horizontal and rocking impedance of a Direct (Flexible (a) 3D Brick rocking harmonic rigid massless circular Volume) force excitation.

foundation.

Horizontal ground 1 Determine SSI response motion excitation of a surface founded 3D Brick, Direct (Flexible prescribed in the form (b) pressurized water reactor 3D Beam Volume) of vertically (PWR) containment propagating SV building.

wave.

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Table 9: SASSI2010 Verification Problem No. 2 Analysis Cases SASSI Element Method of SASSI Model Case Type Forming Excitation Description No. Verified Impedance Scattering response Horizontal ground motion of embedded rigid excitation prescribed in the (a) 3D Brick cylinder, H=0.5,

• Direct form of horizontally uniform soil profile.

• Extended propagating SH wave.

1 Subtraction Horizontal ground motion Same as

• Subtraction excitation prescribed in the (b) Same as Case 1(a).

Case 1(a) form of vertically propagating SV wave.

Scattering response Horizontal ground motion of embedded rigid excitation prescribed in the (a) 3D Brick cylinder, H=1.0,

• Direct form of horizontally uniform soil profile.

• Extended propagating SH wave.

2 Subtraction Horizontal ground motion Same as

• Subtraction excitation prescribed in the (b) Same as Case 2(a).

Case 2(a) form of vertically propagating SV wave.

Scattering response Horizontal ground motion of embedded rigid excitation prescribed in the (a) 3D Brick cylinder, H=2.0,

• Direct form of horizontally uniform soil profile.

• Extended propagating SH wave.

3 Subtraction Horizontal ground motion Same as

• Subtraction excitation prescribed in the (b) Same as Case 3(a).

Case 3(a) form of vertically propagating SV wave.

Scattering response

• Direct Horizontal ground motion of embedded rigid

• Extended excitation prescribed in the 4 - 3D Brick cylinder, H=1.0, Subtraction form of vertically propagating inverted soil profile.

• Subtraction SV wave.

Scattering response

• Direct Horizontal ground motion of embedded rigid

• Extended excitation prescribed in the 5 - 3D Brick cylinder, H=2.0, Subtraction form of vertically propagating inverted soil profile.

• Subtraction SV wave.

Scattering response

• Direct Horizontal ground motion of embedded rigid

• Extended excitation prescribed in the 6 - 3D Brick cylinder, H=1.0, Subtraction form of vertically propagating increasing soil profile.

• Subtraction SV wave.

Scattering response

• Direct Horizontal ground motion of embedded rigid

• Extended excitation prescribed in the 7 - 3D Brick cylinder, H=2.0, Subtraction form of vertically propagating increasing soil profile.

• Subtraction SV wave.

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Table 10: SASSI2010 Verification Problem No. 3 Analysis Cases SASSI Method of Element Type SASSI Model Case Forming Excitation Verified Description No. Impedance Horizontal ground

• Direct (Flexible motion excitation 3D Brick, 3D SSI Response of Volume) prescribed in the 1 Plate/Shell, 3D Lotung 1/4 Scale

• Extended form of vertically Beam Containment Model. Subtraction propagating SV

• Subtraction wave.

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Table 11: SASSI2010 Verification Problem No. 4 Analysis Cases SASSI Method of Element Case SASSI Model Description Forming Excitation Type Verified No. Impedance Horizontal and vertical Horizontal and 3D Brick, 3D response at the pile head of a vertical harmonic 1 Inter-Pile, 3D single pile in a homogeneous Subtraction loading applied at Beam halfspace using inter-pile center of pilecap.

elements.

Horizontal and vertical Horizontal and 3D Brick, 3D response at the pile head of a vertical harmonic 2 Inter-Pile, 3D 2x2 pile group with S/D=2 in Subtraction loading applied at Beam a homogeneous halfspace center of pilecap.

using inter-pile elements.

Horizontal and vertical Horizontal and 3D Brick, 3D response at the pile head of a vertical harmonic 3 Inter-Pile, 3D 2x2 pile group with S/D=5 in Subtraction loading applied at Beam a homogeneous halfspace center of pilecap.

using inter-pile elements.

Horizontal and vertical Horizontal and 3D Brick, 3D response at the pile head of a vertical harmonic 4 Inter-Pile, 3D 3x3 pile group with S/D=2 in Subtraction loading applied at Beam a homogeneous halfspace center of pilecap.

using inter-pile elements.

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Table 12: SASSI2010 Verification Problem No. 5 Analysis Cases SASSI Element Method of Problem Type SASSI Model Description Forming Excitation 5

Verified Impedance Case No.

Horizontal and vertical response at the pile head of Horizontal and 3D Brick, 2x2 pile groups with S/D=2, 5, vertical harmonic 1 Direct 3D Beam and 10 in a homogeneous loading applied at halfspace using the pile center of pilecap.

impedance method.

Horizontal and vertical response at the pile head of Horizontal and 3D Brick, 3x3 pile groups with S/D=2, 5, vertical harmonic 2 Direct 3D Beam and 10 in a homogeneous loading applied at halfspace using the pile center of pilecap.

impedance method.

Horizontal and vertical response at the pile head of Horizontal and 3D Brick, 4x4 pile groups with S/D=2, 5, vertical harmonic 3 Direct 3D Beam and 10 in a homogeneous loading applied at halfspace using the pile center of pilecap.

impedance method.

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Table 13: SASSI2010 Verification Problem No. 6 Analysis Cases SASSI Element Method of Problem SASSI Model Type Forming Excitation 6 Description Verified Impedance Case No.

Horizontal ground Determine SSI response motion excitation 3D Thick of a surface-founded prescribed in the form of 1 Shell, 3D pressurized water reactor Direct horizontally propagating Beam (PWR) containment SV wave. Coherent building. ground motion (30 time histories)

Horizontal ground Determine SSI response motion excitation 3D Thick of a surface-founded prescribed in the form of 2 Shell, 3D pressurized water reactor Direct horizontally propagating Beam (PWR) containment SV wave. Coherent building. ground motion (Random Vibration Theory)

Horizontal ground Determine SSI response motion excitation 3D Thick of a surface-founded prescribed in the form of 3 Shell, 3D pressurized water reactor Direct horizontally propagating Beam (PWR) containment SV wave. Incoherent building. ground motion (30 time histories)

Horizontal ground Determine SSI response motion excitation 3D Thick of a surface-founded prescribed in the form of 4 Shell, 3D pressurized water reactor Direct horizontally propagating Beam (PWR) containment SV wave. Incoherent building. ground motion (Random Vibration Theory)

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Table 14: SASSI2010 Verification Problem No. 7 Analysis Cases SASSI Proble Element Type m7 SASSI Model Description Excitation Verified Case No.

Two elements form a column of 1'x1' in cross section and 4' in height Vertical harmonic (a) Rectangular Brick supported on the surface of a rigid force excitation 1

halfspace.

Four elements form the same column Vertical harmonic (b) Triangular Brick as in Case 1(a) force excitation Harmonic lateral Five elements were used to form a force excitations (a) 3D Beam cantilever beam supported on the applied at the tip of surface of a rigid halfspace.

the beam.

Horizontal ground motion excitation 2

prescribed in the (b) 3D Beam Same as Case 2(a) form of vertically propagating SV wave.

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

A 100'x100' x10' vertical square plate Out-of-plane supported on horizontal plate of the (a) 3D Plate/Shell horizontal harmonic same size supported on a rigid line-load excitations 3 halfspace.

In-plane horizontal (b) same as 3(a) Same as 3(a) except thickness=20' harmonic line-load excitation Two elements form a vertical wall of a Harmonic axial load (a) 2D Plane Strain unit width supported on the surface of a excitation applied at 4 rigid halfspace. top of the wall Same as Case 4(a).

(b) 2D Plane Strain Same as Case 4(a)

Test COMBIN module.

Two elements form two single-degree-Vertical harmonic 5 - 3D Spring of-freedom (SDOF) systems supported force excitations on the surface of a rigid halfspace.

3D Generalized Vertical harmonic 6 - Stiffness/Mass (Same as for 3D Springs) force excitations Matrix A 100'x100' x10' vertical square plate Horizontal and 3D Thick Shell supported on horizontal plate of the 7 - vertical harmonic Element same size supported on a rigid line-load excitations halfspace.

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Table 15: SASSI2010 Verification Problem No. 8 Analysis Cases SASSI Proble Element Type m8 SASSI Model Description Excitation Verified Case No.

A rigid massless strip foundation on the surface of a uniform viscoelastic soil overlaying rigid Vertical 2D Plane (a) rock. The strip foundation was modeled in 2D harmonic force Strain using a one-half model consisting of 5 plane- excitation strain elements and 12 node points.

1 A rigid massless strip foundation on the surface of a uniform viscoelastic soil overlaying rigid Vertical rock. The strip foundation was modeled in 3D (b) 3D Plate/Shell harmonic force as an elongated rectangular foundation using a excitation one-quarter model consisting of 250 3D flat plate/shell elements and 306 node points.

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Table 16: SASSI2010 Verification Problem No. 9 Analysis Cases SASSI Element Problem 9 Type Model Description Excitation Case No. Verified

• Horizontal ground motion excitation prescribed in the A rigid circular disk resting on a form of vertically uniform elastic half space 3D Brick, propagating SV wave.

1 subjected to seismic ground 3D Beam

• Vertical ground motion motion including the effects of excitation prescribed in the incoherency.

form of vertically propagating P wave.

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Table 17: SASSI2010 Verification Problem No. 10 Analysis Cases SASSI Element Problem Methods and Results of Type Model Description 10 Case Verification Verified No.

• Comparing total base reactions due to gravity in the three global directions calculated by SASSI2010 with those verified by SAP2000.

The differences in reactions are less than 0.00015%.

• Comparing the structural frequencies calculated by SASSI2010 with those by verified A surface-founded, fixed- SAP2000.

base nuclear reactor building The major structural frequencies SASSI model described in obtained at the amplification peaks Reference 14 of ER- in the transfer functions calculated F010-6084, Rev. 0. by SASSI2010 are compared with The model has a total weight the corresponding modal of 859,078 kips and consists frequencies by SAP2000.

Brick, of: The differences in structural 1 Beam, frequencies between SASSI2010 32,378 nodes Shell, Link and SAP2000 are less than 8%.

12,075 solid elements The frequency differences are beam 6,453 deemed acceptable. The elements differences can be attributed mostly shell (plate) 18,818 to elements

a. SASSI2010 cannot completely link (spring) 3,306 simulate the fixed-base condition by elements seating the reactor building on a very stiff free-field half space.

b. Different methods in assigning material damping between SASSI2010 (complex damping) and SAP2000 (Rayleigh damping).

c. Two different numerical solution procedures between SASSI2010 (frequency domain) and SAP2000 (time domain).

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• Comparing total base reactions due to gravity in the three global directions calculated by SASSI2010 with those verified by SAP2000.

The differences in reactions are less than 0.0025%.

• Comparing the structural frequencies calculated by SASSI2010 with those by verified SAP2000.

The major structural frequencies A surface-founded, fixed- obtained at the amplification peaks base nuclear control building in the transfer functions calculated SASSI model. by SASSI2010 are compared with The model has a total weight the corresponding modal of 127,750 kips and consists frequencies by SAP2000.

Brick, of: The differences in structural 2 Beam, 9,279 nodes frequencies between SASSI2010 Shell, Link 3,966 solid elements and SAP2000 are less than 4%.

1,393 beam elements The frequency differences are shell (plate) deemed acceptable. The 4,069 elements differences can be attributed mostly link (spring) to 864 elements a. SASSI2010 cannot completely simulate the fixed-base condition by seating the reactor building on a very stiff free-field half space.

b. Different methods in assigning material damping between SASSI2010 (complex damping) and SAP2000 (Rayleigh damping).

c. Two different numerical solution procedures between SASSI2010 (frequency domain) and SAP2000 (time domain).

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Table 18: SHAKE2000 Verification Problems SHAKE2000 SHAKE2000 SHAKE2000 Verification Excitation Problem Capabilities to be Methodology Problem Input No. Verified Description

• Amplification Spectrum, i.e., ratio of acceleration amplitudes between any two layers.

Uniform undamped

• Shear strain/stress elastic half space Free-field time history subjected to a horizontal response calculation Closed-form 1 harmonic ground harmonic

• Calculation of solution motion at the soil acceleration maximum shear surface, i.e., free-strain/stress vs.

field input motion depth

• Calculation of maximum acceleration vs.

depth Two-layered soil

• Amplification subjected to a Free-field Spectrum at any harmonic ground horizontal Closed-form 2 typical layer motion at the soil harmonic solution

• Amplification vs.

surface, i.e., free- acceleration depth field input motion Multi-layered soil Harmonic subjected to a horizontal Amplification Closed-form 3 harmonic ground excitation at Spectrum solution motion at the top of bedrock bedrock.

• Amplification Multi-layered soil Horizontal Spectrum Results subjected to a seismic

• Calculation of calculated by a 4 seismic ground excitation at transient validated motion at the Ground acceleration SHAKE Ground Surface. Surface response time Program history NuScale Nonproprietary

• Calculation of strain-compatible soil shear modulus and

• Manual damping ratios for iteration Multi-layered soil soil layers through Horizontal

• Response subjected to a iteration seismic Spectrum 5 seismic ground

• Calculation of excitation at calculated by motion at the acceleration top of bedrock the validated bedrock. response spectrum SAP2000 of acceleration Program response time history of any soil layer Uniform undamped elastic half -space modeled by 200 Free-field Verify the limitation soil layers horizontal on the maximum Closed-form 6 subjected to a sinusoidal number of layers of solution harmonic ground acceleration 200.

motion at the soil surface, i.e., free-field input motion NuScale Nonproprietary

Table 19: RSPMATCH Verification Problems RspMatchEDT RspMatch2009 Capability to Methodology Test Case No. Verify Modify a seed acceleration time The target spectrum used is from an history so that the response ARES calculation. The seed 1 spectrum of the modified time acceleration time history used is from history closely resembles a published data of an actual recorded target spectrum. earthquake.

The response spectrum calculated by the program for an arbitrary selected Accurately generate a response 2 acceleration time history is compared spectrum.

with one calculated by the validated program SAP2000.

Impact on DCA:

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

NuScale Nonproprietary

NuScale Final Safety Analysis Report Seismic Design 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, Poissons 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.

Tier 2 3.7-377 Draft Revision 1

NuScale Final Safety Analysis Report Seismic Design 3.7.5.2 SAP2000 3.7.5.2.1 Description 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.

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

RAI 03.07.02-7 3.7.5.2.3 Validation and Verification 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.

3.7.5.2.4 Extent of Use 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 3.7.5.3.1 Description RAI 03.07.02-7 Tier 2 3.7-378 Draft Revision 1

NuScale Final Safety Analysis Report Seismic Design 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.

3.7.5.3.2 Version Used SASSI2010 Version 1.0, Berkeley, California RAI 03.07.02-7 3.7.5.3.3 Validation and Verification 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.

3.7.5.3.4 Extent of Use 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 3.7.5.4.1 Description 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.

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

Tier 2 3.7-379 Draft Revision 1

NuScale Final Safety Analysis Report Seismic Design RAI 03.07.02-7 3.7.5.4.3 Validation and Verification 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.

3.7.5.4.4 Extent of Use 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 3.7.5.5.1 Description 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.

3.7.5.5.2 Version Used RspMatch2009, Version 2009 RAI 03.07.02-7 3.7.5.5.3 Validation and Verification 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.

3.7.5.5.4 Extent of Use 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 Tier 2 3.7-380 Draft Revision 1

NuScale Final Safety Analysis Report Seismic Design 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 3.7.5.6.1 Description 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.

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

RAI 03.07.02-7 3.7.5.6.3 Validation and Verification 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.

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

Tier 2 3.7-381 Draft Revision 1