Latest revision as of 10:12, 13 May 2021

Text

Rev 0 to Pistar Program Verification Rept
	ML20215B465
Person / Time
Site:	Arkansas Nuclear
Issue date:	01/31/1977
From:	Arterburn J, Mattison S, Petrokas R; NUTECH ENGINEERS, INC.
To:	;
Shared Package
ML20215B273	List: ML20215B269; ML20215B439; ML20215B465; ML20215B508; ML20215B530; ML20215B545; ML20215B568;
References
	TR-76-001, TR-76-001-R0, TR-76-1, TR-76-1-R, NUDOCS 8706170338
	Download: ML20215B465 (968)
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        -o'    '                                             NUTECH Topical-Report TR-76-001 File Number: 00:800:0004 Revision 0 PISTAR PROGRAM VERIFICATION REPORT i

I l Prepared by Nuclear Technology, Inc. I i

                                                                               --_m.. ..-   ,

L L

                                                               \                          ,

1 i Prepared by: t . Approved by: h< Jon R. Arterburn Robert F. ?etrokas, P.E. Engineering Specialist Engin ring Mgr Mechanical Sys s ing 4 - Released by: . Sandra J. Mattison Robert E. Keever, P.E. Engineering Analyst Executive Vice President

Reviewed by: 8, f /P/ W r =J Date: /977 - D. K. McWilliams, P.E. _ Project Engineer (/ () 8706170338 870612 PDR ADOCK 05000313 nutech P PM

Revision Control Sheet SUBJ ECT: PISTAR PROGRAM VERIFICATION REPORT NUMBER: TR-76-001 REPORT Pre- Accuracy Criteria Pre- Accuracy Criteris: Page Rev pared Check Check Page Rev pared Check Check MfL M

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SUBJECT:

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c. Revision Control Sheet SUBJ ECT: PISTAR PROGRAM VERIFICATION REPORT NUMBER: TR-76-001 REPORT , 1 Pre- Accuracy Criteria Pre- Accuracy Criteria , Page Rev pared Check Check Page Rev pared Check Check 11.11 0 M S#M %4 ' 11.12 0 11.13 0 11.14 0

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TR-76-001

                                                            . Revision 0
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TABLE OF CONTENTS 4 PAGE I l

1.0 INTRODUCTION

AND CRITERIA : 1.1-2.0 GEOMETRY GENERATION PHASE 2.1 ; 2.1 Offset Generator 2.4 'j T 2.2 Optimization of Nodal Bandwidth 2.7 i 3.0 STATIC ANALYSIS 3.1 3.1 Deadweight 3.7 3.2 Thermal. Expansion 3.15 3.3 Anchor Displacement 3.23 i 3.4 Combined Loads 3.31 j 4.0 EIGENVALUE EXTRACTION ANALYSIS 4.1 4.1 Determinant Search Solver 4.6 4.1.1 Frequencies (Determinant Search) 4.7 1 4.1.2 4.2 Mode Shapes (Determinant Search) 4.9 Subspace Iteration Solver 4.11 4.2.1 Frequencies (Subspace Iteration) 4.14 [ 4.2.2 5.0 Mode Shapes (Subspace Iteration) 4.16 RESPONSE SPECTRUM ANALYSIS 5.1 5.1 RSS Modal Response 5.13 1.. 5.2 CSM Modal Response 5.21 6.0 FORCED DYNAMIC TIME HISTORY ANALYSIS 6.1 f- 6.1 Direct Integration Solver 6.7 6.2 Modal Superposition Solver 6.10 i l 7.0 LOAD COMBINATION 71 L 7.1 Direct or Algebraic Summation 7.6 7.2 Absolute Summation 7.14-7.3 RSS Summation 7.22 8.0 HEAT TRANSFER ANALYSIS (HOTPIPE) 8.1 9.0 ASME SECTION III - CLASS 1 EVALUATION 1- 9.1 Flexibility Factors 9.1 9.2 Stress Indices 9.3 Evaluation 10.0 ASME SECTION III - CLASS 2 EVALUATION 10.1 ' n 10.1 Flexibility Factors 10.7 10.2 Stress Intensification Factors 10.9 10.3 Evaluation 10.11 v 1 nutech

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                               '                     TR-76-001              h Revision 0                     .

TABLE OF CONTENTS (Cont) PAGE 11.0 ASME SECTION III CLASS 3 EVALUATION 11.1 11.1 Flexibility Factors 11.7 11.2 Stress Intensification Factors 11.9 f 11.3 Evaluation 11.11 12.0 ANSI B31.1 EVALUATION 12.1 12.1 -Flexibility Factors f 12.2 Stress Intensification Factors I 12.3 Evaluation 13.0 13.1 ANSI B31.7 EVALUATION Flexibility Factors 13.1 f 13.2 Stress Indices 13.3 Evaluation f.

14.0 REFERENCES

14.1 APPENDIX.A* - Computer Output - Geometry Generation Phase (Section 2.0) APPENDIX B* - Computer Output - Static Analysis (Section 3.0) APPENDIX C* - Computer Output - Eigenvalue Extraction Analysis (Section 4.0) f-s APPENDIX D* - Computer Output - Response Spectrum Analysis lL, (Section 5.0)

                                                                        ~
       , APPENDIX E*  -

Computer Output - Forced Dynamic Time History. s (Section 6.0) { APPENDIX F* - Computer Output - Load Combination (Section 7.0) (I k-j APPENDIX G* - Computer Output - Heat Transfer Analysis (HOTPIPE) (Section 8.0) f

APPENDIX H* - Computer Output - ASME Section III Class 1 Evaluation (Section 9.0) l

                                                                             *j v     APPENDIX I*  -

Computer Output - ASME Section III Class 2 Evaluation (Section 10.0) ' j APPENDIX J* - Computer Output - ASME Section III Class 3 Evaluation (Section 11.0) APPENDIX K* - Computer Output - ANSI B31.1 Evaluation , (Section 12.0) APPENDIX L* - Computer Output - ANSI B31.7 Evaluation (Section 13.0) -

Appendices under separate cover vi ._

r-TR-76-001- 9 Revision'.0 1 LIST OF ILLUSTRATIONS s

                                                                                     . I 1
         . FIGURE NUMBER                 TITLE                     PAGE            l 2.0-1       Piping System Model -                    2.3 Geometry Verification 2.1-1      Typical Straight Member                   2.4 1

2.1-2 Elbow Geometry Definition 2.5 l I- 3.0-1 Piping System Model - 3.2 l Static Analysis Verification ! 4.0-1 -Piping System Model - 4.2 Eigenvalue Extraction Analysis [ 5.0-1 Piping System Model_- 5.2 - Response Spectrum Analysis l 5.2-1 Closely Spaced Modes Verification 5.22 6.0-1 Dynamic Time History Analysis 6.2 R Verification 6.0-2 Amplitude Decay Wilson e-Method 6.3 6.0-3 Forcing Function Time History 6.6 7.0-1 Piping System Model - Load Combination 7.2 10.0-1 Piping System Model 'ASME Section 10.2 III Class 2 Verification 11.0-1 Piping System Model - ASME Section 11.2 III Class 3 Verification l. l _ vii j W nutech i i

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                          ,                     TR 76-001

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Revision 0 LIST OF TABLES TABLE NUMBER TITLE 2.0-1 Cross-Sectional Properties 2.2 f I' 2.1-1 Nodal Point Coordinates 2.6 3.0-1 Cross-Sectional Properties 3.4 3.1-1 Member Stress Resultants Deadweight.- Element'l

                                                           .3.8 f

3.1-2 Member Stress Resultants 3. 9' 4 Deadweight - Element:4 ]r. , 3.1-3 Member Stress. Resultants 3.10 . Deadweight - Element 18 3.1-4 Member Stress' Resultants- 3.11 Deadweight - Element 20

3.1-5 Nodal Displacements 3.12 Deadweight - Node 4 3.1-6 Nodal Displacements 3.13 - Deadweight - Node 8 3.1-7 Nodal Displacements 3.14 Deadweight - Node 19 3.2-1 Member Stress Resultants 3.16 Thermal Expansion - Element 1 ~ 3.2-2 Member Stress Resultants Thermal Expansion - Element 4 3.17 {, 3.2-3 Member Stress Resultants 3.18 L Thermal Expansion - Element 18 E-3.2-4 Member Stress Resultants 3.19 [ ! Thermal Expansion - Element 20

                                                                           -i 3.2-5      Nodal Displacements                    3.20 Thermal Expansion - Node 4
                                                                        <=

3.2-6 Nodal Displacements 3.21 Thermal Expansion - Node 8 j 3.2-7 Nodal Displacements . 3.22 Thermal Expansion - Node 19 3.3-1 Member Stress Resultants 3.24- l-Anchor Displacements - Element 1 l l viii 1

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                                  . LIST OF TABLES.(Cont)    Revision 0-t     '

PAGE TABLE-NUMBER TITLE-3.3-2 Member Stress Resultants 3,25 Anchor Displacements - Element 4 3.3-3 Member Stress Resultants 3.26-Anchor Displacements - Element'18

       ,                3.3-4      Member Stress Resultants               3.27
        .                          Anchor Displacements - Element 20 4

1

3.3-5 Nodal Displacements 3.28 -l 1 Anchor Displacements - Node 4 ' 3.3-6 Nodal Displacements 3.29 Anchor Displacements - Node 8 3.3-7 Nodal Displacements 3.30 Anchor Displacements.- Node 19 3.4-1 Member Stress' Resultants 3.32 Combined Loads - Element 1 3.4-2 Member Stress Resultants 3.33 Combined Loads - Element 4-1- 3.4-3 Member Stress Resultants 3.34 j Combined Loads - Element 18 l 3.4-4 Member Stress Resultants 3.35 [ Combined Loads - Element 20 3.4-5 Nodal Displacements 3.36 ; Combined Loads - Node 4 { 3.4-6 . Nodal Displacements 3.37 Combined Loads - Node 8 3.4-7 Nodal Displacements 3.38 Combined Loads - Node 19

4. 0- 1 Cross-Sectional Properties 4.4 i h

4.1.1-1 Modal Frequencies (Determinant Search) 4.8-4.1.2-1 Modal Normalization Points 4.10 (Determinant' Search

4.2.1-1 Modal Frequencies-(Subspace Iteration) 4.15 4.2.2-1 Modal Normalization Points 4.17 (Subspace Iteration) ;

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! .i TR-76-001 . .

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                           ,                      Revision-0
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di ' LIST OF TABLES (Cont) TABLE NUMBER TITLE PAGE F g , 1 5.0-1 Cross-Sectional Properties 5.3 5.0-2 X-Response Spectrum Definition 5.5 f) 1 5.0-3 Y-Response Spectrum Definition 5.7 . 5.0-4 Z-Response Spectrum Definition 5.9 1 5.1-1 Member Stress Resultants RSS Modal Response - Element 1 5.14 f 5.1-2 Member Stress Resultants 5.15 RSS Modal Response - Element 4 ['i 5.1-3 Member Stress Resultants 5.16 3, RSS Modal Response - Element 18 .{ ' 5.1-4 Member Stress Resultants 5.17 RSS Modal Response - Element 20 f 5.1-5 Nodal Displacements . 5.18 RSS Modal Response - Node 4 5.1-6 Nodal Displacements 5.19 RSS Modal Response - Node 8 5.1-7 Nodal Displacements 5.20 RSS Modal Response - Node 19 5.2-1 Nodal Displacements 5.23 - CSM Modal Response 5.2-2 Modal Frequencies 5.25 6.1-1 Step-by-Step Direct Integration 6.8 i Algorithm 6.1-2 Results of Dynamic Time History 6.9 Verification (Direct Integration) }, 7.0-1 Cross-Sectional Properties 7.3 7.'l-1 Member Stress Resultants 7.7 Direct Summation - Element 1 L' 7.1-2 Member Stress Resultants 7.8 Direct Summation - Element 4 L 7.1-3 Member Stress Resultants 7.9 Direct Summation - Element 18 4 X l

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                                       .                  TR-76-001 Revision 0.
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i._ LIST OF TABLES (Cont) j TABLE NUMBER TITLE PAGE 7.1-4 Member Stress Resultants 7.10

     .                      Direct Summation - Element 20 l'

7.1-5 Nodal Displacements Direct. 7.11 Summation - Node 4 1 7.1-6 Nodal Displacements Direct 7.12 Summation -Node 8 7.1-7 Nodal Displacements Direct 7.13 Summation - Node 19 7.2-1 Member Stress Resultants 7.15 3 1 Absolute Summation - Element 1 l 7.2-2 Member Stress Resultants Absolute 7.16 Summation - Element 4 7.2-3 Member Stress Resultants Absolute 7.17 Summation - Element 18 7.2-4 Member Stress Resultants Absolute 7.18-Summation - Element 20 7.2-5 Nodal Displacements Absolute 7.19 Summation - Node 4 ! 7.2-6 Nodal Displacements Absolute 7.20 ; Summation - Node 8 ~ 7.2-7 Nodal Displacements Absolute 7.21 Summation - Node 19 , 7.3-1 Member Stress Resultants RSS 7.23 Summation - Element 1 4 h 7.3-2 Member Stress Resu.ltants RSS 7.24 Summation - Element 4 7.3-3 Member Stress Resultants RSS 7.25

 ,                          Summation - Element 18 7.3-4     Member Stress Resultants RSS              7.26 Summation - Element 20 xi                                         ,

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                      ,                    Revision 0-                       'd e1
                                                                         -     i LIST OF TABLES-(Cont);                                       f TABLE NUMBER             TITL'E                        PAGE                    ]

7.3-5 Nodal Displacements RSS Suramation - 7.27 Node 4 1 7.3-6 Nodal Displacements RSS Summation.- -7.28 Node 8 7.3-7 Nodal Displacements RSS Summation - Node 19

                                                       '7.29~            f 10.0-1      Cross-Sectional Properties                10.3 10.1-1      Flexibility Factor Comparison             10.8 10.2-1      Stress Index Comparison                   10.10 10.3-1      Class 2 - Design Pressure-                10.12                  j 10.3-2      Class 2 - Peak Pressure                   10.13                  ,

1 10.3-3 Class 2 - Sustained Loads 10.'l~4 . l 10.3-4 Class 2 - Occasional Loads 10.15 10.3-5 10.3-6 Class 2 - Thermal Loads Class 2 - Equation #8 10.16 ff 10.17 10.3-7 Class 2 - Equation #9 10'.18 10.3-8 Class 2 - Equation'#10 10.19 10.3-9 Class 2 - Equation #11 10.20 'l 10.3-10 Class 2 - Equation #8 A11owables 10.21 10.3-11 Class 2 - Equation #9 A11owables 10.22 10.3-12 Class 2 - Equation #10 Allowables h) 10.23 l. I 10.3-13 Class 2 - Equation #11 Allowables 10i24 , 11.0-1 Cross-Sectional Properties 11.3 ",1 0 11.1-1 Flexibility Factor Comparison 11.8 I xii

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LIST OF TABLES (Cont) ]

TABLE NUMBER TITLE PAGE'

      ~                                                        '

11.2-1 Stress Index Comparison 11.10 11.3-1 Clars 3 - Design Pressure 11.12 11.3-2 Clu. 3 - Peak Pressure 11.13 11.3-3 Class 3 - Sustained Loads 11.14 11.3-4 Class 3 - Occassional Loads 11.15 11.3-5 Class 3 - Thermal Loads 11.15 11.3-6 Class 3 - Equation #8 11.17 11.3-7 Class 3 - Equation #9 11.18 l 11.3-8 Class 3 - Equation #10 11.19 11.3-9 Class 3 - Equation #11 11.20 11.3-10 Class 3 - Equation 8 A11owables 11.21 11.3-11 Class 3 - Equation 9 A11owables 11.22 11.3-12 { Class 3 - Equation 10 Allowables 11.23 11.3-13 Class 3 - Equation 11 Allowables 11.24 L L 9 xiii nutech _L e

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                                     ,                          TR-76-001 RGvision 0
             '1 ; 0  INTRODUCTION AND CRITERIA This document has been prepared to. demonstrate the accuracy
    ,         and validity of the results, solution techniques, and assump-
 ,          .tions used in the PISTAR computer' program.

PISTAR'is a proprietary software. package' developed by Nuclear i Technology, Inc. to perform analysis-, evaluation, and assist in the design of power plant piping systems'and piping' system e supports, PISTAR consists of a completely integrated system ! of preprocessors, postprocessors, and a number of finite element and heat transfer equation solvers. PISTAR was devel-oped for engineers designing power plant piping. A more complete program description and definition may be obtained I from the PISTAR User's Manual (Reference 1). The program ) has the capability to analyze piping according to nuclear (ASME Section III) an/, non-nuclear (ANSI B31.1* and B31.7*) industry codes. l Three methods of verification are used in.this document: I Comparison of the results obtained from PISTAR with the m results obtained from other accepted public domain computer programs. t Comparison of the results obtained from PISTAR with the results obtained by a series of documented manual calculations. Comparison of the results obtained from PISTAR with the results obtained from accepted documents (see references throughout this text) .

            "Not available in Version 1        y,y_                      IlllIG)()hl
                                                                                "^

_g [ s I TR-76-001 _ . J Revision.0 ) 3 In this document, the most accurate of the three comparison I

                                                                            ' i techniques for the particular area under investigation is' h

reported. Three comercially available structural analysis computer programs were used in the verification of PISTAR:

                        ~ANSYS -(Reference 3)

MRI/STARDYNE. (Reference 4)

                    . ADLPIPE    (Reference 5)                         t!

The basis for PISTA.*'. is the widely accepted computer program ( 1 SAP IV developed at the University of California, Berkeley by ii K.J. Bathe, E.L. Wilson, and F.E. Peterson (Reference 2) . i In its original form, SAP IV ir a general purpose finite element program for performing linear elastic ~ static and- ) dynamic analyses. The straight pipe member, pipe bend member, and the static and dynamic equation solvers from , SAP IV are used in the PISTAR program. All other elements, m , q solvers, preprocessors, and postprocessors are original i NUTECH developments and are NUTECH proprietary information. ] L'

In this document, each critical phase or part of PISTAR is ... found in a unique section. As new and' extended capabilities-and features are added to PISTAR, this document will be revised

with new sections to cover these modifications. All computer ,

l1 s si output associated with this verification report will appear as appendices to this document under a separate cover and . , will be available for review in the NUTECH files. ; 1 1.2 _i

                                                    ' we

f c.' . TR-76-001 1 Revision 0-1 The basic governing criteri on for this verification. report is 5.0% deviation from an accepted solution I result. .Three levels of solution techniques are evaluated l h for validity and are listed below with the appropriate verification criterion. 1 Results which are calculated from a closed form equation solution - l 0.5 basic criterion or 2.5% Results which are calculated from a closed j form matrix solution solver - 1.0 basic criterion or 5.0% ; 1 Results which are calculated from a numerical 1 i method or iterative solution solver - 1.5 basic criterion or 7,5% L This revision (Revision 0) of the verification report is

   ,              applicable to PISTAR Version 1.1. Only the capabilities and features discussed in this report are to be considered
    ~

verified. 1.3 nutech, s

                                                                                   '*d-=en   *g- +=*mo v e -

                                          .                            TR-76-001 Revision 10 l
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l 2.0 GEOMETRY GENERATION-PHASE (. , j The piping system model (Figure 2.0-1) was used for verifying -l 4 the geometry input phase which is processed through the'PISTAR .l

   '                                                                                                    -d input generator.        The main topics of verification are-the'                           4 accuracy of PISTAR's offset generator and.the efficiency of j

the nodal point bandwidth minimization routine. The criterion ] for this verification is 2.5 percent. I S ! G The problem analyzed is Problem Number 6 in Reference 6 L (Static Analysis of a Three-Dimensional Piping Structure Program - i' ANSYS). The data specified in this problem was.directly input into PISTAR with the following exception's: The modulus of elasticity was typed incorrectly 6 as 20.0 x 10 psi in the reference document j (Reference 6). The value.used was 29.9 x.106 psi. l . The valves in the PISTAR model were coded as ] straight pipe sections with the appropriate cross-sectional property values (Table 2.0-1). w PISTAR assum6d a direct spring-to-ground restraint mechanism on nodal point 4. N w d b 2.1 nutech , (

                                                              -TR-76-00'1 .      .
                         ,                                     Ravision 0 The. element' component types:used'in PISTAR to describe'the_                   ~

piping system are PIPE and' ELBOW. f The cross-sectional properties are found in Table 2.0-l. ' Outside Wt Per Unit' l Wall Thickness - f

Component. Dia (Inches) , (Inches) Length ~(Ib) Straight' Pipe 3.5 0.216 0.631313-Elbows 3.5 , 0.216 0.631313 Nodes Valve D 5-6 4.94 l' 0.7619 3.00311 'f Valve E Nodes 14-15 i 4.499 i 1.7153 3 l 4.50466 l. Nodes i Valve F 21-22 5.221 0.3251 i , l 2.00207 ' Table 2.0-1. Cross-Sectional Properties The components in the piping system are made of steel. Young's modulus is 29.9 x 100 psi. Poisson's ratio _is 0.3; and'the coefficient of thermal expansion is 2.178 x 10-5 , L The piping system has been anchored at nodal points 20 and 23. U Nodal point 4 has a direct spring-to-ground restraint mechanism which imposes a translational restraint in'the X,:Y, and Z directions of 1,000 pounds'per inch and a rotational restraint !

                                                                                        '=;.

in the X, Y, and Z directions of 10,000 inch-pounds per radian. - I i. 1 i l 2.2 4 1

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       ., .                                                   TR-76-001                       !

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"                                            *hN Figure 2.0-1. Piping System Model -                                    -

Geometry Verification 2.3 nutech

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                                                    . TR-76-001-      ~'"   (~ l Revision.6-         .

ll 2.1 Offset--Generator PISTAR utilizes an offset generation scheme (Reference 1)'to' develop its coordinate network. This technique uses the following basic equation (1) for developing the coordinates i which occur at the end 'of a' straight member (Figure 2.1-1) : f NODE-I NODE-J f-e e [i gi l Figure 2.1-1. Typical Straight Member ] X = Xy -+ X-OFFSET y f 9 Yy = Y. + Y-OFFSET (1) 7 Zy = 2 + Z-OFFSET 7 l The tangent intersection point _of elbows or pipe bend members 4 are defined by a streight pipe member or point definition s (Figure 2.1-2). The radius of curvature and the convex side (, along the plane of the element are also defined-for elbows d or pipe bend members, o-. u) i

I l J E i s. 2.4 I a%,s

     -      ,                                                                                     i TR-76-001 i

Revision 0 TIP 1 l

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                                                           )2A (90-e/2)                  +                                                l
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l 1 I . i l {- 2B I i Figure 2.1-2. Elbow Geometry Definition l 1 4 C 2 R sin (90-9/2) l=1/2 C[ sin (0/2) (2) L The co ordinates of IB and 2A (Figure 2.1-2) are then found vectorally using a magnitude of L.

      ,       Table 2.1-1 presents the coordinates generated by PISTAR, the actual coordinate values, and the percentage of deviation for the nodal points shown on Figure 2.0-1. All results investiga-ted in tnis section have no deviation from the ANSYS coordinate data input.

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RD 7__ AR TO 0 0 0 0 0 0 0 0 0 0 0 0 0 0 5 0 0 0 0 0 SO . . . . . . . . . . . . . . . . . . . . IC 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 P - 1 1 2 3 _ Z 9 M_ D SR YO SO 0 0 0 0 0 0 0 0 0 0 0 0 0 0 5 0 0 0 0 0 NC 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 A- 1 1 2 3 9 . Z _ V

  %E    0 D

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 W_ _ T RD AR - TO 0 0 0 0 5 0 0 5 5 0 0 0 0 5 0 0 0 0 0 0 SO . . . . . . . . . . . . . . . . . . . . IC 0 0 0 0 5 4 4 9 4 0 0 0 0 4 0 0 0 0 0 P - 9 9 9 9 8 8 8 7 0 6 6 8 7 6 5 Y 5 5 5 5 5 W 9 SR Y0 S0 NC A-Y 0 0 9 0 0 9 0 0 9 9 0 0 5 5 8 0 4 8 4 8 0 7 5 9 5 4 6 0 0 6 0 0 8 0 0 7 6 0 0 5 4 5 0 5 0 0 0 5 0 0 0 0 5 5 0 0 0 0 5

                                                                                                                                                               .      p a

s a m u P V

 %E    0      0     0     0        0      0      0       0         0       0      0          0      0      0 D                                                                                                            0      0        0        0       0       0                    _

g_ _ RD _ AR _ TO 1 1 1 6 1 1 6 1 1 6 1 1 1 1 1 1 1 1 1 7 SO . . . . . . . . . . . . . . . . . . . 1 IC 0 0 0 5 0 0 5 0 0 5 0 0 0 0 0 0 P - 2 3 3 4 4 0 0 0 0 4 5 5 4 4 4 4 4 4 4 4 X 4 4 4 _

                                                                                         !li                                                                                    _

D _ SR _ YO 1 1 1 6 1 1 6 1 1 6 1 1 1 1 1 1 1 1 1 SO . . . . . . . . . . . . . . . . 1 , _ . NC 0 0 0 5 0 0 5 0 0 5 0 0 0 0 0 0 0 0 0 0 A- 2 3 3 4 4 4 5 5 4 4 4 4 4 4 4 4 4 4 X 4 . _ E _ D . 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 OO 1 1 1 2 3 1 1 1 1 1 1 1 1 2 2 2 2 _ NN w6

f' . TR-76-001 Revision Q

 .f.          2.2   Optimization-of Nodal-Bandwidth           -
     ~

PISTAR'uses a minimum wave approach to-minimize the nodal: point bandwidth (Reference 1). The technique'does'not ensure optimum nodal point order in every circumstance. However, it'does ensure minimization of existing nodal point bandwidths. The piping system model under investigation is'shown in~ Figure 2.0-1. The results of the PISTAR optimization, actual optimum nodal order, and original nodal point bandwidth are: 1 J Original Nodal Bandwidth = 11 Optimum Nodal. Bandwidth = ' 3 PISTAR Calculated Nodal Bandwidth =. 4 1 1 L l L

    =
   =

0 2.7 e nutech

TR-76-00] Revision 0

     . -          3.0    STATIC ANALYSIS 1

The piping system model (Figure 3.0"-1) 'was used' for . verifying.

PISTAR's static analysis' solution' technique. The~PISTAR-design and analysis system utilizes the widely used static equation solver developed by E. L. Wilson.at.the University of California, Berkeley (Reference 2) . I A static analysis involves the solution of the equilibrium equation I [K) { u} = { R} (3) l . followed by the calculaticn of element strass resultants. l The load vectors { R} , the structure stiffness matrix [K], and the mass matrix [M], are assembled at the same time. The equation solution is obtained using the large l capacity linear equation solver. This. solver,uses Gauss elimination on the positive-definite symmetrical system of equations. The algorithm performs a minimum number of operations; i.e., there are no operations withizero elements. In the program, the L TDL decomposition of [K] is used. Therefore, i equation 3 can be written as [L]T{v} = {R} (4) and {v)= [D] [L] { u} (5)

      -            where the solution for { v} in equation 4 is obtained by a reduction of the load vectors and the displacement vectors fu}
      ~

are calculated by back substitution. k 3,1 11Utech

c. 4 TR-76-001 Revision d

                                                                          -     j
                                                                     .1          1 I

i'

                \              /                                         c N4/.                                              (

h )

                       $          s                                     {/

6 \ 5 -

                                                                         \\
                                                                              ^\

2 ti i5 h I y \ is , 12 i.7 - is - i 19 .(

                                  /at 22 p

C

ia Y, 25 s

                                      "[pt11 Figure 3.0-1,    Piping System Model                         -(-

Static Analysis Verification 3.2

1 TR-76-001 Revision 0

                                           ,                                                1 f

The piping system model used for.the stati.c' analysis is shown K

     -                                                                                      I
                 . in Figure-3.0-1. The sensitivity of rest 1ts were: verified l

with the widely accepted computer prograta ANSYS (Reference 3). l

i The problem analyzed:is Problem-Number in 6 in Reference 6

   ,               (Static Analysis.of a Three-Dimensional Piping Structure r              Program - ANSYS).

1 j The data specified in problem 6 (Reference 6) was directly 1 { 4. input into PISTAR with the following exceptions: I The modulus of elasticity was +.yped' incorrectly 6 as 20.0 x 10 psi'in the reference document (Reference 6) . The value used was

6 29 x 10 psi. l The valves in the PISTAR model were coded- , as straight pipe sections with the appropriate cross-sectional property values (Table 3.0-1). { . PISTAR assumed a direct spring-to-ground restraint mechanism on nodal point 4. , We ee * .I p 3.3 nutech

7

                                                          'TR-76-001                     -l R9 vision 0 The' element component' types used in PISTAR to describe the piping system are PIPE and. ELBOW.

T q

 ,     The cross-sectional properties are found'in Table 3.0-1.                            '

0\ i 1 Outside Wall Thickness Wt Per-Unit ! Component. Dia (Inches) (Inches) Length (1b) - l Straight Pipe 3.5 0.216 0.631313 l Elbows ' 3.5 0.216 'l 0.631313 j Valve D Nodes 1 5-6 4.94 0.7619 3.00311-Valve E Nodes 14-15 4.499

                        .                      1,7153         4.50466 i                                                         '

i Nodes Valve F 21-22 5.221 0.3251 2.00207 Table 3.0-1. Cross-Sectional Properties Ll I The components in the piping system are made of steel. Young's modulus is 29.9 x 10 6 psi. Poisson's ratio is 0.3; and the ; 1 coefficient of thermal expansion is 2.178 x 10-5 , The piping system has been anchored at nodal points 20.and 23. h Nodal point 4 has a direct spring-to ground restraint mechanism which imposes a translational restraint in the X, Y, and Z s

     ' directions of 1,000 pounds per inch and a rotational restraint in the X, Y, and Z directions of 10,000 inch-pounds per radian.             #

Four structural loading conditions were analyzed for the static piping analysis. These load cases are defined in' problem 6_ . 3.4 h

                                                                                         '1
                                                               -TRi76-001 R9 vision 0 of the.ASME document (Pressure Vessel and. Piping 1972 Computer                  l Programs Verification). Three additional unit loading condi-tions are analyzed. The actual conditions'are:                             -1 q

l t 1. Dead Load - The piping system was subjected to the I This leading was imposed on effects of its own weight. the structure in both ANSYS and PISTAR using'a static , i f

vertical acceleration (Y-axis) of 386.4 inches /second/. i second. This analysis is presented in Subsection 3'.1.

2. Thermal - The piping system was subjected to the effects f of a uniform thermal expansion; 100*F temperature rise l from the stress-free state. This analysis is presented in Subsection 3.2.

3. Anchor Displacement - The piping system was subjected'to the effects of the imposition of displacements at a support location, nodal point 20, (Figure 3.0-1). This analysis is presented in Subsection 3.3. Both the ANSYS and the PISTAR analytical model were subj ected to the following support displacements:

Node 20 Imposed Displacements X-Translation = 0.10 inch Y-Translation = -0.08 inch Z-Translation = 0.05 inch X-Rotation = 0.005 radian , L Y-Rotation = -0.001 radian 2-Rotation = -0.005 radian 3.5 6 nutech

TR-76-001L' ' i Revision 0 l _ i 1 4. Combined Loads - The piping system was subjected to 'i the simultaneous effects of loading conditions defined. in loading condition; e, 2,.and.3. This analysis is { presented in Subsection 3.4. This-condition is also f] defined in the ASME Verification Problem 6 (Reference 6) . I

Analysis results of these loads are presented in_ Subsections T [; 3.1, 3.2, 3.3, and 3.4. Four structural element components and three nodal points were investigated. All resultant f, stresses and displacements for each nodal point were compared-for validity. Listed below are the elements and nodal points . under consideration. '

                                                                                                   .l Element Type          Between Nodes                                          ,

1 Straight Pipe 4 - 5 4 Elbow 7 - 8 18 Straight Pipe .19 - 20 , 20 Elbow - 23 Node Coordinates X Y Z { 4 0.1 90.0 0.0 8 40.1 85.5 0.0 , 19 40.1 50.0 10.0 m h The criterion'used for verification in this section is a 5.0% . . deviation from the ANSYS solution. 1 I

                                                                                                % i 3.6 L

i i Inw

                                                                             -..,a     =                  ,-

.f;. ...- TR-76-001-

    ].                                .                           Revision 0          .

l

l 3.1 Deadweight

               'In the' deadweight analysis,.a static. vertical (Y-axis) accel-      !
                                                                                    .)

eration of 386.4 inches /second/second was imposed on the piping-

                                                                                   'l system (Figure 3.0-1).

i h. Tables 3.1-1 through 3.1-7 present the PISTAR and ANSYS results

.{

and the percentage of deviation from the'ANSYS results for the deadweight analysis. For the various member stress result-1 ants and nodal displacements, the maximum deviation was 3.03%, I which is within the specified criterion. This maximum value i

    .{         is circled on Table 3,1-1 for easy reference.
                                                                                       )
                                                                                      )

l l t i 1 j [ l ! l [' l L L L

~.

3.7 nutech t

1 l TR-76-001 ' ' Revision 0

                                                                                            ,- i e

Table 3.1-1. Member Stress Resultants DEADWEIGHT - Element 1 f ELEMENT NO. 1 TYPE straight Pipe DESCRIPTION Sprinn Attachment at Node 4 - Straight Pine to Node 5. (x. v. 2 = End -I = 1. 90. 0- Fnd-J = 20.1. 90. 01 j DEVI A-MEMBER ANSYS PISTAR TION MEMBER ANSYS PISTAR DEVI TION A-RESULTANTS */. RESULTANTS % 1-Axial Torsional , { Force -3.500 -3.436 1.83 Noment ,-1.31 -1.32 0.76 End-l End-l { Axial . Torsional Force -3.500 -3.436 1.83 Moment -1.31 -1.32 0.76 En d-J End-J l Y-Axis Y-Axis ! Shear -10.580 -10.518 0.59 Moment 0.94 0.94 0 I Endl End-l Y-Axis Y-Axis Shear 2.046 2.108 3.03 Moment -43.40 -43.55 0.35 End-J End-J Z-Axis Z-Axis L. Shear -2.217 -2.224 0.32 Moment 2.25 2.24 0.44 D l End-l End-l l Z-Axis Z-Axis s Shear -2.217 -2.224 0.32 Moment - 87.60 86.34 1.44 End-J End-J Bl 1 L! s

    #f 3.8                                         h, l                                                                                           a_

L

s TR-76-001 ' . Revision 0 _ Table 3.1-2. Member Stress Resultants DEADWEIGHT - Element 4 r ELEMENT NO. 4 TYPE Elbow DESCRIPTION 4.5 Inch Radius Elbow Node 7 6 8 { (x, y, z End-I = 35.6, 90, 0; End-J = 40.1, 85.5, 0) DEVI A- D EVI A-I MEMBER ANSYS PISTAR TION MEMBER ANSYS PISTAR TlON RESULTANTS */. RESULTANTS % Torsional Axial Force -3.500 -3.436 1.83 Noment -1.31 -1.32 0.76

               ' Endl                                            End-l Axial .                                       Torsional                               1 Force      -40.012     -40.074      0.16       Moment    87.75      88.04      0.33 En d-J                                          End J Y-Axis                                         Y-Axis Shear      -35.549     -35.611      0.17       Moment    77.77      78.03      0.33 f-            Endl                                           End-l c            Y-Axis                                          Y-Axis Shear        3.500       3.436     1.83       Moment    11.29      11.33      0.35
       ~

End-J End-J Z-Axis Z-Axis , Shear 2.217 2.224 0.32 Moment 268.99 271.21 0.83 i End-l End-l ;

       -          Z-Axis                                         Z-Axis Shear        2.217        2.224     0.32      Moment   423.26     423.29      0.01 End-J                                           End-J                                ;

4 base him 3.9 MuteCh

r TR-76-001 * -

                                   .                              Revision 0 7

J Table 3.1-3. Member Stress Resultants i DEADWEIGHT - Element 18 1 J ELEMENT NO. 18 TYPE straight Pipe l DESCRIPTION Branch from Node 19 to Node 20 - Node 20 Anchored (x, y, z = End-I = 40.1, 50, 10; End-J = 40.1, 0, 10) , DEVI A- DEVIAj MEMBER ANSYS PISTAR TION MEMBER ANSYS PISTAR TION t y RESULTANTS % RESULTANTS '% fl l j Axial Torsional Force -174.923 -174.996 0.04 Moment 12.04 12.20 1.33 Endl End-l 1 4 Axial Torsional - t Force -206.489 -206.552 0.04 Moment 12.04 12.20 1.33 ! End-J End J Y-Axis Y-Axis I Shear -12.024 -12.090 0.55 Moment -100.03 -97.28 2.75 l Endl End-l .. Y-Axis Y-Axis , Shear -12.024 -12.090 0.55 Moment 40.11 38.91 2.99 ') End-J End-J Z-Axis 2.803 2.724 2.82 Z-Axis

                                                          -404.99    -407.19      0.54 Ll t--

Shear Moment End-l End-l Z-Axis Z-Axis Shear 2.803 2.724 2.82 Moment 196.23 197.30 0.55 End-J End-J i iy 3.10 { m

y TR-76-001 Revision 0 Table 3.1-4. Member Stress Resultants DEADWEIGHT - Element 20

           .                                                                                          i l

ELEMENT NO. 20 . TYPE Straicht Pipe DESCRIPTION End of Piping Structure Nodes 22 6 23 - Node 23

Anchored (x, y, z = End-I = 40.1,'50, 30; End-J = 40.1, 50, 90) DEVI A- DEVI A-MEMBER ANSYS PISTAR TION MEMBER ANSYS PISTAR TION - RESULTANTS % RESULTANTS */. i Axial Torsional i Force 9.807 9.865 0.59 Moment -16.00 -15.59 2.56 i Endl End-l Axial Torsional - Force 9.807 9.865 0.59 Moment -16.00 -15.59 2.56 l L En d-J End J g Y-Axis Y-Axis [~ Shear -17.000 -17.011 0.06 Moment -26.75 -27.23 1.79 Endl End-l Y-Axis Y-Axis

    .         Shear     20.879     20.868     0.05      Moment        15.11        15.50      2.58 End-J                                      End-J                                        i Z-Axis                                     Z-Axis Shear      0.698      0.712     2.01      Moment     -113.82      -114.47       0.57 End-l                                      End-l Z-Axis                                     Z-Axis Shear      0.698. 0.712     2.01      Moment      -230.19     -230.19         o End-J                                      End-J m

l. l w 3.11 nutech

i TR-76-001 Revision 0 l Table 3.1-s. Nodal Displacements [ DEADWEIGHT - Node 4 NODE NUMBER 4 LOCATION End of Model - Spring Restraint x= .1, y = 90, z = 0~ DISPLACEMNT ANSYS PISTAR DEVIATION [ COMPONENT ( X ' 10-2) - ( X 10-2) % I X-Trans -0.3500'47 -0.34361 1.84 Y-Trans -1.0s80- -1.0s18 0.59 [- i Z-Trans -0.22171 -0.22245 0.34. L X-Rotation -0.013143 -0.013174 0'24 g l l Y-Rotation 0.0093874 0.0094044 0.12 L' 2-Rotation 0.022534 0.022374 0.71

\<

h

3.12 -

                                                              ,       \

L

TR-76-001 Revision 0 [ Table 3.1-6.. Nodal Displacements DEADWEIGHT - Node 8 NODE NUMBER 8 LOCATION End of Elbow x = 40.1'. y = 85.5. 2 = 0 DISPLACEMNT -ANSYS PISTAR DEVIATION 1 COMPONENT ( X 10-2) ( X 10-2) %- I X-Trans -0.28241 -0.27678 1.99 I Y-Trans -0.13972 -0'.14018 0.33 2-TranS -0.51523 -0.51647 0.24 L co [lo X-Rotation .1.014025 -J.014058 0 [ Y-R otation 0.0064512 0.0064586 0.11 L Z-Rotation 0.0096513 0.0094761 1.82 L - 3.13 nutech

n

                                                     'TR-76-001  .. .
                                                                         ~

Revision 0 Table 3.1-7 Nodal- Displacements {

DEADWEIGHT - Node 19 NODE NUMBER 19 _ R LOCATION At- Branch x - 40.1. y - so. z --10 f. l DISPLACEMNT ANSYS PISTAR DEVIATION - COMPONENT ( X 10-2) ( X 10-2) % X-Trans -0.0080526 - 0.0079259 1.57

                                                                      'I Y-Trans        -0.014321   -0.014316         0.03 L-Z-TranS        -0.0010959  -0.0011024 0.59 L

) X-Rotation -0.0057852 -0.0058163 0.54 i Y-Rotation 0.00086717 0.00087883 1.3s { Z-Rotation 0.0016604 0.001617s 2.58 M 3.14 b upp

R r- . TR-76-001 l-~' ' Revision 0 I 3.2 Thermal Expansion In the thermal' expansion analysis, a uniform temperature rise above the stress-free temperature of 100 F was imposed on the piping system (Figure 3.0-1). 'I. Tables 3.2-1 through 3.2-7 present the PISTAR and ANSYS ana-lysis results and the percentage of deviation from the ANSYS results for the thermal analysis. For the various member ) stress resultants and nodal displacements, the maximum deviation was 2.07%, which is within the specified criterion.. This maximum 1 I value is circled on Table 3.2-6 for easy reference. . 1 i k L \ L 1 L L l I* i 6 3.15 nutech

TR-76-001 Revision 0 Table 3.2-1. Member Stress Resultants THERMAL EXPANSION - Element 1 f T ELEMENT NO. 1 TYPE Straight Pipe I DESCRIPTION Sprine Attachment at Node 4 - Straicht Pine tn Node 5 (x. v. 2 - End-T - .1 00. 0- Fn c1 .T = ?n 1 on 'ni DEVI A-MEiABER ANSYS PISTAR TlON MEMBER ANSYS PISTAR DEVIA-l TION RESULTANTS % RESULTANTS % g Axiol Torsional i Force -91.594 -91.584 0.01 Noment 2.24 2.23 Endl End-l Axial Torsional 0.45l Force -91.594 -91.584 0.01 Moment 2.24 2.23 En d-J 0.4 5 l End-J L Y-Axis Y-Axis Shear 101.417 101.406 0.01 Moment 0.03 31.67 31.68 Endl End-l Y-Axis Y-Axis ! Shear 101.417 101.406 0.01 Moment -1681.15 -1681.21 0 i End-J End-J Z-Axis Z-Axis U Shear -85.641 -85.645 0 Moment 22.23 22.24 0.04 l End-l End-l 2-Axis Z-Axis - i Shear -85.641 -85.645 0 Moment -2006.10 -2005.87 0.01 End-J End-J 9 Mus uu-3.16

1

q f .- . TR-76-001' ' j , Revision 0 -I f Table 3. 2-2. Member Stress Resultants.- I. THERMAL EXPANSION - Element 4 ; l {

                                                                                         -               1 r

l ELEMENT NO. 4 TYPE Elbow { 4

DESCRIPTION 4.5 Inch Radius Elbow Node 7 6 8 J I- ( x . v ., z - End-I = 35.6. 90. 0 End-J = 40.1, 85.5, 0) DEVI A- D EVI A-I MEMBER ANSYS P! STAR TlON MEMBER ANSYS PISTAR TlON RESULTANTS % RESULTANTS % Axial Torsional f Force -91.594 -91.584 0.01 2.24 2.23 0.45 Moment q Endl End-l Axial Torsional Force -101.417 -101.406 0.01 Moment 3393.96 3394.10 o En d-J End-J - I' ,. Y-Axis Y-Axis Shear -101.417 -101.406 0.01 3008.58 3008.70 0 l Moment l_ Endl End-l Y-Axis Y-Axis Shear 91.594 91.584 0.01 Momen; 383.14 383.17 0.01 En d-J End-J j

Z-Axis Z-Axis { _ Shear 85.641 85.645 0 Moment 3578.06 3577.66 0.01 l End-l End-l Z-Axis Z-Axis .

Shear 85.641 85.645 0 Moment 3622.26 3621.85 0.01 ! End-J End-J

i

                                                                                                       .J 3.17                             nutech               i i

l

TR-76-001 * -' i n< . Revision 0 l Table 3. 2-3. Member Stress Resultants ; THERMAL EXPANSION - Element 18 l 18 ELEMENT NO. TYPE s+"ie* P4r-DESCRIPTION Branch from Node 19 to Node 20 - Node 20 Anchored (x, y, z = End-I = 40.1, 50, 10; End-J = 40.1, 0, 10) DEVI A- D EVI A-l MEMBER ANSYS PISTAR TION MEMBER ANSYS PISTAR TION I RESULTANTS % RESULTANTS % Axial Torsional Force -545.632 -545.426 0.04 Noment 244.90 245.16 0.11 End-l End-l { Axial . Tors;,aol I i Force -545.632 -545.426 -0.04 Moment - 244.90 245.16 En d-J End J 0.11l Y-Axis Y-Axis Shear 1074.78 1074.610 0.02 Moment -629.416 -629.39 0 Endl End-l ) Y-Axis Y-Axis Shear End-J 1074.78 1074.610 0.02 Moment End-J - 1598.25 1598.30 0 [ Z-Axis Z-Axis L Shear 44.553 44.554 0 End-l Moment 23647.10 23641.76 0.02C' End-l a j Z-Axis Z-Axis Shear 44.553 44.554 [ 0 Moment -30091.60 -30088.71 0.01 End-J End-J

                                                                                             'E l

Iem 3.'18 _ y mm.

f . j . TR-76'-001 Revision 0

                    . Table 3. 2-4.           Member Stress Resultants THERMAL EXPANSION - Element 20 l

ELEMENT NO. 20 TYPE Straight Pipe [ DESCRIPTION End of Piping Structure Nodes 22 S 23 - Node 23 Anchored (x. v. 1

End-I = 40.1._ L 30: End -J = 4 0.1 e

50. 001

l. DEVI A- D EVI A- ,

MEMBER ANSYS PISTAR TlON MEMBER ANSYS PISTAR TION ) RESULTANTS % RESULTANTS % j I* Axiol To unal ] Force - 1160.420' -1160.254 0.01 Mune/d 258.73 258.79 0.02

  'I c      .       Endl                          ,

End-l Axial Torsional Force 1160.420 -1160~.254 0.01 Moment 258.'73 258.79 0,02 ! l End-J 'End4

    <               Y-Axis                                       Y-Axis b              Shear      -444.215    -444.020      0.04    Momen?      -1292.32      -1292.49    0.01 Endl                                          Dhl Y-Axis                                         Y-Axis Shear.    -444.215    -444.020      0,04    Moment       1530.10       1529.34     0.05 End-J                                         End-J
       ._           Z-Axis                                         Z-Axis .

Shear 47.040 47.031 0.02 Moment -12353.60 -12351.86 0.01 End-l End-l J

Z-Avis Z-Axis J Shear 47.040 47.031 0.02 Moment 14299.30 '14289.35 .0.07-End-J End-J j

-=

l u , 9 I w 3.19 nutech L-

4 TR-76-001 - . Revision 0 l Table u -s. Nodal Displacements - THERMAL EXPANSION - Node 4 NODE NUMBER 4 LOCATION End of Model - Spring Restraint [l x= .1, y = 90, z=0 f DISPLACEMNT ANSYS PISTAR DEVIATION COMPONENT ( X 10-2) ( X 10-2) % Il 1 X-Trans -9.1594 -9.1584 0.01 ] I

   . Y-Trans        10.142         10.141          0.01 Li Z-Trans        -8.5641        -8.5645           0

[ X-Rotation 0.022416 0.022325 0.41 L e Y-Rotation 0.31677 0.31680 0.01 Z-Rotation 0.22243 0.22238 0.02 L mum 3.20 _ m

TR-76-001 Revision 0

Table 3. 2-6. Nodal Displacements THERMAL EXPANSION - Node 8. NODE NUMBER 8 LOCATION End of Elbow , 2 x - 40.1. y = 85.5,z =0 DISPLACEMNT ANSYS PISTAR DEVIATION COMPONENT ( X 10-2) ( X 10-2) % X-Trans -0.040062 -0.039234 2.07 I Y-Trans 17.080 17.079 0.01 _ Z-TranS -20.463 -20.46s 0.01 X-Rotation -0.008407s -0.0085010 1.11 u Y-Rotation 0.203ss 0.203s8 0.01 Z-Rotation 0.043223 0.043209 0.03 6

3.21 nutech

r

TR-76-001' Revision 0 Table s.2-7. Noda! Displacements - THERMAL EXPANSION - Node 19 7

                                                                           .i '

19 NODE NUMBER h LOCATION At Branch-x - 40.1- v- so. z -to .ll DISPLACEMNT ANSYS PISTAR DEVIATION COMPONENT -( X 10-2) ( X 10-2): % X-Trans 1.2030 1.2031 0.01 l

   ,    Y-Trans             10.849        10.849            0 l'

Z-TranS -17.294 -17.294 0 X-Rotation ' -0 .17859 -0.17869 0.06 L L' t Y-Rotation 0.017645 0.017664 0.11 Z-Rotation -0.026849 -0.026852 0.11 &

 +                                                                        I me, 6

3.22

TR-76-001

                                                               . Revision 0 3.3   Anchor Displacement In the anchor displacement analysis, a movement at nodal

[ point 20 (see Section 3.0) was ' imposed on the piping system (Figure 3.0-1). Tables 3.3-1 through 3.3-7 present the PISTAR and ANSYS results and the percentage of deviation from the-ANSYS results

                . for the anchor displacement analysis. For the various member stress resultants and nodal displacements, the. maximum devia-

}- This tion was 1.20% which is within the specified criterion. .! maximum value is circled on Table 3.3-1 for easy reference. 1 I L d 1 I 1 i nutech 3.23 i

         ~
                                                                                   - .- . -- l

                                                                      .TR-76-001      .          .     '!

Revision-0 f Table 3.3-1. Member Stress Resultants ANCHOR DISPLACEMENTS - Element 1 (< ELEMENT NO. 1 TYPE Spring Attachment at Node 4 Straight Pipe l) DESCRIPTION - Straicht Pine'to . Node'5 fr. v. ? = Fnd-T = .1. on. 0* Fnd .T = 20 1 on_ OT DEVI A-MEMBER' ANSYS PISTAR TION MEMBER ANSYS DEVI A- ' PISTAR TION I-RESULTANTS % RESULTANTS */. Axial Torsional ' Force 143.778 143.779 0 Noment -10.61 -10.62 0.09 Endl End-l Axial . ( Torsional I Force 143.778 143.779 0 Moment -10.61 -10.62 0.09 En d-J Y-Axis End J-Y-Axis fl ' Shear -93.611 -93.602 0.01 Moment Endl 0.83 0.84 1.20 End-l ' Y-Axis Y-Axis Shear -93.611 -93.602 0.01 Moment -1118.66 -1118.45 0.02 End-J End-J - Z-Axis Z-Axis St - -55.974 -55,965 0.02 Moment -4.54 -4.55 JL Erm 1 0.22 i: End-l Z-Axis Z-Axle Shear -55.974 -55.965 0.02 Moment End-J 1867.68 1867.50 0.01 End-J 6 3.24 u. p ee d

   ~
     .      .                                                            TR-76-001 Revision 0 4

Table 3.3-2. Member Stress Resultants l ANCHOR DISPLACEMENTS - Element 4 4 Elbow ELEMENT NO. TYPE c DESCRIPTION 4.5 Inch Radius Elbow Node 7 6 8

1. (x, y, z = End-I = 35.6, 90, 0; End-J = 40.1, 85.5, 0) u DEVI A- D EVI A-f MEMBER ANSYS PISTAR TION MEMBER ANSYS PISTAR TION RESULTANTS */. RESULTANTS %

f Axial Torsional Force 143.778 143.779 0 Moment -10.61 -10.62 0.09 Endl End-l Axial Torsional Force 93.611 93.602 0.01 Moment 2238.15 2237.74 0.02 l En d-J End J t Y-Axis Y-Axis j Shear 93.611 93.602 0.01 Moment 1986.26 1985.90 0.02 (, Endl End-l Y Axis Y-Axis Shear -143.778 -143.779 0 Moment 262.50 262.46 0.02 End-J End-J Z-Axis Z-Axis , i_ Shear 55.974 55.965 0.02 Moment -3318.65 -3318.33 0.01 End-l End-l Z-Axis Z-Axis Shear 55.974 55.965 0.02 Moment -3092.90 -3092.54 0.01 End-J End-J L s e he e 1.- 3.25 nutech Im e e- en m eg

r TR-76-001 . . Revision 0 s

Table 3.3-3. Member Stress Resultants , ANCHOR DISPLACEMENTS - Element 18 fi 18 ELEMENT NO. TYPE Straight Pipe f-DESCRIPTION Branch from Node 19 to Node 20 - Node 20 _ Anchored (v. v. z - End-I = 40.1, 50, 10; End-J = 40.1. 0.-10) DEVIA-MEMBER ANSYS DEVI A-[ PISTAR TlON - MEMBER ANSYS PISTAR TION l RESULTANTS */. RESULTANTS % Axial Torsional Force 23.080 23.083 0.01 Moment -1672.44 -1671.57 0.05l Endl End-l g-Axial Torsional I i Force 23.080 23.083 0.01 Moment -1672.44 -1671.57 0.05 End-J End-J Y-Axis Y-Axis Shear 921.529 921.502 0 Moment -1549.95 -1550.55 0.04 g End-l End-l [, Y-Axis Y-Axis Shear 921.529 921.502 0 Moment -18219.90 -18217.77 End-J End-J 0.01 Z-Axis Z-Axis Shear -333.399 -333.344 0.02 Moment 9404.88 9404.53 0 ( g-End-l End-l Z-Axis Z-Axis Shear -333.399 -333.344 0.02 Moment -36671.60 -36670.57 0 End-J End-J l[ j hi l q -

                                                                                                                                                          ,    4 hum 3.26                                                 _

6 L__.________._____------.-_----_-- - - - - - - - - - - - - - - ' ' ' ' ' '

1 TR-76-001

                                           ,                         Revision 0
  )                                                                                                '

Table 3.3-4. Member Stress Resultants ANCHOR DISPLACEMENTS - Element 20 F L ELEMENT NO. 20 TYPE Straight Pipe End of Piping Structure Nodes 22 6 23 - Node 23 DESCRIPTION _ Anchored ( x, y, z = End-I = 40.1, 50, 30: End-J = 40.1. 50, 901

  }                                          DEVI A-                                   DEVI A-f         MEMBER        ANSYS     PISTAR    TlON     MEMBER       ANSYS      PISTAR   TION RESULTANTS                           %     RESULTANTS                           */.

Axial Torsional Force -977.504 -977.467 0 Moment -461.27 -461.07 0.04 Endl End-l Axial Torsional Force -977.504 -977.467 0 Moment -461. 7 -461.07 0.04 En d-J End4 t Y-Axis Y-Axis Shear -70.531 -70.519 0.02 Moment -1555.95 -1555.79 0.01 Endl End-l Y-Axis Y-Axis Shear -70.531 -70.519 0.02 Moment 9821.32 9818.13 0.03 End-J End-J Z-Axis Z-Axis Shear 189.621 189.565 0.03 Moment -4808.55 -4808.94 0.01 End-l End-l i Z-Axis Z-Axis Shear 189.62'1 189.556 0.03 Moment -576.66 -577.81 0.20 End-J End-J 4

                .                                  3.27                             nutech          !
                                                                                          .4.-..a

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                        ,                         Revision 0            L
                                                                        ,-1 e

j Table 3.3-5. Nodal Displacements j 1 ANCHOR DISPLACEMENTS - Node 4 I NODE NUMBER 4 LOCATION End of Model - Spr{.ng Restraint Il x= .1, y = 90. 2 = 0 DISPLACEMNT ANSYS PISTAR DEVIATION COMPONENT ( X 10-2) ( X 10-2) % u X-Trans 14.378 14.378 0 l 1 [l Y-Trans -9.3611 -9.3602 0.01 L Z-Trans -5.5974 -5.5965 0.02 _

X-Rotation -0.10612 -0.10616 0.04 kl c Y-Rotation 0.0083880 0.0084110 0.29 l Z-Rotation -0.045480 -0.045465 0.03 *i i l 3.28

si 4_ 1

TR-76-001 Revision 0 [

Table 3.3-6. Nodal Displacements

       -                           ANCHOR DISPLACEMNTS - Node 8 NODE NUMBER 8
        -           LOCATION End of Elbow x = 40.1, y = 85.5, z.=    0 DISPLACEMNT        ANSYS        PIST R    DEVIATION f-'                                       -2 COMPONENT         ( X 10 )     ( X 10-2)       %

f. X-Trans 14.723 14.723 o Y-Trans -10.266 -10'.266 o

[- Z-Trans -4.8659 -4.8667 0.02 X-Roiction 0.12717 -0.12721 0.03 Y-Rotation -0.066763 -0.066721 0.06 ? '- Z-Rotation o.11751 0.11750 0.01 l_ j q 3.29 nutech

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                  .                              Revision 0                <

l Table 3.3-7. Nodal Displacements ANCHOR DISPLACEMENTS - Node 19 ._ NODE NUMBER 19 j LOCATION At Branch y = 40.1 y = 50. 2 = 10 i DISPLACEMN1 ANSYS' PISTAR DEVIATION . COMPONENT ( X 10-2) ( X:10-2) % . X-TranS 17.324 17.32s o.01

 ,     Y-TranS        -7.9983        -7.9983       0 Z-TranS         0.10923        0.10923      0 X-Rotation       -0.25s62        -0.25564     0.01 L

ti l Y-Rotation 0.220so 0.22044' o.03 D Z-Rotation 0.047866 0.047842 0.05 "

                                                                             's I

D 3.30 e a e - *w

o

                                                                       .TR-76-001
                                           -                            Revision 0 3.4   Combined Loads
     -                                                                                          l In the combined analysis, all three loading conditions (described in Subsections 3.1, 3.2, and.3.3) are imposed simultaneously                ;
  ,                 on the piping system (Figure 3.0-1).      This condition is presented in the ASME Verification Problem 6 (Reference 6).               l l

Tables 3.4-1 through 3.4-7 present the PISTAR and ANSYS results and the percentage of deviation from the ANSYS results for the f combined loads analysis. For the various member stress resul- ' tants and nodal displacements, the maximum deviation w&; 2.38%, which is within the specified criterion. The maximum-value~is )

circ ~1ed on Table 3.4-1 for easy reference. c. c, ! "L' l 6 I N s , 3.31 nutech W

TR-76-001 * - * 'l

                                     -                              Revision 0                   ,      l Table     3.4-1.          Member Stress Resultants                                           ,

d COMBINEL LOADS Element 1 1 f ELEMENT NO. 1 TYPE Straight Pipe DESCRIPTION Spring Attachment at Node 4 - Straicht Dine en Node 5 fx . v. 7 = End-I = .1. 90, 0: End_,-J = 20.1, 90, 0) 4 DEVIA- DEVIA- r MEMBER ANSYS PISTAR TlON MEMBER ANSYS PISTAR TlON [

                                          %    RESULTANTS                                %

RESULTANTS Axial Torsional 0.21 f Force 48.684 48.759 0.15 Moment -9.68 -9.70 ' EndI End-l < Axial Torsional - Force 48.684 48.759 0.15 Moment -9.68 -9'.70 0.21 . En d-J End-J - Y-Axis Y-Axis Shear -2.775 -2.715 2.16 Moment 33.44 33.46 0.06 Endl End-l . Y Axis Y-Axis Shear 9.852 9.911 0.60 Moment 2843.21 -2843.21 0 End-J End-J . Z-Axis Z-Axis t Shear -143.832 -143.834 0 Moment -19.95- -19.93 0.10 : End-l End-l Z-Axis Z-Axis

                                                                -50.82                  2.38
               -143.832   -143.834         0      Moment                    -52.03 Shear End-J                                          End-J                                       4
                                                                                                 'B t_

t mm. 3.32 '- i.

'f TR-76-001

                                           .                                Revision.0
 -         Table     3.4-2.          Member Stress Resultants e

COMBINED LOADS - Element 4 f 4 ELEMENT NO. TYPE Elbow DESCRIPTION 4.5 Inch Radius Elbow Node 7 8 8 (x, v. z End-I = 35.6. 90. 0: End-J = 40.1. 85.5. 01 DEVI A- D EVI A-MEMBER ANSYS PISTAR TION MEMBER- ANSYS PISTAR TlON RESULTANTS % RESULTANTS % Axial Torsional Force 48.684 48.759 0.15 Noment -9.68 -9.70 0.21 Endl End-l Axial Torsional r Force -47.818 -47.877 0.12 Moment 5719.86 5719.88 0 En d-J End-J Y-Axis Y-Axis Il Shear -43.355 -43.415 0.14 Moment 5072.61 5072.63 0

'-         Endl                                           End-l Y-Axis                                          Y-Axis Shear        -48.684    -48.759     0.15       Moment      656.93       656.95    0 En d-J                                         End-J Z-Axis                                          Z-Axis Shear        143.832    143.834       0        Moment      528.40       530.53   0.40 End-l                                            End-l                                      '
  .       Z-Axis                                          Z-Axis Shear        143.832    143.834       0        Moment      952.62       952.61    0 End -J                                     j    End-J d

3.33 nutech 4..

T TR-76-001 ; Revision 0 r , Table 3.4-3. Member ~ Stress Resultants , COMBINED LOADS - Element 18 f-ELEMENT NO. 18 TYPE. straight Pipe l DESCRIPTION Branch from Node 19 to Node 20 - Node 20 Anchored (x, y, z = End-I = 40.1, 50, 10 End-J = 40.1, 0, 10) DEVI A- DEVI A-MEMBER ANSYS PISTAR TION MEMBER ANSYS PISTAR TION RESULTANTS % RESULTANTS % g Axial Torsional. I' Force -697.476 -697.339 0.02 Moment -1415.51 -1414.22 0.09 End-l End-l [I Axial Torsional i Force -729.041 -728.904 0.02 Moment -1415.51 -1414.22 0.09gl End-J End J Ll Y-Axis Y-Axis Shear 1984.280 1984.022 0.01 Moment -2279.39 -2277.22 0.10 Endl End-l Y-Axis Y-Axis g Shear 1984.280 1984.022 0.01 Moment -16581.60 -16580.55 0.01)' En d-J End-J Z-Axis Z-Axis b Shear -286.043 286.067 0.01 Moment 32647.00 32639.11 0.02 C End-l End-l Z-Axis Z-Axis 1 Shear -286.043 286.067 0.01 Moment -66567.00 -66561.98 0.01 End-J End-J , ei l l l ! h

                                                                                               'b 3.34                                          ,

s e

TR-76-001. Revision 0 i Table 3.4-4. Member Stress Resultants COMBINED LOADS - Element 20 a ELEMENT NO. 20 TYPE Straight Pipe DESCRIPTION End of Piping Structure Nodes 22 6 23 - Node 23 Anchored (x, y, = End-I = 40.1, 50, 30; End-J = 40.1, 50, 90) DEVI A- DEVI A- I MEMBER ANSYS PISTAR TlON MEMBER ANSYS PISTAR TION l RESULTANTS % RESULTANTS % ! \.

       .      Axial                                     Torsional                                              l Force     -2128.110 -2127.855    0.01       Moment      -218.54                -217.87   0.31 Endl                                          End-l                                              l Axial                                     Torsional Force     -2128.110 -2127.855    0.01       Moment      -218.54                -217.87   0.31 En d-J                                       En d-J -

Y-Axis Y-Axis l Shear -531.747 -531.550 0.04 Moment -2875.02 -2875.52 0.02 Endl End-l Y-Axis Y-Axis Shear -493.868 -493.671 0.04 Moment 11366.50 11362.98 0.03 End-J End-J Z-Axis Z-Axis Shear 237.359 237.308 0.02 ' Moment -17276.00 -17275.27 0 End-l End-l Z-Axis Z-Axis Shear 237.359 237.308 0.02 ' Moment 13492.50 13481.35 0.08 End-J End-J W L 3.35 nutech

IN[$is*0 I Table 3.4-5. Nodal Displacements [ COMBINED LOADS - Node 4 NODE NUMBER 4 LOCATION End of Model - Spring Restraint x = .1, y = 90, z=0 DISPLACEMNT ANSYS PISTAR DEVIATION-COMPONENT (' X 10-2) ( X 10-2) % { X-Trans 4.8684 4.8759 0.1s L

 . Y-Trans        -0.27743       -0227150      2.14 Z-Trans         -14.383         -14.383
                                                     -0 L

X-Rotation -0.096843 -0.097012 0.17 g1 t' Y-Rotation 0.33455 0.33462 0.02

m Z-Rotation 0.19948 0.19929 0.10 l I w d I% 3.36 I <._

TR-76-001 Revision 0 4-1 Table 3.4-6. Nodal Displacements i f COMBINED LOADS - Node 8 4 I NODE NUMBER 8 ] LOCATION End of Elbow x = 40.1, y = 85.5, z=0 DISPLACEMNT ANSYS PISTAR DEVIATION !

                                                 -2      -               -

COMPONENT ( X 10 ) ( X 10-2). % X-Trans 14.401 14.407 0.04 b Y-Trans 6.6748 6.6732 0.02 l Z-Trans -25.844 -25.849 0.02 l X-Rotation -0.1.4960 -0.14977 0.11 1 l Y-Rotation 0.14324 0.14331 0.05 L Z-Rotation 0.17038 0.17018 0.12 4

                                                   - 7 nutech l                                                                                     ...

TR-76-001 ' ' Revision 0 - 1 1 Table 3.4-7. Nodal Displacements y; COMBINED LOADS - Node 19 i f' NODE NUMBER 19 l

         ,   LOCATION At Branch x - 40.1, y - 50, z --10

[ DISPLACEMNT ANSYS PISTAR DEVIATION

                                   -2                                   f COMPONENT       ( X 10 )       ( X 10-2)      %

X-Tra ns 18.519 , 18.520 0.01 1 1

 .           Y-Trans          2.8365-       2.836s        0-li
     .                                                                  1 Z-Trans        -17.186      -17.186         'O

[ X-Rotation -0.43910 0.44014 0~.24 luj b Y-Rotation -0.20199 -0.20190 0.04 Z-Rotation 0.022678 0.022607 0.31 - j 3.38 . I

                                                                   .-            l

[ . o TR-76-001 I- - Revision 0 T 4.0 EIGENVALUE EXTRACTION ANALYSIS The piping system model (Figure 4.0-1) was used for verifying

        ~                  PISTAR's modal extraction equation solvers. PISTAR has two equation solvers for performing modal extraction of eigenvalues E                   and eigenvectors. These solvers were developed by E. L. Wilson and K. J. Bathe at the University of California, Berkeley _(Ref-erence 7). The first solver.is the determinant search solver (Subsection 4.1). This solver is an in-core solver used for small problems. The second solver is the inverse iteration solver (Subsection 4.2). This. solver is an out-of-core solver using spill logic and is used for large problems. The program

( automatically selects the best solver for the problem input. In general, the solution to a modal extraction analysis requires the solution of the generalized eigenvalue problem, e

K 4 = ci M4 2 (6) w= Free vibration frequency-4 = Mode shape The mass matrix is diagonal with some zero diagonal elements. The program assumes that only the lowest p eigenvalues and correspond-

           -                            ing eigenvectors are needed. Equation 6 can therefore be written as:
                                                                                ,K 4 = Mon 2                                 (7) where n2 is a diagonal matrix with the p smallest eigenvalues, i.e., 0 2            = diag (w2 ), and 4 stores the corresponding 4.1 nutech

TR-76-001 . I Revision 0 t r s ,l Wh [' h - . s i e, Y [j io l 14

i ll Z /\ X ,,

                                                             ,V
                                                                      ,,i2     l:

g, , is 'f i ! I 19

21 22 1 g as - to g - 9 Figure 4.0-1 Piping System Model - Eigenvalue Extraction Analysis 4.2 1 ik

1

          . t                                                    TR-76-001 Revision 0 l

M-orthonormalized eigenvectors 4 , 4 1 2 '*****p. Two different solution procedures are used in the program: a determinant search technique, or a subspace iteration solution.- The deter-

  .-            minant search solution is used when the stiffness matrix can e              be contained in one block of high-speed storage.      Therefore,    -i for systems of large order and bandwidth, the subspace' iteration     l j

f method is used. Both solution techniques solve the generalized 1 eigenvalue problem directly without a transformation to.the standard form (Reference 7). I I The piping system model used for the eigenvalue- extraction analysis is shown in Figure 4.0-1. The sensitivity of'results ] were verified with the widely accepted computer program ANSYS L (Reference 3). The problem analyzed is Problem Number.6 in Reference 6 (Static IL Analysis of a Three-Dimensional Piping Structure Program - ANSYS). Although this is a static sample problem, its data and charac-teristics are adequate for demonstrating dynamic behavior. The data specified in problem 6 (Reference 6) was directly input into PISTAR with the following exceptions: The modulus of elasticity was typed incorrectly 6 as 20.0 x 10 psi in the reference document (Reference 6). The value used was-29.9 x 100 psi. L 4.3

n TR 76-001, , [ e Revision 0 l.i f

                . The valves in the PISTAR model were coded as straight pipe sections with the appropriate                     .

cross-sectional property values (Table4'.~0-1).

                   -PISTAR assumed a direct spring-to-ground restraint mechanism on nodal point-4.

f i The element component types used in PISTAR to describe the ; piping system are PIPE _and ELBOW. ! The cross-sectional properties are found in Table 4.0-1.

-{!

Outside i Wall Thickness Wt Per Unit Component Dia (Inches) (Inches) Length (1b) f_ Straight Pipe 3.5 0.216 0.631313 i Elbow l 3.5 i 0.216 0.631313 l s ! j Valve D 4,94 0.7619 3.00311 1 s Valve E 4.499 1.7153 4.50466 [ w Valve F s; 5.221 0.3251 2.00207 l Table 4.0-1. Cross-Sectional Properties L The components in the' piping system are made of steel.- Young's modulus is 29.9 x 10 0 psi. Poisson's ratio is 0.3; and the _]

                                                          -5 coefficient of thermal expansion is 2.178 x 10           ,
  ,                                   4.4 L)

I

       * '                                              TR-76-001 Revision 0 Ti.e piping system has been anchored at noda1' points 20 and 23.-

1 Nodal point 4 has a direct spring-to-ground restraint mechanism which imposes a translational restraint in the X, Y, and Z directions of 1,000 pounds per inch and a rotational restraint in the X, Y, and Z directions of 10,000 inch-pounds per radian. For verification, a total of 15 eigenvalues and eigenvectors were extracted. The results of these analyses are presented

4 in Subsections 4.1 and 4.2. For' verification, modal' frequencies and modal normalization points were compared.

The criterion used for verification in this section is a 7.5% deviation from the accepted ANSYS solution. 1 b P h-- 4.5 nutech e 4hmen,

K TR-76-001 - Revision 0 ' 4.1 Determinant Search Solver The determinant search modal extraction solver is examined for solution technique' accuracy in this section.- The piping model described in Section 4.0 was used for this analysis. The deter-minant search technique is best suited for the analysis of { largesystemsinwhichKandM(Equation 8)havesmallbandwidths,f or for problems with few degrees of freedom. Basically, the solution algorithm combines triangular factorization and vector inverse iteration in an optimum. manner to calculate the required - eigenvalues and eigenvectors; these are obtained in sequence starting from the least dominant eigenpair w 2 #. 1 An efficient accelerated secant iteration procedure which operates on the j characteristic polynomial p(w2) = det(K - w M) 2 y (8) is used to obtain a shift near the next unknown eigenvalue. The eigenvalue separation theorem (Sturm sequence property) is used in this iteration. Each determinant evaluation requires a ( triangular factorization of the matrix K - e M.2 When there is E a shift near the unknown eigenvalue, the inverse iteration solution calculates the eigenvector; the eigenvalue is obtained { by adding the Rayleigh quotient correction to the shift value. ,i i The modal frequency values and the modal normalization points ') were compared with the results obtained from the ANSYS computer program for solver verification.

4.6

f =. o TR-76-001-

 -l                                    ,
                                                             ' Revision 0          <    l 4.1.1   Frequencies (Determinant Search)-        ,

i Table 4.1.1-1 presents the PISTAR and ANSYS modal frequency results using the piping model defined in'Section 4.0. The solution algorithm used was the determinant search technique. For: the various modal frequencies, the ' maximum deviation was 0.46%, which is within the specified criterion. .The maximum { value is circled in Table 4.1.1-1 for easy reference. 1 '! i l 1 i I . J l ! 1

                                                                                     -)   i L

k \.

                                            '7 nutech       !

1

                                                         .     . r!

TR-76-001 Revision 0 l! Table 4.1.1-1. f Modal Frequencies (Determinant Search) Mode PISTAR 'ANSYS % Number Results (eps) Results (eps) Deviati'on{ 1 12.64 12.60 0.32 - 2- 15.44 15.37 0.46 -l 3 34.70 34.70 0 f, 4 39.73 39.68 0.13 ! 5 53.50 53.47- 0.06' - 6 95.40 95.16 0.25 7 105.8 105.69 0.10 I. 8 143'.1 142.93 0.12 l 9 176.9 176.79 0.06 i 10 246.7 246.38 I 0.13 f 11 277.9 277.58 0.12 l j 12 322.5 321.95 0.17 l 13 332.7 332.06 0.19- '(

        !     14            424.9           424.63         0.06    b i

l 15 l 515.3 513.54 0.34 4 I l E w ! L. 4.8 L

7 ;, p mrpg .3

                                                                                                           ?
                                                                                                                     ~

3 ,'; . 1,;

                                                                  , .. c; . . )q.      D d; g'- 'y l ::t
                                                                                  ',1-'f                                                    ~ TR-76-001' f                                                                                                                                                         q
                                                                ,.l q,,
                                                                                          .g       ..                           ,
                                                                                                                                          ' \ Revi'sion 0                   'j
                                                           , . gf > , ,.                ,
                                                                                               ,                                             ; s.                           _
                   -                                         n-                                            a                               , p,                              3

n 1

s. \

4'.1.2 Mode Shapes (Determinant Search)'

4 j--

                                                                                                                                                                          .l Table 4.1.2-1 pre'sents the PISTAR and                                             SYS modal normalizaticn results using .the piping inodel.. defined"in Section 4.0.

The d

,' u ., V b .. solution.nigorithm used was the" determinant' search. technique.

                   .t"         r.
                         ..     ;                                    +.                                      '

p,]",F ,x l 4 The modal normalization pointsiwere the same for the PISTAR and ANSYS runs. T h

              )!                                                                                                         s y

n ; L 1

I 1

i

            . f I

l m k i i

'- i e

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l nutech 49 L

j

                                                       .TR-76-001 ,. ,

3 Revision 0 Table'4.1.2-1. j Modal' Normalization Points - .i; 1

                     '(Determinant Search)                                       i
                          .PISTAR               ANSYS                          -

Mode: Results Results Number i (Node-DOF) (Node-DOF) g ', J-) 1- 7-X 7-X 2 7-Z 7-Z- l

      !     3               4-Y                  4-Y
      !     4               4-Z                  4-Z 5               4-Y                  4-Y l                                                               )

6 22-Y 22-Y i 7 17-X 17-X l i 8 22-Y I 22-Y 9 12-Z 12-Z i 10 , 11-Z ll-Z l 11 4-Y 4-Y I ; 12 4-Z 4-Z t i l 13 l 12-Z 12-Z 14 i 19-Z 19-Z bi ; Ei 15 : 17-X 17-X ! W i i j b u. I, 5 b-l 4.10 c. 1 i In

Revision 0-4.2 Subspace Iteration Solver The modal extraction solver is examined for solution technique accuracy in this section. The piping model described.in Section 4.0 was used for this analysis. The subspace iteration technique was designed for large problems and for piping systems that are too large to be

   -          completely solved in core.. The iteration can be interpreted as a repeated application of the Ritz method; the computed eigenvectors from one step are used as the    base vectors for the next iteration, until convergence with the required p f              eigenvalues and eigenvectoIs.

The solution is found by iterating simultaneously with q linearly independent vectors, where q > p. In the k'th iteration, the vectors span the'q-dimensional subspace ck and' 1 best eigenvalue and eigenvector approximatio- ..e calculated; l i.e., when the vectors spsn the p-dimensional least dominant subspace, the required eigenvalues and eigenvectors are obtained, Let V g store the starting vectors, then the k'th iteration is described as follows: { , Solve for vectors V which k span ek KVk* # k-1 4.11 nutech

^+

TR-76-001 Revision 0

                                                                                        '[e Calcuate the projections of'K and M onto ck (i.e., the general-                        -

ized stiffness matrix and mass matrix corresponding to ek)* ! T (10) . f K k YkE k I-T- (11) Mk " Vk" k Solve for the eigensystem of K k and Mk 2 K g Qp = MgQk U k (12) and calculate the k'th improved approximation to the eigenvectors i

                                      "                                          (13)

V k k Ak 10 Provided that the starting subspace is not orthogonal to any of-the required eigenvectors, the iteration converges to the-desired result, i.e.,af+O 2 and Vp + e as k + . { I The number of vectors q used in the iteration is greater e; than the desired number of eigenvectors to accelerate the con-vergence of the process. The number of iterations required to achieve satisfactory convergence depends on the quality of.the s starting vectors V g. The. program generates q starting vectors, where q equals the minimum of (2p) or (p+8) . At convergence, t : a Sturm sequence check is performed to verify that the lowest p- , eigenvalues have been found. 4.12 q

                                                                                           =
                                                                          .m.*--

f~ .- . TR-76-001 l- , Revision 0 The comparative results of this solver with the ANSYS program can be found in Subsections 4.2.1 and 4.2'.2. ' Subsection 4.2.1 presents the results of the-frequency calculations and Subsection 4.2.2 presents the results of the eigenvector extraction calcu-lations. { l l I I ; a l fL b b 1 1 1 i b l b 4.13 nutech

TR-76-001 * - Revision 0 - {.1

4.2.1 Frequencies-(Subspace Iteration) f Table.4.2.1-1 presents PISTAR.and ANSYS resul'st for the modal f extraction analysis'using the' piping model defined in Section ?

                                                                                      .1
                                                                                      -j 4.0. The' solution algorithm used.was.the subspace iteration                      J l

solution technique. For.the various modal frequencies, the' maximum deviation was.0.46%, which is within the.specified criterion. The maximum value is circled in Table 4.2.1-1 h< for easy reference. - I l l' I

                                                                                      -l  :

J L;

4.14 y on m.

l

      ~ '                                                                  1 TR-76-001               i
                          .                       Revision 0 i

Table 4.2.1-1. 1 _ Modal Frequencies. [ (Subspace Iteration) i i FISTAR ANSYS I Mode Results Results % Number (cps) (cps) Deviation

            -         1        12.64            12.60            0.32    ,

2 15.44 '15.37 0.46 3 '34.70 34.70 0 4 39.73 39.68 0.13 i 5 53.50 53.47 0.06 I- f i 6 95.40 95.16 0.25

7 105.8 105.69 0.10 8 143.1 142.93 0.12 9 176.9 176.79 0.06 10 246.7 , 246.38 0.13 11 277.9 277.58 0.12 12 322.5 321.95 I 0.17 13 332.7 332.06 0.19 _ 14 424.9 , 424.63 ! 0.06 l l 15 515.3 l 513.54 ' O.34 l 1 1 4.15 nutech 2 ,h_

TR-76-001 - . [ Revision'0 l 4.2.2 Mode Shapes (Subspace. Iteration) Table 4.2.2-1 presents the PISTAR and ANSYS results for'the

-{

modal extraction analysis using the piping model defined in Section 4.0. The solution algorithm used was the subspace f iteration technique. The modal normalization points were the same for the PISTAR and ANSYS runs. f I I 4 l L L L L' L L

4 4.16 i J l l

a TR-76-001 Revision 0 . f' 1 ^ !

Table 4.2.2-1.- Modal Normalization Points F e (Subspace Iteration) PISTAR ANSYS Results Results Mode Number (Node-DOF) (Node-DOF) 7-X 7-X 1 .c 7-2 7-Z l 2 4-Y 4-Y 3 4-Z 4-Z 4 4-Y 4-Y 5 , 22-Y 22-Y-6 i 7 17-X 17-X l 8 22-Y 22-Y 9 12-Z 12-Z 10 11-Z ll-Z 11 4-Y 4-Y 12 4-Z 4-Z 13 12-Z 12-Z 19 , 14 , 19-Z i 15 17-X 17-X nutech I 4.17

                                                                           - .   - I U

' ~ TR-76-001 Revision 0 J

     -       -5. 0  RESPONSE SPECTRUM ANALYSIS.

The' piping system model shown in. Figure.5.0-1 was used for E verifying.PISTAR's response spectrum analysis equation solver. The sensitivity of results were verified with the widely accepted computer program ANSYS (Reference 3).

             -The problem used in this analysis is Problem Number 6 in Reference 6 (Static Analysis of a Three-Dimensional Piping Structure Program-ANSYS). Although this is a static sample problem, its data and characteristics are adequate for demonstrating' dynamic behavior.

l I The data specified in problem 6 (Reference 6) was directly input into PISTAR with the following_ exceptions. [ . The modulus of elasticity was typed incorrectly as 20.0 x 10 6 psi in the reference document l 0 (Reference 6). The value used was 29.9 x'10 psi. !

                            . The valves in the PISTAR model were coded as straight pipe sections with the appropriate cross-sectional property values.(Table 5.0-1).

1 l l j I 5.1 nutech 4 _ l _ _j

TR-76-001- ,. Revision 0 f x , , W h. I g s s - y 14

                                                                 ,,               r
                                                                          ,,      I Z
                         /\              X 16             'l2 l

g7

                                                             ,   13
                                               /
                                                     ../                          I;
                                                                                          /

zi . 22

~!

L L. E' 23

                                                   *hd Figure 5.0-1. Piping System Model - Response Spectrum Analysis                            i M

5.2 l _. . _ . . _ j

                                                                               .a  ,v  vv.   ;
             . . .                                                             Revision 0    i l

f . PISTAR assumed a direct spring-to-ground' } restraint mechanism on nodal point 4. ) The element component types used in PISTAR to describe the

'~

i piping system are PIPE and ELBOW. The cross-secticnal properties are found in Table 5.0-1. Outside Wall Thickness Wt Per Unit ) Component Dia (Inches) (Inches) Length (1b) { Straight Pipe 3.5 .0.216 0,631313 Elbows 3.5 0.216 0.631313 Value D No es 4.94 0.7619 3.00311 { Value E f$ 4.499 1.7153 4.50466 s

           .         Value F                     5.221            0.3251       2.00207 Table 5.0-1.       Cross-Sectional-Properties-I 1

The components in the piping system are made-of steel. Young's i 6 modulus is 29.9 x 10 psi. Poisson's ratio is 0.3; and the coefficient of thermal expansion is 2.178 x 10 -5 , The piping system has been anchored at nodal points 20'and 23. ' Nodal point 4 has a spring-to-ground restraint mechanism which !

  ,.               imposes a translational restraint in the X, Y, and Z directions of 1,000 pounds per inch and a rotational restraint in the
 \-

5. 3 nutech

                                                                                                            --------------a TR-76-001      ' -
                                                                   ,                          -Revision 0                {D i

4 X, Y, and Z directions of 10,000 inch-pounds per radian. {.s The piping model.first went through a modal extraction analysis where a total of 15 eigenvalues and.eigenvectors were extracted using the determinant search eigensolver. . The modal superposition technique was used for:the solution

                      -of the               ynamic equations for all 15 modes.

The structure (Figure 5.0-1) was. subj ected to 3 uncoupled fL j shock vectors imposed along the global X, Y, and Z-directions. ; These solutions were combined to give the total Il solution. The response spectra are defined by a series of frequency versus acceleration points found in Tables 5.0-2 through 5.0-4. In general, a dynamic structural analysis involves the solution ) of the system of equations Mu + Cu (14) r r

E"r = R (t )

for the displacements. R(t) can be an effective load which results from ground motion. Specifically, if the structure ;_ is uniformly subjected to a ground acceleration, you may assume the following: " 1 R(t) = -MU S (15) , U r is the relative displacement of the structure with respect to the ground.

                                                                          ~5. 4                                         C l      t
                                                                                                                           ==

J

TR-76-001 Revision 0

 .                  Table 5.0-2. X-Response Spectrum Definition c-          SPECTRAL POINT                                 SPECTRAL 1              NUMBER            FREQUENCY (CPS)         VALUE- (gs) 1                     0.25               0.075'                        ;

2 0.45 0.20 - y 3 0.50 0.22 4 0.64 0.28 , 5 1.0 0.36 6 1.6 0.45 [ 7 2.1 0.58

                                       .                                                    i 8                     2.3                0.65 4

9 3.1 0.65 10 3.4 0.90 t - 11 3.6 1.40 12 3.7 1.55 L 13 5.3 1.55 1 14 7.0 1.55 3 l

  .-               15                      8.0                0.75 8.2                0.60 1

_ '16 i u 5.5 nutech !

p eudeen

1 i TR-76-001

                                         -Revision 0 Table 5.0-2. X-Response Spectrum Definition (Cont)                                                 {'l     .

SPECTRAL' POINT SPECTRAL VALUE - (g 's) f-NUMBER- FREQUENCY (CPS) l)

17 9.0 0.55 18 10.0 0.50 .

                                                                         -l 19                  10.5                  0.50                       :

20 11.5 0.25 - j 21 13.0 0.22 fl l 22 15.0 0.17 j 23 18.0 0.18 j 24 20.0 0.18- [ 25 24.0 0.18 l! Li 26 25.0 0.15 27 1000.0 0.15 {l w h I L; L'

b. '

i l i l l 6 5.6

<1

3

                                                                                                    -1 f     . ..
                                                         -TR-76-001                                   1

-l1 Revision 0

                                                                                                      )
 ;_.                 Table 5.0-3. Y-Response Spectrum Definition-
                                                                                                      )

SPECTRAL POINT SPECTRAL NUMBER FREQUENCY (CPS) VALUE (g's)

  -                   1                    0.25                  0.07 1

2 O.5 -0.12 3 i I 0.8 3 0.24 I 4 0.94 0.24 j 1 T :) 1 5 1.0 0.26 ) l 6 1.5 0.41 , i 1 7 2. 0 0.51 8 2.5 0.59

j 9 3.5 0.618 0 10 7.4 0.618 l 11 8.0 0.6.5 1 L 12 9.0 0.60 13 10.0 0.585 4 14 12.0 0.57 u. 15 13.75 0.4 16 15.0 0.29 u 5.7 nutech

w. h4e . g m-.-n , %

2 TR-76-001- * '

                   .                      Revision 0 Table 5.0-3. Y-Response Spectrum Defini t i~on                r (Cont)-                                                         lL SPECTIML POINT                                -SPECTRAL NUMBER-          FREQUENCY (CPS)-         VA'.UE (g 's) f 17                    18.0                    0.29 18                    20.0-                   0.258 19                    20.1                    0.23 f

20 22.0 0.22 . 21 25.0 0.22 22 1000.0 0.22 1 i 1.. IL l c 1!. 1, 1 l s o i

i . e i 1 I 5.8

==

TR-76-001 l Revision 0 Table; 5. 0- 4. - Z-Response Spectrum Definition 1 SPECTRAL POINT SPECTRAL g NUMBER FREQUENCY (CPS) VALUE (g's) 1 0.25 0.075 iL

          -               2                      0.45                0.20 3                     0.5                  0.22 4                      0.64                 0.28

v 5 1. 0 ' O.36 1 I i d 6 1.6 0.45 l

7 2.1 0.58 i 8 2.3 0.65 i 3.1 9 0.65 E, 10 3.4 0.90 I

  <u 11                       3.6                 1.40 12                      3.7                  1.55
    ~

13 5.3 1.55 1 i 14 7.0 1.55 t 1

 ,                     15                      8.0                  0.75 16                      8.2                  0.60 m

6 5.9 (1

TR-76-001 -- Revision 0-Table 5'.0-4. Z-Response Spectrum Definition 7 (Cont) p, SPECTRAL POINT SPECTRAL f1 NUMBER FREQUENCY (CPS) VALUE (g's) {l 17 9.0 0.55 18 10.0 0.50 p)j (4 19 10.5 '0.50 20 11.5 0.25 21 13.0 0.22 22 15.0 0.17 1'! 23 18.0 0.18' , 24 20.0 0.18 f' 25 24.0 0.18 ll 1., j i 26 25.0 0.15 q j 27 1000.0 0.15 g, , n l L L N 4 W 5.10 t 4

TR-76-001 Revision 0 I In this analysis, the ground acceleration vector in equation i

   '                                                                                                i 15 is written as                                                                     {
                                                                                                     \

u=n g gx

                                                    +0 gy
                                                            +u gz                   (16) where 5          gy, and U gz    are the, ground accelerations in the 8x'                                                                     .l X, Y and Z-directions, respectively.               The equation for theJ f

response in the r'th mode is therefore 1 2 Rr + 2Cr *r*r* "r*r " T rx

                                                       *T     +r ry . rz                -(17) where x r is the r'th element in X and                                       -

T r Tx =-4 r gx; I ry =-$rMu gy; r rz =-$rMu gz (18) 3 Using the definition of the spectral. displacement (.Re ference

 ,              10), the maximum absolute modal displacements of the structure

n. subjected to an acceleration in the X-direction are u ax),, ,g7 3x ("r) (19) where S x (wr

                                 ) is the spectral displacement in the X-direction corresponding to the frequency w r

I x is a null vector-except for those elements which correspond to the X-translational degree of freedom. These, elements equal 1.0. Similarly, the equation for responses caused by ground acceleration l--

5.11 e nutech-

1

TR-76-001 b Revision 0 o l'- in'the Y and.Z directions is u "*) (

            = $r!* M Iy!8y I"r)     I' "
                                             }"*r!* M Iz !  z f "r)   (20) and the total maximum response in the r'th mode is assumed to f

be ur (max)- rx u (*^*) +ryu (max)rz+ u (max) (21)- f 1 PISTAR calculates the maximum responses.in each of the p lowest modes. The total response for displacements and stress - resultants is calculated by various modal superposition techniques. PISTAR presently has four modal superposition ~ techniques available to the user. {R f Direct or Algebraic Summation (j Absolute Summation Square root of the sum of'the. squares (RSS) i,1-

Closely spaced modes (Reference-10) Ll k: l The square root of the sum of the squares and the closely 5 o spaced modes techniques are presented for verification in Sections 5.1 and 5.2. h , The criterion used for verification in this section is 7.5%. - deviation from the accepted ANSYS and manual' calculation solutions. '~ I l i I gy. # 5.12 i

TR-76-001' q l Revision 0 l I 5.1 RSS Modal Response i i Tables 5.1-1 through 5.1-7 present the PISTAR and ANSYS response spectra analysis results and the percentage of. deviation from the accepted ANSYS.results. The piping 1 model used was that. defined in Section 5.0. In this ana-lysis, the square root of the sum of the squares technique (RSS) is used to superimpose individual-one degree of free- l

                                                                                                 .q dom nodal solutions-. The uncoupled spacial components                       {

1 are also combined using RSS techniques. The maximum deviation was 3.80%, which is within the specified criterion. ' The maximum value is circled on Table 5.1-3 for easy reference.- l s f l l i I. I . J I l k u 5.13 nutech eee awestp--

TR- 7 6 - 0 01- - [ Revision 0 } p Table 5.1-1. Member Stress Resultants RSS Modal Response - Element 1 [ ELEMENT NO. 1 TYPE Straight Pine <, DESCRIPTION Sprine Attachment at Node 4 - strnight Pipe to ; Node 5. (X. Y. Z = End-I = .1. 90. 0: End-J = 20.1. 90. 0) , 'f DEVI A- UEVIA-4 i MEMBER MANUAL PISTAR TION MEMBER MANUAL PISTAR TION L ! RESULTANTS % RESULTANTS % Axial Torsional Force 15.473 15.336 0.89 Noment 2.59 2.60 0.39( End-l End-l y Axial Torsional . Il Force 15.473 15.336 0.89 Moment 2.59 2.60 End-J End J 0.39 l ~ I Y-Axis Y-Axis ' Shear- 5.560 5.478 1.48 Moment 1.36 1.36 0 ll Endl End-! ( l Y Axis Y-Axis ; Shear 5.560 5.478 1.48 Moment 105.58 104.70 0.83 En d-J End-J Z-Axis Z-Axis L Shear 5.316 5.273 0.81 Moment 1.42 1.41 0.70 c End-l End-l 2-Axis Z-Axis Shear 5.316 5.273 0.81 Moment 112.47- 110.81 1.48[ End-J End-J y 4p s. Ii 5.14 t

TR-76-001 [ Revision 0 [ Table 5.1-2. Member Stress Resultants RSS Modal Response - Element 4 ,

~-

4 ELEMENT NO. TYPE Elbow , DESCRIPTION 4.5 Inch Radius Elbow Node 7 5 8 (X, Y, Z End-I = 35.6, 90, 0; End-J = 40.1. 85.5. 0) - i DEVIA- D EVI A- ; F MEMBER MANUAL PISTAR TION MEMBER MANUAL PISTAR TION j RESULTANTS % RESULTANTS % l Axial Torsional Force 4.774 4.765 0.19 Noment 2.61 2.60 0.38 End-l End-l Axial Torsional Force 6.649 6.643 0.09 Moment 98.95 97.84 1.12

  ,-         En d-J                                       End-J
    !-       Y-Axis                                     Y-Axis Shear       6.649      6.643      0.09     Moment   108.18  107.14     0.96 Endl                                        End-l
            'Y Axis                                      Y-Axis c           Shear       4.774      4.765      0.19     Moment    18.12   17.76     1.99

[ End-J End-J

Z-Axis Z-Axis Shear 4.518 4.446 1.59 Moment 387.20 184.50 1.44 L End-l End-l 2-Axis Z-Axis

  .          Shear       4.518      4.446     1.59      Moment   223.84- 220.42     1.53 En d-J                                      End-J I

b-5.15 nutech W -+p-=g e is e,

TR-76-001

                                 .                         Revision 0                        s T

Table 5.1-3. Member Stress Resultants oI RSS Modal Response - Element 18 [ 1 ELEMENT NO. 18 TYPE straight Pipe DESCRIPTION Branch from Node 19 to Node 20 - Node 20 Anchored . { (X , Y . 2 = End-T = 40.1. 50. 10- End-J = 40.1 0. 1 01 ANsys D EVI A- AtJsYs DEVIA MEMBER IWANWRL PISTAR TlON MEMBER 41W$H#iE PISTAR TION i RESULTANTS % RESULTANTS % Axial Torsional Forc e 25.479 25.683 0.80 Noment 157.64 156.33 0.83 ( l End-I End-l y Axial Torsional 'I. Force 25.479 25.683 0.80 Moment 157.64 156.33 En d-J ~ End-J 0.83l W u Y-Axis Y-Axis Shear 7.943 7.775 2.12 Moment 119.53 119.30 0.19 . Endl End-l ( Y Axis Y-Axis Shear 7.943 7.775 2.12 Moment 784.45 775.28 1.17 End-J End-J ' - Z-Axis Z-Axis Shear 17.174 16.992 1.06 266.63 263.20 L Moment 1.29 c-End-l End-l Z-Axis Z-Axis , Shear 17.174 16.992 1.06 Moment 130.53 125.57 3.80 End-J End-J

                                                                                              }
                                                                                            ' fr 1

o ; c 5.16 - i !

I TR-76-001 Revision 0 - Table 5.1-4. Member Stress Resultants r . RSS Modal Response - Element 20 straicht Pine !

 ,              ELEMENT NO.          20                TYPE DESCRIPTION End of Piping Structure Nodes 22 & 23 - Node 23                         f l

Anchored (X, Y. Z = End-I = 40.1. 50. 30- Fnd-J = 40.1 50. o03 DEVI A- 4+Jsys DEVI A- ; At/sys N PISTAR TION MEMBER -1tWtNt#M: PISTAR TlON MEMBER

                                                 %      RESULTANTS                              %

RESULTANTS Axial Torsional 24.440 24.119 0.13 Moment 192.94 l'0.50 1.27 l Force

          . Endl                                        End-l l

Axial . Torsional 24.440 24.119 0.13 Moment 192.94 190.50 1.27 Force

         .      En d-J                                      End-J Y-Axis                                     Y-Axis 4.428     4.428      0        Moment       77.20      77.00      0.26 i Shear Endl                                       End-l                                  ;

Y-Axis l Y Axis ' s 4.428 4.428 0 Moment 350.02 348,12 0.54 Shear End-J End-J Z-Axis 2-Axis

   '                         6.087      6.068   0.31       Moment      155.32     155.89      0.37 Shear
 ,.              End-l                                       End-l
    ,            2-Axis                                     Z-Axis 6.087      6.068   0.31       Moment      110.41-    109.80      0.55 Shear End-J                                       End-J l

L I 4 57 nutech

                                                                                       *    *. 2,

TR-76-001- ! Revision 0 - i 31 Table 5.1-5. Nodal Displacements ! RSS Modal Response - Node 4 1 NODE NUMBER 4 LOCATION 'End of Model - snring na< train + {l X= .1, Y = 90, Z = 0-DISPLACEMNT ' ^ ^ ^~1 PISTAR DEVIATION- 1 COMPONENT (y'( X 10 -2 ) ( X 10-2) % MNsys -[- \ X-Trons 1.7248 1.7103 0.84 [ i

Y-Trons 0.63367 0.62450 1.45 Z-Trons 0.60966 0.60842 0.20 { X-Rotation 0.026098 0.025960 0.53

-L!

C Y-Rototion 0.013690 0.013580 0.80 i i s, Z-Rotation 0.014234 0.014059 1.23 p P 5.13 k t w' avi e. e

[ . . TR-76-001 Revision 0 i

    ?
                                   ,                                             l Table       3.1-6. Nodal Displacements                       ]

RSS Modal Response - Node 8 i 8 NODE NUMBER-LOCATION End of Elbow

l. x - 40.1. Y = 83.5, Z=0 DISPLACEMNT " "M PISTAR DEVIATION L

COMPONENT 10-2) ( X 10-2) %

                                     \ A+#4%

b X-Trans 1.6358 1.6227 o.80 ) 4 Y-Trans 0.085554 0.085743 0.22 n

l. Z-Trans o.087032 0.0867s4 o.32 1

e X-Rotation 0.026617 0.026474 0.54 L Y-Rotation 0.012620 0.012307 o.90 Z-Rotation 0.022702 0.022352 1.s4 I. b'- s.19 nutech

TR-76.-001 r Revision 0 ll 1

                                                                       )      i
                                                                          '1 Table s.1-7.       Nodal Displacements RSS Modal Response - Node 19

{) NODE NUMBER 19 LOCATION At Branch fI) X = 40.1. Y = 50. 2 = 10 !! DISPLACEMNT I ""' PISTAR DEVIATION COMPONENT ( X 10-2) ( X 10-2) % l

                      \ Mss                                          .        I X-Tr0ns          0.69438-     0.69243       0.28                 ,

i Y-Trans 0.0019119 0.0019273 0.81 Z-Trans 0.0027102 0.0026738 1.34 t I X-Rototion 0.0037717 0.0038141 1.12 l Y-Rotation 0.011358 0.011264 0.83 L t s Z-Refation 0.020020 0.019766 1.27 y q! W 4 1 5.20 J-y t x

L ' TR-76-001

                                              ,                     Revision 0 f.

5.2 CSM Modal Response i The piping system model shown in Figure 5.2-1 was used.for j l i

                     . verifying the closely spaced modes (CSM) option for combining
 .[1-modal response. The model consists of a straight pipe run of 100 inches, pinned at both ends with rigid restraints, and               l rigidly fixed at node 1 against rotation about its longitudinal i

axis. Listed below are che.important properties: ; i i Young's modulus 29.7E+06 psi Poisson's ratio 0.3- ! I Weight per length 0.1808 lb/ inch Outside diameter 1.315 inch Wall thickness 0.154 inch The structure was subjected to a response spectra excitation f- - in the global X, Y, and Z-directions (see Tables 5.0.2 through a I

5.0-4 for the spectra definition). l 1 5 l [ The modal results for nodal point 6 were combined by manual calculations using the ten percent method, as specified in Nuclear Regulatory Guide 1. 92 (Reference .10) . These results were compared with PISTAR results. These comparative results are presented in Table 5.2-1. s. c The input for all manual calculations was PISTAR's mode response

   %                 output.

t u 5.2 nutech

                                                                                      -e  em

TR-76-001 ' Revision 0 ' i hY f.

                                    / Z             X f

NRIGID i - A '2 RIGID f 3 4

                     %:; '        .                                      L g.

8 e l 10 , j

                                                                    !I RIGID u
                                                                         <L !

l e FIGURE 5.2-1. CLOSELY SPACED MODES VERIFICATION, p L 5.22

            ,                                                                                 D

[ . - , 'TR-76-001 l J J' Revision 0 Table s.2-1. Nodal Displacements CSM Modal Response 4 6 NODE NUMBER LOCATION X= 50.0. Y = 0 0. 2 = 0.0, f

    ,                   . .DISPLACEMNT MANUAL

PISTAR DEVIATION

COMPONENT ( X 10-2) ( X 10~2) % i X-Trans o.0013580 0.0013580 o 1 l l Y-Trans 0.057024 .o.057024 o l l, Z-Trans 0.057024 0.057024 0

  .                                                                                                1 X-Rotation              0.0           0.0            o Y-Rotation         0.74898E-14 0.74898E-14          0
  ~

l

                                                                                                  ,l
  ~

Z-Rotation 0.10971E-15 0.'10971E-1s 0 f [ ("1" + "2") 2 + ("3") 2 + ("4" + "s") 2 ' ("6" + "7")_2 .

CSM =

("8" + "9") 2 + ("10 + "11") 2) I

s.23 - t nutech j

TR-76-001

                                                      ~ Revision                                                                               r Table 5.2-2 lists the. major results'of~the modal::extrac-'           i tion analysis. performed on this.model. . Eleven modes were extracted andthey are reported with their corresponding modal characteristic frequency.                      ,
                                                                      -{,

I;

                                                                      ;I; T

[ I t I L i-.. I P I ne i, W . 5.24 C, t I w, 4

               ~
                  .       c TR-76-001                   l Revision 0               )

1 l l

               -                                                                                                      l Table 5.2-2.

MODAL FREQUENCIES j 1 l MODE NUMBER FREQUENCY (CPS) i 1 11.63 ' r c 2 11.63 3 32.89 L 4 39.52 S 39.52 6 68.96 7 68.96 8 100.80 9 100.80 10 153.20 u 11 153.20 L i 1 i l i >. f g, 5.25 nutech q

-i

c l l TR-76-001' Revision 0

        ,            6.0   FORCED DYNAMIC TIME HISTORY ANALYSIS i

L- The' mathematical codel in Figure 6.0-1 was used for verify- , i ing'the dynamic time history solvers in PISTAR. ]

1 In dynamic response analysis the solution of the equation l M 6 + C 6 + K u = R(t) -(22) { is required, where R(t) can be ~a vector of arbitrary ' time varying loads. (Direct integration techniques or modal superposition.

techniques are used for the time history solution to Equation 22.) l The user must decide to use moda1' superposition or direct ; integration for an effective response history analysis. The i e direct integration is equivalent to a modal superposition analysis in which all the eigenvalues and vectors have been calculated, and the uncoupled equations'are integrated with L a common time step At. The integration can only be' accurate-for modes where at is smaller than a certain fraction of the period T. Using the Wilson e-method, the integration errors effectively filter out of solution the high mode response, for which At/T is large. This filtering it;- caused by amplitude decay la the numerical solution when At/T is large. Figure 7.0-2 shows the amplitude decay using the Wilson

'~

0-method. . L 6.1 nutech,

m i

                                ,                           TR-76-001          -l'                    '

Revision 0 Mk f -I r t GLOBAL r f U' z x j j e j l i i MASS =lO KlPS 4 i-l 2 J c

                         #8 ',

0 18.0" S CH-STD 1 I OUTSIDE DIAMETER = 18" 3 WALL THICKNESS = 0.375" P 'Po e, , l ELASTIC MODULUS = 30.0 x 10 KSI PolSON'S RATIO = 0.3 b P = 20 KIPS Ej

                                                                           }ju1' I

i Figure 6.0-1. Dynamic Time History Analysis _ Verification i

i

(

                                                                         ;                  1 6.2                                                      '-

4 ms

f. )

                                       '                                  TR-76-001 Revision 0 l

1 I, 23.0 19.0 'I -

L AD

                                     \        #      I T

O 15.0 ' b g e = i.4 O b l1.0 j W Q D

     .y           y.

L 3 Q. 3 7.0 r m w CD

      ^
                 % 5.0
       "         z                                                                            ,

W O < 2 { W i Q. t 3.0 i i l l.O L 3 0.02 0.06 0.10 0.14 0.18 0.22 at/T 1

Figure 6.0-2. Amplitude Decay Wilson e-Method 4 4

      .                                     6.3 nutech w.._

1 TR-76-001 7 i Revision 0 '{

                                                                                 -1
 .The effective filtering.of the high frequency response-from.                  j l l

the solution may be beneficial. Integration accuracy cannot be obtained in the response of.the modes for which At/T is fj

                                                                                   .j large. The filtering process allows one to obtain a total system solution in which the low mode response is accurately observed.
                                                                             'h Therefore, a direct integration analysis is equivalent to                  '

a modal superposition analysis when only the lowest modes of the system are considered. (A sufficient number of modes are used for the applied loading .) The exact number o'f modes l' effectively included in the analysis depends on the time step ' size (ot) and the distribution of the periods. The advantanges of modal superposition are essentially: Frequencies and mode shapes are obtained

                                                                             '{ !

A variety of response history and response spectrum analyses can be obtained with a relatively small I additional cost. L Small structural changes or additional eigenvalues E or eigenvectors can be added to an existing eigen- L u system to reduce the cost of the new eigensystem solution. (The frequency domain under analysis is , extended.) The direct step-by-step integration technique is more effect- [ ; ive when there are many modes in the analysis and the response 6.4 s

[ 4 TR-76-001 Revision 0 i J J- is required over relatively few time steps- (i . e . , in shock problems).

     ,            The model under investigation (see Figure 6.0-1) is a mathematical representstion.of a 240.0 inch run of 18.0 inch schedule STD pipe. This problem is presented in Structural Dynamics (Reference 11). The material is carbon
    ~

i steel with Young's modulus of 30.0E06 f.si and Poisson's ratio I of 0.3. The pipe is simply supported on either end (i.e., at nodal points 1 and 3) . The finite element representation cons.sts of three nodal points connected by two straight .f pipe members. A 10 kip mass is located 120.0 inches from either end of the straight pipe model (i.e., at the center of the span). Since PISTAR uses a lumped mass matrix for this f problem, the mass may be input using the appropriate weight per unit length. The specific cross-sectional properties are* Outside Diameter ' = 18.0 inches Wall Thickness = 0.575 inches Weight / Length = 0.083398 kips / inch i The force excitation is a time history forcing function with 1 a magnitude of 20.0 kips. The force consists of a point force applied at nodal point 2 in the positive global Y-direction. 4 Figure 6.0-3 is a graphic representation of this forcing function with respect to time. W e 6.5 nutech e

                                                                                                  *        # 3 TR-76-001
                                                    -                                  Revision 0                !

l r j i l I I l 1 r 20.0- - - - - - - - - - - - - - - - - - - -

                                                                                             $f li                                          I-     ,

l I i 15.0 - 1

    '                                                        l l

a I i to i CL l :

      -                                                                                                          i I

M w i : 10.0 - i i i I Ltl i : O I D H I I l

      .J                                                    l                                             [-;l l

Q. i 4 2 5.0- i i 4 3 I

L i

t e i

                                                           ,! .                                            L 0.0                 e             i             i            a      i     i                     i s

0.0 0.025 0.050 0.075 0.10 0 0.125 0.15 0 TIME (SECONDS) . t Figure 6.0-3. Forcing Function Time History 6.6 [

                                                                                                    . .ww        7

TR-76-001: y Revision 0 i

    - .        6.1    Direct Integration Solver The solution of the equations of motion (Equation 15) can be obtained using the direct integration method of analysis.

In the PISTAR computer program, the Wilson 0-method _is used, which is unconditionally stable. The algorithm used is summarized in Table 6.1-1. Rayleigh damping.is assumed; 1 therefore, C = a M + SK. This form of damping required no storage and no multiplications for a damping matrix. I For ver.ification, the solutions'obtained from PISTAR were compared with those obtained from the ANSYS computer program and a classical hand solution (Reference 11). Displacement component magnitudes (along with-peak' times) and the damping val < " for damped and undamped dynamic response were compared and tabulated in Table 6.1-2. All results are within the ;tpecified criterion of + 7.5%. L L: L . e d 6.7 4_ nutech

i TR-76-001' ' ,

                              ..                                       Revision 0            ,

Table 6.1-1, STEP-BY-STEP DIRECT INTEGRATION ALGORITHM ~f 1* Initial Calculations

1. Calculate the following constants (Assume C = aM +-8K). j e = 1.4, T = eat _b l

                                                         = sa 4 2

6/(T 2) ag = _ (6 ' + 3at)/ (T +5Br) a 5

                                                         = 3by /T    -

8 f b sa g

         = a    -

a o 6 = 2b1 - 6/(TO) a 1

6/r 2 + 3bg /r a 7

                                                         =b l T/2 +1-3/6                   I a

2 = 6/T + 2b g a = at/2 ' 8 a 3

2 + Tbg /2 ag = at 2/3 2 a +T 4 = 6/[e(3st 33 "10

                                                         =    ag L.

2. Form effective stiffness matrix K* = K + a M. g

3. Triangularize K For Each Time Increment l

1. Form effective load vector R t

         =        +

3t l* R R

t ( t+At' t) * "E"1"t 2t 8

2. Solve for effective displacement vector'u '

L" t

E K u t

                       =R   t

3. Calculate new acceleration, velocity and displacement-vectors,i. )

Ut +At =au4t + "5"t + "6 t +aE 7t

bt +at " t + "8 ( t+6t t) - 1 "t+at " "t + at U t + agt6 + "10 t+at

4. Ca.'.culate element stresses if desired.

6.8 '- 1 up

8

                        .                                    4 ? S-i U3m O
   '              N O

I N T 6 7 O %A 3 0 1 0 - I I . . . . 1 T V 0 0 0 0 ~ A E - M D - R ) O 6 1 n f F S 8 6 o E Y 9 6 2 8 i D S 4 9 9 0 t N 3 0 2 1 a R A . . . . r A 0 0 0 0 g

     >       E                                                   e l

i R 1 1 t S A 1 6 2 8 n T 5 9 9 0 I S 3 0 2 1 ~ I . . . t P 0 0 0 0 c e -

r - N i O D I ( -. T 2 _ N %A 8 0 n O I . . - - o I V 0 0 i - T E t A D a . M c -

 "           R O

F S Y 5 2 1 2 i f i E S 3 9 r D N 3 0 - - e A . . V m R P A 0 0 y E L r l i A o S C 4 2 t I 3 9 s N O N S S 3 0

                                             -         -       i I

I A 0 0 L e . C m _ i F A 1 1 T T E 0 0 0 0 c

                            .       .          .               i                     =

B 0 0 0 0 m F a . n N A y - O l i 0 0 0 0 D I P . . . . T L 0 0 1 1 f F U L A o O s S G t N l I S S u F P M O N O N E Y E Y s e A R D F t n e t n 2 E e - L. m m 1 1- e e . A c c 6 r I a a R l l e A kp ke kp ke l V as am as am b , ei PD ei ei ei a PT PD PT T r P' e " I

                                           -                         C*G(:
                                                                       )3

TR-76-001* ' Revision 0 t. 6.2 Modal Superposition Solver f f I' I! i Il! 4 Not Available in Version 1.1 of PISTAR. ,

                                                              -l     1
                                                            <1 L'

e, L W

                                                            'E e

b 6.10 c, i, 6 L L

TR-76-001 Revision 0 -

                =7.0   LOAD COMBINATION The load combination postprocessing' module.of PISTAR combines

_ the analysis results of two or more loading conditions. PISTAR presently has three' combination techniques available.

                            . Direct or Algebraic Summation
                            . Absolute Summation
                            . Square Root of the Sum of the Squares (RSS)

I Summation I The problem used in this analysis is-Problem Number 6 of Reference 6 (Static Analysis of a Three-Dimensional Piping Structure Program - ANSYS) shown on Figure 7.0-1. The data specified in problem 6 (Reference 6) was directly ! I L input into PISTAR with the following exceptions: 'l l

      -                                                                                   1 The modulus of elasticity was typed incorrectly             I

{ as 20.0 x 10 6 psi in the reference document i 0 (Reference 6). The value used.was 29.9 x 10 psi. - L The valves in the PISTAR model were coded as L straight pipe sections with the appropriate cross-sectional property valdes (Table 7.0-1). 1 7-nutech

TR-76-001 . Revision 0 , l i 7'1 g-h [ l N4/' ) h 1 8 N 6 s.,' to 'yg. \ f4 ll - 15 k 2 X is '12

p. is f.

I 19

,/

21

22 }j L-s

                                   /                                                   L L

c-(_ 23

                                                   *hd Figure 7.0-1. Piping System Model - Load Combination i

I _ i 7.2 4 .

I f TR-76-001 1- . Revision 0

                        . PISTAR assumed a direct. spring-to-ground restraint mechanism on nodal point 4.

The' element component types used in.PISTAR to describe the piping system are PIPE and ELBOW. The cross-sectional properties-are found in Table'7.0-1. 1 4 On' side Wall Thickness Wt Per Unit .I Component Dia (Inches)- (Inches) . Length (1b) I f Straight Pipe 3.5 0.216 0.631313-Elbows 3.5 0.216 0.631313 l N s Value D 4.94 0.7619 3.00311 s Value E 4.499 1.7153 4.50466 s Value F 5.221 0.3251 2.00207 Table 7.0-1. Cross-Sectional Properties The components in the piping system are inade of steel. Young's modulus is 29.9 x 10 6 psi. Poisson's ratio is 0.3; and the coefficient of thermal expansion is 2.178 x 10 -5 , The piping system has been anchored at nodal points 20 and 23. Nodal point 4 has a spring-to-ground restraint mechanism which imposes a translational restraint in the X, Y, and Z directions of 1,000 pounds per inch and a rotational restraint in the X, Y, and Z directions of 10,000 inch-pounds per radian. - 7.3 Outech

1 TR-76-00I * [j

                          ,                              Revision 0       r, i

Two structural loading conditions were analyzed for the load combination. A modal extraction. analysis was made prior to -' performing the dynamic respon'se spec

rum analysis. The actual loading conditions are~ described below:-

1. Secondary Seismic - The piping system was subjected'to ]

i the effects of seismic anchor displacements .(see Subsec-

        . tion 3.3. for actual anchor displacements).                              -1 1

I.

2. Primary Seismic - The piping system was subjected to .

the inertia effects of a dynamic response spectrum ana-lysis. After the extraction of 15 i..; des (Section 4.0), the structure was loaded with 3 uncoupled simultaneous. f 1 response spectra (Section 5.0). . The results of these combinations are presented in Subsections ! 7.1, 7.2, and 7.3. Four structural element components and three nodal points were investigated. All of.the resultant i- , stresses and all of the displacements for each nodal point s'4 were compared for validity. Listed below are the elements and nodal points under consideration. l Element Type Between Nodes to 1 Straight Pipe 4 ,7 4 Elbow 7 - 8 18 Straight Pipe 19 - 20

20 Elbow 22 -

23 6 h 6 7.4 t ,- ~ L.

TR-76'-001

                                                                                   ' Revision 0 J

Node I Coordinates .

.\

X Y -2

                   ,                          4              0.1     90.0      0.0 8            -40.1    85.5       0.0                       '
        ~

i 19 40.1 ~50.0 10.0 } e i j ( j The sensitivity of results were compared.with-manual ca'1cula- I ' \ tions of various quantities. The criterion for-acceptable- I 1.

   ]                        results is 2.5% deviation from the manual ~ calculations.

I i, 1 4 ( l t l L ! L' l l L L u L L u t 75 nutech

TR-76-001'

                                         ,                          Revision'0-7.1~ Direct or Algebraic Summation Tables 7.1-1 through 7.1-7 give.the results:obtained from-          -

PISTAR and manual calculations fcr the direct summation: tech-nique.and the percentage of deviation from.the~ manual.~calcula - - {: ' tions results. The maximum deviation was 0.'30%, which is-within the specified criterion. The maximum value.is circled { on Table 7.1-1 for easy reference.- f! i IR Il 1, l l L L Li ; j l 1 7.6 a

                                                                                  <       "j   .

l

TR-76-001 Revision 0 , Table 7.1-1. Member Stress Resultants l 1 i DIRECT SUMMATION - Element 1 l I ELEMENT NO. 1 TYPE Straight Pipe DESCRIPTION Spring Attachment at Node 4 - Straight Pine to I-- Node 5, fx, v. z - End-I. 90 0: End-J = 20.1, 90 0) DEVI A- D EVI A-I MEMBER MANUAL PISTAR TlON MEMBER MANUAL PISTAR TION ; RESULTANTS % RESULTANTS % { Axial Torsional Force 159.019 159.019 0 Noment -8.75 -8.74 0.11 l Endl End-l Axial Torsional Force 159.019 159.019 0 Moment -8.75 -8.74 0.11 1_ En d-J End-J Y-Axis Y-Axis Shear -88.262 -88.263 0 Moment 2.72 2.72 0 ! Endl End-l ! Y Axis Y-Axis

                          -88.262     -88.263 Shear                                0        Moment           -1032.70   -1032.70      ,0 End-J                                          En d-J
                                                                                                            ~

2-Axis Z-Axis Snear -51.667 -51.667 0 Moment -3.33 -3.34 0.30 End-l End-l

2-Axis Z-Axis Shear -51.667 .-51.667 0 Moment 1980.67 1980.67 0 { End-J j End-J um a O. 7.7 nutech

TR-76-001 Revision 0 1 2 l Table 7.1-2. Member Stress Resultants DIRECT SUhD4ATION - Element 4 , [ f ELEMENT NO. 4 ' TYPE _ Elbow f DESCRIPTION __4.5 Inch Radius Elbow Node 7 6 8 (x, y, z End-I = 35.6, 90, 0; End-J = 40.1, 85.5, 0) DEVI A-PISTAR D EVI A-TION g' PISTAR TION MEMBER MANUAL s MEMBER MANUAL.

                                       */o    RESULTANTS RESULTANTS Axial 148.471 Torsional Moment         -8.75          -8.74     0.11 ll    !

Force 148.471 0 End-l g: Endl I Axial Torsional ' 100.373 100.373 Moment 2372.06 2372.06 0 li 0 Force En d-J End J Y-Axis Y-Axis 100.373 100.373 0 Moment 2125.32 2125.32 0 i Shear End-l l - Endl Y-Axis Y-Axis

             -138.900  -139.000      0.07        Moment        285.35        285.35      0 Shear                                                                                                 -

End-J End-J 2-Axis L.I Z-Axis C' Shear 61.391 61.391 0 Moment -3138.64 -3138.64 0 End-l End-l 2-Axis Z-Axis _ 61.391 61.391 0 Moment -2877.82 -2877.82 0 Shear End-J End-J t e i m 7.8

                                                                                            * *i .
                                                                             ^

TR-76-001 Revision 0 Table 7.1-3. Member Stress Resultants l DIRECT SUMMATION - Element 18 l 18 straight Pipe ELEMENT NO. TYPE DESCRIPTION Tr'omNode to 10Node N N i

               '"c hc rc4 (x , y , z = End-I = 40.1, 5 0 , -1:#                             so End-J = 40.1.50, 0    t@)

I

   ;                                             DEVI A-                                        D EVI A-      .

I MEMBER MANUAL PISTAR TlON MEMBER MANUAL PISTAR TION I RESULTANTS % RESULTANTS % Axial Torsional Forc e -971.463 -971.463 0 Noment -254.13 -254.13 0 Endl End-l Axial Torsional Force -971.463 -971.463 0 Moment -254.13 -254.13 0 i_ En d-J En d-J

Y-A 4is Y-Axis l l- Shear -71.694 -71.694 0 Moment -3429.14 -3429.14 0 En d-l End-l l Y Axis Y-Axis 't Shear -71.694 -71.694 Moment -1527.23 0 -1527.23 0 End-J End-J Z-Axis Z-Axis Shear 194.706 194.706 0 Moment -5789.15 -5789.15 0 End-l End-l L Z-Axis Z-Axis Shear 194.706 194.706 Moment 0 -5002.'44 -5002.44 0 End -J End-J nutech

l TR-76-001*

Revision 0 l .-

Table 7.1-4. Member Stress Resultants , DIRECT SUMMATION - Element 20 f-( ELEMENT NO. 2 TYPE Straight Pipe DESCRIPTION End of Piping Structure Nodes 22 6 23 - Node 23 Anchored ( x , y , z = End-I = 40.1, 50. 30: End-J = 40.1. 50. 901 f li DEVI A- DEVI A-MEMBER MANUAL PISTAR TlON MEMBER MANUAL PISTAR RESULTANTS % RESULTANTS TION

                                                                                                            %       l, Axiol                                       Torsional                                      q Force      -970.862   -969.863     0.10      Mom ent -  -254.13    -254.13     0 End-l                                          End-l Axial                                       Torsional                              -l
           ,               Force      -970.862   -969.863     0.10      Noment     -254.13    -254.13     0 En d-J                                        En d-J                                g Y-Axis                                       Y-Axis                                 I-Shear       -76.075    -76.076     0        Moment     -1527.23   -1527.23     0 Endl                                          End-l l

Y-Axis Y-Axis Shear -76.075 -76.076 0 Moment 10175.82 10175.82 .0 En d-J l End4 L i Z-Axis Z-Axis ' Shear 196.636 196.636 0 Moment -5002.44 -5002.44 0 h C End-l End-l 2-Axis Z-Axis I Shear 196.636 196.636 0 Moment -231.87 -231.87 0 ,! End-J End-J l l l M 7.10 '-

                                                                                                     ~;                   1 j
                                         -                                . TR:- 7 6 - 0 01                                  ,

Revision 0 j

   )~                   Table 7.1-s. Nodal Displacements-
   ~

DIRECT SUl@tATION - Node . 4

4 NODE NUMBER ! LOCATION End of Model - Spring-Restraint

'~

x = .1. y = 90. z=0 DISPLACEMNT MANUAL ' 'PISTAR DEVIATION COMPONENT ( X 10-2) ( X 10-2) % ,. -- . X-Trans 16.079 16.079 0- .,

;-)

Y-TranS -8.7491 -8.7491 0 . Z-Trans -s.0856 -s.osss 0 1 l l X-Rotation -0.087449 .j0.087349 0 'l I i

^;

Y-Rotation o.027187 'O.027187 o-Z-Rotation -0.03337s -0.033375 o

                                                                                                                          ,I g                            1 7'                                            '

s nutech

.\

t

TR-76-001 Revision 0 t , l.

  )                                                                      #
                                                                  ,f s.

c l able 7.ie6. .N o ao. l D .isplacements

                 ,i s
                                                                                .g

g. '

9 DIRECT SUMMATION '- Node 8 u ;

                                                                                                                                                                                                                                     . g.
                                                                                                                                                                                                                                                -s'u,.     ,j
         ~

NODE NUMBER- 8 c t

                                                                                                                                                                                                                                                  ,h LOCATION l.nd                       f Elbow                                                                                        "'        '
                                                                                           >s
                                                                                                                                                                                                                                          ,A
                                                                                . ,,.x m 4 0. 1, S '= 8 5 . 5 , _ z L = - 0' t'                                                             DISPLACEMNT ' MANUAL -                                          PISTAR-                              DEVIATION                                       .,
                                                                                                                                 -2 COMFO_NEN'T ./( X 10 )                                        ( X'l0-2)                                               %                                                   -

1 s

                                        \        ,

r x s' s . X-Trans ' 16.'328 16.328. 1, ' 0, . > ; g . , m]

s e( - n (. s. y , t 3 s f

                                                                                                                                                                          \\                        3 v
                      ,     4 Y-Trans                       -10.274                      -10.274 'i                                                0-           <

/ 3 A 5: c ! cr., e v -

d \ , Yh * 'Q Z-Rotation 0.13810 0.13 n 0 0

1 pt i , 4

) m. z , , 1,y , 1 i i s (1: , , _ J. s ! i y 'I I lm_ 7.12 s ) - h .. I -.. j ' a ' -TR-76-001 Revision O' 1 r-f Table 7.1-7. Nodal Displacements J DIRECT SUMMATION - Node 19 q 19 NODE NUMBER LOCATION At branch j j_. x - 40.1, y - 50, z-- 10 ! DISPLACEMNT MANUAL. PISTAR DEVIATION l [ COMPONENT ( X 10-2) ( X 10'2) % $ X-Trons 17.964 17.964 0 1 1 Y-Trons -7.9972 -7.9972 0 L Z-TronS 0.11395 0.11396 0.01 ~ L X-Rotatio7 , -0.26159 -0.26158 0 L i [ Y-Rototion -0.20722 -0.20722 0 L l Z-Rotation 0.06s801 0.065801 0 ! i 'l L 7.13 nutech ' i . TR'- 7 6 - 0 01 Revision 0

7. 2' Absolute Summation Tables.7.7-1 through 7.2-7 give,the resul'ts obtained-from h

PISTAR and manual calculat' ions for the absolute summation-- . technique and the percentage of deviation from the manual. calculation results. The' maximum deviation.was'0.01%,.which . is:within the specified criterion. The' maximum value is circled on Table 7.2-7 for easy reference, f I I I t .. t ) Li E dumm W 7.14 Imp [ TR-76-001 l_ , Revision 0-r 1 $ Table-7.2-1. Member Stress Resultants ' [ ABSOLUTE SUMMATION - Element 1 i iPe 1 Straight Pipe ' ELEMENT NO. TYPE -l DESCRIPTION Spring Attachment at Node 4 - Straight Pipe to l Node 5, (-x, y, 2 - End'I = 1, 90, 0;'End-J = 20.1, 90, 0) DEVI A- DEVI A-MEMBER MANUAL PISTAR TlON - MEMBER MANUAL PISTAR TION RESULTANTS */. RESULTANTS % Axial f Force l'59.019 159.019 0 Torsional Noment 13.89 13.89 -0 1 .En d-l End-l Axial Torsional Force 159.019 159.019 0 Moment 11.39 13.89 0 ) f ~ En d-J -Axis End J Y-Axis l Shear 99.208 9P,208 0 Moment 2.72 2.72 0 L End! End-l j Y-Axis Y-Axis Shear 99.208 99.208 Moment 1241.14 1241.14 .0 f End-J 0 End-J Z-Axis Z-Axis { Shear 62.163 62.163 0 Moment 6.15' 6.15 0 End-l End-l 2-Axis Z-Axis Shear 62.163 62.163 0 Moment 1980.67 1980.67 0 l End-J End-J -l L __ l 7.15 Mutech 1 TR-76-001 Revision 0 i Table - 7. 2.-2 Member Stress Resultants ! ABSOLUTE SUMMATION - Element 4 [lj f ELEMENT NO. 4 TYPE Elbow f DESCRIPTION 4.5 Inch Radius Elbow Node 7 8 8 (x, v. z End-I = 35.6 90, 0; End-J = 40.1 85.5 0) i DEV1 A-MEMBER DEVI A-[' I !] MANUAL PISTAR T10N MEMBER MANUAL RESULTANTS PISTAR TION % RESULTANTS % ,; Axial Torsional Force 148.471 148.471 0 Noment 13.89 l1 13.89 0 ; End-l End-l {' Axial . Torsional i Force 100.373 100.373 0 Moment End-J 2372.06 2372.06 0 End J Y-Axis l Y-Axis Shear 100.373 100.373 0 2125.32 Moment 2125.32 0 ! Endl End-l Y-Axis Y-Axis She r 148.471 148.471 0 Moment - 285.35 285.35 .0 End-J EndM Z-Axis Z-Axis L-Shear 61.391 61.391 0 3507.06 End-l Moment 3507.06 0 El> End-l ' t Z-Axis Z-Axis Shear 61.391 L l_ 61.391 0 Moment 3317.88 3317.89 0 . End-J End-J }. "1 I, Iw 7.16 < ~l TR-76-001 Revision 0 [ i - Table 7.2-3. Member Stress Resultants- ; ABS 0*UTE SUMMATION - Element 18 18 Straight Pipe ELEMENT NO. TYPE ^ DESCRIPTION

c: Node h to Node $ -Nede10 20 50 Anchored (x, y, = End-I = 40.1, 50, M: End-J - 40.1,A;0, 3) l DEVI A- DEVI A-f MEMBER MANUAL PISTAR TION MEMBER MANUAL PISTAR TION j

RESULTANTS % RESULTANTS % ! 4 Axial Torsional Force 1019.36 1019.36 0 Moment 634.15 634.15 0 Endl End-l Axial . Torsional ] Force 1019.36 1019.36 0 Moment - 634.15 634.15' 0 3 I- En d-J End-J l Y-Axis Y-Axis ] Shear 88.774 88.774 0 Moment 3589.58 3589.58 0 l i End-l End-l Y-Axis Y-Axis { Sheer 88.774 88.774 D Moment 1680.83 1680.82 .0 End-J End-J Z-Axis Z-Axis Shear 194.706 194.706 0 Moment- 6113.43 6113.43 0 End-l End-l 2-Axis Z-Axis Shear 194.706 194.706 0 Moment 5295.46 5295.46 0 End-J End-J g i *l 1 7' 7 nutech __ _.. . ..i... . . TR-76-001 _. Revision 0 Table- 7.2-4. Member Stress Resultants I~ il ABSOLUTE SUMMATION - Element 20 II f ELEMENT'O. N 2 TYPE Straight Pipe { DESCRIPTION End of Piping Structure Nodes 22 6 23 - Node 23 Anchored ( x , y, z = End-I 40.1, 50, 30; End-J'40.1, 50, 90) . I D EVI A-MEMBER MANUAL PISTAR TION MEMBER MANU^L PISTAR DEVI A g l TION l RESULTANTS % RESULTANTS % l Axial Torsional l'19.96 . Force 0 1019.96 0 Noment 634'.15 634.15 'O ) End-l End-l g Axial . Torsional ' I: , Force 1019.96 1019.96 0 Moment 634.15 634.15- 0 En d-J Y-Axis End-J l-{] Shear 84.393 84.393 0 _ Y-Axis Moment 1680.83 1680.82 0 ~f g End-l End-l [. Y Axis Y-Axis Shear 84.393 84.393 0 10175.82 L0175.82 End-J Moment End-J 0 { Z-Axis Z-Axis 'h Shear 196.636 196.636 0 Moment 5295.46 5295.46 0 O1 End-l End-l' . , 2-Axis Z-Axis ' Shear 196.636 196.636 0 Moment 437.93 437.93 0 End-J End-J . L 4_ , l

8 i

c I m e 7.18 l , ~ .m w - TR-76-001 Revision 0 j 1 -i T Table 7.2-s. Nodal Displacements i ~ ABSOLUTE SUMMATION - Node 4 i I NODE NUMBER' 4 LOCAT'ON End of Model - Spring Restraint -l' ' x= .1 v = 90. >=0 _ l DISPLACEMNT MANUAL PISTAR DEVIATION [- ' COMPONENT ( X 10-2) ( X 10-2)- % __ l- X-TranS 16.079 16.079 0 f 1 Y-TranS 9.9979 [ 9'.9979 0-l- i ~/-Tra n S 6.2974 6'.2975 0 l 1 L l 1 X-Rotation 0.13893 0.13893 0 l Y-Rotation 0.027187 0.027187 0 L Z-Rotation 0.061s21 0.061s21 0 l .[ - ] 'l 7- . nutech . TR-76-001 - Revision 0 Table 7.2-6 Nodal Displacements [. ABSOLUTE SUMMATION - Node 8 8 NODE NUMBER LOCATION End of Elbow x = 40.1, y =.85.5, z=0 DISPLACEMNT MANUAL COMPONENT ( X 10-2) PISTAR ( X 10-2) DEVIATION {' ' X-Trans 16.328 16.328 o Y-Trans 10.440 10.440 o { . Z-Trans 5.9951 5.9951 0 L l X-R.,rion 0.16087 0.16087 o , , 1 5l 1 Y-R otation 0.074937 0.074937 0 ' -l i Z-Rotation o.13810 0.13810 o , e 'g. 7.20 1 TR-76-001 Revision 0 Table 7. 2-7. Nodal Displacements { ABSOLUTE SUMMATION - Node 19 i NODE NUMBER 19 LOCATION At Branch .j x = 40.1, y = 50, z = 10 __ DISPLACEMNT MANUAL DISTAR DEVIATION ~2 o COMPONENT ( X 10 ) ( X 10-2) % e l X frans 17.964 17.964 0 1 Y-Trans 8.0009 8.0009 0 . l 4 l Z-Trans 0.11395 0.11396 0.01 l t X-Rotation 0.26865 0.26865 0 i t [ Y-Rotation 0.22948 0.22948 0 Z-Rotation 0.065801 0.06s801 0 l 4 nutech i L ~ i TR-76-001' ' Revision 0 'l i 7.3 RSS Summation Tables 7.3-1 through 7.3-7 give the results.obtained from. f - PISTAR and manual calculations for the.RSS summation technique-and the percentage of deviation.from the manual'calcul'ation l i results. The maximum deviation was 0.01%, which is within-the specified criterion. The maximum value is circled on Table 7.3-5 for easy reference. f..) I .1 Ia 3 II 1 b i. i. l' L' l 'h 7.22 ) h l fR-76-001 Revision 0 , Table 7.3-1. Member Stress Resultants - RSS SUMMATION - Element 1 l 1 " ELEMENT NO. TYPE Straight Pipe ^ DESCRIPTION Spring Attachment at Node 4 - Straight Pipe to 1 ;- Node 5, tx, y, z - End-I = 1, 90, 0; End-J = 20.1, 90, 0) . I DEVI A- D EVI A- ' MEMBER MANUAL PISTAR TlON MEMBER MANUAL PISTAR TION RESULTANTS % RESULTANTS */. 1 Axiol Torsional Force 144.545 144.546 0 Noment 11.61 11.61 0 l Endl End-l ~ Axial Torsional Force 144.545 144.546 0 Moment 11.61 l End-J 11.61 0 i En d-J Y-Axis 4 . tis l Shear 93.895 93.895 j l End-l 0 Moment 1.92 1.92 0 End-l Y-Axis ~ Y-Axis Shear 93.895 93.895 0 Moment 1141.69 En d-J 1141.69 0 End-J [ 2-Axis Shear 57.156 57.156 0 Z-Axis Moment 4.95 i End-l 4.95 0 End-l Z-Axis Z-Axis Shear 57.156 57.156 '0 Moment 1873.23 1873.23 0 1 End -J End-J . y 1 l s. 7' 5 nutech I. TR-76-001 Revision 0 Table 7.3-2. Member Stress Resultants I RSS SUMMATION - Element 4 I TYPE Elbow 4 ELEMENT NO. DESCRIPTION 4.5 Inch Radius Elbow Node 7 8 8 - .(x, y, z End-I = 35.6, 90, 0; End-J = 40.1, 85.5, 0) ' DEVI A- D EVI A-MEMBER MANUAL PISTAR TlON MEMBER MANUAL- PISTAR - TION RESULTANTS % RESULTANTS % 7 Axial Force 143.813 143.813 Torsional { 0 Moment 11.61 11.61 0 Endl End-l { Axiol Torsional- ' Force 93.97 93.97 0 Moment 2277.28 2277.28 0 .g En d-J End J [ Y-Axis Y-Axis Shear 93.97 93.97 0 Moment 2021.89 2021.89 0 End-l End-l. L~ Y-Axis Y-Axis Shear 143.813 143.813 0 Moment 268.04 268.04 0 ,. En d-J End-J Z-Axis Z-Axis L Shear 57.091 57.091 0 Moment 3327.95 3327.96 0 C End-l End-l Z-Axis Z-Axis Shear 57.091 57.091 0 Moment 3105.65 3105.66 0-End-J End-J = 1 1 l b li 7.24 ' l' L -['11 - TR-76-001 ~ Revision 0 l Table 7.3-3. Member Stress Resultants ' ' j r RSS SUMMATION - Element 18 l 18 Straight Pipe ELEMENT NO. TYPE 21 22 str @ =y Nom Node if to Node 2G --Neu% 2 I DESCRIPTION a m= Anchored (x, y, z = End-I = 40.1, 5 0, N ; End -J = 4 0.1, *:0, b) DEVI A- - DEVI A-MEMBER MANUAL PISTAR TION MEMBER MANUAL PISTAR TION [ RESULTANTS % RESULTANTS % [ Axial Torsional . t I Force 995.699 995.699 0 Noment 483.08 483.08 0 I Endl .End-l Axial Torsional , Force 995.699 995.699 0 Moment 483.08 483.08 0 En d-J End-J l Y-Axis Y-Axis I L Shear 80.687 80.687 0 Moment 3510.28 3510.28 0 .Endl End-l . Y-Axis Y-Axis Shear 80.687 80.687 0 Moment 1605.87 1605.87 0 End-J End-J Z-Axis 2-Axis Shear 190.579 190.579 0 Moment 5953.5 5953.5 0 End-l End-l 2-Axis . Z-Axis Shear 190.579 190.579 0 Moment 5151.03 5151.03 0 End-J End-J L . b e 7.25 nutech TR-76-001- l Revision 0' [1 Table 7.3-4. Member Stress Resultants [1 RSS SUMMATION - Element 20- i i ELEMENT NO. 2 TYPE Straight Pipe - DESCRIPTION End of Piping Structure Nodes 22 6 23 - Node 23 Anchored (x, y. z = End-I = 40.1, 50, 30; End-J = 40.1, 50, 90) , l-DEVI A- D EVI A- l-MEMBER MANUAL PISTAR TlON MEMBER MANUAL PISTAR TION RESULTANTS % RESULTANTS %- p Axial - Torsional l Force .995.714 995.714 0 Moment 483.08' 483.08 0 , Endl End-l l Axial . Torsional i Force 995.714 995.714 0 Moment 483.08 483.08 0 En d-J End-J - . Y-Axis Y-Axis i Shear 80.342 80.342 0 Moment 1605.87 1605.87 0 Endl End-l Y-Axis Y-Axis { Shear 80.342 80.342 0 Moment 9834.12 9834.12 0 _; End-J End-J l l Z-Axis Z-Axis i' Shear 190.631 190.631 0 Moment 5151.03 5151.03 0 ~ End-l End-l Z-Axis Z-Axis Shear 190.631 190.631 0 Moment 350.39 350.39 0 End-J End-J 6 , '4 I y e. ! 7.26 . TR-76-001 -Revision 0 i Table 7.3-s. Nodal Displacements. ' ~ RSS SUMMATION - Node 4-a 4 NODE NUMBER LOCATION End of Model - Spring Restraint x= .1, y = 90, z=0-1 DISPLACEMNT MANUAL- PISTAR DEVlATION 1 COMPONENT ( X 10-2) ( X 10-2) % 1 X-Trans 14.475 14'.474 0.01 ) I 1 Y-T rans 9.3943 9.3943 0- { Z-Trans 5.7237 s.7237 0 ; i X-Rotation 0.11608 0.11608 0 [ Y-Rotation 0.019226 0.019226 0 ; L Z-Rotation 0.049491 0.049491 0 L L . q L. 7.27 nutech TR-76-Ob1 Revision 0 Table 7.3-6. Nodal Displacements [l RSS SUMMATION - Node 8. u NODE NUMBER 8 LOCATION End of Elbow ej j x 46.1, y - 85.s z o hl DISPLACEMNT MANUAL PISTAR DEVIATION COMPONENT ( X 10-2) ( X'10-2) '% X-Trans 14.800 14.800 'o h, 1 Y-Trans 10.357 10.358 If 0.01 , 1 !. l Z-Trans s.2073 s.2073 o X-Rotation 0.13716 0.13716 o ! L e 1 Y-Rotation 0.063794 0.063794 0 Z-Rotation 0.11789 0.11789 0 i l r 7.28 f ' ~' TR-76-001 1._ , Revision.0 Table 7.3-7. Nodal Displacements { RSS SUMMATION - Node 19 19 ' NODE NUMBER LOCATION At Branch . l. x - 40.1 v- so. z - to DISPLACEMNT MANUAL PISTAR DEVIATION -2 COMPONENT ( X 10 ) ( X 10-2) % ! X-Trans 17.290 17.289 0.01 1 Y-Trans 7.999 7.999 0 [ Z-Trans o.11126 0.11127 0.01 1' X-Rotation 0.26514 0.26514 o L. l Y-Rotation o.21863 0.21863 o [ i ' Z-Rotation o.05012s 0.050125 o l L = ~ 7.29 nutech ' .masues 4.=m c ,. . o ~ TR-76-001 Revision 0-l~ r 8. 0 - HEAT TRANSFER ANALYSIS (HOTPIPE)- i .j. i f i i l l 1 \ l Not Available in Version-1.1 of PISTAR. 3 j j i ~ l i I m L L L - 8.1 'nutech- , i 'a .l'- 7-TR-76-001 ' Revision.O 9.0 ASME SECTION III - CLASS 1 EVALUATION.' ' 1 1 I : 4 I l Not Available in Version 1.1 of PISTAR. L L . t .. L t L. 'b 9.1 nutech .,m. _p .. . l' ' TR-76-001. e Revision 0 a p 10.0 ASME SECTION III - CLASS 2 EVALUATION { The piping system model shown in Figure.10.0-1 was used'for: verifying PISTAR's ASME Section III - Class 2 evaluation ' postprocessing module. The PISTAR evaluation is in accordance with the ASME Boiler j and Pressure. Vessel Code, Section III NC-3600'(Reference 8). The sensitivity of results were compared with manual calcula-tions of various quantities in accordance with ASME NC-3600. The raw data used for these calculations was the output from the analysis portion of the PISTAR analysis and design computer program. The criterion for acceptable results was less than or equal to 2.5% deviation from the manually calculated results. l The piping system for the ASME Section III - Class 2 evaluation ) { is shown in Figure 10.0-1. This problem is Problem Number 6 in Reference 6 (Static Analysis of a Three-Dimensional Piping Structure Program - ANSYS). L The data specified in problem 6 (Reference 6) was directly input into PISTAR with the following exceptions: The modulus of elasticity was typed incorrectly 6 as 20.0 x 10 psi in the reference document (Reference 6) . The value used was 29.9 x 10 6 psi. nutech. + .....-u..-.._..-m ~ TR-76-061 . Revision 0~ r , NV h fi 8 N . f. 6 Y s, 10 14 < ll . Z X 16 12 ' 33 17 19 / 22 L L C 23 2 p 1a Figure 10.0-1. Piping System Model - ASME Section III - Class J Verification , f 10.2 - m j 'I 8 S TR-76-001 . . Revision-0 The valves in the PISTAR model.were coded as straight pipe sections with the appropriate-cross-sectional property values (Table 10.0-1), 1 PISTAR assumed.a direct-spring-to-ground restraint mechanism on nodal point 4. l The element component types used in PISTAR to descril'e the l piping system are PIPE, ELBOW, and TEE (forged). , .f I ! The cross-sectional properties are found in Table 10.0-1. Outside Wall Thickness Wt Per Unit Component Dia (Inches) (Inches)- Length (1b) [ Straigh+. Pipe 3.5 0.216' O.631313 , l Elbows , 3.5 0.216 0.631313-L Valve D Nodes 5-6 4.94 0.7619 3.00311 1 Valve E Nodes 14-15 4.499 1.7153 4.50466 L Valve F Nodes 21-22 2.00207 I 5.221 0.3251 s l [. Table 10.0-1. Cross-Sectional Properties , I .I 1' The components in the piping system are made of steel. Young's . modulus is 29.9 x 10 6 psi. Poisson's ratio is 0.3; and the coefficient of thermal expansion is 2'.178 x 10 -5 , j 10.3 Mutech i - I l TR-76-001,. . Revision 0 ~ The piping system-has been anchored'at nodal points 20 and c

23. Nodal point 4 has a direct spring-to-ground restraint mechanism which imposes a.translational restraint in the X, Y, and Z directions of 1,000 pounds per inch and a rotational restraint in the X, Y- and Z directions of-10,000 inch-pounds per. radian.

f Five structural loading conditions were analyzed for the ASME Section III - Class 2 piping stress analysis and evaluation. A modal extraction analysis was made prior to performing the f dynamic response spectrum analysis. The actual loading . conditions are described below. !

1. Dead Load - The piping system was subj ected bl !

{ to the effects of its_own. weight. This loading -l .1 was imposed on the structure in PISTAR using.a static vertical acceleration - (Y-axis) of 386.4 inches /second/second. ' *

2. Thermal - The piping system was subjected to the I.

6i effects of a 150*F temperature rise from the zero ; stress state; and the effects of. thermal anchor m displacements (see Subsection 3.3 for the actual anchor displacements) were considered. " 4 s

3. Secondary Seismi: .The piping system was c ,

subjected to the effects of seismic anchor . displacements (see Subsection 3.3 for the actual u , anchor displacements). ' 10.4 F em ~ ' TR-76-001 .. Revision 0

4. Primary Seismic - The piping system was subjected to the. inertia effects.of a dynamic )

response spectrum analysis. After the-extraction of 15 modes (Section 4.0), the structure was loaded with~3 uncoupled simultaneous response. . spectra.(Section 5.0).

5. Total Seismic - The results of the loading conditions for primary seismic were' absolutely superimposed with the results of secondary f seismic analysis, l

) f- The following list specifies the conditions assigned to the .l .j 1 resultant moment calculatior.., used in the ASME NC-3600 j equations. I. ASME NC-3600 PISTAR Equations Loading Conditions Sustained Loads - Dead Load Occasional Loads - Total Seismic Thermal Loads - Thermal L l L L i 4 Eup 10.5 nutech TR-76-001-Revision 0. L. H The following-list givesia'dditional-information' required by ASME NC-3600 for evaluation of this. piping system lij j .\ (Figure 10.0-1). .) Design Pressure = 500 psi . Design Temperature =- 700*F 't Peak Pressure = - 750 psiL . Operational Cycles = less than 7,000 (for thermal.) ! Cold Allowable = 15,000.0 psi 1 i Hot Allowable = 14,300.0. psi-l; l ] 1 I r h I 'l i I l .i i -j 3 1 i ;h .1 9 10.6 [,____ ^ { s - TR-76-001 Revision 0 F 10.1 Flexibility Factors l The flexibility factors for this piping system (Figure 10.0-1) were calculated in accordance with ASME Section III, NC-3600. ' i Table 10.1-1 gives the results obtained from PISTAR, manual calculations (based on Section NC-3600 of Reference 8), and ] the percentage of deviation from the manual calculations. There were no deviations for the various structural members investigated. I l l I l- [ t I L l L L L L L c 7 nutech 1 1 TR-76-0d1 Revision 0 Table 10.1-1. FLEXIBILITY FACTOR COMPARISON { f . NODE ELEMENT ELEMENT FLEXIBILITY FACTORS % NUMBER NUMBER TYPE PISTAR MANUAL

DEVIATIO.N 4 1 PIPE 1.0 1.0 0 5 PIPE 1 1.0 1.0 7 4 ELBOW 4.58 4.58 0

0-f ) 8 4 ELBOW 4.58 4.58 0 19 19 TEE 1.0 1.0 0 i 20 19 TEE 1.0 1.0 0 22 20 PIPE 1.0 1.0 0 j 23 20 PIPE 1.0 1.0 0 l *For - Pipe . k = 1.0 Figure NC-3673.2 (b)-1 (Reference 8) I, - Elbow: k = 1.65 (Reference 8) where: L h = flexibility characteristic (Reference 8) h h=tR n Figure NC-3673-2 (b)-1 (Reference 8) r' ; j R = Bend Radius (Reference 8) ! r = Mean Pipe Radius (Reference 8) tg = Wall Thickness (Reference 8) . - Tee : k = 1.0 (Reference 8) ~l 10.8 ~ ise l~ - TR-76-001 I . Revision 0 f 10.2~ Stress Intensification Factors The stress intensification factors for this piping system (see Figure 10.0-1) were calculated in accordance with'ASME Section III, NC-3600. Table 10.2-1 presents the results obtained from PISTAR, f manual calculations (based on Table NC3673.2(b)-1 of Reference 8), and the percentage of deviation from manual l calculations. There were no deviations for the various structural members investigated. l . , l j I.- 1 1 I_ I L L L L L 1 10.9 nutech ,

c. - . . . - - . - . . . . . . .. - - - . . . . . . . - . .. . . . . . . . . _ . -- . . - - . .

~ TR-76-001' Revision 0 i ri Table 10.2-1. STRESS INDEX COMPARISON i [1 NODE ELEMENT ELEMENT STRESS INDEX (i) . g NUMBER NUMBER _ T'iPE PISTAR MANUA L

DEVIATION-4 PIPE 1 1.0 3.0 0 -

5 1 PIPE 1.0 1.0 0 7 4 ELBOW 1.8 1.8 0 8 19 19 4 ELBOW 1.8 1.8 0 l-TEE 1.3 1.3 0 20 19 TEE 1.0 1.0 1 0 2 20 PIPE 1.0 1.0 0 23 20 PIPE 1.0 1.0 0 !

l. .

*For - Pipe : i = 1.0 Figure NC-3673.2(b)-1 (Reference 8) l1 - Elbow; 9 Lj i= jj3 Figure NC-3673.2(b)-1 (Reference 8) where: I h = Flexibility Characterist!.c (Reference 8) h=tR n Figure NC-3673.2(b)-1 Teference 8) 2 r F R = Bend Radius (Reference 8) r = Mean Pipe Radius (Reference 8) - Tee : i= Figure NC-3673.2(b)-1 (Reference 8) '! vhere: ' h = 4.4t n Figure NC-3673. 2 (b)-1 (Reference 8) r 10.10 -I -l l . TR-76-001 Revision 0 _ 10.3 }i7aluation The ASME Section III (Code) Class 2 evaluation was performed - in accordance witL the rules of NC-3600 (Reference 8). For l verification, the following items were compared with manual j

f. calculations (using PISTAR moment file output for calculations). i i ITEM TABLE Design Pressure Stress 10.3-1 !

Peak Pressure Stress 10.3-2 Sustained Loads Stress' '10.3-3 Occasional Loads Stress 10.3-4 Thermal Loads Stress 10.3-5 Equation #8 Solution 10.3-6 Equation #9 Solution ) 10.3-7 ) Equation #10 Solution 10.3-8 Equation #11 Solution 10.3-9 Equation #8 Allowables 10.3-10 Equation #9 Allowables 10.3-11 . L Equation #10 Allowables 10.3-12 l Equation #11 Allowables_ 10.3-13 ( Tables 10.3-1 through 10.3-13 present the comparative results for this verification. There were no deviations for the L t various structural members investigated. L nutech TR-76-001 Revision 0 Table.10.3-1. CLASS 2 - DESIGN PRESSURE i f r j (STRESS) NODE ELEMENT ELEMENT , nF9TGN PRESSURE TERM % l NUMBER NUMBER TYPE l PISTAR MANUAL

j DEVIATIO 4 PIPE 1 2025.5 2025.5 0 5 PIPE 1 2025.5 2025.5 0 7 4 ELBOW 2025.5 2025.5

{ 0 8 4 ELBOW 2025.5 2025.5 0 ( 19 19 TEE 2025.5 2025.S 0 20 19 TEE 2025.5 2025.5 0 22 20 PIPE 2025.5 2025.5 0 23 20 PIPE 2025.5 2025.5 0 I ll PD g , #. = DP NC-3652 4t n (Reference 8) ~j where: l P = Internal Design Pressure (Reference 8) t Dg = Outside Diaioeter of Pipe (Reference 8) = l t n Nominal Pipe Wall Thickness (Reference 8) ' j - 1 e t I ' m uun 10.12 - A TR-76-001 Revision 0 f. Table 10.3-2. CLASS 2 - PEAK PRESSURE I y . j' (STRESS) NODE ELEMENT ELEhENT PEAK PRESSURE TERM % NUMBER ' NUMBER TYPE PISTAR MANUAL

DEVIATION 'l 4 1 PIPE 3038.2 3038.2 0 h 5 1 PIPE 3038.2 3038.2 0 7 4 ELBOW 3038.2 3038.2 0 8 4 ELBOW 3038.2 3038.2 0 l 19 19 TEE 3038.2 3038.2 0 20 19 TEE 3038.2 3038.2 0 22 20 PIPE 3038.2 3038.2.

l 0 23 20 PIPE 3038.2 3038.2 o I. "PP =P Max D NC-3652 (Reference 8) 4t n I- where: { PMax = Peak Pressure (Refe-ance 8) D o = Outside Diameter of Pipe (keference 8) t n = Nominal Wall Thickness .(Reference 8) 1. 10.13 nutech . . ? TR-76'-001 Revision 0 I r Table 10.3-3. CLASS 2 - SUSTAINED LOADS ; ^ I r1 (STRESS) l l NODE ELEMENT ELEMENT SUSTAINED LOADS TERM % I NUMBER NUMBER TYPE PISTAR MANUAL

DEVIATIOlf l'

4 1 PIPE 1.50 1.50 0 i 1 52.24 52.24 5 1 PIPE 0 f' 7 4 ELBOW 206.09 206.09 0 \ 8 4 ELBOW 315.77 315.77 0 19 19 TEE 230.64 230.64 0 20 19 TEE 116.57 116.57 0 22 20 PIPE 56.70 56.70 o j 23 20 PIPE 132.04 132.04 O I, I J , y SL = 0.75 i MA NC-3652-b 7 (Reference 8) Nhere: i = Stress Intensification Factor (Reference 8) {l M Resultant Moment on Cross-Section (Reference 8) e; A = Due'to Sustained Loads 1 Z = Section Modulus of Pipe (Reference 8) i NOTE: 0.75 i Never Less Than 1.0. (Reference 8) . = *1 10.14 .TR-76-001 Revision 0 i Table 10.3-4. CLASS 2 - OCCASIONAL LOADS . i f ~ N0DE ELEMENT ELEMENT ( OCCASIONAL , LOADS(STRESS) TERM % __ NUMBER NUMBER TYPE l PISTAR MANUAL

DEVIATION 4 1 PIPE 9.4~/ 8.435 0 l

5 1 PIPE 1277.6 1277.6 0 7 4 ELBOW 2986.8 2986.8 0 l 8 4 ELBOW 2977.9 2977.9 0 - 19 19 TEE 4974.6 4974.6 0 20 19 TEE 22707. 22707. " l 22 20 PIPE 3120.9 3120.9 0 l i 23 20 PIPE 5808.6 5808.6 0 ; I L 0.75 i M

o 0L Z

NC- 3652 (Reference 8) l where: I-y i = Stress Intensification Factor (Reference 8) g M B = Resultant Moment Due to (Reference 8) [ Occasional Loads Z = Section Modulus of Pipe (Reference 8) NOTE: 0.75 i Never Less Than 1.0 (Reference 8) L " 5 nutech 1 TR-76-001. . [ Revision 0 l -l - Table 10.3-5. CLASS 2 - THERMAL LOADS i -NODE NUMBER ELEMENT NUMBER ELEMENT TYPE (STRESS) THERMAL LOADS TERM PISTAR % l! ' l MANUAL

DEVIATION .

4 1 PIPE 32.191 32.192 0 5 1 PIPE 2134.6 2134.6 0 7 4 ELBOW 6774.5 6774.5 0 ) 8' ELBOW 7694.2 7694.2 4 0 f 19 19 TEE 30632. 30632. 0 .- 20 19 TEE 46272. 46272. 0 l 22 20 PIPE 13805. 13805. O. 23 20 PIPE 13761. 13761. 0 _L iM

O =

NC-3652 T (Reference 8) . where: i = Stress Intensification Factor (Reference 8) MC = Resultant Moment Due to Thermal Loads (Reference 8)- Z = Pipe Section Modulus (Reference 8) u L 't !== s l_ 10.16 L m m*m TR-76-001 Revision 0 ._ j l i \ Table 10.3-6. CLASS 2 - EQUATION #8 l l 4 l NODE SOLUTION TO ELEMENT ELEMENT EQUATION #8 % ! NUMBER NUMBER TYPE PISTAR MANUAL

DEVIATION 4 1 PIPE 2027.0 2027.0 0 ;

f 5 1 PIPE 2077.7 2077.7 0 7 4 ELBOW 2231.6 2231.6 0 8 4 ELBOW 2341.2 2341.3 0 19 19 TEE 2256.1 2256.1 0 20 19. TEE 2142.0 2142.1 ' 0 22 20 PIPE 2082.2 f' 2082.2 0 23 20 PIPE 2157.5 2157.5 0 I i PD N 0.75i A I, *S = + 3g 4t n Z NC-3652.1 (Reference 8) [ where: = P Internal Design Pressure (Reference 8) f Dg = Outside Diameter (Reference 8) t n = Wall Thickness Nominal (Reference 8) i = Stress Intensification Factor (Reference 8) l M A = Resultant Moment Due to (Reference 8) {' Sustained Loads j Z = Pipe Section Modulus (Reference 8) ' NOTE: 0.75 i Never Less Than 1.0 (Reference 8) 0 m 10.17 I nutech . s E TR-76-001 . Revision 0 r i i U Table 10.3-7. CLASS 2 - EQUATION #9 4 SOLUTION TO l ; N0DE' ELEMENT ELEMENT EQUATION #9 % t j NUMBER NUMBER TYPE PISTAR MANUAL

DEVI AT10L_ '

4 1 PIPE 5 1 7 4 I j 8 4 0 OL 4t n Z where: P Max = Peak Pressure Dg = Outside Diameter = t n Wall Thickness = i Stress Intensification Factor M A = Loads = MB Resultant Loads i Z = Pipe Section Modulus NOTE: 0.75 i Never Less Than 1.0 r 10.18 - , . TR-76-001 Revision 0 Table 10.3-8. i HUMBER NUMBER 3048.1 3048.1 0 ~ PIPE 4368.0 4368.0 0 l ELBOW 6231.1 6231.1 0 ; ELBOW 6331.9 6331.9 0 .i 19 19 TEE 8243.5 8243.4 0 20 19 TEE 25862. 25862. 0 6215.8 6215.8 22 23 20 20 PIPE PIPE 8978.8 8978.8 0 )l K .1 1 P Dg 3 , Max . 0.75i (MA+M) B NC-3652.2 (Reference 8) (Reference 8) (Reference 8) (Reference 8) (Reference 8) _ Resultant Moment Due to Sustained (Reference 8) - Moment Due'to Occasional (Reference 8) (Reference 8) (Reference 8) '.j L 1 .e I 1 - l i. CLASS 2 - EQUATION #10 1 -) SOLUTION TO NODE ELEMENT ELEMENT EOUATION #10 % TYPE PISTAR MANUAL

DEVIATI,Q,5 I

4 1 PIPE 32,191 32.192 0 ) 5 PIPE 2134.6 2134.6 -f 1 0 7 4 ELBOW 6774.5 6774.5 0 ] l , 8 4 ELBOW 7694.2 7694.2 0 , 19 19 TEE 30632. 30632. 0 20 19 TEE 46272. 46272. 0 3 22 20 PIPE 13805. 13805. O I 23 20 PIPE 13761. 13761. 0 1 - iM {

S E

Z NC-3652.3 (Reference 8) ~ i = Stress Intensification Factor (Reference 8) M = Resultant Moment Due to Thermal (Reference 8) C Loads Z = Pipe Section Modulus i (Reference 8) [ , i l N 6 10.19 nutech TR- 7 6 - 0 01- - C Revision 0 J ' Table 10.3-9. CLASS 2 - EQUATION #11 f. SOLUTION TO f NODE ELEMENT ELEhENT _ ' EQUATION #11- _% - {; _liUMBER' NUMBER TYPE PISIAR MANUAL

DEy1ATR X 4 1 PIPE 2059.2 2059.2 0 ,

5 1 PIPE 4212.3 4212.3 0 4 ELBOW 9006.0 9006.1 0 8 4 ELBOW 10035. 10035. O f! 19- 19 TEE 32888. 32888. 0 20 19 TEE 48414. 48414. 0 22 20 PIPE 15888. 15887. 0 23 20 PIPE 15918. 15918. O {', L PD

S " + M + NC TE 0.75i A i NC-3652.3 4t n T T (Reference 5) F l

where: P = Design Pressure (Reference 8) Dg = Outside Diameter (Reference 8) t n = Wall Thickness (Reference 8) k' i = Stress Intensification Factor (Reference 8) 9! M = Resultant Moment Due to Sustained A Loads (Reference 8) - M = Resultant Moment Due to Thermal i C Loads (Reference 8) p-Z = Pipe Section Modulus (Reference 8) , j t NOTE: 0.75 i Never Less Than 1.0 ~j (Reference 8) s; q $ 10.20 l! Lj ,i 1 .l ._._ __ j TR-76-001 Revision 0 Table 10.3-10. CLASS EQUATION #8 ALLOWABLES l EQUATION #8 4 , NODE ELEMENT ELEMENT ALLOWABLE % NUMBER NUMBER TYPE PISTAR MANUAL

DEVIATION 4 1 PIPE 14300. 14300. !

O 5 1 PIPE 14300. 14300. 0 7 4 ELBOW 14300. 14300. O f 8 4 ELBOW 14300. 14300. 0 19 19 TEE 14300. 14300. 0 20 19 TEE 14300. 14300. O i 22 20 PIPE 14300. 14300. 0 23 20 PIPE 14300. 14300. O { Allowable Stress = 1.0 S h NC-3652.1 (Reference 8) where: 1- b h = Basic Material Allowable (Reference 8) Stress at Design Temperature f i eBS _ 10.21 nutech TR-76-001 , , Revision 0 ' r f i i Table 10.3-11. CLASS 2 - EQUATION.#9 ALLOWABLES U Fi h ,j EQUATION #9 NODE ELEMENT. ELEMENT ALLOWABLE .% .f:l 3 NUMBER NUMBER TYPE PISTAR MANUAL

DEVIATION 4 1 PIPE 17160. 17160. O _

5 1 PIPE 17160. 17160. 0 - 1, 7 4 ELBOW 17160. 17160. 0 8 4 ELBOW 17160. 17160. 0 19 19 TEE 17160. 17160. 0 20 19 TEE 17160. 17160. 0 - 22 20 PIPE 17160. 17160. 0 . 23 20 PIPE 17160. 17160. 0 'I Allowable Stress = 1.2 S h NC-3652.2 (Reference 8) where: i S h = Basic Material Allowable (Reference 8) ] at Design Temperature - 4 I i 1-I o L i i t . t 6 II i 10.22 .i I f- - TR-76-001' Revision 0 L Table 10.3-12. CLASS 2 - EQUATION #10.ALLOWABLES f i NODE NUMBER ELEMENT NUMBER ELEMENT TYPE hh LE % DEVIATION PIST R MANUAL

7 4 ELBOW 25342. 25342. 0 i

8 4 ELBOW 25315. 25315. 0 I- 19 19 TEE 25336. 25336. O l f 20 19 TEE 25364. 25364. 0 22 20 PIPE 25379. 25379. 0 23 20 PIPE 25361. 25361. 0-l *S A = f (1.25 S c + 0.25 (2 S h -bSL)). NC-3611.2 (Reference 8) where: f = Stress Range Reduction Factor (Reference 8) S c = Basic Material Allowable Stress (Reference 8) at Minimum Temperature I- S = Basic Material Allowable Stress h at Design Temperature (Reference 8) , ,f- S SL = Stress Due to Pressure and (Reference 8) Sustained Loads f t L I 10.23 u nutech . . . . - - . - . ~ . _ . _ ...n-.- .. . . . . - . ~ TR-76-001 Revision 0 Table 10'.3-13. CLASS 2 EQUATION #11 ALLOWABLES g. NODE NUMBER ELEMENT NUMBER ELEMENT TYPE f 39ffth % DEVIATION - ft, PISTAR MANUAL

7 4 ELBOW 39642. 39642. 0 '

8 4 ELBOW 39615. 39615. 0 [, 19 19 TEE 39636. 39636. 0 20 19 TEE 39664. 39664. 0 ,! 22 20 PIPE 39679. 39679. 0 23 20 PIPE 39661. 39661. 0 l-Allowable Stress = Sh+8A: SA = f(1. 5 S c + 0.25 (2 Sh-SSL)) NC-3652.3 (Reference where: S = h Basic Material Allowable Stress-(Reference 8) at Design Temperature f = Stress Range Reduction Factor (Reference 8) i S c = Basic Material Allowable Stress at Minimum Temperature (Reference 8) b , t: S 8b = Stress Due to Pressure and Sustained Loads- (Reference 8), u t ?. 10.24 1 ' y - gum TR-76-001 l Revision 0 -J ) i 11.0 ASME SECTION III - CLASS 3 EVALUATION The piping system model shown in Figure 11.0-1 was used for y verifying PISTAR's ASME Section III - Class 3 evaluation l q i t postprocessing module. l The PISTAR evaluation is in accordance with the ASME Boiler and Pressure Vessel Code, Section III ND-3600 (Reference 8). The sensitivity of results were compared with manual calcula-tions of various quantitles in accorcance with ASME ND-3600. i t I The raw data used for these calculations was the output from I the analysis portion of the PISTAR analysis and design. computer ) program. The criterion for acceptable results was less than q . or equal to 2.5% deviation from the manually calculated results. I l I' The piping system for the ASME Section III - Class 3 evaluati.on is shown in Figure 11.0-1. This problem is Problem Number 6 in Reference 6 (Static Analysis of a Three-Dimensional Piping Structure Program - ANSYS). k The data specified in problem 6 '(Reference 6) was directly input into PISTAR with the following exceptions: The modulus of elasticity was typed incorrectly 6 as 20.0 x 10 psi in the reference document. (Reference 6). The value used was 29.9 x 106 psi. nutech TR-76-0D1 . Revision O' (i N ,. Y r N4/ ;l h A S A 8 I' ! Y .' s ,, 14 l3 Z /\ X is 12 I

g. , is -

1 l9 21 l 22 . Lie g ; g as l u 2 t. Figure 11.0-1. Piping System Model - ASME Section III - Class 3 Verification <; 11.2 q 4 k , I. [ TR-76-001 l- , Revision 0 l q I. , The valves in the PISTAR model were coded as p i l ! k straight pipe sections with the appropriate ) cross-sectional property values-(Table 11.0-1). h l [ PISTAR assumed a direct spring-to-ground restraint i i mechanism on nodal point 4. J The element component types used in PISTAR to describe the piping system are PIPE, ELBON, and TEE (forged). ! L i The cross-sectional properties are found in Table 11.0-1. l l J. Outside Wall Thickness- Wt Per Unit l

1. Component Dia (Inches) (Inches) Length (1b) i Straight Pipe 3.5 0.216 0.631313 Elbows ,

3.5 0.216 0.631313 1 Valve D Nodes 5-6 ! 4.94 0.7619 3.00311 alve E ] 4.499 1.7153 4.50466 Nodes Valve F 21-22 5.221 0.3251 2.00207 W Table 11.0-1. Cross-Sectional Properties The components in the piping system are made of steel. Young's modulus is 29.9 x 10 0 psi. Poisson's ratio is 0.3; and the coefficient of thermal expansion is 2.178 x 10-5 , 11.3 nutech u. .. . e-TR-76-001 .c ' Revision 0 The piping system has been' anchored at nodal points 20 and

23. Nodal point 4 has a direct spring-to-ground restraint d, i

mechanism which imposes a translational restraint in the X, n Y, and Z directions of 1,000 pounds per inch and a rotational restraint in the X, Y, and Z directions of 10,000 inch-pounds per radian. Five structural loading conditions were analyzed for the l ASME Section III - Class 3 piping stress analysis and evaluation. -] A modal extraction analysis was made prior to performing the 1 dynamic response spectrum analysis. The actual loading conditions are described below. f

1. Dead Load - The piping system was subj ected L-L ,1 to the effects of its own weight. This loading i

i was imposed on the structure in PISTAR using a a static vertical acceleration -(Y-axis) of 386.4 - , . 1i inches /second/second. - L

2. 1.

Thermal - The piping system was subjected to the t-effects of a 150 F temperature rise from the zero 4 stress state; and the effects of thermal anchor '- displacements (see Subsection 3.3 for the actual iP anchor displacements) were considered.

3. Secondary Seismic - The piping system was "

subjected to the effects of seismic anchor I L displacement s (see Subsection 3.3 for the actual t anchor displacements). ( 11.4 a- ; Ig' TR-76-001' j Revision 0 i

4. Primary Seismic - The piping system was subjected to the inertia effects of a-dynamic. i response spectrum analysis. After the extraction F of 15 modes (Section 4.0), the structure was ,

l ' loaded with 3 uncoupled simultaneous response spectra (Section 5.0).

5. Total Seismic - The results of the loading conditions for primary seismic were absolutely superimposed with the results'of secondary c seismic analysis.

The following list specifies.the conditions assigned to'the resultant moment calculations used in the ASME ND-3600 n, ~ equations. 1 ASME ND-3600 PISTAR Equations Loading Conditions Sustained Loads - Dead Load ( Occasional Loads - Total Seismic Thermal Loads - Thermal 6 '+ 8 t i 11.5 nutech TR-76-001

7 Revision 0 0.i e

The following list gives additional information required by 0' ASME ND-3600 for evaluation of this piping system q l (Figure 11.0-1). 1 - Design Pressure = 500 psi Design Temperature = 700*F l Peak Pressure = 750 psi' c Operational Cycles = less than 7,000 (for thermal) , Cold Allowable = 15,000.0 psi ! Hot Allowable = 14,300.0 psi-L l 7 l l l l l %l L l 2 1 l . w1 E' l= i N b I 4 11.6 i.' ' s s , ?W -[f f-TR-76-001 l Revision 0 I I 1 11.1 Flexibility Factors i 1 The flexibility factors for this piping system (Figure 11.0-1) 1 were calculated in accordance with ASME Section III, ND-3600. I Table 11.1-1 gives the results obtained from PISTAR, manual e calculations (based on Section ND-3600 of Reference 8), and . . the percentage of deviation from the manual calculations. There were no deviacions for the various structural members investigated. I t 1 4 a 1 1 ; 1 i l L I w 'N e 11.7 m nutech ~1 TR-76-001 c) h 'l Revision 0 ] T\ dj Table 11.1-1. FLEXIBILITY FACTOR COMPARISON J p1 d r 1 NODE ELEMENT ELEMENT FLEXIBILITY FACTORS g 1 Il __XUXBER NUMBER TYPE PISIM MANUAL

DEVIATI_0N

' Q, 4 1 PIPE 1.0 1.0 O 5 1 PIPE l '. 0 1.0 0 1 7 4 ELBOW 4.58 4.58 0 f .1 8 4 ELBOW 4.58 4.58 0. . 19 19 TEE 1.0 1.0 0 (;l 1 20 19 TEE. 1.0 1.0 0 - 22 20 - PIPE 1.0 1.0 0 - 23 20 PIPE 1.0 1.0 0 i Li 'l '~ *For - Pipe : k = 1. 0 Figure ND -3673. 2 (b)-1 (Reference 8) - Elbow: k = 1.65 (Reference 8) ( where: h = flexibility characteristic L: (Reference 8) e h=tR n Figure ND-3673-2 (b)-1 (Reference 8) g A r R = Bend Radius (Reference 8) r = Mean Pipe Radius (Reference 8) I t n = Wall Thickness (Reference 8) - Tee : k = 1.0 (Reference 8) \. I 6 11.8 t ' =r TR-76 001 Revision 0 11.2 Stress Intensification Factors The stress intensification factors for this piping system (see Figure 11.0-1) were calculated in accordance with ASME 'l Section III, ND-3600. [ Table 11.2-1 presents the results obtained from PISTAR, manual calculations (based on Table ND-3673.2(b)-1 of l Reference 8), and the percentage of deviation from manual calculations. T1ere were no deviations for the various ' structural members investigated. 1 1 L L l l i w l = l 'w e e 11.9 u nutech TR-76-001- - Revision 0 Table 11.2-1. STRESS INDEX COMPARISON c l i, r NODE ELEMENT ELEMENT STRESS INDEX (i) g I NUMBER NQQER TYPE PISL\R hW!UAL* DEVIATIO , 4 -1 PIPE 1.0 1.0 0 5 1 PIPE 1.0 1.0 0 fi 7 4 ELBOW 1.8 1.8 0-t 8 4 ELBOW 1.8 1.8 0, 19 19 TEE 1.3 1.3 0 , 20 19 TEE 1.0 1.0 0 22 23 20 20 PIPE PIPE 1.0 1.0 1.0 1.0 0 f 0

For Pipe : i = 1.0 Figure ND-3673.2(b)-1 (Reference 8)

- Elbow: i= Figure ND-3673.2(b) '(Reference 8) where: h = Flexibility Characteristic (Reference 8)

h=tR n Figure ND-3673.2(b)-1 (Reference 8) c A '

r .- R = Bend Radius (Reference 8) r = Mean Pipe Radius (Reference 8) _,' - Tee : i- Figure ND-3673.2(t)-1 (Reference 8) where: ' h = 4.4t n Figure ND-3673.2(b)-1 (Reference 8) r '- l 11.10 '- ' TR-76-001 } Revision 0 l .{ c 11.3 Evaluation l The ASME Section. III (Code) Class 3 evaluation was performed in accordance with the rules of ND-3600 (Reference 8). For i verification, the following items were compared with manual ,, calculations (using PISTAR moment file output for calculations). { t P i ITEM TABLE j Design Pressure Stress 11 . 3-1 i Peak Pressure Stress. 11 . 3 - 2 ! Sustained Loads Stress { 11 .3 -3 Occasional Loads Stress 11.3-4 Thermal Loads Stress 11 . 3 - S i Equation #8 Solution 11 .3-6 l 1- Equation #9 Solution kl.3-7 t Equation #10 Solution 11 . 3 -8 Equation #11 Solution 11 . 3-9 Equation #8 A11owables 11 . 3 - 1 0 Equation #9 A11owables 11 . 3 - 1 1 Equation #10 A11owables 11 . 3 - 1 2 l Equation #11 A11owables 11 . 3 - 1 3 L ' Tables .11.3-1 thrcugh 11.5-13 present the comparative results i for this verification. There were no deviations far the various structural members investigated. i - j l u i i 11.11 11utech : 1 1 ?l TR-76-001' , -Revision 0 R r Table 11.3-1. CLASS 3 - DESIGN PRESSURE' NODE (STRESS) ELEMENT ELEMENT nFATCN PRESSURE TERM % l NtT}1BER NUMBER TYPE PISTAR MANUAL

DEVIATIO?!

4 PIPE 1 2025.5- 2025.5 0 5 1 PIPE 2025.5 2025.5 0-7 4 ELBOW' 2025.5 2025.5 0 19 8 4 19 ELBOW TEE 2025.5 2025.5 2025.5 0 f ~ 2025.5 0 20 19 TEE 2025.5 2025.5 22 20 PIPE 2025.5 2025.5 0' 1] 0 23 20 PIPE 2025.5 2025.5 0 h PD, 'DP = ND-3652 4t D (Reference 8) l El where: i i (' P = Internal Design Pressure (Reference 8)- ; D o = Outside Diameter of Pipe' (Reference 8) - t = n Nominal Pipe Wall Thickness (Reference 8) c . 15 a t he i i Im. 11.12 y '4 m_ l ( .- . TR-76-001 Revision 0 ~ ) l-j" Table 11.3-2. CLASS'3 - PEAK PRESSURE j l l , l 1 {)' NODE ELEMENT ELEMENT (STRESS) PEAK PRESSURE TERM % NUMBER NUIjBER TYPE PISTAR MANUAL

DEVI ATJ,0F_

4 1 PIPE 3038.2 3038.2 0 f( 5 1 PIPE 3038.2 3038.2 0 I 7 4 ELBOW 3038.2 3038.2 0 t 8 4 ELBOW 3038.2 3038.2 0 , [. 19 19 TEE 3038.2 3038.2 0 L i 20 19 TEE 3038.2 3038.2 0 22 20 PIPE 3038.2 3038.2 0 23 20 PIPE 30To.2 3038.2 o PP =PMax D ND-3652 (Reference 8) 4t n L. where: P Max = Peak Pressure (Reference 8) Dg = Outside Diameter of Pipe (Reference 8) L t n = Nominal Wall Thickness :(Reference 8) L I 11.13 nutech

u. . . - . . - - _ .

TR-76-001 i , Revision 0 Gl Table 11.3-3. CLASS 3 - SUSTAINED' LOADS (STRESS) 1 l! NODE ELEMENT ELEMENT SUSTAINED LOADS TERM t. NU\fBER NUMBER TYPE PISTAR MANUAL

DEVIATION.

PIPE 1.50- -1.50 ~ 4 1 0 5- 1 PIPE 52.24 ,52.24 0 ,- 7 4 ELBOW 206.09 206.09 0 , 8 19 4 19 ELBOW TEE 315.77 230.64 315.77 230.64-0 0 f 20 19 TEE 116.57 116.57 0 22 20 PIPE 56.70. 56.70 0 - 23 20 PIPE 132.04 132.04 0 , 0.75 i M ,SL = A z ND-3652 (Reference 8)'. where: i = Stress Intensification Factor . .(Reference 8) MA = Resultant Moment on Cross-Section (Reference 8) h Due to Sustained Loads Z = Section Modulus of Pipe (Reference 8) h. NOTE: 0.75 i Never Less Than 1.0. (Reference 8) j ',J .1 t ; l i: 11.14 I! l TR-76-001 Revision 0 l Table 11.3-4. CLASS 3 - OCCASIONAL LOADS I ~~ ' (STRESS) NODE ELEMENT ELEMENT OCCASIONAL LOADS TFRM % ; J'py_ER NUMBER TYPE PISTAR MANUAL

DEVIAT,J 01. #

4 1 PIPE 8.437 8.435 0 5 1 PIPE 1277.6 1277.6 0 t 7 4 ELBOW 2986.8 2986.8 0 ) - 1 ( 8 4 ELBOW ,. 2977.9 2977.9 0 19 19 TEE 4974.6 4974.6 0 20 19 TEE 22707. 22707, 0 e 22 20 PIPE 3120.9 3120.9 0 23 20 PIPE 5808.6 S808.6 0 I l 0.7S i M OL I ND- 3652 (Reference 8] where: { a i Stress Intensification Factor (Reference 8) [ MB = Resultant Moment Due to (Reference 8) Occasional Loads i Z = Section Modulus of Pipe (Reference 8) l h-NOTE: 0.75 i Never Less Than 1.0 (Reference 8) ; i i b t 11.15 rititenc:ti ~ TR-76-001 Revision 0 e. J ! Table 11. 3-5. CLASS 3 - THERMAL LOADS \ r1 / g. NODE (STRESS) ELEMENT ELEMENT THERNML LOADS TERM % _NLt}1BER NUMBER TYPE PISTAR MANUAL

DEVIAT_IjQN 1

4 1 PIPE 32.191 32.192 0' . 5 1 PIPE 2134.6 2134.6 O < l 7 4 ELBOW 6774.5 .6774.5 0 e { 8 i 4 ELBOW 7694.2 7694.2 0 \ ' 19 19 TEE 30632. 30632. 0 20 19 TEE 46272. 46272. 0 22 20 - PIPE 13805. 13805. 0 .; 23 20 PIPE 13761. 13761. 0 iM

o =

T 7 ND-36 5 2 (Reference 8)' where: k 1 = i Stress Intensification Factor (Reference 8) L ) M = C Resultant Moment Due to Thermal I.oads (Reference 8) b Z = Pipe Section Modulus (Reference 8) l 'E - ?i i.! ! 6 11.16 6 b l= TR-76-001 Revision 0 i Table 11.3-6. CLASS 3 - EQUATION #8 SOLUTION TO NODE ELEMENT ELEMENT EQUATION #8 % { .. NINEER NUMBER TYPE PIJ_ TAR MANUAL

DEYJAT_LOL-)

{ 4 PIPE 2027.0 1 2027.0 0 i 5 PIPE l 1 2077.7 2077.7 0 7 4 ELBOW 2231.6 2231.6 0 8 4 L ELBOW 2341.2 2341.3 0 ! 19 19 TEE 2256.1 2256.1 0 l) i 20 19 TEE 2142.0 2142.1 0 22 20 PIPE 2082.2 2082.2 0 23 20 PIPE 2157.5 2157.5 0 1 PD N 0.75i A f

S gt

= 47 + 3 ND-3652.1 (Reference 8) n where: P = Internal Design Pressure (Reference 8) { D o = Outside Diameter (Reference 8) { l t n = Wall Thickness Nominal (Reference 8) l t i = Stress Intensification Factor (Reference 8) M = Resultfant Moment Due to 'A (Reference 8) Sustained Loads Z = Pipe Section Modulus (Reference 8) NOTE: 0.75 i Never Less Than 1.0 l 't (Reference 8) l e 1, s 'n 1 L i 11.17 nutech 1 TR-76-001'

f!

Revision 0 {L C' d ; Table 11.3-7. CLASS 3 - EQUATION #9 rl U -i SOLUTION TO g' NODE ELEMENT ELEMENT EQUATION #9 % NUMBER NU)1BER TYPr. PISTAR MANUAL

DEXIAT10)) >

4 1 PIPE 3048.1 3048.1 ' 0 - 5 7 4 1 PIPE ELBOW 4368.0 6231.1 4368.0 6231.1 0 0 f' 8 4 ELBOW 6331.9 6331.9 0 -( , 19 19 TEE 8243.5 8243,4 0 20 19 TEE 25862. 25862. 0 1 22 20 PIPE 6215.8 6215.8 0 23 20 PIPE 8978.8 8978.8 { 0 q; l P Dg 3 , Max 0.75i (MA+N) B ND -365 2. 2 (Reference 8) ) OL 4t Z ' n '; where: P Max = Peak Pressure (Reference 8) D o = Outside Diameter (Reference 8) h t n = Wall Thickness (Reference 8) g i = Stress Intensification Factor (Reference 8)- - M 4 = Resultant Moment Due to Sustained (Reference 8) Loads M " B = Resultant Moment Due to Occasional (Reference 8) Loads Z = Pipe Section Modulus (Reference 8)~ ,_ NOTE: 0.75 i Never Less Than 1.0 (Reference 8) w 11.18 6 ^) , e l TR-76-001 Fevision 0 j .- 8 Table 11.3-8. CLASS 3 - EQUATION #10 l SOLUTION TO , NODE ELEMENT ELEMENT EOUATION #10 % NUstBER NUMBER TYPE PISTAR MANUAL

DEVI ATJ,0),' ,

4 1 PIPE 32.191 32.192 0 [ 5 1 PIPE 2134.6 2134.6 0 7 4 ELBOW 6774.5 6774.5 0 8 4 ELBOW 7694.2 7694.2 0 ] 19 19 TEE 30632. 30632. 0 I l 20 19 TEE 46272. 46272. O 22 20 PIPE 13805. 13805. 0 1 23 20 PIPE 13761. 13761. O I o b iM {

S E

= ND - 3 65 2. 3 (Reference 8) i = Stress Intensification Factor (Reference 8) M C = Resultant Moment Due to Thermal (Reference 8) Loads ' Z = Pipe Section Modulus (Reference 8) % 11.19 ' nutech TR-76-00S Revision 0 7 Table 11. 3 - 9. - CLASS 3 - EQUATION #11 SOLUTION TO [ NODE ELEMENT ELEMENT ~ EQUATION #11 % 3 _XUMBER KUMBER TYPE l PISTAR MANUAL

DEVIATION 4 1 PIPE 2059.2 2059.2 0 5 1 PIPE 4212.3 4212.3 0 7 4 ELBOW 9006.0 9006.1 0 8 4 ELBOW 10035. 10035. O f 19 19 TEE 32888. 32888. 0 -

20 19 TEE 48414. 48414. 0 - 22 20 PIPE 15888. 15887. 0 23 20 PIPE 15918. 15918. ~ O b PD

0 N S

TE = 4t + 0.75i "A + i C ND-3652.3 n ~T- T (Reference 8) Ll where: P = Design Pressure = (Reference 8) D, Outside Diameter (Reference 8) L t n = Wall Thickness C' (Reference 8) = i Stress Intensification Factor (Reference 8) M = _ A Resultant Moment Due to Sustained (Reference 8) Loads M = C Resultant Moment Due to Thermal (Reference 8) 'E Loads Z = Pipe Section Modulus (Reference 8) NOTE: 0.75 i Never Less Than 1.0 (Reference 8) < I m 11.20 l-i) l l i TR-76-001-Revision 0 l, Table 11.3-10. CLASS 3 - EQUATION 8 ALLOWABLES 1 NODE EQUATION #8 ELEMENT ELEMENT. ALLOWABLE E lBER NUMBER TYPE PISTAR MANUAL

DEVIATION l 4 1 PIPE 14300. 14300. 0 5 1 PIPE 14300. 14300. 0 7 4 ELBOW' 14300. 14300, 0 8 4 ELBOW 14300. 14300. O i 15 19 TEE 14300. k 14300. 0 I ,

19 1 TEE 14300. 14300, 0 ;I L 20 PIPE 14300. 14300. 1 O

2. 20 PIPE 14300. 14300. 0 l 1

1 I Allowable Stress = 1.0 S 3 ND-3652.1 1 (Reference 8) { where: 4 b h = Basic Material. Allowable Stress at Design Temperature (Reference 8) L ! i v 11.21 3 L. nutech TR-76-00 Revision 0 r Table 11.3-11. CLASS 3 - EQUATION 9 ALLOWABLE 3 r } NODE EQUATION #9 f ELEMENT NtNBER ELEMENT ALLOWABLE % j. NINBEk TYPE PISTAR MANUAL

DEVIATTQN 4 1 PIPE 17160. 17160. 0 5 1 PIPE 17160. 17160. O r 7 4 ELBOW 17160. 17160. 0 l.

8 4 ELBOW 17160. 17160. 0 19 19 TEE 17160. 1716'0. 0 20 19 TEE 17160. 17160. 0 22 20 PIPE 17160. 17160. 0 23 20 PIPE 17160. 17160. O h h Allowable Stress = 1.2 S h ND-3652.2 (Reference 8) i where: '- S h = Basic Material Allowable (Reference 8) at Design Temperature L k-I W '6 i 1 11.22 i- ! p w TR-76-001 Revision 0 Table 11.3-12. CLASS 3 - EQUATION 10 ALLOWABLES NODE ELEMENT f$h.fftfl0 ELEMENT g ? NUMBER NUMBER TYPE DEVIATION PISTAR MANUAL

l 7 4 ELBOW- 25342. 25342. 0 8 J 4 ELBOW 25315. 25315. O l 19 19 TEE 25336. 25336. 0 20 19 TEE- 25364. 25364. 0 22 20 PIPE 25379. 25379. O f 23 20 ' PIPE 25361. 25361. 0 1

*S A = f (1.25 S c + 0.25 (2 Sh~85L)) ND-3611.2 (Reference 8) - t where: [ f = Stress Range Reduction Factor (Reference 8) S c = Basic Material Allowable Stress (Reference 8) g at Minimum Temperature t S h = Basic Material Allowable Stress (Reference 8) at Design Temperature . l S gg = Stress Due to Pressure and (Reference 8) L Sustained Loads ' L L U u 11.23 nutech . . ,.I . TR-76-001 Revision 0 r! Table 11.3-13. CLASS 3 - EQUATION 11 ALLOWABLES l c l NODE ELEMENT ELEMENT ' I' A LE NUMBER NUMBER TYPE PISTAR MANUAL

DEVIATION a

p' 1 7 4 ELB0W 39642. 39642. 0 i 8 4 ELBOW 39615. 39615. O f 19 19 TEE 39636. 39636. . O J 20 19 TEE 39664. 39664. 0 22 20 PIPE 39679. 39679. 0 23 20 PIPE 39661. 39661. 0 l Allowable Stress = # 8 ^8 A = f(1.25 S c S h A + 0.25 (2 Sh-85L)) ND-3652.3 (Reference 8) where: l. I1 = S h Basic Material Allowable Stress (Reference 8) , at Design Temperature = Stress Range Reduction Factor f (Reference.8) S c = Basic Material Allowable Stress (Reference 8) L , at Minimum Temperature b. S 8b = Stress Due to Pressure and ' Sustained Loads (Reference 8) is L 11.24 6 I u f TR-76-001 ] . Revision 0 12.0 ANSI B31.7 EVALUATION I . l .' l I Not Available in Version 1.1 of PISTAR, L i L c L De 12.1 Mutech R_ e i ' ' 1 ['l. TR-76-001 1 I . Revision 0 13.0 ANSI B31.7 EVALUATION - f. 1 I O l I Not Available in Version 1.1 of PISTAR. L I 1 L L L L h 4 _ 13.1 nutech m _m_. .. - - i- - .. - - 4 i . - - -- ' - - - -J . lQ; f - -TR-76-001 Revision 0

14.0 REFERENCES

1. PISTAR User's Manual. . Nuclear Technology,.Inc., TR-76-002.

i

2. SAP IV, A Structural Analysis Program for Static and .

Dynamic Response of Linear Systems. Bathe, K. J., et al, J

.[

1973, EERC 73-11.

3. ANSYS Engineering Analysis System User's Manual. Swanson Analysis Systems, Inc., 1975.

4 '. MRI/STARDYNE Static and Dynamic Structural Analysis Systems. j Control Data Corporation, 1974. 1 1

5. Dingwell, I. W., ADLPIPE.... Static, Thermal, Dynamic Pipe Stress Analysis Input Preparation. Arthur D. Little, Inc.,

1974.

6. Pressure Vessel and Piping 1972 Computer Programs Verifi-cation. The American Society of Mechanical Engineers, )

I 1972, 72-94235. j

7. Bathe, K. J., et al, " Solution Methods for Eigenvalue l 1 Problems in Structural Mechanics." International Journal of Engineering Mechanics Division, Volume 6, Number 2, 1973. I l

l 8. ASME Boiler and Pressure Vessel Code, Section III, Nuclear [ Power Plant Components. 1974 with addendums up to and including Winter 1975.

9. Clough, R. W., " Earthquake Analysis by Response Spectrum I- Superposition." Bulletin of the Seismological Society of America, Volume 52, July 1962.

       .                    10.           " Combination of Modes and Spatial Components in Seismic Response Analysis." Regulatory Guide 1.92, U. S. Atomic Energy Commission Directorate of Regulatory Standards, December 1974.

11. Introduction to Structural Dynamics. Biggs, J.,

McGraw-Hill Book Company, 1964. ~ L L L 14.1

                                                                   .                                        nutech

f ' PSD-01-016 Revision 2 -- File: 08.210.0020 l I {- PISTAR f PIPING ANALYSIS COMPUTER PROGRAM

                                                                                                                -l VERIFICATION TO                                                !

NRC BENCHMARK PROBLEMS I l VOLUME I . l l I ^ Prepared for the Office of Nuclear Reactor Regulation Nuclear Regulatory Commission L Prepared by ) Nuclear Technology, Inc. San Jose, California L Project Approval: (. - A J. R. Arterburn, P.E. i L NUTECH Approval and Release: N [gh[ --- - A. B. Higginbotham, P.E. Date: ,

I7/80/

                                                                                                           . I m

toao'r*%Mutech

                                 .                                                tupp-

l REVISION CONTROL SHEET PICTAR PIPING ANALYSIS COMPUTER

SUBJECT:

PROGRAM VERIFICATION TO NRC REPORT NUMBER: PSD-01-016 BENCHMARK PROBLEMS, VOLUME I d b NJ M NAME/ TITLE W. H.'Estrada/ INITIAL S ecialist

                                             . $.                                          Eh NAME/ TITLE J. R. Arterburn/                                                  INITIAL Project    n     er                                                                                            l Y

NAME/TITL h B. Higg botham/ INITIAL Engineerip[gManager _//b/fduh fl0 NAME/ TITLE A. S. Crowder / INITIAL Specialist . D P. #74-)d/G DFM ' NAME/ TITLE D. K. McWilliams/ INITIAL Staff Engineer b PRE- ACCURACY CRITERIA b PRE- ACCUPACY CRlTERIA PAGE(S; REV PARED GECK OIECK PAGE(S) REV PARED GECK CHECK ii 0 dde fJ/p W/A I-A.3 0 g @ % ll iii 0 l I-A.4 0 [ iv 0 I-A.5 0 I-1.1 0 I-A.6 0 I-1.2 I-A.7 0 g 0 I-1.3 I-A.8 0 g 0 I-2.1 0 I-A.9 0 I-2.2 0 I-A.10 0 I-2.3 0 I-A.ll 0 I-2.4 0 I-A.12 0 1-2.5 0 I-A.13 0 I-2.6 0 I-B.O O . I-2.7 0 I-B.1 0 I-3.1 0 I-B.2 0 I-3.2 0 I-B.3 0 I-4.1 0 I-B.4 0 - I-4.2 0 I-B.5 0 I-5.1 I-A.0 0 0 d@ g h& I-B.6 I~ 0

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f. REVISION CONTROL SHEET

[ (Continuation) R TITLE: PISTAR PIPING ANALYSIS COMPUTER PROGRAM VERIFICATION REPORT NUMBER: PSD-01-016 TO NRC BENCHMARK PROBLEMS , VOLUME I PRE- ACCURACY CRITERIA PRE- ACCURACY CRITERIA PAGE REV PARED CHECK CHECK PAGE REV PARED CHECK CHECK .

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REVISION CONTROL SHEET (Continuation) TITLE: PISTAR PIPING ANALYSIS ' REPORT NUMBER: PSD-01-016 COMPUTER PROGRAM VERIFICATION TO N_RC BENCHMARK PROBLEMS, VOLUME I PRE- ACCURACY CRITERIA PRE- ' ACCURACY CRITERIA I PAGE REV PARED CHECK CHECK PAGE REV PARED CHECK CHECK i I-A.8 2 d]& TrA D/#7 I-A.9 2 1 I-A. lC 2 J ( ^ I-A.ll 2 I-A.12 2 I-A.1: 2 ! I-B.8 2 E-B. 9 2 [-B.1C 2 E-B.ll 2 [-B.12 2

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_, -1 i 1 PSD-01-016 i j i

                                  .             PREFACE                                 1 This report presents verification of the ' PISTAR piping analysis l_          computer program in response to a request made by the Office of Nuclear   Reactor      Regulation    of the   Nuclear   Regulatory     >

[ Commission. This verification is directed specifically at the response spectrum solution for determining responses of piping systems subjected to earthquake loading. Verification of the other capabilities of the PISTAR computer program is presented in the PISTAR Verification Report (Reference 1). 1 Iei It II I i L ' M m4u.p> b L W 11 ._ nutech

F G . t i I L PSD-01-016 Revision 1 TABLE OF CONTENTS I VOLUME I PAGE 1.0

2.0 INTRODUCTION

PROGRAM DESCRIPTION.............................. I-1.1 1-2.1 f 1 i 2.1 PISTAR Features and Capabilities........... I-2.1 2.2 Theoretical Basis.......................... I-2.4 3.0

SUMMARY

OF RESULTS............................... 1-3.1 4.0 PROGRAM REFERENCE LIST........................... I-4.1

5.0 REFERENCES

....................................... 1-5.1 APPENDIX A: RESULTS FOR BENCHMARK PROBLEM NO. 1.................................... I-A.0 APPENDIX B: 'RESULTS FOR BENCHMARK PROBLEM do. 2.................................... I-B.O I! APPENDIX C: RESULTS FOR BENCHMARK PROBLEM NO. 3.................................... I-C.0 'I. y) APPENDIX D: RESULTS FOR BENCHMARK PROBLEM No. 323A................................. I-D.0 - APPENDIX E: RESULTS FOR BENCHMARK PROBLEM - No. 4.................................... I-E.0 b iii - nutech f

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PSD-01-016 ) Revision 1 l 1 TABLE OF CONTENTS (Concluded) i VOLUME II . PAGE l

1.0 INTRODUCTION

..................................... 11-1.1 APPENDIX A: PISTAR COMPUTER PRINT-0UT FOR BENCHMARK PROBLEM NO. 1.................. II-A.0 APPENDIX B: PISTAR COMPUTER PRINT-0UT FOR BENCHMARK PROBLEM NO. 2.................. II-B.0 APPENDIX C: f PISTAR COMPUTER PRINT-0UT FOR BENCRMARK PROBLEM NO. 3.................. II-C.0 APPENDIX D: PISTAR COMPUTER PRINT-0UT FOR BENCHMARK PROBLEM No. 323A............... II-D.0 VOLUME III !

1.0 INTRODUCTION

.................................... 111-1.1 APPENDIX A: PISTAR COMPUTER PRINT-0UT FOR BENCHMARK PROBLEM No. 4..................III-A.0 nutech

e J PSD-01-016 J Revision 1

1.0 INTRODUCTION

H This report has been prepared to demonstrate, to the Office of Nuclear Reactor Regulation (ONRR) of the Nuclear Regulatory j Commission (NRC), the accuracy and validity of NUTECH's proprie-tary piping analysis computer program, PISTAR. This report is provided - in response to an ONRR request for additional verifi-cation of structural computer programs used for static and dynamic analysis of nuclear piping systems. The additional veri-fication requested by the ONRR consists of a comparison of results obtained from a program such as PISTAR to the results provided by the ONRR for a set of benchmark problems. f

                                                                         , f<

A total of seven (7) benchmark problems were provided by the ONRR along with a sketch of each structure, and the full or partial g solutions to each problem. The structures analyzed are assumed I to experience linear elastic behavior when subj ected to dynamic loading induced by earthquake type excitation in three direc- f. tions. The structural responses due to the earthquake loading are determined by the response spectrum method using the inter-modal combination technique in accordance with the provisions of NRC Regulatory Guide 1.92 (Reference 3). The information requested by the ONRR, to document the results of this additional verification, include: ;

1. Classification of the program development as either inter-nally or externally developed. For externally developed programs such as PISTAR, only four of the seven benchmark problems need to be solved. These four benchmark problems ~

consist of Problems 1, 2, 3, and 323A. Par an additional request by the ONRR, Benchmark Problem 4 is also to be 1 J solved. i j

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PSD-01-016 Revision 1 c

2. Program name, version, and a general description of the program including identification of the capabilities used for f piping analysis and the theoretical basis of the program.

3. Computer print-out of the solution to each benchmark prob-lem showing the following:

a. Listing of input data

{ I b. Natural frequencies and associated mode shapes

c. Modal participation factors

d. Combined modal displacements and rotations

e. Combined element stress resultants (internal forces and moments) j

f. Combined element stresses )

As discussed in Section 2, the PISTAR computer program has four (4) maj or phases. These phases are the Input Processing phase, Analysis ph:se, Load Combination phase and the Code Evaluation phase. The Input Processing, Load Combination and Code { Evaluation phases were developed totally by NUTECH and are NUTECH proprietary. The Analysis phase is taken from the well-known , structural analysis computer program SAP IV (Reference 4), devel- I l oped at the University of California at Berkeley. The pipe, elbow and boundary element formulations, and the static and dynamic equation solution solvers are also from the SAP IV g computer program. Since the analytical solution techniques of L the Analysis phase, particularly the response spectrum solver, are of most interest in this verification, PISTAR was considered

as an externally developed computer program for the purposes of this verification. This report thus presents the information requested by the ONRR, for Benchmark Problems 1, 2, 3, 323A, and 4 as solved with the computer program PISTAR. The name, version, general description b and theoretical basis , particularly the method used for inter-

                                                                                                 .i I-1. 2                                              !

_ nutech 4

PSD-01-016 (d Revision 1 j modal L and intramodal combination for the response spectrum analysis of the program, is given in Section 2. A summary of the results. of this verification is presented in Section 3 and Section 4 provides the reference list for the PISTAR computer program. The reference itst for this report is contained in ' Section 5. Appendices A through E contain the detailed informa- j tion for the five benchmark problems solved using PISTAR. Each I h appendix contains the following: ' A sketch of the PISTAR model for the benchmark problem. l) l Graphs of the input response spectra. f Comparison tables containing results from PISTAR and the results provided by the ONRR. Deviation from the results provided by the ONRR are also shown. ~ Volumes 11 and III of this report contains the PISTAR - computer print-out for each benchmark problem. The PISTAR print-out 7 includes the information requested by the ONRR in Item 3, above. [ l L L

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PSD-01-016 2.0 PROGRAM DESCRIPTION PISTAR (Piping Stress Analysis and Reporting) is a computer pro-

  '{               gram ana'ysis.

developed explicitly for piping system design T'ie program was developed by Nuclear Technology, Inc. and (NUTECH) with the assistance of McDonnell Douglas Automation I' Company (MCAUTC) . The features and capabilities , and the theo-retical basis of the PISTA'1 computer program are described below.

2.1 PISTAR Features and Capabilities l The PISTAR computer program was developed with, up-to-date L ' engineering techniques in piping . analysis

using the finite ele-ment method. The pip:.ng system i;eoreatry Jefinition, analytical,

, e load combination, and code evaluation capatilities in PISTAR provide a complete piping design and analysis tool to assure compliance with the ASME and ANSI power piping codes require-ments. State-of-the-art programming te.hniques were used to implement the engineering requirements while making the program i efficient, user-oriented, and versatile. ,

   '              The piping system ' geometry is defined 'in PISTAR with piping component, support and stiffness elements.               Seven piping com-ponent elements are currently available.              These are the PIPE, u               ELBOW, REDUCER, VALVE, TEE, BRANCH and SWEEP 0LET elements.             Each of these are beam elements having different geometries (straight

_ or curved), girth welds, and stress intensification factors and indices. i

   ~                                           '

The cross-sectional and material properties, and weight are specified for. each element. Other information such as code l classification, girth and longitudinal weld specification, stress j intensification factors and indices can also be specified to more i accurately define the geometry of the piping system. I-2.1 nutech

PSD-01-016 i Five types of support. elements are used to define the restraints ' which are commonly 'found in power piping systems. The five types are the ANCliOR, RESTRAINT, ' GUIDE, HANGER and SNUBBER elements. These supports are linear, translational and rotational springs-to-ground having a specified direction and stiffness value. A general stiffneas element is also available which gives the capability of apecifying an arbitrary 6 x 6 stiffness matrix between any two points in the model. [ The analytical capabilities in PISTAR include static analysis, modal extraction, response spectrum analysis, and dynamic time- g history analysie. Deadweight, thermal expansion , concentrated (' forces and moments, static displacements and rotations, and static accelerations can be imposed on the piping system using the static analysis capability. The frequencies and normalized f mode shapes of the piping system are determined using the modal extraction capability. Two methods are available for performing [ the. modal extraction, the Determinant Search and the Subspace Iteration methods. The response spectrum analysis capability can be used to deter-mine response of the piping system when subj ected to an arbri-trary seismic or other dynamic acceleration (or_ displacement) response spectrum in the X, h Y and Z dire c t a.ons . The methods , available in performing the intermodal and intramodal combinations for the response spectrum analysis are discussed in Section 2.2 of this report. ! i l The response of the piping system to an arbitrary force or dis-placemeit time-history is determined using the dynamic time-history analysis capability. The Wilson-e direct integration s technique is used in PISTAR to compute the responses due to the input time-history. '

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PSD-01-016 ]

I The analytical capabilities described above are carried out by ,

)
~

the matrix solution of a system of simultaneous equations.- A 1 bandwidth reducer internally reorders the node numbers to f 1 minimize the cost of performing the matrix solutions. j - Nodal displacements, support reactions, and piping forces and moments are the results obtained from the static, response _ spectrum and dynamic time-history. solutions . The results from any analysis load case un be combined with the results of other analysis load cases using the load combination capability in PISTAR. The results from each analysis can be multiplied by a l scalar factor and then combined with results from other analysis (' load cases by direct, absolute, or square-roct-sum-of-the-squares ; (SRSS) summation techniques. I The results from any of the above analysis capabilities can be saved for later processing by use of the restart feature in j PISTAR. The program can be restarted at various convenient ! stages while performing a piping analysis. e l The code evaluation capability in PISTAR includes the stress l evalue. tion of piping system in accordance with Section III, Sub- ' sect: ions NC and ND of the ASME Soiler and Pressure Vessel Code (Reference 5) and with the ANSI B31.1 Code (Reference 6) . The program compares the calculated stresses in the piping component elements to the applicable code allowable stresses for the ten maximum stressed elements in the system. The program indicates those elements having stresses which exceeds the allowables. The input for PISTAR has been formatted for ease in defining the required information. Extensive use of alphanumeric identifiers ) ' I and a semi-free format (i.e., no right or left data justification required) makes checking easier and reduces the chances for input 1 1-2.3 l

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PSD-01-016 1 errors. All commonly used pipe cross-sectional properties, 4 J material properties, and stress intensification factors and ,) indices are stored in the program and can be easily accessed. L Output from the PISTAR computer program is in a format suitable j to insert directly in a stress report. It has block headers on every page and all pertinent tables are printed in an 8-1/2 x 11 area requiring no reduction for insertion into reports . Double H spacing is used wherever possible for easy reading.

Extensive checking and sorting of the input data is performed by H PISTAR to minimize the computational costs attributable to . input M errors. Data is processed through the entire checking phase, re- j gardless of errors, to ensure that all input errors' are found. Error diagnostics are identified by PISTAR as either Fatal, f Warning, or Informative errors. [ PISTAR has plotting options available to th'e user to assist in model verification and interpretation of r,esults and can f interface with any commonly available plotting hardware. The ' PISTAR geometric plotting package will produce computer isomet- { ric, plan and elevation views with full headings, annotations and support configurations as needed to describe the piping system in f the stress report. PISTAR also has the capabilities to plot dynamic time history results. { The current version of the PISTAR program is Release 1.5. This release was utilized to obtain the solutions to the benchmark problems. ,

2.2 Theoretical Basis

                                                                               'l The PISTAR computer program consists of four (4) main phases.

These phases are the Input Processing, Analysis, Load Combination , and Code Evaluation Phases. The Input Processing phase reads and H i 1-2.4 -: nutech ..

PSD-01-016 l _ interprets the F15 TAR input data, performs the detailed data j checking, and generates intermediate input files for the other I phases of the program. The Analysis phase performs the geometry J formation, and the static, responsa spectrum and dynamic time-history analysee of the piping system. The Load Combination phase combines the results obtained for any load case performed in the Analysis phase of the program. The Code Evaluation phase y performs the stress evaluation of the piping system in accordance I with the ASME Boiler and Pressure Vessel Code (Reference 5) and ANSI B31.1 Code (Reference 6). t The Input Processing, Load Combination, and Code Evaluation phases of the program were developed by NUTECH. The Analysis i l phase of the program is based on the SAP IV computer program (Reference 4) that was developed at the University of California at Berkeley. The pipe , bend , and boundary elements formulations , and the static and dynamic solution solvers have been extracted c from the SAP IV computer program. Only minor changes were made to the routines taken from the SAP IV program. These' changes

]           consisted of 1) making the routines compatible with PISTAR, and            l

2) adding additional summation techniques for intermodal and I

intramodal combinations for the response spectrum analysis. The l theoretical basis of the element formulations and the static and dynamic solution solvers can- be found in the documentation , available on the SAP IV computer program (Reference 4). The intermodal and intramodal combinations for the response spec-trum analysis in PISTAR are based on the SAP IV computer program. Additional summation techniques have been added to PISTAR to allow user-specified options for the intermodal and intramodal combinations. A description of the intermodal and intramodal combinations for the response spectrum analysis in PISTAR follows. A response spectrum analysis of a structure subjected to inde-I- 2. 5 nutech

r PSD-01-016 I Revision 1 _; pendent excitation in the three spatial directions X, Y and Z, I! ? results in individua?. modal responses of the structure for each p excitation. Letting the modal responses for the r' th mode be tl represented by u rx' "ry, and u rz f r the X, Y and Z excitation, tespectively, the intermodal and intramodal combinations of the responses are given below. f The intramodal responses , i.e., the responses for the r' th 1 : mode due to excitation in the X, Y and Z directions, are combined first. The intramodal responses are combined as i follows: Algebraic Suml : ur " "rx + "ry + u rz I Absolute Sun: ur" !"rx! + !"ry! + !"rz! SRSS Sum2 : ur I

ufx+u ry * "rz ur" " x + "ry + lu rz I SRSS with - 2 Absolute. Sum 3 <u r = u + luyxl 7 +ufz ur = u +u rx

A 3 !"ry! where: ,

ur = combined modal response for the r' th mode i J. I A warning is issueel by PISTAR if the algebraic sum combination technique is specified. 2 The SRSS sum combination technique is the method in the SAP IV computer program. 3 ' The user must specify one of the three options indicated. c. 1-2.6 nutech :

{, . PSD-01-016 - Revision 1 ! f 1

  ;                With    the  intramodal     responses- combined,               the intermodal      !

responses are then combined as follows: u n Algebraic Sum l: u= I u r ! r r=1 [- n Absolute Sum: u= E lur ! r,= 1 . L 2 2 V2 SRSS Sum : u= r=1 u# . {

                                                                              ~                       ;

SRSS Sum with Provisions for 'm 1 2 /2 Closely Spaced Modes 3: u= I u i q f - where.

                                                                              ~
 '.                                                                                                  (

u = total combined response u = combined response for the q'th closely i spaced group 4 l c u: r for modes not closely spaced

=<

j - ( l(ur)kl : f r modes closely spaced l l n = number of modes ' k m = number of closely spaced modal groups i = first mode of the q'th group (lowest frequency) L I A warning is issued by PISTAR if the algebraic sum combination technique is specified. 2 The SRSS sum combination technique is the method in the SAP IV s computer program. 3 This definition is in accordance with the Grouping Method as ., defined in the NRC Regulatory Guide 1.92 (Reference 3). 4 The groups are formed by starting with the mode with the lowest frequency and working towards modes with successively higher ~ frequency. A mode is included in one group only. l I-2.7 ilutech

I PSD-01-016 , , p Revision 1 .lI l e j = last mode of the q'th group. The j'th mode "- is the mode with the highest frequencylessih than or equal to the frequency of the i'th mode increased by ten percent. 1

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PSD-01-016 Revision 1

       -       3.0

SUMMARY

OF RESULTS The results for Benchmark Problems 1, 2, 3, 323A, and 4 are ; presented in Appendices A through E, respectively. The results ; from PISTAR are tabulated in the appendicies along with the results provided by the ONRR where available. Each table' ! indicates the page in the PISTAR computer print-out (provided in Volumes II and III of this ~ report) which contains the results L used in the tables. The results tabulated include the natural ! 7 frequencies, modal participation factors, and selected combined nodal displacements, piping forces and moments, and piping stresses. The deviation from the ONRR results are also shown in [ the tables. Results from PISTAR or from the ONRR results smaller than 1.0 x 10-6 were taken as zero. The results 2 rom the* PISTAR computer program were obtained by usina modeling and analysis techniques which produce results compar able to the results obtained from the ONRR. In some cases, this required the use of special modeling or analysis techniques L-to obtain results similar to those obtained from the ONRR. The j special techniques used are discussed below. N For Benchmark Problem 3, short pipe elements, numbers 7, 9,

  ,                   10, 12, 15, 17, 18, 20, 21, and 23, were used in modeling the structure as shown in Figure C-1 in Appendix C. .These
  ~

short pipe elements were required because 1) PISTAR limits the maximum number of elements that can attach to a node point to four (4) and 2) the directional orientation of elbows and bends must be defined in PISTAR by the piping elements attaching to the elbow or bend. For Benchmark Problem 4 short pipe elements, numbers 5, 10,' _ 45, and 80 were used in modeling the structure as shown in Figure E-1 in Appendix E. These short elements were used

                                                                                         /k  '

. for the same reason as described above for Problem 3. Flutech d

PSD-01-016- ' ' Revision 1 i

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. For Benchmark Problems 2, 3, and 4, the X, Y, and Z earth-quake excitations were analyzed using three independent <j response spectrum analysis cases. The results from these ' l cases were then combined by the SRSS summations. technique < using. the Load Combination phase in PISTAR. The three independent cases were required for these three problems I because these problems had clustered natural frequencies (closely spaced modes). Since PISTAR- combines the intramodal respon.ses first and then the intermodal responses which is opposite the order the ONRR used in " obtaining the combine'd responses , the results. obtained from R PISTAR if all three excitation were applied simultaneously, would be higher than the results provided by the ONRR. L An additional case was included in the PISTAR analysis in which the three earthquake excitations were applied simul- ) taneously. Results from this case are not tab:.ulated . . For Benchmark Problem 323A, the SRSS intermodal combination technique was used in the PISTAR analysis. This cechnique

was used because an intermodal combination cluster factor g of 0.00001 was specifi ed in the analysis performed by the { ONRR. This cluster factor was sufficiently small that no structural natural frequencies were clustered. h The ~ deviation of the PISTAR results from the ONRR results fo/ Benchmark Problems 3 and 4, as shown in Appendices C and L: , respectively, are higher than the deviation calculated for the other benchmark problems. The higher deviations for these ' problems were determined to be attributed to different methods being used for combining the intermodal responses. As described u in Section 2.2, PISTAR computes the intermodal responses using ,< the Grouping method whereas the ONRR results were computed using L the Ten Percent method. The Grouping and Ten Percent methods are 4 defined in the NRC Regulatory Guide 1.92 (Reference 3). m 1-3.2 nutech +

PSD-01-016 4.0 PROGRAM REFERENCE LIST ' The reference list for the PISTAR computer program as given in

      ~     Volume I, Section 6 of the PISTAR User's Manual (Reference 2) is ahown below.

i

            . PISTAR Verification Report, Nuclear Technology, Inc., TR-76-001.
            . Poley,   S.,   " Mesh Analysis of Piping Systems" IBM New York      .

Scientific Center Technical Report Number 320-2939, March I 1968.

            . Hall,  A. S.,   et al, " Curved Beam Stiffness Coefficients",

ASCE Journal of Engineering Structural Division, February

   '.             1969.

I i' . Wilson, E., et al, " Direct Solution of Large Systems of Linear Equations", Computers and Structures. Bathe, K. , et al, " Solution Methods for Eigenvalue Problems in Structural Mechanics", International Journal of Engineering Mechanics Division , Volume 6, Number 2, 1973 d

            . Bathe,    K.,    et   al,  "Eigensolution of Large Structural Systems with Small Bandwidth", ASCE Journal' of Engineering Mechanical Division, June, 1973.

i, . Bache, K., et al, "Large Eigenvalue Problems in Dynamic Analysis", ASCE Journal of Engineering Mechanical Division, ' June, 1973.

            . Clough, R. W., " Analysis of Structural Vibrations and Dynamic Response", Proceedings from the First U.S.-Jaoan           '

Symposium on Recent Advances in Matrix Methods of i Structural Analysis and Design , Tokyo , Japan , 1968. j . Bathe, K, et al, " Stability and Accuracy Analysis of' Di-L rect Integration Methods", International Journal of Earth-quake Engineering and Structural Dynamics, Volume 1, Number 2, 1973.

            . Clough,    R. W.,    " Earthquake Analysis By Response Spectrum Superposition",      Bulletin of the Seismological Society of America, Volume 52, July, 1962.
            . ASME Boiler and Pressure Vessel Code, Section III,_ Rules for Construction of Nuclear Power Plant Components, 1974,

_ with addend'um up to and including Winter 1975. 1-4.1 nutech .

PSD-01-016 American National Standard Code for Pressure Piping", Power Piping, ANSI B31.1 and B31.lb, June 1973, with 1973 Addendum. 4

   . USA   Standard    Code    For   Pressure- Piping,   Nuclear    Power.

Piping, USAS B31.7, 1969. j (

     " Combination of Modes and Spatial Components in Seismic Response Analysis", Regulatory Guide 1.92, U. S. Atomic Energy   Commission,      Directorate   of  Regulatory Standards,             j December 1974.                                                               4-
     " Sample Analysis of a Piping System - Class 1 Nuclear", The American Society of Mechanical Engineers, Working Group on Piping, 1972.

i..

   . Brock,  J.,   et a l ., " Speed Charts for Calculation of' Tran-sient Temperatures on Pipes", Heating, Piping,              and Air.

L Conditioning, Volume 43, Number 11, November 1971.

   . Arpaci,   V.,   Conduction Heat      Transfer,  Addison   -

Wesley Publishing Company, 1966. .

   . Rohsenow, W., et al, Heat,      Mass, and Momentum Transfer,                "

Prentice - Hall, 1961. f

   . Stress   Intensification      Factors and Stress Indices For              b Bonney Forge Sweepolets , Gulf & Western Industrial Products Company, Bonney Forge Division, January 1971..                            1 d

I i I m u I ma

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PSD-01-016 Revision 1

5.0 REFERENCES

1. PISIAR Verification R: Lort, Nucl22r Technology, .Inc.,

TR-76-001, Revision 0.

2. PISTAR User's Manual, Nuclear Technology, Inc., TR-76-002, Revision 2. ,

3. " Combination of Modes and Spctial Components in Seismic Response Analysis", Reculatory Guide 1.92, U.S. Atomic Energy Commission, Directorate of Regulatory Standards,

f. Revision 1, February 1976.

F 4. Klaus-Jurgen Blake, Edward L._ Wilson, Fred E. Peterson, SAP IV, A Structural Analysis Program for Static and Dynamic Response. of Linear Systems, Report No. EERC 73-11, University of California, Berkeley, CA.

5. ASME Boiler and Pressure Vcssel Code, Section III, Rules for Construction of Nuclear Power Plant Comoonents, 1974, with addendum up to and including Winter 1975.

6. American National Standard Code for Pressure Pioine, Power Pioing, ANSI B31. I and B31.Ib, June 1973 with 197T j; Addendum.

1 L f m. has e m hans I-5.1 L nutech

g m PSD-01-016 o l H

\'

e i APPENDIX A {

            - RESULTS FOR                                 ..

BENCILMARK PROBLEM NO. 1 - a 1 l' t m I m e l I-A.0 - nutech _

PSD-01-016 APPENDIX A

LIST OF TABLES PAGE i Table A-1: Natural Frequencies........................... I-A.5 Table A-2: Modal Participation Factors................... I-A.6 Table A-3: Combined Nodal Displacements, Node 2.......... I-A.8 Table A-4: Combined Nodal Displacements, Node 6.......... I-A.9 f Table A-5: Combined Element Stress Resultants, Element 1.................................... I-A.10 i L Table A-6: Combined Element Stress Resultants, Element 5.................................... I-A.11 Table A-7: Combined Element Stress Resultants. Element 8.................................... I-A.12 q Table A-8: Combined Element Stresses, Maximum Ten....... I-A.13 L L LIST OF FIGURES 1 PAGE Figure A-1: PISTAR Piping Mode 1.......................... I-A.2 Figure A-2: Input Response Spectrum, X- and.............. I-A.3 Z-Directions Figure A-3: Input Response Spectrum, Y-Direction... 0 .... I-A.4 i 1 1 ~

l l I-A.1 1 nutech ! i l

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II ;O 1'7' C N [! KW,)'I NOTE : L CIRCLED NUMBERS ARE ELEliENT NUMBERS. ~ l FIGURE A-1 BENCHMARK PROBLEM NO. 1 ' PISTAR PIPING MODEL i. n lay i I-A.2 nutech m

6

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PSD-01-016 i Revision 2 ; f TABLE A-1 f BENCRMARK PROBLEM NO. 1 NATURAL FREQUENCIES T MODE NUMBER PISTAR1 ONRR RESULTS DEVIATION 7. I 1 28.53 28.53 0.00 2 55.76 55.77 0.02 l 1 3 81.49 81.50 0.01 1 4 141.7 141.7 0.00 5 162.8 162.8 0.00 l 1 l L L I i I Natu' cal frequencies are shown on page 16 of the PISTAR computer print-out. The PISTAR computer print-out for this problem is b contained in Appendix A of Volume II. I-A.5 nutech

PSD-01'-016 , , Revision 2-TABLE A-2 BENCHMARK PROBLEM NO. 1 MODAL PARTICIPATION FACTORS MODE DIRECTION PISTAR1 ONRR RESULTS DEVIATION 7. X 0.1753 0.1752 0.06 1 Y 0.02593 0.02593 0.00 Z 0.3308 0.3308 0.00 f X 0.3628 0.3628 0.00 2 Y 0.002081 0.002074 0.34 Z 0.1478 0.1478 0.00 ; 1 X 0.05397 0.05397 0.00 l! 3 Y 0.2582 0.2582 0.00 Z 0.02793 0.02793 0.00 ll ' X 0.08359 0.08361 -0.02 4 Y 0.05267 0.05268 -0.02 Z 0.01176 0.01174 0.17 .. 1 Modal participation factors are shown on page 23 of the PISTAR d computer print-out. The PISTAR computer print-out. for this l_ problem is contained in Appendix A of Volume II. I-A.6 nutech j l

PSD-01-016 Revision 2 f TABLE A-2 (CONCLUDED) i BENCRMARK PROBLEM NO. 1 MODAL PARTICIPATION FACTORS MODE DIRECTION PISTARI ONRR RESULTS DEVIATION % X 0.07925 0.07925 0.00 5 Y 0.06604 , 0.06605 -0.02

Z 0.01114 0.01115 -0.09 e

i . T' t I-I Modal participation factors are shown on page 23 of the PISTARl/h computer print-out. The PISTAR computer print-out for this problem is contained in Appendix A of Volume II. I-A.7 m nutech

PSD-01-016-

Revision 2
TABLE A-3 BENCHMARK PROBLEM NO. 1 COMBINED NODAL DISPLACEMENTS N0DE 21 DISPLACEMENT PISTAR2 ONRR RESULTS DEVIATION 2

COMPONENT (x10 ) 2 (x10 ) y, j

                                                                                   ,I X-TRANSLATION         0.20445            0.20436             0.04               b l

Y-TRANSLATION 0.00021084 0.00021082

    ,                                                           0.01 l

Z-TRANSLATION 0.48656 0.48638 0.04 ' i X-ROTATION 0.015326 0.015322 l 0.03 Y-ROTATION 0.0056019 0.0056005 0.02 Z-ROTATION 0.0062957 0.0062938 n 0.03 1 l l I 1 Refer to Figure A-1 for nodal locations. U 2 Nodal displacements print-out. are shown on page 27 ofthePISTARcomputerIb The PISTAR contained in Appendix A of computer print-out for this problem is Volume II. v I-A.8 I nutech J

PSD-01-016 Revision 2 TABLE A-4 BENCHMARK PROBLEM'NO. 1 { COMBINED NODAL DISPLACEMENTS I NODE 61 l 1 f DISPLACEMENT PISTAR2 2 ONRR RESULTS 2 DEVIATION COMPONENT (x10 ) (x10 ) 7, j I X-TRANSLATION 0.78411 0.78382 0.04

I l 1 Y-TRANSLATION 0.21167 0.21159 0.04 I Z-TRANSLATION 1.0600 1.0597 0.03 4 i X-ROTATION 0.010161 0.010159 0.02 ; Y-ROTATION 0.021054 0.021050 0.02 q Z-ROTATION 0.0024369 0.002436 0.04 L l. 1 Refer to Figure A-1 for nodal locations. 2 Nodal displacements are shown on page 27 ofthePISTARcomputerld print-out. The PISTAR computer print-out for this problem is contained in Appendix A of Volume II.

I-A.9 nutech

57SA$ 71l8i w - ~ l= N , O

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Refer to Figure A-1 for element and nodal locations. 2 Stresnes are shown on page 30 of the PISTAR computer print-out. The PISTAR computer print-out for this problem is contained in lb Appendix A of Volume II. 3 _ Stress calculated per Eq. (9) of Paragraph NC-3652 of the ASME Code (Reference 5) . Pressure and sustained loads are taken as zero. 4

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L !. PSD-01-016 . 1 1 APPENDIX B ' f LIST OF TABLES PAGE -l l- 1 l Table B-1: Natural Frequencies........................... I-B.5 j Table B-2: Modal Participation Factors . . . . . . . . . . . . . . . . . . . I-B. 6 Table B-3: Combined Nodal Displacements, Node 1.......... I-B.8 j Table B-4: Combined Nodal Displacements , Node 6. . . . . . . . . . I-B. 9 ' Table B-5 Combined Nodal Displacements,-Node 12.........I-B.10 , Table B-6 : Combined Element Stress Resultants, Element 1....................................I-B.11 ; Table B-7: Combined Element Stress Resultants, ! E l eme n t 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I- B .1 2 Table B-8: Combined Element Stress Resultants,. Element 14................................... I-B.13 Table B-9: Combined Element Stres ses , Maximum Ten . . . . . . . I-B.14 LIST OF FIGURES PAGE Figure B-1: PISTAR Piping Model.......................... I-B.2 L Figure B-2: Input Respons e Spectrum , X- and . . . . . . . . . . . . . . I-B. 3 Z-Directions _ Figure B-3: Input Response Spectrum, Y-Direction......... I-B.4 i nutech

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f PSD-01-016 TABLE B-1 f BENCHMARK PROBLEM No. 2

       -                            NATURAL FREQUENCIES i

i MODE NUMBER PISTAR1 ONRR RESULTS DEVIATION 7. 1 8.712 8.712 0.00 i I-2 8.806 8.806 0.00 1 3 17.51 17.51 0.00 1 4 40.37 40.37 0.00 5 41.63 41.63 0.00

L l L L L L I Natural frequencies are shown on page 24 of the PISTAR computer print-out. The PISTAR shown in Appendix computer B of Volume II. print-out for this problem is l-B 5 nutech

PSD-01-016 s. TABLE B-2 ~ BENCHMARK PROBLEM No. 2 - MODAL PARTICIPATION FACTORS - MODE DIRECTION PISTAR I ONRR RESULTS DEVIATION 7. X 0.6066 0.6066 0.00 1 Y 0.00 0.00 0.00 Z 0.00 0.00 0.00 X 0.00 0.00 0.00 2 Y 0.00 0.00 0.00 l Z -0.6074 -0.6074 0.00 l X 0.00 0.00 0.00 gi I: 3 Y 0.00 0.00 0.00 , Z 0.00 0.00 0.00

                                                                                                                                                                 ;i X               0.00                                                0.00          0.00 4                                                   Y               0.008728                                            0.008728      0.00 Z               0.00                                                0.00          0.00             ~

I Modal participation factors are shown on page 31 of-the PISTAR computer print-out. The PISTAR computer print-out for this problem is contained in Appendix B of Volume II. I-B.6 nutech 1

{. Pso-01-016 f TABLE B-2 (CONCLUDED)

~~

BENCRMARK PROBLEM No. 2 MODAL PARTICIPATION FACTORS f MODE DIRECTION PISTAR I ONRR RESULTS DEVIATION % f X 0.00 0.00 0.00 i f 5 Y 0.002450 0.002450 0.00 Z 0.00 0.00 0.00' I . I L i 1 4-i t u L I _ Modal participation factors are shown on page 31 of the PISTAR computer print-out. The PISTAR computer print-out for this problem is contained in Appendix B of Volume II. ; I-B.7 nutech 1

PSD-01-016 , , Revision 2 , TABLE B-3 BENCHMARK PROBLEM NO. 2 COMBINED NODAL DISPLACEMENTS NODE 11 o DIGPLACEMENT COMPONENT PISTp)2 (x10 ONRRRgULTS (x10 DEVIgTION Wa f X-TRANSLATION 23.027 23.025 0.01 Y-TRANSLATION 0.092636 0.092622 0.02 Z-TRANSLATION 22.516 22.512 0.02 X-ROTATION 1 0.65401 0.6'5397 0.01 Y-ROTATION 0.00056358 0.00056353 0.01 Z-ROTATION 0.67212 0.67209 0.00 li l; L l

iR l 1 Refer to Figure B-1 for nodal locations. ' 2 Nodal displacements are shown on page.61 of the PISTAR computer print-out. The PISTAR computer print-out for this problem is jg contained in Appendix B of Volume II. -- I-B.8 f nutech [;

PSD-01-016 l Revision 2 l f TABLE B-4 i BENCHMARK PROBLEM NO. 2 COMBINED NODAL DISPLACEMENTS NODE 61 f DISPLACEMENT COMPONENT PISTf)2 (x10 ONRRRgULTS (x10 DEVIgTION X-TRANSLATION 46.191 46.188 0.01 Y-TRANSLATION 0.097832 0.097827 0.01 Z-TRANSLATION 44.630 44.623 0.02 l r X-ROTATION 0.0052933 0.0052930 0.01 g Y-ROTATION 0.00028994 0.00028991 0.01 > i. Z-ROTATION 0.11133 0.11132 0.01 L. t L s 1 Refer to Figure B-1 for nodal locations. i 2 Nodal displacements are shown on page 61.of the PISTAR computer ; print-out. The PISTAR computer print-out for this problem is lj u contained in Appendix B of Volume II. nutech

1 PSD-01-016 .' , Revision 2 TABLE B-5 BENCRMARK PROBLEM NO. 2 COMBINED NODAL DISPLACEMENTS NODE 121 I t DISPLACEMENT il COMPONENT PISTf)2 (x10 ONRRRg1SULTS (x10 DEVIgTION X-TRANSLATION 46.186 46.183 0.01

                                                         ,_                              t-Y-TRANSLATION       0.18270             0.18268            0.01                  1 l     i Z-TRANSLATION      44.630              44.623              0.02 X-ROTATION          0.088571            0.088560           0.01 f

l t' Y-ROTATE 0N C.0011116 0.00111.6 0.00 ,ii Z-ROTATION 0.11133 0.11132 0.01 c t L 1 Refer to Figure B-1 for nodal locations. 2 Nodal displacements print-out. are shown on page 61 of the PISTAR computer contained in The PISTARB ofcomputer print-out for this problem is !j . Appendix Volume II. <! L I-B.10 tititenc:F1 [ i

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N #X4 1 Revision 2 , , TABLE B-9 BENCHMARK PROBLEM NO. 2 COMBINED ELEMENT STRESSES MAXIMUM TEN ELEMENTI NODE 1 STRESS PISTAR2 ,3 ONRR DEVIATION % [ NO. ID INTENSIFICATION RESULTS ( 15 17 1.0 12284.0 N/A 4 N/A 11 16 1.0 12284.0 N/A N/A f 6 18 1.0 12284.0 N/A N/A f 1 15 1.0 12284.0 N/A N/A 14 12 1.0 9590.3 N/A N/A e; [: 2 7 1.0 9590.3 N/A N/A t, 1.0 10 10 9590.3 N/A N/A 5 5 1.0 9590.3 N/A N/A 16 12 1.0 6787.4 N/A N/A b' 7 7 1.0 6787.4 N/A N/A i 1 Refer to Figure B-1 for element and noda'l location. 2 Stresses are shown on page 66 of the PISTAR computer print-out. The PISTAR computer print-out for this problem is contained in g Appendix B of Volume II. 3 Stress calculated per Eq. (9) of Paragraph NC-3652 of the ASME ' Code (Reference 5) . Pressure and sustained loads are taken as zero. ( 4 Not Available. ( i. l I-B.14 nutech !

                                                        -l 1

PSD-01-016 [ APPENDIX C e RESULTS FOR BENCHMARK PROBLEM No. 3 A h.m j m 1 haue k

b a b-I-C.0 a nutech

PSD-01-016 APPENDIX C LIST OF TABLES PAGE Table C-1: Natural Frequencie:....................... I-C.5 I Table C-2: Modal Participation Factors . . . . . . . . . . . . . . . I-C.6 l c Table C-3: Combined Nodal Displacements, Node 3....... I-C.8 , Table C-4: Combined Nodal Displacements, Node 8...... I-C.9 Table C-5: ' Combined Nodal Displacements , Node 13. . . . .I-C.10 Table C-6: Combined Element Stress Resultants, [ i Element 1................................I-C.11 Table C-7: Combined Element Stress Resultants, Element 1 6 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I - C .1 2 : Table C-8: Combined Element Stress Resultants, I i Element 27...............................I-C.13 g Table C-9: Combined Element Stresses, Maximum Ten... I-C.14 8 fi i LIST OF FIGURES PAGE Figure C-1: PISTAR Piping Mode 1................... .. I-C.2 Figure C-2: Input Response Spectrum, X- and.......... I-C.3 Z-Directions tl Figure C-3: Input Response Spectrum, Y-Direction..... I-C.4 i II) 1i k! w: I-C.1 rititeac:t1 j. t< 4

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_ I-C.2 nutech

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J PSD-01-016 TABLE C-1 BENCHMARK PROBLEM NO. 3 NATURAL FREQUENCIES I MODE NUMBER PISTAR I ONRR RESULTS DEVIATION 7. I, 1 1.792 1.793 -0.06 I , 2 1.827 1.828 -0.05 i 3 3.206 3.205 0.03 4 3.363 3 365 0.06 5 3.540 3.539 0.03 6 3.645 3.645 0.00 1 i i I , 2 w I s I Natural frequencies are shown on page 26 of the PISTAR computer print-out. The PISTAR computer print-out for this problem is ' shown in Appendix C of Volume II. , I-C.5 l nutech 1 L;

c l PSD-01-016

TABLE C-2 BENCHMARK PROBLEM NO. 3 j- MODAL PARTICIPATION FACTORS h

[ MODE DIRECTION PISTAR l ONRR RESULTS DEVIATION % i X 0.00 0.00 0.00 1

         ,           1           Y         0.00             0.00             0.00 I'

Z 0.8943 0'.8960 -0.19 X 0.8978 0.8997 0.21 1' I 2 Y 0.00 0.00 0.00 Z 0.00 0.00 0.00-l X 1.395 1.407 -0.85 L 3 Y 0.00 0.00 0.00 s Z 0.00 0.00 0.00 i X 0.00 0.00 0.00 4 Y 0.05324 0.05415 -1,68 Z 0.00 0.00 0.00 I Modal participation factors are shown on page 40 of the PISTAR computer print-out. The PISTAR computer print-out for this problem is contained in Appendix C of Volume II. I-C.6 rititenc:li L -

I PSD-01-016 i TABLE C-2 (CONCLUDED) i BENCRMARK PROBLEM No. 3 f MODAL PARTICIPATION FACTORS , i MODE DIRECTION PISTAR I ONRR RESULTS. DEVIATION 7. f X 0.00 0.00 0.00 5 Y 0.00 0.00 0.00 L Z 1.289 1.299 -0.77 i X 0.00 0.00 0.00 6 Y 0.00 0.00 0.00 Z 0.00 0.00 0.00 i i. i l g l: 1 I w , I Modal participation factors are shown on page 40 of the PISTAR ' computer print-out. The PISTAR computer print-out for this ,: problem is contained in Appendix C of Volume II. I-C.7 nutech t s

PSD-01-016 i Revision 2 TABLE C-3 BENCHMARK PROBLEM NO. 3 ! COMBINED NODAL DISPLACEMENTS NODE 31 l DISPLACEMENT COMPONENT PISTp)2 (x10 ONRRR{SULTS (x10 > DEVIgTION , 1 l X-TRANSLATION 11.550 11.688 -1.18

    .-                                                                                                            J l                Y-TRANSLATION     0.24408            0.24574           -0.68 Z-TRANSLATION    10.740             10.882                                                    f f                                                                        -1.30                                 1 1

X-ROTATION ( E 0.47363 0.47997 -1.32 y

Y-ROTATION 0.044984 0.045533 -1.21 ' t Z-ROTATION 0.56555 0.57205 -1.14 L - i 1 1 i l L l l l

                                                                                                                    )
                                                                                                                   '1 1

Refer to Figure C-1 for nodal locations. 2

~                  Nodal displacements are shown on page 79 of the PISTAR computer print-out.

The PISTAR computer print-out for this problem is k contained in Appendix C of Volume II. I-C.8 nutech

p PSD-01-016 Revision 2 TABLE C-4 BENCHMARK PROBLEM NO. 3 o COMBINED NODAL DISPLACEMENTS NODE 81 i II; DISPLACEMENT COMPONENT PISTp)2 (x10 ONRRRgyULTS (x10 DEVIp* TION [ X-TRANSLATION 20.224 20.455 1.13 4 Y-TRANSLATION 0.083850 0.083804~ 0. 0 5 I l Z-TRANSLATION 16.270 16.492 -1.35 f

                                                                            .m X-ROTATION        0.30597            0.30079         1.72               ai 1

1:l Y-ROTATION 0.00 0.00 0.00 Z-ROTATION 0.15874 I 0.15524 2.25 1 p li 1 RI i 1 Refer to Figure C-1 for nodal locations. ' 2 Nodal displacements are shown on page 78 of the PISTAR computer print-out. di The PISTAR computer print-out for this problem is " contained in Appendix C of Volume II. I-C.9 nutech ,

             .                                                              L$

PSD-01-016 Revision 2 TABLE C-5 BENCHMARK PROBLEM NO. 3 ' COMBINED NODAL DISPLACEMENTS NODE 131 DISPLACEMENT PIST 2 ONRR R ULTS DEVI TION COMPONENT (x10 (x10 X-TRANSLATION 342.99 343.35 -0.10 Y-TRANSLATION 0.083918 0.083872 0.05 Z-TRANSLATION 355.12 355.30 -0.05 , L I X-ROTATION 5.9686 5.9744 -0.10 Y-ROTATION 0.00 0.00 0.00 I w Z-ROTATION 5.8297 5.8380 -0.14-l l i l l - i.

I Refer to Figure C-1 for nodal locations. 2 Nodal displacements are shown on page 78 of the PISTAR computer Jh print-out. The PISTAR computer print-out for this problem is contained in Appendix C of Volume II. _ I-C.10 nutech

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PSD-01-016 Revision 2

TABLE C-9 BENCHMARK PROBLEM No. 3 COMBINED ELEMENT STRESSES MAXIMUM TEN

ELEMENTI NODE 1 STRESS PISTAR2 ,3 ONRR DEVIATION 7. NO. ID INTENSIFICATION RESULTS

16 8 1.0 58106. N/A4 N/A 31 10 1.0 49494. N/A N/A f 14 6 1.0 49494. I?/A N/A 15 8 1.0 29279. N/A N/A 17 8 29278. 1.0 N/A N/A b f 15 8B 1.0 29156. N/A N/A 17 8A 1.0 29154. N/A N/A 13 6 1.0 22714. N/A N/A u l 30 10 1.0 22714. N/A N/A l L l 26 10 1.0 20751. i N/A N/A I 1 Refer to Figure C-1 for element and nodal location. 2 stresses are shown on page 84 of the PISTAR computer print-out. g The PISTAR computer print-out for this problem is contained in j Appendix C of Volume II. 3 Stress calculated per Eq. (9) of Paragraph NC-3652 of the ASME Code (Reference 5). Pressure and sustained loads are taken as zero.. 0 Not available I-C.14 nutech

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                                                                                                                      -1 PSD-01-016            7}

3

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APPENDIX D s n! t RESULTS FOR '

             T BENCHMARK PROBLEM NO. 323A                                .lI i
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PSD-01-016 APPENDIX D l LIST OF TABLES PAGE Table D-1: Natural Frequencies........................... I-D.4 f Table D-2 : Modal Participation Factors................... I-D.7 l Table D-3: Combined Nodal Displacements , Node 6. . . . . . . . . I-D.15 Table D-4 : { Table D-5: Combined Nodal Displacements , Node 23. . . . . . . . I-D.16 Combined Nodal Displacements , Node 34. . . . . . . . .I-D.17 c i Table D-6: Combined Element Stress Resultants, i Element 1.....................................I-D.18 Table D-7 : Combined Elemen? Stress Resultants, j Element 11...................................I-D.19 Table D-8 : Combined Element Stress Resultants, Element 33................................... I-D.20 Table-D-9: Combined Element Stress Resultants, Element 40................................... I-D.21 Table D-10: Combined Element Stresses , Maximum Ten. . . . . . . I-D.22 l LIST OF FIGURES 1. PAGE l Figurc D-1: PISTAR Piping Model.......................... I-D.2 Figure D-2: Input Response Spectrum, X , Y , and Z-Directions............................. I-D.3 ! ~ w 4 b I-D.1 nutech 9

4 e PSD-01-016 AY f I 4 d

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                                         $                                                                      NOTE:

CIRCLED !!U!iDERS ARE ELEMENT NUMBERS. l J

i l, FIGURE D-1 k u BENCHMARK PROBLEM NO. 323A

                                                                                                                                                          \
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PISTAR PIPING MODEL 6

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I-D.2 nutech i l t

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PSD-01-016 TABLE D-1 g BENCHMARK PROBLEM NO. 323A U NATURAL FREQUENCIES MODE NUMBER PISTAR I ONRR RESULTS DEVIATION 7. i 0 1 6.391 6.391 0.00 2 9.993 9.993 0.00 3 13.27 13.27 0.00 4 14.48 14.49 0.07 5 15.33 15.33 0.00 t i 6 17.50 17.50 0.00 , t 7 19.09 19.09 0.00 8 19.62 19.62 0.00 s [. 9 21.44 21.44 0.00 L

                                                                                                                      'B-10      28.71                                               28.71         0.00 I'

I , 1

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I Natural frequencies are shown on pages 31 and 32 of the PISTAR , computer print-out. The PISTAR computer print-out for this ' problem is shown in Appendix D of Volume II. 4;i t u nutech t

1 PSD-01-016 l TABLE D-1 (CONTINUED) BENCHMARK PROBLEM NO. 323A NATURAL FREQUENCIES l 1 _ MODE NW4BER PISTAR I ONRR RESULTS DEVIATION % 11 29.87 29.86 0.03 l 12 31.49 31.48 0.03 13 32.01 32.01 0.00

   !                   14           36.37           36.37             0.00         q l

15 40.98 40.98 0.00 i 16 41.37 41.37 0.00 l 17 47.39 47.39 0.00

18 49.77 49.77 0.00'

 '-                                                                                 j 19           50.13           50.13             0.00
'-                    20            52.93           52.93             0.00 l

l l I Natural frequencies are shown on pages 31 and 32 of the PISTAR computer print-out. The PISTAR computer print-out for this problem is shown in Appendix D of Volume II. I-D.5 j nutech 3

PSD-01-016 TABLE D-1'(CONCLUDED) j BENCHMARK PROBLEM NO. 323A l NATURAL FREQUENCIES MODE NUMBER PISTAR I ONRR RESULTS DEVIATION 7.

                                                                          .I 21             56.90            56.90             0.00 22            58.51            58.51             0,00 li 23            67.47            67.47             0.00 24            70.46            70.46              0.00                 .

25 75.41 75.41 0.00 - l 26 79.18 79.18 0.00 j 27 80.74 80.74 0.00 ' 28' 86.10 86.11 0.01 . 29 88.28 88.28 0.00- b 30 92.74 92.74 0.00 31 99.36 99.36 0.00 l Natural frequencies are shown on page 31 and 32 of the PISTAR i computer print-out. The PISTAR computer print-out for this problem is shown in Appendix D of Volume II. I-D.6 nutech

PSD-01-016 i l TABLE D-2 BENCHMARK PROBLEM NO. 323A l MODAL PARTICIPATION FACTORS I_ l

MODE DIRECTION PISTAR I ONRR RESULTS DEVIATION 7. X 0.6082 0.6081 0.02 3 l l 1 Y 5.977 5.977 0.00 ) Z 0.1234 0.1234 0.00 X 5.761 5.761 0.00 2 Y 0.1995 0.1995 0.00 Z 2.996 2.996 0.00 X 0.5596 0.5583 0.23 3 Y 3.153 3.156 -0.10 Z 1.950 1.951 -0.05 X . 2.037 2.036 0.05 4 Y 0.09965 0.09930 0.35 Z 3.540 3.540 0.00 I Modal participation factors are shown on pages 127 through 129 of the PISTAR computer print-out. The PISTAR computer print-out for this problem is contained in Appendix D of Volume II. I-D.7 L

a D PSD-01-016 Revision 1. TABLE D-2 (CONTINUED) BENCHMARK PROBLEM NO. 323A MODAL PARTICIPATION FACTORS 1 MODE DIRECTION PISTARI ONRR RESULTS DEVIATION 7. ' X 3.312 3.312 0.00 5 Y 0.0008028 0.0004261 88. (.006)2 g' Z 7.389 7.389 0.00' X 4.789 4.790 0.02 6 Y 3.025 3.024 0.03 Z 2.999 2.998 0.03 1, X 3.711 3.71 2 -0.03 7 Y 0.1286 1 0.1287 -0.08 Z 3.637 3.637 0.00 X 1.375 1.375 0.00 8 Y 0.01999 0.02015 -0.79 Z 0.3466 0.3465 0.03 E' I ofModal participation the PISTAR factors computer are shown on pages 127 through 129 print-out. for this problem is contained in Appendix D of Volume II.The PISTAR computer 2 The deviation maximum when computed by normalizing this value to the participatio- - parenthesis. factor in that direction shown in - 4 I I-D.8 nutech

I 1 PSD-01-016 j

TABLE D-2 (CONTINUED) BENCHMARK PROBLEM NO. 323A MODAL PARTICIPATION FACTORS PISTAR I

MODE DIRECTION ONRR RESULTS DEVIATION % l 7 X 5.872 5.872 0.00 9 Y 1.796 1.797 -0.06 I 1; j Z 4.261 4.262 0.02 1 X 0.5583 0.5580 0.05 10 Y 0.4289 0.4298 -0.21 j Z 2.992 2.992 0.00 I l X 0.1568 0.1568 0.00 11 Y 6.778 6.780 -0.03 Z .8905 0.8920 0.17 X 0.950 0.9426 0.79 12 Y 0.8976 0.8841 1.53 1.069 Z 1.059 0.94 I Modal participation factors are shown on pages 127 through 129 of the PISTAR computer print-out. The PISTAR computer print-out for this problem is contained in Appendix D of Volume II. I-D.9 [1(jt()()() u

PSD-01-016 Revision 1 TABLE D-2 (CONTINUED) BENCHMARK-PROBLEM No. 323A MODAL PARTICIPATION FACTORS { 1 l MODE DIRECTION PISTARI ONRR RESULTS DEVIATION 7. b X 1.045 1.052 0.67 [ 13 Y .1349 0.1175 14.80 (0.26)2 g' Z 1.527 1.533 -0.39 l l X 1.944 1.943 0.05 14 Y 0.1117 0.1115 0.18 ; Z 1.565 1.564 0.06 l X 3.199 3.199 l 0.0 1 15 Y 1.092 1.091 0.09 Z 1.981 1.981 0.00 X 0.002586 0.004581 -44. (0.0)2 16 Y 0.6152 0.61 78 0.42 - Z 0.003690 0.0007525 390. (0.0)2 ; I ofModal participation the PISTAR factors computer are shown on pages 127 through 129 print-out. The PISTAR computer print-out for this problem is contained in Appendix D of Volume II. 2 The deviation when computed by normalizing this value to the maximum participation factor in that direction is shown in A parenthesis. Q1

I-D.10 nutech 4 i

)._

PSD-01-016 Revision 1 TABLE D-2 (CONTINUED) BENCHMARK PROBLEM NO. 323A MODAL PARTICIPATION FACTORS MODE DIRECTION PISTARI ONRR RESULTS DEVIATION 7. I X 0.7425 0.7430 -0.07 17 Y 1. 711 1. 711 0.00 1'

    ;                        Z        1.777           1.777           0.00 i

X 1.393 1. 3 91 0.14 18 Y 4.444 4.445 L 0.02-Z 0.3828 0.3822 0.16 X 1.403 1.40'5 0.14 L 19 Y 2.162 2.158 6') Z 0.1577 0.1577 0.00 X 0.002557 0.002703 5.40 (0.0)2 M 20 Y 0.5129 0.51'16 0.25 Z 1.092 1.092 0.00 I Modal participation factors are shown on pages 127 through 129 of the PISTAR computer print-out. The PISTAR computer print-out for this problem is contained in Appendix D of Volume II. 2 The deviation when computed by normalizing this value to the maximum parenthesis. participation factor in that direction is shown in g 1-D.11 nu ech

PSD-01-016 TABLE D-2 (CONTINUED) BENCHMARK PROBLEM NO. 323A MODAL' PARTICIPATION FACTORS I MODE DIRECTION I PISTAR 'ONRR RESULTS DEVIATION % X 0.8630 0.8638 -0.09' ! 21 Y 2.134 2.137 -0.14 Z 0.3519 0.3519 0.00 X 0.1731 0.1718 0.76 q 22 Y 2.132 2.128 0.19 , Z 0.09070 0.09082 -0.13 X 0.6175 0.6176 -0.02

             ,            i 23           Y         0.7950         0.7944        0.08 l-Z         1.388          1.388         0.00 X         0.5036         0.5035        0.02 24           Y         0.3016         0.3020      -0.13              -

i Z 0.06632 0.06644 -0.18 i I Modal participation factors are shown on pages 127 through 129 of the PISTAR computer print-out. The PISTAR computer print-out ,.. for this problem is contained in Appendix D of Volume II. I-D.12 nutech I I-

l PSD-01-016 , l TABLE D-2 (CONTINUED) BENCHMARK PROBLEM NO. 323A

MODAL PARTICIPATION FACTORS e- > l MODE DIRECTION PISTAR I ONRR RESULTS DEVIATION % X 0.4891 0.4893 -0.04 r 25 Y 0.1005 0.1008 -0.30 L

  ,                          Z        0.2771         0.2774         -0.11 t

X 0.8695 0.8700 -0.06 1 l 26 Y 1.095 1.094 0.09 Z 0.8925 0.891s' O.07 X 0.9506 0.9497 0.09 27 Y 0.1144 0.1141 0.26 h Z 0.6465 0.6471 -0.09 X 0.7150 0.7154 -0.06 28 Y 0.2179 0.2176 0.14 Z 0.9144 0.9148 -0.04 i I Modal participation factors are shown on pages 127 through 129 of the PISTAR computer print-out. The PISTAR computer print-out for this problem is contained in Appendix D of Volume II. I-D.13 IllitEB( Il e

PSD-01-016 TABLE D-2 (CONCLUDED) / BENCHMARK' PROBLEM No. 323A- }; MODAL PARTICIPATION FACTORS- ! l ! i. MODE- DIRECTION PISTARI ONRR RESULTS DEVIATION 7. i X 1.405 1.405 0.00 29 1 Y 1.393 1.393 0.00 Z 0.6966 0.6969 -0.04 X 0.4062 ~0.4065 -0.07 30 Y 0.3429 0.3429 0.00 i Z 0.2215 0.2216 -0.05 <, i X 0.7983 0.7980 0.04 31 Y 0.1626 0.1621 0.31- ; Z 0.02885 0.02862 0.80 l IB I I i Modal participation factors' are shown on pages 127 thr'ough 129 of the PISTAR computer print-out. The PISTAR computer print-out . '! for this problem is contained in Appendix D of Volume II. l l I-D.14 nutech I

                                                                         ,1 Li l

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PSD-01-016

      .-.                                                           Revision 2                        .
    <                                                                                              -1

{ ( TABLE D-3 BENCHMARK PROBLEM No. 323A i

                                                                                                     'l COMBINED NODAL DISPLACEMENTS h                                           NODE 61 DISPLACEMENT-       PIST   2 ONRR R   ULTS   DEVI TION COMPONENT         (x10              (x10

{ X-TRANSLATION 0.97820 0.97812 0.01 l Y-TRANSLATION 0.20522 0.20565 -0.21 f Z-TRANSLATION 0.92643 0.92659 -0.02 X-ROTATION 0.00087673 0.00087859 -0.21 1 Y-ROTATION 0.0055876 0.0055902 -0.05 lu Z-ROTATION 0.00050637 0.00050687 -0.10

L L 4 I Refer to Figure D-1 for nodal locations. 2 Nodal displacements are shown on page 133 of the PISTAR computer print-out. The PISTAR computer print-out for this problem is g contained in Appendix D of Volume II. I-D.15 4

PSD-01-016 ' Revision 2 i TABLE D-4 BENCHMARK PROBLEM No. 323A l COMBINED NODAL DISPLACEMENTS NODE 231 1 DISPLACEMENT COMPONENT PISTp)2 (x10 ONRRRgSULTS (x10 > DEVIgTION E l X-TRANSLATION 0.57367 0.57370 -0.01 l Y-TRANSLATION 0.43994 0.43965 0.07 Z-TRANSLATION 0.38633 0.38634 0.00 1 X-ROTATION 0.0011924 0.0011919 0.04 Y-ROTATION 0.0016021 1 0.0016018- 0.02 Z-ROTATION 0.0023855 0.0023846 0.04 Il ' l' 11 1 i. i 1 Refer to Figure D-1 for nodal locations. 2 Nodal displacements are shown on page 134 of the PISTAR computer 8' print-out. The PISTAR computer print-out for this problem is contained in Appendix D of Volume II. 1-D.16 nutech l

PSD-01-016 Revision'2' 1 i 1

TABLE D-5" u BENCHMARK PROBLEM NO. 323A COMBINED NODAL DISPLACEMENTS l- NODE 341 I DISPLACEMENT i COMPONENT PISTp)2 (x10 ONRRR{SULTS (x10 >- DEVIgTION ! X-TRANSLATION 1.6649 1.6649 0.00 L Y-TRANSLATION 6.1942 6.1937 0 01 Z-TRANSLATION 0.48346 0.48328 0.04 1 X-ROTATION 0.031807 0.031805 0.01 L 3 Y-ROTATION 0.0085753 0.0085750 - 0.00 L Z-ROTATION 0.0024491 0.0024481 0.04 k t 1 l 1 l i 1 Refer to Figure D-1 for nodal locations. 2 Nodal displacements are shown on page 134 of the PISTAR computer Jh ) print-out. The PISTAR computer print-out for this problem is contained in Appendix D of Volume II. I-D.17 nutech

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                                                                                                                                              .......--____y PSD-01-016 Revision 2 J
                                                                                                                                                                   .l TABLE D                                                                                                                                                                           l BENCHMARK PROBLEM No. 323A                                                         h COMBINED ELEMENT STRESSES MAXIMUM TEN                                                    -

k ELEMENTI NODEI STRESS PISTAR2 ,3 ONRR DEVIATION 7. l NO. ID INTENSIFICATION RESULTS - 39 40 3.0 751.12 N/A4 N/A 29 30 1.0 734.98 N/A N/A i 30 '30 1.0 734.98- N/A N/A 1 30 31 1.0 571.74 -N/A N/A 1

                                                                                                                                                                -fd 31                                                     1.0 31                                                        571.74            N/A          N/A                  f I'

28 29 1.0 534.55 N/A N/A 29 29 1.0 534.55 N/A N/A 39 39 3.0 463.64 N/A N/A .I l 31 32 1.0 409.45 N/A N/A 32 32 1.0 409.45 N/A N/A < 1 Refer to Figure D-1 for element and nodal location. 2 Stresses are shown on page 142 of the PISTAR computer print-out. 8 is The PISTAR computer print-out for this problem is contained in Appendix D of Volume II. c, 3 Stress calculated per Eq. (9) of Paragraph NC-3652 of the ASME - " Code (Reference 5). Pressure and sustained loads are taken as zero. O Not available I-D.22

nutech ' i 1 c

i-

             -O< '.'%.

PSD-01-01'6 Revision'1 M f APPENDIX E RESULTS FOR BENCHMARK PROBLEM.NO. 4

     'i iL
                                                                     ]

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                                                             .nutech

c ( PSD-01-016 Revision 1 , I

                                                                                                                            't APPENDIX E i

I LIST'OF TABLES l PAGE Table E-1: Natural Frequencies........................... I-E.5 ~ C Table E-2: Modal Participation Factors . . . . . . . . . . . . . . . . . . . I-E. 8 Table E-3: Combined-Nodal Displacements, Node 9......... I-E.16 u Table E-4: Combined Nodal Displacements, Node 19........ I-E.17 Table E-5: Combined Nodal Displacements, Node 48. . . . . . . . .I-E.18 h Table E-6: Combined Element Stress. Resultants, il J i E l em e n t 6 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . - I - E .1 9 Table E-7: Combined Element Stress Resultants, j Element 37................................... I-E.20 -g l Table E-8: Combined Element Stress Resultants, c Element 43................................... I-E.21 l Table E-9: Combined Element Stresses,' Maximum Ten....... I-E.22 f LIST OF FIGURES PAGE Figure E-1: PISTAR Piping Mode 1.......................... I-E.2 F1gure E-2: Input Response Spectrum, X- and.............. I-E.3 h Z-Directions i Figure E-3: Input Response Spectrum, Y-Direction......... I-F.4 w f.}}

ML20215B465: Difference between revisions

Latest revision as of 10:12, 13 May 2021

Contents

Text

SUBJECT:

1.0 INTRODUCTION

14.0 REFERENCES

14.0 REFERENCES

SUBJECT:

2.0 INTRODUCTION

SUMMARY

5.0 REFERENCES

1.0 INTRODUCTION

1.0 INTRODUCTION

1.0 INTRODUCTION

SUMMARY

5.0 REFERENCES

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