ML13004A052

Units 1 and 2, Updated Final Safety Analysis Report, Revision 14, Appendix D - Computer Programs

ML13004A052
Person / Time
Site:	Byron, Braidwood
Issue date:	12/14/2012
From:	Exelon Generation Co
To:	Office of Nuclear Material Safety and Safeguards, Office of Nuclear Reactor Regulation
References
RS-12-221
Download: ML13004A052 (187)

Text

B/B-UFSAR D.0-i REVISION 7 - DECEMBER 1998 APPENDIX D - COMPUTER PROGRAMS TABLE OF CONTENTS

PAGE D.0 COMPUTER PROGRAMS D.0-1 D.1 CBEAM D.1-1

D.2 CONCRETE D.2-1 D.3 DYNAS D.3-1 D.4 DYNAX D.4-1

D.5 LAFD D.5-1 D.6 SIMULATE D.6-1 D.7 PCAUC D.7-1 D.8 PIPING ANALYSIS PROGRAMS D.8-1 D.9 PLFEM II D.9-1 D.10 RSG D.10-1

D.11 SEISHANG D.11-1 D.12 SHAKE D.12-1 D.13 SLOPE D.13-1 D.14 SLSAP1 D.14-1

D.15.1 SLSAP-IV D.15-1 D.15.2 SAP90 D.15-4 D.16 SOR-III D.16-1

D.17 STAND D.17-1 D.18 STRUDL-II D.18-1 D.19 TEMCO D.19-1 D.20 PENAN D.20-1

D.21 SEEPAGE D.21-1

B/B-UFSAR D.0-ii REVISION 7 - DECEMBER 1998 TABLE OF CONTENTS, (Cont'd)

PAGE D.22 COLID D.22-1 D.23 COMPONENT ANALYSIS PROGRAMS D.23-1 D.24 MISLODS D.24-1

D.25 BSAP D.25-1 D.26 BWSPAN/BWSCAN D.26-1 D.27 BWSPEC D.27-1

D.28 RESPECT D.28-1 D.29 ATHOSBWI D.29-1 D.30 EasyFIV D.30-1 D.31 CIRC D.31-1

D.32 CRAFT2 D.32-1 D.33 COMPAR2 D.33-1

D.34 REFERENCES D.34-1

B/B-UFSAR D.0-iii APPENDIX D - COMPUTER PROGRAMS LIST OF TABLES

NUMBER TITLE PAGE D-1 Span 1 Character istics and Design Results D.T-1 D-2 Span 2 Character istics and Design Results D.T-2 D-3 Span 3 Character istics and Design Results D.T-3 D-4 Results for 28-Day Strength D.T-4 D-5 Structural Frequencies D.T-5 D-6 Probable Maximum Story Displacements D.T-6 D-7 Absolute Maximum Story Shears D.T-7 D-8 Probable Maximum Story Shears D.T-8 D-9 Natural Periods for the Eight Lowest Flexural Modes D.T-9 D-10 Computer Output Displacements D.T-10 D-11 Computer Output Anchor Forces D.T-11 D-12 Comparison of P 2 Values from MISLODS and SEMANDERES D.T-12 D-13 Comparison of Mo ments for Selected Members D.T-13 D-14 Summary of Load Sets at Girth Butt Weld with Change in Material and Wall Thickness D.T-14 D-15 Six Highest Values of Stress Intensity, Girth Butt Weld with Change in Material and Wall Thickness D.T-15 D-16 Summary of Calcu lations of Cumulative Usage Factor, Gi rth Butt Weld with Change in Material and Wall Thickness D.T-16 D-17 Modal Frequencies D.T-17 D-18 Allowable Shea r, Moment and Span of Cable Tray D.T-18 D-19 Response of the Ceiling-Mounted Support D.T-19 D-20 Response of the Wall-Mounted Support D.T-20 D-21 Interaction Coeffici ents of the Ceiling- Mounted Support D.T-21 D-22 Applied Loads for SLSAP Pipe Network D.T-22 D-23 Force Equilibrium Reactions D.T-23 D-24 Periods of Plane Frame D.T-24 D-25 Comparison of Mo ment (SLSAPIV and PIPDYN) D.T-25 D-26 Cantilever Beam Analysis - Natural Periods for the Eight Lowest Flexural Modes D.T-26 D-27 Cylindrical Tube Analysis - Selected Natural Periods D.T-27

B/B-UFSAR D.0-iv LIST OF TABL ES (Cont'd)

NUMBER TITLE PAGE D-28 Rolled Beam Design Problem D.T-28 D-29 Composite Beam Design Problem D.T-29 D-30 Column Design Problem D.T-30 D-31 Plate Girder Design Problem D.T-31 D-32 Section and Material Properties D.T-32 D-33 Results of TEMCO Problems D.T-33 D-34 Input for Tensile Force and Biaxial Bending Problem D.T-34 D-35 Results from T ensile Force and Biaxial Bending Problem D.T-35 D-36 Parameters for COLID Rectangular Section Stress Factor Example D.T-36 D-37 Comparison of COLID Results and Hand Calculations for Rectangular Section Stress Factor Example D.T-37 D-38 Parameters for COLID Rectangular Section Ultimate Capacity and ACI Ultimate Capacity Options D.T-38 D-39 Comparison of COLID Results and Hand Calculations for Rectangular Section Ultimate Capacity and ACI Ultimate Capacity Options D.T-39 D-40 Parameters for C OLID Solid Circular Column Test D.T-40 D-41 Comparison of COLID Results and Hand Calculations for Solid Circular Column D.T-41 D-42 Parameters for C OLID Hollow Circular Column Example D.T-42 D-43 Comparison of COLID Results and Hand Calculations f or Hollow Circular Column D.T-43 D-44 Comparison of COLID Results for Metric and British Units D.T-44 D-45 Allowable Slenderness Ratios D.T-45

B/B-UFSAR D.0-v APPENDIX D - COMPUTER PROGRAMS LIST OF FIGURES

NUMBER TITLE D-1 Three-Story Shear Building D-2 Response History Analy sis of Cantilever Beam for DYNAS Program D-3 Cantilever Response D-4 Shallow Spherical Shell D-5 Axial Displace ment Shallow S pherical Shell D-6 Meridional Moment Sh allow Spherical Shell D-7 Finite Element Ideal ization of Thick-Walled Cylinder D-8 Stresses and Displac ements in Thick-Walled Cylinders D-9 Cylinder Under Harmonic Loads D-10 Meridional Mom ents and Deflectio ns of Cylinder - N=0 and N=2 D-11 Meridional Mom ents and Deflectio ns of Cylinder - N=5 and N=20 D-12 Suddenly Applied Ring Line Load D-13 Radial Displ acement vs. Time D-14 Bending Moment v

s. Time - Sudden ly Applied Ring (Line) Load D-15 Spherical Cap D-16 Axial Displacement of Sp herical Cap Under Dynamic Load D-17 Meridional Tension of Spherical Cap Under Dynamic Load D-18 Hyperbolic Cooling Tower D-19 Spectrum of De sign Earthquake D-20 Cooling Tower Meridional Force D-21 Idealized Model of A nchor-Panel System Used in LAFD Validation Problem D-22 Design of Tied Colum n - Compression Controls D-23 Design of Tied C olumn - Tension Controls D-24 Design of Tied C olumn - Biaxial Bending D-25 Example Frame for PIPSYS Static Analysis D-26 Piping System for Combined Stress Analysis (PIPSYS) D-27 Structural Model of Pi ping System (PIPSYS) D-28 Load Time History (PIPSYS) D-29 Force vs. Ti me Joint 8 Z Dir ection (PIPSYS) D-30 Rectangular Tank Filled with Water D-31 Moment of M y at Horizontal Cro ss Section of Walls D-32 Moment M y at Top of Wall D-33 Moment M x Along Cross Se ction of Long Wall D-34 Plate With Circular Hole Under U niform Tension D-35 Stresses in Plate With C ircular Hole U nder Uniform Tension B/B-UFSAR D.0-vi LIST OF FIGU RES (Cont'd)

NUMBER TITLE D-36 Square Plate W ith Rectangular Ho le Subjected to Temperature Variation D-37 Moments in Plate Due to Temperature Variation D-38 Validation for a One-Degree-of-F reedom Damped System (RSG)

D-39 Cable Tray Model for SEISHANG Program D-40 Ceiling Mounted Support Model for SE ISHANG Program D-41 Wall Mounted Support Model f or SEISHANG Program D-42 Soil Profile and Layered Representation Used for Sample Problem D-43 Comparison of Shear St resses and Accelerations D-44 Comparison of Spectral Values for Surface Motions D-45 Circular Plate on a Ri gid Foundation for SLSAP and NOBEC D-46 Comparison of Displace ment and M oment Variation of Circular Plate from SLSAP and NOBEC D-47 Model of Pipe Network for SLSAP and SAPIV (SLSAP Validation Problem 1) D-48 Comparison of Surfac e Stresses in a Clamped Spherical Shell Under Ex ternal Pressure for SLSAP and SAPIV (SLSAP Validation Problem 2) D-49 Model of Plane Frame for SLSAP and SAPIV (SLSAP Validation Problem 3) D-50 Model of Pipe Assembla ge for SLSAP and SAPIV (SLSAP Validation Problem 4) D-51 Bending Moments in a Cantilever Beam D-52 Bending Moments in a Simply Supported Plate D-53 Model for Response History Analysis for SLSAP and SAPIV (SLSAP Validation Problem 7) D-54 Comparison of SL SAP and SAPIV Transverse Deflections of the Can tilever Beam (SLSAP Validation Problem 7) D-55 Comparison of SLSAP and SAPIV Be nding Moments of the Cantilever Beam (SLSAP Validation Problem 7) D-56 Cylindrical Tube and L oad History for SLSAP and SAPIV Mode Super position and Direct Integration Analyses (SL SAP Validation Problem 8) D-57 Displacement Compari son of SLSAP Mode Super- position and Reference 39 for the Cylindrical Tube (SLSAP Validation Problem 8) D-58 Displacement Com parison of SLSAP Dir ect Integration and Reference 39 for the Cylindr ical Tube (SLSAP Validation Problem 8) D-59 Circular Plate for SOR-III Example D-60 Moment Comparison of SABOR-III and SOR-III

B/B-UFSAR D.0-vii LIST OF FIGU RES (Cont'd)

NUMBER TITLE D-61 Radial Shear C omparison for SABOR-II I and SOR-III D-62 Shear and Moment Diagrams D-63 Plane Flow Problem with Finite Element Mesh D-64 Comparison of Free Surfa ces Obtained from SEEPAGE and Analytical Method D-65 Finite Element M esh for Axisymmetric Flow Problem D-66 COLID Rectangular Sect ion Parameters and Sign Convention D-67 COLID Interaction Diagram for Rectangular Section Stress Factor Problem

B/B-UFSAR D.0-1 APPENDIX D COMPUTER PROGRAMS

The computer programs referred to in Sec tions 2.5, 3.7, 3.8, 3.9, and 3.10, Attachment C.A of Appendix C, by their acronyms are described herein.

All programs are verified within the stated assumptions and limitations, for correctness of utilized theory and validity of obtained results for a variety of typical problems. Res ults are check ed against known solutions, solutions obtained f rom other programs, or hand calculations.

Examples of validation p roblems are included with the program descriptions. Whene ver applicable, inte rnal checks such as equilibrium and orthogon ality checks are inclu ded as an aid in checking the validit y of the results.

B/B-UFSAR D.1-1 D.1 CBEAM CBEAM (Reinforced Concre te Beam Design and S chedule) is written to perform the routi ne work of reinforce ment selection for rectangular cross section beams.

The program is based on the design methods of the ACI 318-71 Code and Sargent & Lundy's structural design standards.

In CBEAM, all beam sections are assumed to be rectangular sections. For stirrup reinforcement, each beam is divided into three portions: left 1/4 length, middle 1/2 length, and right 1/4 length. The program assumes that constant shear forces are applied within each regi on. Design forces (bending moments and shear forces) for continuous f rames should be obtained from analysis programs such as STRUDL.

Design forces for individual members should be obta ined by any acce ptable analytical procedure.

Required input data in cludes identificat ion titles, dimensions of the member se ctions and design me mber forces. Output includes a beam schedule suitable for direct release for construction use and a l ongitudinal bar schedule.

To demonstrate the v alidity of CBEAM, a typi cal three span beam design was proce ssed on CBEAM and the results compar ed to hand calculations.

Tables D-1 through D

-3 show the beam cha racteristics and the resulting output for the three b eams. As shown, the results compare very favorably.

B/B-UFSAR D.2-1 D.2 CONCRETE CONCRETE is a computer program used for stat istical evaluation of concrete strength.

It sorts and anal yzes the field data collected on concrete samples and presents it in a convenient form for interpretation.

CONCRETE was developed and is maintained by Sargent & Lundy.

Since 1972 the p rogram has been used at Sargent

& Lundy on UNIVAC 1100 hardware ope rating under EXEC 8.

The compressive strength test results of concr ete cylinders are statistically analyzed to obtain the mean, standard deviation, coefficient of variation, moving averages, a nd other statistical parameters required in the quality app raisal of concrete according to ACI 214-65. The strength results a re also compared with the quality control limits fixe d according to t he ACI 318-71 Code and the ASTM Manual on Qual ity Control of Mater ials, 15-C.

Any violations or inadeq uacies are clearly p ointed out in the output. To demonstrate the v alidity of the progr am, a sample problem from "Notes on ACI 3 18-71 Building Code Requirements with Design Applications" (Reference 1) was p rocessed on CONCRETE.

The problem determines the average 28-day st rength and standard deviation for 46 test cylinders.

CONCRETE's r esults, shown in Table D-4, are i dentical to the hand cal culation solutions in the ACI notes.

B/B-UFSAR D.3-1 D.3 DYNAS DYNAS (Dynamic Analy sis of Structures) is designed to perform dynamic analysis of st ructures which c an be idealized as three-dimensional sp ace frames and/or ri gid slabs connected together by translational or tor sional springs.

The program considers the combined effects of translatio nal, torsional, and rocking motions on the structure. The program uses either the response spectrum or the time history method of analysis, depending on the type of forci ng function available. Each method uses a normal mode approach. In the case of time history analysis, th e decoupled differen tial equations of motion are numer ically integrated using Newmark's -method (Reference 3).

The DYNAS program is capable of analyzing st ructures having parts with different a ssociated dampings.

An option is also available to analyze a large structural system using a modal synthesis technique. In this option, the system is divided into subsystems whos e modal characteri stics are computed separately and then sy nthesized to obtain the response of the complete system. The input base motion can be applied simultaneously in tw o orthogonal directi ons. A response spectrum can be generated at specified s labs or joints.

The program output includes modal responses, p robable maximum responses, a time history of structural response, and a response spectrum at specified joints.

The DYNAS program was original ly developed by Sargent & Lundy in 1970. The program is curre ntly maintained on UNIVAC 1100 series hardware operat ing under EXEC 8.

The solutions of two of the problems used for validating DYNAS are presented.

In the first problem , a three-story shear building is analyzed and compared to a so lution obtained by B iggs (Reference 4).

The structure in conju nction with the applicable masses and stiffness values is represented by the closed-coupled system shown in Figure D-1.

For this analysis the following response spectrum was used:

Frequency Displacement 1.00 cps 3.30 in. 2.18 cps 1.40 in.

3.18 cps 0.66 in.

The results obtained by Biggs and from DYNAS are compared in Tables D-5 t hrough D-8.

B/B-UFSAR D.3-2 In the second ex ample, results of DYNAS are comp ared to those obtained by Wilson et al. (Reference

2) using the SAP-IV program.

An acceleration is a pplied at the fixed end of a cantilever beam (Figure D-2).

The natural periods calculated by both SAP-IV and DYNAS are s hown in Table D-9.

A comparison of the bending moment at the fi xed end of the cantile ver beam is shown in Figure D-3.

As demonstrated in b oth examples, DYNAS performs an accurate analysis.

B/B-UFSAR D.4-1 D.4 DYNAX DYNAX (Dynamic Analy sis of Axisymmetric Structures) is a finite element program capable of performing both s tatic and dynamic analyses of axisymmetric structures.

Its formulation is based on the theory of small displacement.

Three types of finite el ements are available

quadrilateral, triangular, and shell. The geometry of the structure can be general as long as it is axisymmetric.

Both isotropic and orthotropic elastic ma terial properties can be modeled.

Discrete and distributed springs can be used to model elastic foundations, etc.

For static analysis, input loads can be structural weight, nodal forces, nodal di splacements, dis tributed loads, or thermal loads. Loads can be axisymmetric or nonaxisymmetric.

For solids of revolution, the pr ogram outputs nodal displacements and element stresses in the global system (radial, circumferential, and axial) and element and nodal stress resultants in a shel l coordinate system.

For shells of revolution, the output c onsists of nodal displ acements as well as element and nodal stress resulta nts in a shell coordinate system (meridional, circumfer ential, and normal).

For dynamic analysis, three meth ods are available: direct integration method, modal supe rposition method, and response spectrum method. Dynamic anal ysis by direct integration or modal superposition meth od uses a forcing function input via either 1) nodal force components versus time for any number of nodes, or 2) vertica l or horizontal ground acceleration versus time. For nonaxisym metric loads, the equivalent Fourier expansion is used. Dynamic an alysis by the re sponse spectrum method uses a spectral velocity versus natur al frequency input with up to four damp ing constants. The output of dynamic analysis provides nodal displa cements, element stresses, and resultant forces and moments at specified time s teps. When the modal superposition meth od is used for e arthquake response analysis, the prescribed number of frequencies a nd mode shapes are computed and printed along w ith the cumulati ve response of all specified modes by t he root sum square (RSS) method and the absolute sum method.

DYNAX was originally developed under t he acronym ASHAD by S. Ghosh and E. L. Wilson of the University of California, Berkeley, in 1969 (Reference 5).

It was acquired by Sargent &

Lundy in 1972 and is maintained on UNIVAC 1100 series hardware operating under EXEC 8.

Validation of the ma jor analytical capab ilities of DYNAX is demonstrated by a comparison of the resu lts from six documented problems with DYNAX results.

B/B-UFSAR D.4-2 The first problem is tak en from S. Timoshenko and S. Woinowsky-Kri eger's book Theory of Plates and Shells (Reference 6). A cl amped shallow sphe rical shell, shown in Figure D-4, is analyzed for displacements an d stresses produced by a uniform pressure applied on its outside s urface. DYNAX and the Timoshenko/Woino wski-Krieger solutio ns are compared in Figures D-5 and D-6.

The second problem, taken from Theory of Elasticity by Timoshenko and Goodi er (Reference 7), is a plane strain analysis of a thick-wa lled cylinder subj ected to external pressure. The finit e element idealization and the loading system used for this c ase are shown in Figur e D-7. Results of the DYNAX analysis a re compared with t he exact solution in Figure D-8. The agree ment for both stresses and displacements is excellent.

The third problem is taken f rom an article by Budiansky and Radkowski (Reference 8). The structure, illustr ated in Figure D-9, is a short, wide cylind er with a modera te thickness to radius ratio. The a pplied loads and t he output stresses are pure uncoupled harmonics.

For this finite element analysis, the cylinder is divided into 50 elements of equal size. This problem solves for harmonic deflections, element stresses, and forces. Figures D-10 and D-11 compare DYNAX results with the results given in the article.

The fourth problem is taken from an article by Reismann and Padlog (Reference 9).

A ring (line) load of magnitude P (500 pounds) is suddenly appl ied to the center of a freely supported cylindrical shell.

The dimensions of the shell and the time-history of the load are shown in Figure D-12. Because of symmetry, only one-half of the cylinder is modeled using 80 elements of equal size. The t ime-history of radial deflection and meridional moments from DYNAX and from Rei smann and Padlog are compared and are shown in Figures D-13 and D-14, respectively.

For the fifth problem, the method of mode superposition is used to solve a shallow spherical cap with clamped support under the action of a suddenly a pplied uniformly distr ibuted load. The dimensions of the sh ell and the load tim e-history are shown in Figure D-15. The fi rst 12 modes were co nsidered to formulate the uncoupled equations of motion. Each of these equations was solved by the step-by-step integration metho d using a time step of 0.1 x 10

-4 seconds. The resul ts are compared graphically with those obtained by S. Klein (Reference 1

0) in Figures D-16 and D-17.

The sixth problem is a hyperbolic cooling tower, as shown in Figure D-18. The to wer is analyzed for horizontal earthquake motion. A response spectrum for 2% damp ing, as shown in Figure

B/B-UFSAR D.4-3 D-19, was used for this analysis. The R MS values of the meridional force are com pared with those obtained by Abel et al. (Reference 11) in Figure D-20.

As shown in these six examples, DYNAX is capable of producing accurate results for both static and dynamic analyses of shells.

B/B-UFSAR D.5-1 D.5 LAFD LAFD (Analysis of Li near Anchor Forces a nd Displacements) calculates the maxim um force and displ acement of anchors resulting from local buckling of thin plate liners anchored to concrete walls. The sol ution method used in L AFD is described in Reference 12.

First, anchor displa cements are found for an assumed postbuckling load by a relaxation technique. Then, u sing this maximum displacement, the anchor force a nd the strain in the buckled plate are calculated.

The stress-strain relation given in a paper by Young and Tate (Reference 13) is reestablished in the program. Using the ca lculated strain, first stress is found and then a new load. Th e new load is then u sed to find a new set of displacements. The proc edure is repeated to find a second new load. This load is then compared to the load used in the previous cycle. The p rocedure is repeated u ntil the difference between the loads obtained in the last two cycles is approximately zero.

The program is capable of analyz ing four types of anchors:

Nelson studs of 1/2-, 5/8-, and 3/4-inch diameter, and 3- x 3-1/4-inch angle conti nuous rib anchors. Th e force-deformation relations of these a nchors are obtai ned from the manufacturer's publication (Reference 14).

The program output includes the maximum anchor force, the maximum anchor deforma tion, and the postbuck ling load of the buckled plate.

LAFD was developed by Sargent &

Lundy in 1971 and is currently maintained on UNIVAC 1100 series hardware operating under EXEC 8.

To validate the progra m, significant calcula tions were verified with hand calculatio ns. As an example of this validation, a comparison of these calculations is presented for a strip of liner having the fol lowing properties:

Strip span a = 17.5 in., Plate thickness t = 0.375 in., Strip width w = 9 in., Modulus of Elasticity E = 30 x 10 3 ksi, and Yield Stress o = 36 ksi.

5/8-inch-diameter Nelson stu ds are used as anchors.

The anchor displacements, U i , the force in the anchor adjacent to the buckled panel, f 1 , and the postb uckling load P as calculated by the program a re shown in Table D-10.

Substituting these

B/B-UFSAR D.5-2 displacements into the a ppropriate force-defor mation relationship for a 5/8-inch-diameter Nelson stud yields the anchor forces contained in Table D-11.

The validity of the so lution is checked usin g the displacements and anchor forces given in Tables D-10 a nd D-11 for the system shown in Figure D-21 to verify the equal ity of the original equations:

f + )U- U (a EA = P-Fo 1 2 1 (1) f + )U - U - U (2 a EA = O n 1+n 1-n n (2) 3....N 2, 1, = n The postbuckling load, P, as det ermined by Equat ion 1, is equal to 21.864K as compared to 21.978K obtained from the program.

Substitution into Equation 2 sat isfies the equat ion; equilibrium having been verified, the results obtained from the program are valid.

B/B-UFSAR D.6-1 D.6 SIMULATE SIMULATE (A Monte-Carlo Analysis of the Turbine Hazard) performs a Monte Carlo Si mulation analysis of the turbine missile hazard to nuclear power plants. It models the plan t structures, safety-related equipment and turbine disc characteristics.

SIMULATE traces each m issile's path through the plant structures, considering cases of perforation and ricochet, a nd recording damage to the safety-r elated equipment until the energy of the missile drops below a pr eselected level or t he missile leaves the plant region.

The program also stores informat ion on a system file, such as the trial number in which one or more targets are hit, the hit target names, and th e corresponding miss ile weight. Such information may be used subsequently to dete rmine frequencies of those combinations (of target s) which are detrimental to the safety of the plant.

SIMULATE was developed at Sargent

& Lundy in 1977. It is currently maintained in UNIVAC 1100 series hardware operating under EXEC 8.

The input consists of information describing the plant structures and safety-related com ponents as well as the postulated missile characteristics.

The output includes the information necessar y to evaluate the probability of damage that would interfe re with normal safe shutdown beyond certain limits.

To validate SIMULATE, five problems were use

d. The first two problems are for the validation of the modified NDRC formula and CEA-EDF formula for the perf oration of con crete barriers, and the Ballistic Research L aboratory (BRL) formula for the perforation of steel b arriers. The other three problems deal with the extraction of f requencies of a given set of combinations defining a damage state from a given set of targets which are hit in a given number of trials.

B/B-UFSAR D.7-1 D.7 PCAUC PCAUC (Portland Cement A ssociation Ultimate Design of Columns) is used to design or to investigate rein forced concrete columns using the ultimate s trength theory in accordance with ACI 318-71 Code. The program is capable of designing or investigating tied col umns subjected to an axial load combined with uniaxial or biaxial bendi ng moment. The program input consists of the dimensions of sections, materi al properties, reinforcement requirement and lo ading data. The applied forces output includes the load fac tors per ACI. The slenderness effect is not included in the present program.

Output from the design p art of the program includes the steel reinforcement arrangemen t, ultimate capacity for all loading cases, and inter action control p oints data. Output from the investigation part of the program either includes biaxial or uniaxial interaction data. Sa rgent & Lundy has modified the original PCA program to follow 1971 ACI buil ding code and to provide more design opti ons and greater capacity.

PCAUC is a modified ve rsion of the program "Ultimate Strength Design of Concrete C olumns", developed by the Portla nd Cement Association. The program was ob tained by Sargent & Lundy in 1972 and modified. It is curr ently maintained on UNIVAC 1100 series hardware operat ing under EXEC 8.

To validate PCAUC, d ocumented results from several problems were compared with PCAUC results.

Three of these problems are presented here.

The first problem is taken from Wang and Salmon's book (Reference 19). The reinforcement for a 17-inch x 17-inch square tied column is designed for compressi on control loads.

The loads include a dead-loa d axial load of 214 kips and bending moment of 47 ft/kips, and a live-load axial load of 132 kips and a bending moment of 23 ft/kips. Th e reinforcement is designed according to the ACI Code with f c' = 3,000 psi and f y = 40,000 psi.

The solution as given in Wang and Salmon's book is identical to the solution obtained fr om PCAUC, shown in Figure D-22. It should be noted that the ultimate capaci ty provided by PCAUC has been reduced by a factor of 0.7.

The second problem is also t aken from Reference 19. The reinforcement for a ti ed column 14 inches wide and 20 inches deep is designed for t ension control loa ds with a dead-load axial load of 43 kips and bend ing moment of 96 kips, and a live-load axial load of 32 kips and be nding moment of 85 ft/kips. The reinforc ement is designed accord ing to ACI Code using symmetrical rein forcement with respect to its width and with f c' = 4,500 psi and f y = 50,000 psi.

B/B-UFSAR D.7-2 The solution as given in Wang and Salmon's book is identical to the solution obtained from PCAUC, shown in Figure D-23.

The third problem is taken from Notes on ACI 318-71 Building Code Requirements with Design Applications (Reference 20). A square tied column 28 inches x 28 inch es is designed for biaxial bending load s for the follow ing service loads:

Dead Live Axial 550 kips 300 kips M x 320 ft/kips 200 ft/kips M y 160 ft/kips 100 ft/kips The bending is designed according to the ACI Code with fc' =

5,000 psi and f y = 60,000 psi.

The selected reinforce ment obtained from PCA UC, shown in Figure D-24, is identical to that from Reference 20. It should also be noted that the interaction control points o btained by both show good agreement.

B/B-UFSAR D.8-1 D.8.1 PIPING ANALYSIS PROGRAMS PIPSYS (Integrated Piping Analysis Sys tem) analyzes piping systems of power plants for static and d ynamic loadings, and computes the combined stresses. The f ollowing analyses are performed:

a. Static: Analysis of thermal, displacement, distributed, and concent rated weight loadings on piping systems;

b. Dynamic: Analysis of piping system response to seismic and fluid transient loads;

c. Stress Combinati on: Computes the combined stresses in the piping components in accordance with the ASME Boiler and Pressure Vessel Code,Section III (Reference 21).

The static, dynamic, and stress combination analyses can be performed independently or in sequence. Resul ts of the static and dynamic analyses can be stor ed on magnetic tape for use at a later date to perf orm the stress combi nation analysis. The piping configuration can be plotted on a Calcomp plotter.

The input consists of the pi ping system geometry, material properties, static and d ynamic loadings. Vari ous options exist to control the lengt h of the output. The default option generally prints only the summary of input data and final results. PIPSYS was devel oped at Sargent

& Lundy in 1972. It is currently maintained on UNIVAC 1100 series hardware operating under EXEC 8.

To demonstrate the validity of the PIPSYS program the following three examples a re presented.

To illustrate the validity of the static portion of PIPSYS, the problem shown in Figure D-25 was analyzed and the results compared to those given in Reference 22. Ta ble D-13 shows the comparison of member end moments.

As shown, the results from PIPSYS and Refer ence 22 are in good agreement.

To illustrate the validity of the stress combination analysis portion of PIPSYS, t he problem outlined in Reference 23 was reanalyzed on the PIPSYS program.

The layout of the piping system is shown in Figure D-26. The stress analysis is performed at location 19. The summary of load sets and descriptions is presented in Table D-14. The results of the str ess analysis are presented in Tables D-15 and D

-16. The notati ons and equation numbers correspond to the ASME Boiler and Pr essure Vessel Code (Reference 21).

B/B-UFSAR D.8-2 It is observed that the PIPSYS results are very close to those presented in Reference 23.

To illustrate the validity of the dynamic analysis portion of PIPSYS, a problem wa s analyzed and the r esults obtained from PIPSYS were compared w ith those from two public domain computer programs, DYNAL (Referen ce 24) and NASTRAN (References 25 and 26). Figure D-27 shows a schematic representation of the piping system analyzed. Th e system is modeled with simple beam elements with a total of 136 deg rees of freedom. Figure D-28 shows the time depende nt blow-down forces at the relief valves locations. Results of PIPSYS are compar ed with DYNAL and NASTRAN in Table D-17 and Figu re D-29. The results from all three programs a re quite close.

D.8.2 WESTDYN The WESTDYN computer pro gram is a Westinghou se proprietary code for the analysis of thre e-dimensional piping systems. WESTDYN performs linear, elastic analyses of piping sy stems subjected to internal pressure, st atic, thermal, a nd seismic loads. The program combines output loads in accordance with ASME Section III (Reference 21) or ANSI B31.1 piping stress criteria to arrive at actual piping stresses.

The piping system to be analyzed may c ontain a number of sections, a section being defined as a sequence of straight and/or curved me mbers lying between two network points. A network point is: (a) a junction of two or m ore pipes; (b) an anchor or any point at which motion is presc ribed; or (c) a position of lumped mass. A ne twork point may be defined as completely unrestrained, or one or more of i ts six degrees of freedom may be rigidly or el astically constrained or displaced. Any member in the system may sustain prescribed loads. Also, at any l ocation within the system members may be changed, masses concen trated, springs in serted, temperature conditions varied, m aterials and weld co nfigurations changed, and body forces altered.

WESTDYN computes at each point w ithin the piping system the forces, moments, transla tions, and rot ations which result from the imposed anchor or junction loads, therma l gradients in the system, and gravitational loads in any combination of the three orthogonal axes. For seismic effects, a normal mode analysis is performed using three-dimensional r esponse spectra. The resultant internal forces and moments are comp uted from the square root of the sum of the squares of the modal forces and moments.

B/B-UFSAR D.8-3 D.8.3 CPASYS CPASYS (Conversational P iping Analysis S ystem) is a comprehensive system of interactive computer programs that were designed to automate and simplify piping des ign calculations.

Pipe geometry and loading condition de scriptions are permanently stored on project unique data base files. The control system program will retrieve the information and all ow the piping an alyst to maintain it.

The interactive progra ms in the system allow an analyst to perform all operations necessary to analyze a pi ping system, review the design of its interfa ces, design weld ed attachments, and document all work performed.

Design control tool documents are also generated.

Origin of Program:

Sargent & Lundy D.8.4 SIPDA SIPDA (Simplified Piping Dynamic Ana lysis) is used to seismically qualify small piping subsystems 2 inches in diameter. In compliance with the limi ting allowable stress and deflections, it considers the effects of pressure, weight and se ismic loadings to calculate the maximum allowable span len gths. SIPDA was validated by comparison of sample problem re sults with previously validated results.

Origin of Program:

Sargent & Lundy D.8.5 NOHEAT NOHEAT (Nonlinear Heat T ransfer Analysis) uses the finite-element method to calculate the temp erature distribution in an axisymmetric solid which results from nonlinear heat transfer.

Stresses resulting from linear thermal expansi on are calculated for the applicable mod el and for certain app ropriate sections.

NOHEAT was validated by comparison of sample problem results to previously validated results and manual calculation results.

Origin of Program: Universi ty of Califo rnia (Berkeley)

D.8.6 HYTRAN HYTRAN (Hydraulic Tr ansient Analysis) ca lculates pressures, velocities and f orce transients in a l iquid filled piping network due to transients that are initiated by valve closure, pump trip, or by pressure changes at a piping te rminal. HYTRAN was validated by comparison of sample problem results to results given in publi shed documents.

Origin of Program:

Sargent & Lundy

B/B-UFSAR D.8-4 D.8.7 PWRRA PWRRA (Pipe Whip Restr aint Reaction Anal ysis) computes the response of the simple pipe-whip analysis models to an applied time dependent b lowdown force. It pro vides the load data required for the pipe whip restr aint and the support structure.

PWRRA was validated by comparison of s ample problem results with available a nalytical results in published technical literature.

Origin of Program:

Sargent & Lundy D.8.8 RELVAD RELVAD (Relief Valve Design Program) is used in the design of safety/relief valve asse mblies. The program calculates fluid forces at valve discha rge exit and vent stack inlet and exit, moments and stresses in the discharge elbow, discharge flange, valve inlet weld and b ranch connection to th e run. RELVAD was validated by comparison of sample problem results with results of example problem in ANSI C ode For Pressure Piping, Winter 1975 Addenda to Power Pi ping ANSI B31.1g-1976.

Origin of Program:

Sargent & Lundy D.8.9 PWUR PWUR (Rupture Analysis for Unrestrained Pipe s) calculates the effect of a pipe rupture on the surr ounding area.

This program calculates the steady-st ate thrust coefficient as a function of the resistance coefficie nt of the piping sys tem for steam and saturated on subcooled water, calculation of the component of the blowdown force due to steady state and the duration of the wave force and, calculation of the a rea affected by jet impingement as a function of t he resistance coefficient. PWUR was validated by comparison of sample problem results with results of manual calculations.

Origin of Program:

Sargent & Lundy D.8.10 SRVA

SRVA (Safety Relief Valve Blowdown Ana lysis) is a finite difference program f or the analysis of transient flow in a relief valve line discharging into a suppression pool.

Transient forces and the pressur es at the water column and the valve outlet are calculated.

SRVA was validat ed by comparison of sample problem results with published results and analytical problem solutions.

Origin of Program:

Sargent & Lundy

B/B-UFSAR D.8-5 D.8.11 NONLIN NONLIN (Nonlinear Dynamic Analys is of 2-D Structures) determines the nonlinear response of a complex structural or piping system model. Various material properties, forces and other parameters are input to generate the resp onse. NONLIN was validated by comparison of sample problem r esults with results from an existing validated p rogram (DRAIN-2).

Origin of Program:

Sargent & Lundy D.8.12 RELAP 4/MOD 5 RELAP 4/MOD 5 was used to obtain fluid veloc ities, densities and pressures for each time step which was used to calculate blowdown forces. These force time histories were then input into the PWRRA program.

RELAP was validated by comparison of results of sample prob lem contained in the program file with previously valid ated results.

Origin of Program: EG&G D.8.13 AXTRAN

AXTRAN (Axial Te mperature Transients in Welds) performs a thermal transient anal ysis and generates an axial temperature profile on the s tagnant line. A XTRAN was valida ted by comparison of sample problem results with results from an e xisting validated program (NOHEAT).

Origin of Program:

Sargent & Lundy D.8.14 ADINA ADINA (Automatic Dynamic Incremental Nonlinear Analysis) performs nonlinear and linear static and dynamic fini te element analysis.

ADINA was validated by running test problems contained in the ADINA User's Manual.

Origin of Program:

Massachusetts Inst itute of Technology D.8.15 ANCHOR

ANCHOR (Analysis of Intermediate Anchors on Piping Systems) performs the anchor load combination for ASME Code NC and NF Loads. ANCHOR was val idated by comparison of sample problem results with results of manual calculations.

Origin of Program:

Sargent & Lundy

BRAIDWOOD-UFSAR D.8-6 REVISION 1 - DECEMBER 1989 Subsections D.8.16 and D.8.17 describe piping analys is programs used on the Brai dwood project only.

D.8.16 QUICKPIPE

QUICKPIPE performs support opt imization and rigo rous computer analysis of 4 inch and under, Class 2/3 small bore p iping. The QUICKPIPE verificati on includes approxim ately 40 test runs, selected to "exercise" e very portion of the program. Each run's results were ver ified against parallel SUPERPIPE results.

SUPERPIPE is a compu ter program for the rigo rous analysis and design checking of piping systems. It was developed by Impell Corporation in 1974.

SUPERPIPE was benchmarked by c omparison with r esults published by the NRC in NUREG/

CR-1677 for seven sa mple problems. The comparison was p erformed in accordance w ith the NRC request for additional verification of computer codes used for analysis of nuclear piping systems.

The verificat ion specification addressed the response spectrum method of dynamic analysis commonly used in seismic qualification of nuclear piping. The program has also been thoroughly tested and verified for a comprehensive set of sample problems, includ ing extensive comparison with several publicly available programs and ASME benchmark problems.

QUICKPIPE utilizes t he 1974 ASME Code up to and including the Summer 1975 Addenda.

All verification a nalyses have been documented in accordance with established Impell Quality Assurance procedures.

D.8.17 AUTOHANG AUTOHANG is an interacti ve graphics computer program which designs pipe supports.

It selects and analyzes component hardware, performs frame quali fications, and produces final drawings.

INTERSUPPORT is a comprehensive comput er program for the structural analysis and design checking of pipe support structures. It uses a finite element beam analysis to calculate stresses a nd displacements. T he program also performs a Raleigh f requency evaluation.

INTERSUPPORT was developed by Impell Corporation in 1981 and has been verified against results of the hand calculations and several publicly ava ilable programs.

AUTOHANG reads the service l evel allowables from a plant-specific database. Faulted allo wables may be preset to a specific value, or AUT OHANG can determine th e correct factor to be applied to the normal allowab les, as specified in the ASME BRAIDWOOD-UFSAR D.8-7 code. AUTOHANG utilizes the 1974 AS ME Code including the Summer 1975 Addenda and the AICS 7th Edition.

The results of AUTOHANG anal yses, as well as the methodology of these analyses, has be en extensively ver ified. Approximately 100 benchmark cases were run.

The AUTOHANG results were compared to hand calculations.

D.8.18 MLT*MOMENT.MOX

MLT*MOMENT.MOX (Moment Range and Trans ient Conversion) calculates moment ranges betwe en user supplied load set data (e.g., moments, load set ID, multiplicat ion factors) using a method consistent with the method used in the Byron fatigue data. This was done so that one-to-one comparisons could be made between Braidwo od and Byron moment ranges for e ach load set pair.

Origin of Program:

Sargent & Lundy D.8.19 MLT*MOMENT.TRAN MLT*MOMENT.TRAN (Moment Range and Tran sient Conversion) calculates NB-3650 the rmal transient stress quantities for each specified enveloped load set usi ng Byron fatigue data temperature values (which are in degrees Fahrenheit) and other input parameters. The resulting therm al transient s tress quantities are then used as input for Sargent & Lundy f atigue elevations on Braidwood.

Origin of Program:

Sargent & Lundy

B/B-UFSAR D.8-8 D.8.20 OPTPIPE The OPTPIPE computer pro gram, developed by NUTECH Engineers, is a special purpose program wh ich performs linear elastic static and dynamic analysis of three-dimensional piping systems arbitrarily oriented in space. The prog ram can perform static analyses for dead weight, intern al pressure, t hermal effects, support displacements and externally applied loads. Dynamic analyses can be performed for ea rthquake loading represented by either an acceleration response spectrum or a time history.

For dynamic time history analyses, e ither the modal superposition or direct integratio n procedure can be used.

In the response spectrum approach, diffe rent spectra at different supports may be provided. In the time histo ry analysis approa ch, different acceleration time histories at different supports may be provided, and different damping for each mode of the system may be input. The progr am has the option of com puting modal damping by considering d ifferent damping in each component of the piping system. In static analysis, joint di splacements, mem ber forces, and support reactions are output for the com plete system. For dynamic time history analysis, the time histories of these parameters and t heir maximums are obta ined for s elected nodes and members. For dynamic resp onse spectrum an alysis, maximum joint displacements, m ember forces, and supp ort reactions are determined by a combination of each of these parameters for each mode and for each set of earthquake directions.

The total response due to the different modes may be obtained by the absolute summation method, square root of sum of the squares method, or by the closely spac ed modes summation procedure (ten percent method or gr ouping method).

The piping system may be composed of four different types of elements.

a. Three-dimensional straig ht and curved pipe elements.

b. Three-dimensional beam e lements which can be used to model rigid h angers, valves, etc.

c. Boundary elements which can be used to m odel spring hangers and may also be used to determine support reactions.

d. Substructure sti ffness input element. For curved pipes and tee or bran ch connections, stiffness and stress modification effects are automatically taken into account. For curved and straight pipes, convent ional effective stress magnitudes are computed.

OPTPIPE contains plotting capa bilities for p lotting the geometry of a structure. It also has the ability to perform

B/B-UFSAR D.8-9 stress checks for ASME Class 1, Class 2 and Class 3 piping, based on the requirements of t he 1977 Edition of the ASME Code including Addenda through Summer 1979.

D.8.21 ANSYS The ANSYS computer program is a large-scale, g eneral purpose computer program for the solution of several classes of engineering problems.

Analysis capabilities include static and dynamic; elastic, plastic, cre ep and swelling; buckling; small and large deflections; stead y state and transient heat transfer, electrostatics, magn etostatics, and fluid flow.

The matrix displacement method of analysis based upon finite element idealization is employed throughout the program. The ANSYS program is capable of analyzing two- and three-dimensional frame stru ctures, piping systems, two-dimensional plane and axisymmetr ic solids, three-dimensional solids, fl at plates, axisy mmetric and three-dimensional shells and nonlinear problems including interfaces a nd cables.

Loading on the struc ture may be forc es, displacements, pressures, temperatures or response spectra.

Loadings may be arbitrary functions of time for linear and n onlinear dynamic analyses. Loadings for heat transfer an alyses include internal heat generation, con vection and radiation boundaries, and specified temperatur es or heat flows.

ANSYS is a proprietary engineering analysis computer program developed by Swanson A nalysis Systems, Incorporated.

B/B-UFSAR D.8-10 REVISION 7 - DECEMBER 1998 D.8.22 GAPPIPE The GAPPIPE computer p rogram is a general purpose piping analysis program developed by Robert L. Clou d & Associates, Inc., and sponsored by t he Electric Power Re search Institute.

GAPPIPE performs both li near and nonlinear e lastic analyses of three-dimensional piping systems subjected to thermal expansion, imposed displacements, i nternal pressure, ex ternally applied loads, and seism ic and fluid t ransient loads or motions. In addition, GAPPIPE contains a pos tprocessor capable of performing stress evaluation of p iping components in ac cordance with the ASME Boiler and Pressu re Vessel Code, Sectio n III requirements.

GAPPIPE differs from other piping comp uter programs in that it has the capability to analyze piping systems containing gaps.

GAPPIPE has two anal ysis methods to co mpute the dynamic responses of such systems. The first method is nonlinear time history analysis by modal su perposition and pseudoforce representation of gap responses. This m ethod is most suitable for the simulation of piping responses induced by fluid transient loads or e xcitations where the input cannot be easily or adequately characteri zed by response spectra.

For excitation defined by response spect ra, GAPPIPE offers a second analysis method t hat uses the respons e spectrum analysis technique and the method of equi valent linearization to account for the nonlinear behavi or of gaps. In this method, GAPPIPE can use either uniform e nveloped response spectra or different spectra at different supports using the independent support motion technique.

The GAPPIPE element library contains the following types of elements.

a. Three-dimensional pipe e lements (straight and curved segments), b. Boundary elements which are used to model supports, anchors, gaps and springs, c. Three-dimensional truss elements, and

d. Three-dimensional beam elements.

Using the truss and beam element s, complex structures and equipment can be modeled and coupled with the piping models. A GAPPIPE analysis model c an be a combination of one or more of the above element types.

This program is NRC-approved, as stated in Reference 55.

B/B-UFSAR D.9-1 D.9 PLFEM-II PLFEM (Plate Finite El ement Method) analyzes plane elastic bodies, plates, and shell structures by the stiffness matrix method. The program uses two finite e lements, a rectangular element and a triang ular element.

Elastic spring supports and/or an elastic foundation may be considered in the analysis. O rthotropic materia ls may also be considered in conjunction with the rectangul ar element.

Pressure loads, concentr ated forces, nodal displacements, and thermal loads may be considered in the a nalysis. All loading cases may be factored and/or combined in any manner.

The program output includes de flections and ro tations of all joints and membrane st resses (normal, sh earing, and principal) at the center of each element, the resultant moments (X, Y, twisting principal), and shears and reaction forces. An equilibrium check is made to determine the a ccuracy of the results. PLFEM was developed and is maintained by Sargent & Lundy. It was originally developed on a UNIVAC 1108 in 1966. Since May 1972 it has been suc cessfully operating on the UNIVAC 1100 series hardware operat ing under EXEC 8.

Three sample problems are presen ted to demonstrate the validity of PLFEM. Plots of the comput er results obtained are compared with theoretical results and results by other methods.

The first problem is an analys is of a rectangular tank filled with water which was presented by Y. K.

Cheung and J. D. Davies (Reference 27). The finite element used was presented by Zienkiewicz and Cheung in Au gust 1964 (Reference 28).

Experimental results agreed exactly with the finite element results except at a few isolated points where very small differences were noted.

The PLFEM grid and loading for the tank problem are shown in Fi gure D-30. The grid used is the same size as the one used by Cheung and Davi es. Moments in three regions of the tank are plotted along with the PLFEM results in Figures D-31 through D-33.

As a second example, a rectangular plate sub jected to a uniform plane stress and having a circular hole in its center is analyzed. The grid used in the PLFEM analysis is shown in Figure D-34. Be cause of double symmetry, only one quarter of the plate is analyzed. Resu lts obtained from the PLFEM analysis are plotted in Figure D-35 against the exact values as given by S. Timoshenko and J.

Goodier in Reference 7.

As a final example, a square pla te having a rect angular hole in its center is analyzed for the effect of a thermal gradient through the plate. The grid used in t he PLFEM analysis is shown in Figure D-36.

Only one quarter of the plate is

B/B-UFSAR D.9-2 analyzed because of the double symmetry. Moment values obtained by PLFEM are plotted for two regions of the plate in Figure D-37. For comp arison, values of the moments obtained by an analysis based on the Hrenn ekoff framework an alogy are also shown.

B/B-UFSAR D.10-1 REVISION 3 - DECEMBER 1991 D.10 RSG RSG (Response Spectrum Generator) genera tes dynamic response spectra (displacement, velocity, and a cceleration) for single-degree-of-freedom elastic systems with various damping, subjected to a prescribed ti me-dependent acceleration. The differential equation of motion is solved us ing Newmark's method of numerical int egration (Reference 3).

The program may also be used to obtain a response-spectrum-consistent time-history in which the res ponse spectrum of the generated time-histo ry closely envelops the given spectrum.

The program has the capability of plotting the input time, acceleration functio n, and the response spectra output on tripartite and/or ac celeration versus period frequency grids.

Depending on the option, the pro gram output includes the spectra of a given time-history or t he response-spec trum consistent time-history.

RSG was developed by S argent & Lundy in 1969. Since 1972 the program has been maintained on U NIVAC 1100 series hardware operating under EXEC 8.

One of the compariso ns used for validati on is presented.

The response spectrum for a one-degree-of-freedom damped system as presented by Bigg s (Reference 4) was dete rmined using RSG.

The system was subject ed to the sinusoidal g round acceleration shown in Figure D-38.

A damping factor of 0

.2 was used for this example. The response spectra obtained by B iggs and from RSG are also shown in Figure D-38.

As demonstra ted by this comparison, RSG genera tes an accurate response spectrum.

B/B-UFSAR D.11-1 D.11 SEISHANG SEISHANG (Seismic Analysis of Ha ngers) is used f or the analysis and design of electrical cable and HVAC duct support systems.

The program computes t he allowable spans for cable trays and selects the proper mem ber sections for various types of supports. The input load functions can be in the form of dead load, live load, or dyna mic response spectra.

Program input consists of geometric data, ma terial properties, member properties, and external loadings.

Program output consists of allowable spans, member size s, and mechanical response.

The allowable slenderness ratios used for design of compression members in HVAC and ca ble tray support d esigns are shown in Table D-45.

SEISHANG was developed at Sargent

& Lundy in 1976. It is currently maintained on UNIVAC 1100 series har dware under EXEC 8.

To demonstrate the v alidity of the progr am, two problems are presented.

A typical cable tray, shown in Figure D-39, is analyzed and compared to the solution obtained by hand calculation. The results obtained from SEISHANG and by ha nd calculation are compared in Table D-18. The r esults show good agreement.

Two typical HVAC supports, shown in Figures D-40 and D-41 are analyzed and compared to the s olution obtained from the DYNAS (see Subsection D.3).

The results obtai ned from SEISHANG and from DYNAS are compared in Tables D-19 and D-20. The HVAC support shown in Figure D-40 is also analyze d with PlPSYS (see Subsection D.8.). T he results obtained from SEISHANG and from PIPSYS are compared in Table D-21. The results show good agreement.

B/B-UFSAR D.12-1 REVISION 1 - DECEMBER 1989 D.12 SHAKE SHAKE (Soil Layer Pr operties and Respo nse/Earthquake) is a program which computes response in a hor izontally layered semi-infinite system s ubjected to vertically traveling shear waves. Strain-compatible soil properties are computed within the program. Earthq uake motion can be s pecified at any level of the soil profile, and a resulting m otion can be computed anywhere else in the profile. T he method is based on the continuous solution of the shear wave equati on. For soil liquefaction studies, plots of stress time-histories at various levels in a soil profile can also be obtained.

The input for the program incl udes property data for the soil profile, curves of strain vers us shear moduli and damping ratios, and the input earthquake motion.

The output includes the strain-compatible soil properties, response spectra of object and computed motion s, printer and CALCOMP plots of time-histories, Fourier spe ctra, and response spectra. Stress time-histor y plots are also included.

SHAKE originally was d eveloped by John L ysmer and P. B.

Schnabel of the University of Ca lifornia, Berkeley (Reference 29). It was modified by and is now maintained by Sargent &

Lundy. It has been used on a UN IVAC 1100 series hardware operating under EXEC 8 at Sargent & Lundy since October 1972.

To verify Sargent & Lundy's ve rsion of SHAKE, re sults from the program were compare d with results f rom a problem in a paper by Idriss and Seed (Reference 30).

The 100-foot layer of dense sand shown in Figure D-42 was analyzed. The propert ies of the sand we re considered to be as follows: Total unit wei ght = 125 pcf, (K 2)max = 65, and K o = 0.5.

The parameter (K 2)max relates the maximum shear modulus, G max , and effective mean pressure at any depth, y, bel ow the surface as follows: max G = 2/1'm 2 max)K 1000( Where 'm = ' 3)2K + (1'v o ,

B/B-UFSAR D.12-2 K o = coefficient of lateral pressure at rest, and v = effective vertical pressure at depth y.

Damping values and the variation of modu lus values with strain were based on pu blished data for san ds (Reference 31).

The response of the sand layer w as evaluated u sing the time-history of accelerations recorded at Taft during the 1952 Kern County earthquake as b ase excitation. The ordinates of this time-history were adjusted to provide a maximum acceleration of 0.15g. The results obtained f rom SHAKE and the publ ished results are compared in Figures D-43 and D-4

4. The maximum shear stresses and accelerations from both solu tions are compared in Figure D-43; the response spectra of the surface motions are compared in Figure D-44.

As illustrated in the se figures, the two solutions compare favorably.

B/B-UFSAR D.13-1 D.13 SLOPE SLOPE (Slope Stabili ty Analysis) utilizes the theory of equilibrium of forces to determine the facto r of safety against sliding of any embankment or slope. It contains the Bishop, Fellenius, and Morge nstern-Price methods of two-dimensional stability analysis. In the Bish op and Fellenius methods, the factor of safety against failu re is estimated along a circular surface of failure, wh ereas any arbitrary fa ilure surface may be chosen for the Mo rgenstern-Price method.

The input includes t he slope geometry, s oil profile, soil properties (density, cohesion, and the f riction angle) and the piezometric surface(s).

The program also ha s the capability to introduce an ear thquake loading assumed as a horizontal gravitational force.

Once the problem is input, several options can be used to determine the factor of safet y by the various methods. In addition, d ifferent stages such as end-of-construction, full-lake, and sudd en-drawdown, can be considered in a single run.

The output includes factors of s afety for each t rial surface and a plot of the sl ope cross section having slope profile, soil profile, water table conditions, and failure surface for the minimum factor of safety.

SLOPE was developed and put under ICES (Integrated Civil Engineering Systems) by William A. Bailey at the Massachusetts Institute of Technology. It has been in the public domain since 1967. Sargent

& Lundy currently u ses the SLOPE version maintained by the McDonnell Do uglas Automation C ompany on IBM 370 Series hardw are (Reference 32).

B/B-UFSAR D.14-1 D.14 SLSAP1 SLSAP1 (Sargent &

Lundy Structural Analy sis Program) performs static analysis for stru ctures consisting of any of the following element types: three-di mensional truss, three-dimensional beam, plane stress or plane strain, two-di mensional axisymmetric solid, three-dimensional solid, thin shell and boundary. The stiffnesses of the ele ments are evaluated fo r linear elastic isotropic or orthotropic materia ls. The structural stiffness is obtained by assembling a ll the individual el ement stiffnesses.

In static analysis e ach load case may in clude element loadings -

thermal loads, pressure loads, gravity loads , and concentrated nodal loads. The program calcul ates the nodal d isplacements and forces or stresses in elemen ts for multiple load cases.

The original version of the program, SAP, was developed by E. L. Wilson of the University of Califo rnia at Berkeley and released in September 1970 (Refe rence 33). In 1973 Sargent &

Lundy modified the progr am to enable it to analyze a mat on a nonlinear elastic foundation, with zero foundation stiffness in regions of mat u plift. The regions of z ero stiffness represent the fact that the soil foundat ion can not carry tension stresses. The progr am operates on the U NIVAC 1100 series hardware operating under EXEC 8.

To show the validity of the program, a circular plate on a rigid no-tension foundation, as shown in Figure D-45, is analyzed. The p rogram results are c ompared with results obtained Timoshenko and Woinowsk i-Krieger's meth od of solution (Reference 35). As sh own in Figure D-46, the results are in excellent agreement.

B/B-UFSAR D.15-1 REVISION 7 - DECEMBER 1998 D.15.1 SLSAP-IV SLSAPIV (Sargent & Lundy Structu ral Analysis P rogram) performs static and dynamic structural analyses.

The structure may consist of any of the fo llowing element types: three-dimensional truss, thr ee-dimensional beam, three-dimensional solid, plane stress or p lane strain, two-dimen sional axisymmetric solid thick shell, thin shell, isoparametric shell, boundary spring or pipe. The stiffnesses of the elements are evaluated for linear elastic i sotropic or orthot ropic materials. The structural stiffness is obtained by assembling all the individual element stiffnesses.

In static analysis each load case may include element loadings -

thermal loads, pres sure loads, gravity loads and concentrated nodal loads. The program calculates the nodal displacements and forces or stress es in elements for multiple load cases. Th ere are four options a vailable in SLSAPIV dynamic analysis: frequency calculations only, frequency calculations followed by response history anal ysis, frequency calculations followed by response sp ectrum analysis, and response history analysis by direct integration. The p rogram performs the solution for eigenvalu e/vectors using either the determinant search algorithm or the subspace iteration alg orithm depending on the size of the problem. The ou tput for the time-history analysis and the response spectrum analysis includes displacement of the nodes and the element stresses.

The post processor, developed by Sar gent & Lundy, enhances the working application of t he static analysis portion of the SLSAPIV program. Its primar y purpose is to perform load combination analyses for structures with multiple loading cases.

The postprocessor comb ines files from indepe ndent runs into a single file, selects output requested by the user and checks for the absolute upper limits of the combined element stresses. It also has the capability to calculate the plate/shell minimum required moment capacities in two orthogonal dir ections or to calculate the principal stresses of the elemen ts. In addition, computer graphic capabilities for co ntours have been implemented for the mat foundation.

SAP was originally dev eloped by E. L. Wi lson of the University of California at Berkeley in 1 968. Sargent &

Lundy currently maintains a modified SAPIV version rel eased in 1973 (Reference

36) on UNIVAC 1100 series hardware ope rating under EXEC 8.

To demonstrate the v alidity of the major analytical capabilities of SLSAPIV, eight of the probl ems used for validation are presented. These prob lems are taken from Reference 36, which also contains comparis ons with several other static and dynamic computer programs and classical solutions.

In the first problem , the pipe network s hown in Figure D-47 is analyzed by SLSAPIV. The stat ic response of the system is calculated under the combine d effects of concentrated loads, B/B-UFSAR D.15-2 vertical (y-direction) gravity loads, un iform temperature increase, and non-zero displacements imp osed at one support point. The applied loads ar e shown in Table D-22.

The results from both pr ograms are compared in Table D-23.

Also shown are t he results from Reference

37. As shown, all of the results compare favorably.

In the second proble m, a clamped spheric al shell shown in Figure D-48 is analyzed for stre sses produced by a uniform pressure applied on its outside surface. The model represents a 5-degree wedge of the shell with eight een thin-shell elements along the 39-d egree meridian.

The curves in Figure D-48 are plots of t he meridian () and circumferential () direction surface predicted by SAPIV (Reference 36) and S LSAPIV at the element centroid. The results are almo st identical.

In the third pro blem a plane frame is analyzed to de termine the three lowest frequencies and c orresponding-mode shapes. The frame is shown in Figu re D-49 (part a), and the beam element is shown in Figure D-49 (part b).

Results from Reference 36 and SLSAPIV are compared in Table D-24. As shown, the r esults compare favorably.

The fourth problem deals with the response spect rum analysis of a pipe assemblage.

This problem was ori ginally presented in Reference 38.

The model of the pipe assemblage is shown in Figure D-50.

Z-moments are predic ted for the local co ordinates of the thirteen elements for the five lowest modes.

Table D-25 shows a comparison of the moment pr edictions from SLSAPIV and Reference 36. T he proportional horizontal and vertical spectra are simultaneou sly specified.

PIPDYN results, as documented in the SAPIV user manual, are also shown. All program results are in good agreement.

In the fifth problem a cantilever beam, shown in Figure D-51 (part a), is analyze d under both uniform and concentrated loads. The beam is modeled using 10 equal-length beam elements. It has a cross-sect ional area of 1 x 2 inches, a length of 10 inches, and a Y oung's modulus equal to 30 x 10 3 ksi. A uniform load equal to 2 kips/inch and a concentrated load of 10 kips are applied at one e nd of the beam.

The results from SLSAPIV are c ompared to analytical results obtained by Timoshenko a nd Gere (Reference 3 4). Figure D-51 (part b) shows excellent agreement between the bending moments obtained by both solutions.

B/B-UFSAR D.15-3 In the sixth problem a simply supported square plate under uniform loading is analyzed. A 10-inch-square by 1-inch-thick plate with Poisson's ratio e qual to 0.3 and Young's modulus equal to 30 x 10 3 ksi is loaded with 1 ksi pressure.

The results obtained are compared to those pre sented by S.

Timoshenko and S. Wo inowski-Krieger (Referen ce 35). Bending moments M xx and M yy for both x and y sym metry lines obtained in the two solutions ar e shown in Figure D-

52. The maximum bending moment which occurs at the center of the plate differs by only 1.05%.

In the seventh p roblem a cantilever beam, shown in Figure D-53 (part a) is analyzed for ground acceleration.

The response history of eight flexural mo des is calculated by mode superposition analysis.

The ground accelera tion applied at node 1 is shown in Fi gure D-53 (part b).

The natural periods for the eight lowest flexural modes as calculated by SLSAPIV and Refe rence 36 are given in Table D-26. The transvers e deflection versus time for nodes 5 and 9 is plotted in Figure D-54. The fixed end moment versus time at element 1 is plotted in Figure D-55.

The results show a favorable comparison.

For the eighth problem, the ti me history response of a cylindrical tube to a su ddenly applied load is analyzed by mode superposition and direct integra tion. Results are compared with SAPIV and solut ions by Reismann and Padlog (Reference 39).

One half of the tube, shown in Figure D-56 (part a) is idealized as an assemblage of axisymmetric elements with a total of 61 degrees-of-f reedom. The time variation of the applied load is shown in Figure D-56 (part b).

The 20 lowest modes calc ulated by SLSAPIV an d Reference 36 by mode superposition are listed in Table D

-27. Figure D-57 shows the radial displacem ent versus time for SLSAPIV and Reference

39. Figure D-58 shows the plot for dire ct time integration results from SLSAPIV and Reference 39. As shown, results from SLSAPIV compare favora bly with results f rom both SAPIV and Reference 39.

B/B-UFSAR D.15-4 REVISION 7 - DECEMBER 1998 D.15.2 SAP90 SAP90 is a finite element program for the static and dynamic analyses of structural s ystems. The structu ral systems that can be analyzed on SAP90 may be modeled by one or a combination of the following element types:

a. three-dimensional frame (beam) element, b. three-dimensional shell element, c. two-dimensional solid element, and

d. three-dimensio nal solid element The two-dimensional frame, truss, membrane, plate bending, axisymmetric, and plane strain elements are all available as special cases of the four elemen ts named above. A boundary element in the form of translational or rotational spring supports is also available in the program. The type of loads allowed by the progr am include gravity, thermal, prestress, distributed, or noda l forces and presc ribed displacements.

The program can perform static, steady-state , eigenvalue, and dynamic analyses. T he static and dynamic analyses may be activated together in the same run, and load c ombinations may include results from both analyses. The dynamic analyses may include response spectrum or t ime-history anal yses. In the time-history analyse s, loading can be nodal load or base acceleration, and the so lution is obtained u sing standard modal superposition or the Ritz vectors.

The effect of an axial load on the transverse bending be havior of frame element can be considered by using the P-Delta analysis.

Two design postprocess ors are available for frames analyzed by SAP90. SAPSTL uses the American Institute of Steel Construction Specifications (ASD-89 or PD-89 or LRFD-86) to check the design of steel frames analyzed by SAP9

0. SAPCON uses the American Concrete Institute Building Code Requirements for Reinforced Concrete (ACI 318-89) to design or check the design of concrete frames. The input data consists of nodal coordin ates, element members, loads, etc. The data are input to SAP90 in an unformatted file.

The input file can be create d interactively using SAPIN preprocessor program or noninteractively usi ng a text editor.

When SAPIN is used, the finite element model and input file for SAP90 analysis are generated graphically using pulldown menus to place joints and elements on the screen. Before executing SAP90, the user can use the interactive grap hics program SAPLOT to plot the model on the scree n, or on a hardcopy drawing.

Important debugging options avai lable through SA PLOT include display of joint restrai nts, element propert y ID, loading, and blowups of local ized regions.

B/B-UFSAR D.15-5 REVISION 7 - DECEMBER 1998 The output data consist of nodal displacemen ts, element stresses or forces, and s upport reactions. All r esults are org anized in output files stored on d isk during the executi on. Output data can be interactively p lotted using SAPLOT and SAPTIME graphics programs. Important plottin g options available through SAPLOT and SAPTIME include:

deformed shape, no dal and element time history responses, con tours of element stres sed, principal and Von Mises stresses. Response s pectrum curves f or acceleration time history generat ed by SAP90 run can be generated and displayed using SAPSPEC.

SAP90 was developed by E. L. Wilson and A. Habibullah of Computers & Structur es, Inc. (CSI), Be rkeley, California.

B/B-UFSAR D.16-1 D.16 SOR-III SOR-III (Shell of Re volution) is a com puter program used to analyze thin shells of revolution subj ected to axisymmetric loading by employing a generalized Ada ms-Moulton method to integrate numerically the go verning differential equations.

Arbitrary distribution of normal, tangential, and moment surface loadings as well as edge forces and deflections may be analyzed in the axisym metric loadings.

Input of boundary conditions allows for the cons ideration of ela stic support conditions. Temperature varia tions along the meridian or across the thi ckness may also be considered.

The program output includes shell displacement s, outer fiber stresses, and strains and stress resultants.

SOR-III was developed at Knolls Atomic Power Laboratory for the United States Atomic Energy Commission (Refe rence 40). Version III was acquired by Sargent & Lu ndy in 1969 and is currently maintained on Sargen t & Lundy's UNIVAC 1 100 series hardware operating under EXEC 8.

The Sargent & L undy version has been modified to punch da ta for plotting.

Results from this program ha ve been frequently compared with other available solutions and other computer programs to check the validity of the prog ram. One of these comparisons is the analysis of a circular flat reinforced c oncrete plate. The details of the p roblem and the b oundary conditions are shown in Figure D-59. Re sults of the SOR-III a nalysis were compared with the finite element program, SABOR-III (Reference 41).

Figure D-60 shows the bending moment in the meridional and hoop directions, respectively. Figure D-61 shows t he comparison of radial shear. As sh own in these figures, results compare favorably.

B/B-UFSAR D.17-1 REVISION 1 - DECEMBER 1989 D.17 STAND STAND (Structural Anal ysis and Design) is an integrated structural code whic h is programmed to p erform analysis and design of structural s teel members accor ding to the 1969 AISC Specification. It c onsists of the fol lowing subsystems:

a. beam edit, b. rolled beam design,

c. composite beam design, d. plate girder design, e. column edit,

f. column design, and

g. column base plate design.

The program input consists of member geometry and basic loadings. The desig n is performed for s pecified combinations of basic loadings and overstress factors. For floor framing systems, the program is capable of aut omatic transfer of reactions from tributa ry beams to supporting members. There are many design control parameters available , such as minimum and maximum depth limitations, s hape of the ro lled section, location of the lateral support of the c ompression flange, material grade or yield stress, deflection limitations, flange cutoff criterion, and lo cation of stiffeners.

For columns, the program is ca pable of account ing for axial loading as well as uniaxial or biaxial bending.

For column base plat e design, only axial load and column combinations are considered.

The program output includes the complete final design and provides the designer with suf ficient intermedia te information to enable him to evaluate the results.

For rolled and composite beam desig ns, complete details of shop-welded and field-bolted end connections are contained in the output.

Supplementary information for economic evaluation of the design is also provided.

STAND was developed and is maintained by Sargent & Lundy.

Since May 1972, the program has been u sed extensively at Sargent & Lundy on U NIVAC 1100 series ha rdware operating under EXEC 8. Some of the principal applicati ons include the design of steel floor framing using various t ypes of horizontal structural elements and the design of co lumns or beam columns.

B/B-UFSAR D.17-2 To validate STAND, r esults from the prog ram were compared with results from example des ign problems in the Manual of Steel Construction (Reference 42). Fo ur problems are given.

The first is a rolled beam design problem (Example 1, pp.

2-5). A beam of 36-ksi steel is designed for a 125-kip/ft bending moment, assuming its compression flange is braced at 6-foot intervals. The results, listed in Ta ble D-28, show that STAND selects a more efficient section.

The second is a composite beam design problem (E xample 1, pp.

2-143 and 2-144). A noncove rplated composite interior floor beam is designed. L imits of 1 1/2 inc hes for dead load deflection and 1 2/10 inches for live lo ad deflection are imposed. The results, shown in Table D-29, are nearly identical.

The third is a colum n design problem w ith three examples, (Examples 1, 2 and 5, pp. 3-4, 5, and 9).

The first of these exa mples is the design of a W12 column of 36-ksi steel that wi ll support a concentric load of 670 kips.

The effective length with respect to its minor axis is 16 feet and to its major axis, 31 feet.

The second example is the design of an 1 1-foot-long W12 interior bay column of 36-ks i steel that will support a concentric load of 540 kips. The column, rigidly framed at the top by 30-foot-long W30 x 116 girders connected to each flange, is braced normal to its web at the top a nd the base.

The third example is the design of a W14 column of 36-ksi steel for a tier building of 18-foot story height that will support a 600-kip gravity load and a 190-kip/ft maximum wind moment, assuming K = 1 relative to both axes and bending is about the major axis.

The results from all three checks are identical to those in the AISC Manual, and are shown in Table D-30.

The fourth problem is a plate gi rder design prob lem (Example 1, p. 2-108). A welded plate girder is designed to support a uniform load of 3 kips/ft and two concen trated loads of 70 kips as shown in Figure D-62. The compression flan ge of the girder is supported lateral ly only at points of concentrated load.

The results are show n in Table D-31.

B/B-UFSAR D.18-1 D.18 STRUDL-II STRUDL-II (Structural Design L anguage) is used primarily for static analysis of frame and truss str uctures. The program is, however, capable of performing linear static or dynamic analyses for finite element repr esentations of struc tures using stiffness matrix methods. N onlinear static problems and stability problems may also be treated.

The program is capable of analyz ing plane trusses and frames, grids and elastic bodies, sp ace trusses and fr ames, or three-dimensional elastic so lids subjected to arbitrary loads, temperature changes, or specified disp lacements. Either earthquake accelerations or time-history force may be used for dynamic analysis. Ani sotropic materials may a lso be used. In addition to analysis, the program is capable of performing structural steel design according to AISC Code and reinforced or prestressed c oncrete design accor ding to ACI Code.

The program output depen ds upon the type of fi nite element used and the analysis that was perfor med. Included in the output are displacements and member forces and moments or element stresses and moments.

Eigen values, e igen vectors, and time-history response or nodal response may be obtained for dynamic analyses. M ember sizes may be o btained if t he design portion is used.

STRUDL-II was developed as part of the Integrated Civil Engineering System at the Massac husetts Institute of Technology (Reference 43).

The program has been in the publ ic domain since 1968. Two versions are currently being used, one m aintained by the McDonnell Douglas Automation C ompany on IBM 370 series hardware (Reference 44) a nd one maintained by U NIVAC on the 1100 series hardware (Reference 45).

B/B-UFSAR D.19-1 D.19 TEMCO TEMCO (Reinforced Concrete Secti ons Under Eccentric Loads and Thermal Gradients) a nalyzes reinforced concrete sections subject to separate or combined action of ec centric loads and thermal gradients.

The program can also analyze reinforced concrete sections subjected to axial force and biaxial bending. The effect of temperature is induc ed in the section by reactions created by the curvature restra int. No thermal gradient can be specified when analysis under ax ial force and biaxial bending is desired.

The analysis may be done assuming either a cracked or an uncracked section.

Material properties can be assumed to be either linear or nonline ar. The program is capable of handling rectangular as well as n onrectangular sections.

The program input consists of section dimensio ns, areas and location of each layer of rein forcing steel, loads, load combinations, and ma terial properties.

The curvature and ax ial strain correspon ding to the given eccentric loads (axi al load and bending moment) are determined by an iterative proced ure. Thermal gradient is applied on the section by inducing reactions created by the curvature restraint, i.e., there is no curvature chang e due to a thermal gradient on the section. The axial expansion is assumed to be free after thermal g radient is applied.

An iterative procedure is employed again fo r finding the final strain distribution such that equilibrium of inter nal and extern al loads is satisfied.

The program output consists of an echo print of the input, the combined loads, final lo cation of neutral ax is, final stresses in steel and concrete, and fina l internal force

s. Similar intermediate results (before thermal gra dient is applied) can also be output if desired.

The program can be used to analyze a wide va riety of reinforced concrete beams and col umns, slabs, and conta inment structures subject to various c ombinations of exter nal loads and thermal gradients.

The program was developed by and is maintain ed by Sargent &

Lundy. Since February 1 972, the program has been extensively used at Sargent &

Lundy on UNIVAC 1100 serie s hardware operating under EXEC 8.

To demonstrate the validity of TEMCO, program results are compared with hand calculated re sults. Four exa mple problems are considered. The s ection and material properties for each problem are given in Table D-32, along w ith the applied external forces and thermal grad ients. Those for the fourth problem are given in Table D-34.

B/B-UFSAR D.19-2 REVISION 1 - DECEMBER 1989 The first problem considered i nvolves a section with two layers of steel under the act ion of a compressive force applied at the centerline of the section, a b ending moment, and a thermal gradient. A cracked analysis of the section is required assuming nonlinear materi al properties.

The second problem considered involves a section with two layers of steel under the action of a te nsile force applied at the centerline of the section, a bending mom ent, and a thermal gradient. A cracked analysi s of the section is required assuming nonlinear m aterial properties.

The third problem considered i nvolves a section with two layers of steel under the act ion of a tensile f orce applied at the centerline of the section, a b ending moment, and a thermal gradient. A cracked analysis of the section is required assuming linear material properties.

The fourth problem inv olves a section with 10 reinforcing steel bars under the a ction of a tensile force and biaxial bending.

A cracked analysis of the section is required assuming nonlinear materi al properties.

The hand-calculated so lutions were obtai ned according to the following procedure:

a. Assume the loc ation of neutral a xis and the stress distribution to be the same as those given by the program under the given mechanical loading.

b. Compute the stra in distribution under the given mechanical loading.

c. Compute the stre ss resultants by integration and using the proper stres s-strain relationships.

d. Check for equilibrium wi th external me chanical loads.

e. If equilibrium is satisf ied, compute the curvature imposed on the secti on by the given thermal gradient.

f. Compute the final curv ature by subtr acting the thermal curvature from t he mechanical curvature.

g. Compute the new axial strain such that equilibrium is satisfied keeping the curvature constant.

h. Compute the final stre ss resultants by integration and using the proper str ess-strain relationships.

B/B-UFSAR D.19-3 i. Compute the thermal moment.

j. Check for equilibrium and co mpare program results with hand-calculated results.

Results obtained using this procedure to gether with those computed by TEMCO for all four problems are pres ented in Tables D-33 and D-35.

It is concluded that r esults given by the program agree very well with results obtained by hand calculations and that equilibrium between internal and external forces is satisfied for all three problems.

B/B-UFSAR D.20-1 D.20 PENAN PENAN handles the analysis of axially symmet ric solids of revolution, which are composed of orthot ropic materials with temperature-dependent pr operties, and which are subjected to asymmetric and t ime-dependent heatin g and loading.

Mainly, the structure of this program is a c ombination of two suitably modified, axi symmetric finite eleme nt programs. The two programs are:

a. NOHEAT (Nonlinear Heat Transfer Analysis Program) by I. Farhoomand and E. Wilson, and

b. ASAL (Finite Element A nalysis-Axisymmetric Solids with Arbitrary Loads

), Dunham & Nickell.

Outlined below is a brief desc ription of the program's most significant features.

a. PENAN is designed to handle automatic finite element mesh gen eration and plotting for various penetration assembly configurations.

b. It has a built-in mate rial property bank covering temperature-dependent me chanical and thermal properties (including fa tigue design parameters) for all Section III materials.

c. It forms optimal load and load-range combinations for the various code-specifi ed loading categories and generates Fourie r series coefficients for all asymmetrically a pplied loads.

d. Through repeated use of the same sti ffness matrix and unit-load-stresses, the program can carry out multiple stress evaluations.

The program calculates the a llowable stresses for all stress categorie s, makes the necessary stress comparisons, and generates the entire Penetration Assembly Stress Analysis Report.

B/B-UFSAR D.21-1 D.21 SEEPAGE SEEPAGE (Two-Dimension al Steady-State Seepag e Analysis Program) is a finite element program de veloped for analyzing various types of two-dimensional ste ady seepage flows through non-homogeneous anisotropic poro us media such as flow through an earth dike; flow in to wells; and seepage losses through a bed of canals, lakes, etc.

The program is capable of comp uting the pressure, potential function, stream function values, velocities in two directions on a vertical plane, and dischar ge values through vertical section lines in the flow domain.

It can also determine the position of the free s urface line and plot the flow net.

Input for this program consists of the g eometry of the flow domain, directional permeability coefficients, a nd available pressure heads on the boundaries.

Output consists of nodal point pressures, potential value s, stream function values, velocities in two directions in every element, a nd discharge through specified sect ions. For seepage problems involving free surface, additional input is required, including the initial trial free surface, number of iterations for free surface, free surface correction fac tor, and error tolerance.

SEEPAGE was originally developed by Robert L. Taylor of the University of Californ ia at Berkeley. It has been extensively modified by Sargent & Lundy since 1972. It is n ow maintained by Sargent & Lundy on UNIVAC 1 100 series hardware under EXEC

8. In order to validate the SEEPAGE p rogram, two validation runs were made and the results were comp ared with solutions obtained by other an alytical methods.

Figure D-63 shows a plane flow p roblem along with the finite element representation u sed in the SEEPAGE c omputer run. The discharge per foot width of dam computed by SEEPAGE is 90.26 x 10-4 cfs; that obtained by using Dupuit's The ory (Reference 46) is 90.00 x 10

-4 cfs. Comparison of f ree surfaces determined by using SEEPAGE and those using Kozeny's solut ion (Reference 47) is shown in Figure D-64.

They are in close agreement.

For the second problem, groundwater flowing into a well is analyzed by SEEPAGE and hand calculations. The hand calculations are based on the well formula for steady radial flow in an unconfined aquifer as given in Reference 48.

Figure D-65 shows the finite element mesh configuration and permeability coefficients. The disch arge obtained from SEE PAGE is 0.6791 cfs; that from the hand cal culations is 0.6567 cfs.

B/B-UFSAR D.22-1 D.22 COLID COLID (Column Interaction Diagra m) calculates the axial load and bending moment c apacities using allo wable material and section properties f or rectangular and circular (solid and hollow) reinforced concr ete sections to be o utput as plotted interaction curves. The program uses the ACI 318-77 Building Code (Reference 49) and ASME (Reference

50) Code Factors.

These factors may be rep laced by user-defined values.

The axial load and ben ding moment capacities are generated by moving the neutral a xis from the extreme compression fiber across the section a nd by checking the strain compatibility between the steel and the conc rete. A compl ete interaction diagram is obtained for all sections for bot h compression and tension axial loads as well as positive and negative bending moments.

COLID was originally d eveloped at Sargent &

Lundy in 1973. It is now maintained on UNIVAC 1100 series hardware under EXEC 8.

To demonstrate the v alidity of the progr am, four rectangular and circular reinfor ced concrete sections are considered.

The first problem is a test of t he Stress Factors option for a rectangular section.

The sign convention and definition of parameters for r ectangular sections are shown in Figure D-66.

Design parameters and st ress factors used for the problem are given in Table D-36.

Results from t he program compare favorably with hand calc ulations, as shown in Table D-37, for the locations on the interaction diagram shown in Figure D-67.

The second problem tes ts the Ultimate Capaci ty and ACI Ultimate Capacity options for rectangular sec tions. Table D-38 contains the design input param eters. COLID resu lts compare favorably with hand calculations, as shown in Table D-39.

The third problem is a solid circula r tied column used to test the ACI ultimate capacity option.

Design parameters are given in Table D-40. As shown in Ta ble D-41, the re sults obtained from COLID compare favor ably with ha nd calculations.

The fourth problem is a hollow circular tied column used to test the Hollow Colu mn option for ACI ultimate capacity.

Design parameters are given in Table D-42.

The hand-calculated results shown in Table D

-43 compare favorably.

The final problem is an ultima te capacity rectangular section analysis to test metric units.

Parameters in Problem 2 were converted to metric and the problem was rean alyzed. English results were converted using hand calcul ations and compared with the COLID metric results. As shown in Table D-44, the results compare favorably.

B/B-UFSAR D.23-1 REVISION 3 - DECEMBER 1991 D.23 COMPONENT AN ALYSIS PROGRAMS D.23.1 THERST THERST is a Westinghouse proprie tary computer co de that is a one-dimensional heat t ransfer code used to calculate the time history throughwall tr ansient effects. The program is used to calculate the following on a time-history basis:

• Throughwall temperature dist ribution (printed values at 11 points through the wall)

• Average temperature

• Linear temperatu re distribution, T 1

• Nonlinear temper ature distribution, T 2 using a finite difference solution technique for circular cross sections with an adiabatic outsi de surface. The temperature variation on the ins ide surface is speci fic as series of linear ramps. A convection film coefficient is applied as a "resistance" between the input temperature distribution and the inside surface.

The time-history film coefficient can be specified directly either as a series of linear ramps or the time variation in velo city. The code will calculate the film coefficient, h. The following method is used to calculate the film coefficient:

h = hforce + h free (Btu/hr-ft 2-°F) where hforce = forced convection film coefficient hfree = free convection film coefficient This method was chosen to give a continu ous variation in film coefficient when velocity goes to zero; also, it is slightly conservative to incl ude both forced and free convection coefficients. The forced convection film coefficient for flow inside a pipe is Pr )v D ( D K 26.461 = h 0.4 0.8 forceµ where K = thermal conductivity (Btu/hr-ft-

°F)

D = inside diameter (in.) = fluid density (lb/ft

3)

B/B-UFSAR D.23-2 REVISION 1 - DECEMBER 1989 fluid veloci ty (ft/sec) µ = viscosity (lb/hr-ft) Pr = Prandtl number =

K C pµ C p = specific heat at constant pressure (Btu/lb-

°F) The free convection film coeffic ient for a vertical pipe is hfree = Pr D T g D K 0.555 0.25 i 3 2 2µ where g = gravitational constant = temperature coefficient of thermal expansion (1/°F) D i = inside diameter (ft) T = temperature difference between insid e surface of pipe and fluid (°F) THERST uses the temper ature-dependent materi al properties (C p , µ, K, etc.) in the c alculation of the film coefficient.

The results of THERST are saved on TAPE19 for later input to MAXTRAN79. This tape contains the run title , the time variation in water tempe rature, average temperature, T 1 , and T 2. D.23.2 MAXTRAN79 The program MAXTRAN79 is a Wes tinghouse propri etary computer code that calculates the secon dary and peak st ress intensities as defined by ASME S ection III NB-36 50, on a time-history basis for only the the rmal effects (T 1 , T 2 , T a , and T b). The stresses are calculated for one transient; t hat is, ranges are not considered.

The secondary (S s) and peak (S p) stress intensity equations become:

T - T E C = S b b a a ab 3 s T-1 E + T - T E C K + T )-2(1 E K = S 2 b b a a ab 3 3 1 3 p where all terms are as defined in ASME Secti on III NB-3650 and = 0.3 and = a.

B/B-UFSAR D.23-3 MAXTRAN79 finds the time(s) of m aximum/minimum s econdary stress and maximum/minimum peak stress to be used in the postulation of pipe break lo cations and the calculat ion of usage factors, respectively. The v alue of maximum peak str ess is chosen at the time of maximum alte rnating stress, where S alt = [S p] K e/2.0 and where S n = an input primary-plus-secondary stress representing the range in pressure and moment stress plus the thermal transient stress (T a - T b) from another transient S n = S + S s'n 'n S = secondary pressu re and moment stress K e = -2.3 + 1.1 S S m n 1 and 1.0 K e 3.3 (austenitic st ainless steel)

The input of MAXTRAN 79 consists of car ds describing a node number and types of members (tee, branch, straig ht run, weld, and the like) for which the Code cal culates the stress indices. Also input are the tap es generated from the THERST program. One tape must be available for each cross section and transient being consider ed. If a point of t hermal discontinuity is being analyzed (for instance, the weld at a v alve), two tapes must be input. The ta pe containing the pipe cross-section data is used to obtain (T 1 , T 2 , and T a. The tape containing the valve cross-section data is used to obtain T

b. The output of MAXTRAN79 consists of the following:

• An echo of the input

• A table giving t he maximum and minimum secondary and peak stresses and the corresponding time, Twater , (T 1 , T 2 , T a , and T b

• An output tape for FAT CON input givi ng member data, (T 1 , T 2 , (T a - T b) and T a for the condition yielding maximum and minimum secondary and peak stresses

• Plots of secondary peak and alternating stresses versus time

B/B-UFSAR D.23-4 D.23.3 FATCON Program FATCON is a Westinghouse proprie tary computer code which is used to perform fatigue ana lysis in accordance with the ASME B and PV Co de,Section III, Sub section NB-3600, 1977 Edition through and including the Summer 1979 Addenda.

The program input consists of a combination of c ard images and cataloged MAXTRAN thermal tran sient tapes. The card images identify member type, pr operties, fatigue cy cle data, and other problem specific informa tion. The tapes -

consisting of up to 19 separate tapes per proble m run - supply temperature transient data for use in evaluation of Code equations (10), (11), 13), and (14).

The program is divided into two dist inct portions. The purpose of the first portion is to calculate the cumulative usage factor using the peak st ress data from MAXTR AN. Included in this portion of the program are the spec ific transients by label and type, temp erature data (input) associated with each transient, number of cycles for each tra nsient, and the pressure, along with the stress indices for the member. The transient combinations are identified in dividually and all pertinent data are lis ted including cumulati ve usage factor.

When equation (10) is exceeded, a message appears and equation (13) without moment is printed. The second portion, identified by the heading S ECONDARY, is used to maximize equation (13) independently of the usage factor calculations a nd prints out equation (13) without moment for various transient combinations.

D.23.4 WECAN The WECAN computer program is a Westinghouse proprietary computer program that can be used to solve a large variety of structural analysis pr oblems. These pro blems can be one-, two-, or three-dimensional in nature. It has the capability to do static elastic and inelas tic analyses, st eady-state and transient heat condition analy sis, steady-st ate hydraulic analysis, standard and reduced modal analysis, harmonic response analysis, and t ransient dynamic analysis.

The WECAN program is based on the finite element method of analysis. The analy st must model, or id ealize, the structure in terms of discrete elements and apply loadings and boundary conditions to these el ements. The stiff ness (or conductivity) matrix for each element is assembled into a system of simultaneous linear equa tions for the entire s tructure. This set of equations is then solved by a variati on of the Gaussian elimination method known as the wave front t echnique. This type of solution makes it possibl e to solve syste ms with a large number of degrees of freedom using a m inimum amount of core storage. The maximum nu mber of allowed degrees of freedom in the wave front depends on the amou nt of core available which, in turn, depends on the type of analysis be ing performed.

B/B-UFSAR D.23-5 The library of finite elements includes spar s, beams, pipes, plane elements, axisym metric solids of r evolution elements, three-dimensional solids, pl ates, plane and axisymmetric shells, three-dimensional shells, friction interface elements, springs, masses, dampers, heat c onduction elements, hydraulic conducting elements, c onvection elements, an d radiation elements.

WECAN is organized so that add itional structural elements can be added with a minimum of effort. Input formats are similar for all elements and all types of analyses. I nput data are used in the static analysis with only minor modifications.

The program is in a continual st ate of development.

No version is made available un til it has been chec ked and determined to be free of errors.

B/B-UFSAR D.24-1 D.24 MISLODS MISLODS (Probability of Turbine Missile Damage), pronounced "missile odds," calculat es the probability of damage to power plant structures due to turbine missiles.

This probability, P 4 , can be expressed as P 4 = P 1 P 2 P 3 where P 1 = probability of missile ejection, P 2 = probability of the mis sile striking selected barriers, given the missile ejection, P 3 = probability that the m issile will penetrate the barriers, given the missile ejection and strike. P 1 issupplied as input. MISL ODS calculates the values of P 2 and P 3 , which are dependent on the missile characteristics, plant geometry, struct ural materials, and thicknesses. The methodology is based on references 5 1, 52, and 53.

MISLODS was developed by Sargent

& Lundy in 1975. It is currently maintained on UNIVAC 1100 series hardware operating under EXEC 8.

To demonstrate the v alidity of MISLODS, the program's solution is compared to t he problem presented by Semanderes on pages 7 through 10 of refere nce 54. In this problem, strike probabilities are determined for 3 types of targ ets and 4 types of missiles. The comparison b etween MISLODS and Semanderes' results is shown in Table D-12. The com parison is n ot exact, however, because of the differences in the t wo methods. Where Semanderes uses a Mo nte Carlo simulation, MISLODS uses a more definitive numerical integration procedure.

However, as shown in Table D-12 the independen t solutions comp are favorably.

B/B-UFSAR D.25-1 REVISION 7 - DECEMBER 1998 D.25 BSAP BSAP (Bechtel Structural Analysis Program) is a general purpose, finite-element computer program for analysis of structural systems subject to s tatic, dynamic, and thermal loads. The program incorporates an extensive library of beam, shell, and solid elements, such that virtually any type of structure can be represented. The Bechtel version of the BSAP is based upon and incorporates features of the S AP program developed at the University of California at Berkeley by Professor E. L. Wilson.

BSAP has been extensively used in the design and analysis of nuclear power plant stru ctures since the mid-1 970s. BSAP has been used to analyze the Byron a nd Braidwood Unit 1 containment structures to assess the effec ts of the temporary construction opening created to accommodate activities associated with the steam generator repl acement project.

A thin quadrilat eral and triangular shell element that has membrane and bending propert ies has been used to develop a three-dimensional, fin ite-element model of the containment structure. Each node of the she ll element has five degrees of freedom (three translati ons and two rotations).

The rotation about an axis normal to the plane of the ele ment is not defined.

Static loads whi ch may be considered i nclude nodal forces, distributed pressures, differential temperat ures, and boundary movements. The static solution is obtai ned using Gaussian elimination techniqu e or Crout elimina tion technique.

The validation process f or BSAP consists of a number of problems designed to check the full range of available BSAP capabilities.

The BSAP results are compared wi th the benchmark results derived from independent methods of solu tion that have been previously validated or are generally c onsidered to be correct. Hand calculations employing well-established comp utation methods were used for some problems.

For many proble ms, a benchmark solution was obtained by using an independently program med public domain program.

B/B-UFSAR D.26-1 REVISION 9 - DECEMBER 2002 D.26 BWSPAN/BWSCAN BWSPAN is a large, fin ite-element program using beam elements for the analysis of stru ctural systems.

BWSPAN's library of elements include various pipe and structural e lements. BWSPAN performs static, response spectrum, and time history analyses of structural systems.

Stress analysis opt ions include ASME Section III Class 1, 2, and 3; ANSI B31.7 and B31.1 for piping; and ASME NF and AISC for str uctural steel. Additional capabilities include nonlinear (gapped) static and dynamic analyses and thermal stratificat ion analyses. B WSPAN is capable of evaluating thermal stratification. BWSCAN is a stress postprocessor of BWSPAN.

B/B-UFSAR D.27-1 REVISION 7 - DECEMBER 1998 D.27 BWSPEC BWSPEC reads and process es output files genera ted by BWSPAN and presents the results in a consistent, logical fashion that can be readily understood by equipment designers wh o require interface loading information.

B/B-UFSAR D.28-1 REVISION 7 - DECEMBER 1998 D.28 RESPECT RESPECT generates respon se spectra from time histories. It also generates time histories in st ructures and s pectra for attachments.

B/B-UFSAR D.29-1 REVISION 7 - DECEMBER 1998 D.29 ATHOSBWI ATHOS is a three-dimensional, th ermal-hydraulic code using the methods of computational flu id dynamics (CFD

). ATHOS is comprised of two programs: the geometric preprocessor GPP module and the thermal-hydraulic program ATHOS module.

Part of the output from the GPP modu le is used as input to the ATHOS module.

ATHOS3 Mod-01, developed by CFD Research Corpora tion (CFDRC) and licensed by EPRI, was acquired in March 1993 by B&W. B&W corrected some inconsi stencies and m ade further modifications.

The update was verified against field measur ements and another CFD code, THIRST, which was de veloped by AECL.

The program was renamed ATHOSBWI and h as been used extensive ly at B&W for PWR replacement steam generator designs.

Major modifications to the original code ATHOS3 Mod-01 include corrections to the the rmodynamic properties of the secondary fluid and the tube g ap velocity calculations for flow-induced vibration (FIV) analysis. Since the latter is n ot used in the present study, only the thermodynamic proper ty modification is described below. When ATHOS3 Mod-01 was obtai ned, it was found that the secondary saturation co nditions were incons istent with ASME steam tables.

ATHOS3 Mod-01 co rrelations were then replaced with "IFC for mulation for industria l use" from the ASME steam tables. These modifications were tested by comparisons with the saturation temperatures of the steam ta bles and with field measurements perfo rmed by Westinghouse.

The ATHOS3 code comput es the steady-state and time-dependent behavior of the thermal-hydraulic parameters of PWR steam generators. The calcu lated overall (i.e., g lobal) parameters of a steady-state analysis are:

a. Inlet temperature of the primary fluid,

b. Circulation ratio, c. Secondary side invento ry (i.e., liquid "collapse" level and associated liquid "hold-up" volume fraction) in the shell (excluding the do wncomer region), d. Enthalpy and flow rate of recirculating mixture, and

e. Downcomer liquid inven tory, mass flow rates and average enthalpies.

In a transient analysis, the f ollowing overall p arameters are calculated as a function of time:

a. Temperature drop of the primary fluid, B/B-UFSAR D.29-2 REVISION 7 - DECEMBER 1998 b. circulation ratio, c. Shroud secondary side in ventory (i.e., c ollapse level and hold-up v olume fraction),

d. Enthalpy and flow rate of recirculating mixture, e. Downcomer mass flow rates and average enthalpies, f. Height of the water level in the downcomer, and

g. Rates of heat transfer f rom the primary side and to the secondary side; and eith er: (a) mass outflow rate of steam leaving the dome, or (b) steam dome pressure, depending on user-specified outlet boundary condition.

In order to calculate the above overall/global p arameters, the ATHOS3 code first comp utes the three-dim ensional distributions of the followi ng parameters:

a. Primary-flui d temperature, b. Tube-metal mid-wall temperature,

c. Heat flux to the seconda ry side fluid (s team and water mixture), d. Enthalpy and temperature of the secondary side fluid,

e. Mass quality and void fr action of the se condary side fluid, f. Three velocity c omponents of the steam and water phases, g. Secondary si de pressure, and

h. Various other au xiliary parameters.

B/B-UFSAR D.30-1 REVISION 7 - DECEMBER 1998 D.30 EasyFIV EasyFIV is a PC-based, user-friendly, flow-i nduced vibration code used for predicting the r esponse of tube bundles (or single tubes) subjected to cros sflow. It provides default values and ranges for the c onstants needed for the anal ysis. However, some background knowledge in FIV is necessa ry for the user to judiciously select t he constants for the application.

The FIV calculations in EasyFIV are performe d in two steps.

First, a commercially available, finite-elem ent software (PAL2) integrated within EasyFIV calcul ates the natural frequencies and mode shapes of t he tubes. Then the na tural frequency and mode shape information along with the crossflow velocity distribution and other FIV parameters provided by the user are used to predict the FIV respon se of the tubes. The results of the FIV analysis can be displayed graphi cally or in tabular form. Hard copies of the tables a nd graphs can be obtained.

There are four mechanisms that cause tube bu ndles (subjected to crossflow) to vibrate.

They are as follows:

1. Fluid-elasti c instability,

2. Vortex shedding, 3. Turbulence buffeting, and

4. Acoustic resonance EasyFIV predicts the tube resp onse due to the first three mechanisms. Response due to acoustic resona nce is not predicted since acoustic resonance is not of concern in liquid and two-phase crossflow situations.

The most common tube g eometries that are used for EasyFIV analysis are straight tubes and U-tubes. Ho wever, EasyFIV has the capability of mode ling any complex-shape d tube geometry.

The only restriction is that the entire tube lie in one plane.

B/B-UFSAR D.31-1 REVISION 7 - DECEMBER 1998 D.31 CIRC The BWC computer code, C IRC provides a one-d imensional, thermal-hydraulic analysis of natural circulation, i nverted U-tube nuclear steam generators.

Heat transfer, ci rculation ratio, and water level analysis c apabilities are availa ble. The code is capable of analyzing steam generator s with integral or nonintegral preheaters.

As a minimum, the program determines the thermal performance based on the inp ut parameters. The program can also do partial power cases, specified as a fraction of the full-power steam flow where the prima ry inlet conditions are recalculated by CIRC.

Inputs vary depending on the scope of an alysis required, but basic geometry, terminal point parameters, f low characteristics, and fluid properties are required.

Output for the i nput case, as well as for specified full-power and partial power cases, includes steam flow rat e, heat duty, secondary side fluid q ualities and densities , circulation ratio, circulation loop pressure losses, and a water level/inventory analysis.

The BWC thermal-hydraulic analys is program, CIRC, provides a one-dimensional analys is of a natural recirc ulating inverted U-tube steam generator with ei ther light or he avy water primary fluid. The code has the capabil ity of performing heat transfer, circulation, and water level/invento ry analyses.

Heat Transfer Analysis The CIRC code calculates the heat transferred in the boiler.

The basic case of no primary fluid inlet quality and no integral preheater will be co nsidered first. T he surface area of the boiling zone (B-Zone) is divided into ten eq ual area zones and the heat transferred is determined for each zone with the secondary side modeled as an infinite he at sink of constant temperature equal to secondary side saturati on. The heat transfer across the tube wall ac counts for con vection at the tube inside diameter (ID), tube wall met al conductivity, tube outside diameter (OD) fo uling, and pool boil ing at the tube OD.

The analysis for the case of p rimary side quality proceeds similarly with the fol lowing exceptions. Th e tube area (A-Zone) required to condense the prima ry side quality is determined by calculating the heat t ransfer necessary to r educe the enthalpy of the incoming primary fluid to saturated conditions. The heat transfer coefficient again i ncludes ID convection, metal conductivity, foulin g, and boiling coefficient at the tube OD.

This area is deducte d from the total boi ler area input and the remaining area is divided into t en zones. The remainder of the heat transfer analysis proceeds as above.

B/B-UFSAR D.31-2 REVISION 7 - DECEMBER 1998 For the case of the in tegral preheater, the boiling area heat transfer analysis prior to the preheater is as discussed above.

At the preheater, boil ing, subcooled boi ling, and convective heat transfer zones (C, D, and E Zones, respectively) are considered. The heat transfer analysis in the preheater pool boiling zone is simi lar to the analysis outside of the preheater. The subcooled boiling region is determined as the region where the boiling heat tr ansfer coefficie nt is larger than the convective coefficient.

In the convective zone, countercurrent heat tran sfer is assumed (as re flected in the log mean temperature difference) a nd the input convective heat transfer coefficient at the tube OD is used.

The basic solution technique assumes an enthalpy for the secondary fluid leaving the preheater and calc ulates the corresp onding feedwater inlet temperature.

This calculated temper ature is compared with the input value, and the outlet enthalpy is adjusted until the calculated value converges to the inp ut feedwater tempera ture. Effects of leakage through the thermal plate to the hot leg are included in the heat transfer analysis of the convective z one below the thermal plate (F Zone).

In this zone, count ercurrent convective heat transfer is assumed with a secondary flow equal to the outlet steam flow.

Circulation Analysis The circulation analysis portion of the CIRC c ode determines the circulation ratio of the generat or. All irrecov erable component pressure losses, as well as static heat, are d etermined around the circulation loop, ba sed on local fluid p roperties. When the flow losses equal the static pumping head, a converged solution is obtained.

The circulation analysis first considers the h eat transferred in the thermal-hydraulic zones and redistribute s it over geometric zones, i.e., tube support spans and U-bend. The fluid properties are then determined at the planes of the tube supports and in the spans between the supports.

Slip effects due to the two-phase secondary mixture a re considered when calculating pumping head. Values are determined for all dynamic losses (shock, friction, etc.) around the loop and combined with pumping head and static head until conve rgence is obtained, i.e., circulation loss es equal total pumping head. The final circulation ratio is then determined.

During a requested partial p ower calculation, a water level analysis is performed during each circ ulation iteration.

B/B-UFSAR D.31-3 REVISION 7 - DECEMBER 1998 Water Level/Inve ntory Analysis This segment of the CIRC program determines the steam generator's secondary si de inventory or wate r level for a series of geometric volumes input by the user. The r outine works for two modes of input: water l evel versus power and inventory versus power. For s pecified water lev el, the inventory is calculated based on the previously deter mined average volume densities and the input volumes.

For specified inventory, the water level is determine

d. In addition, for partial power cases, the change in inventory (from 100

%) or the new water level can be specified and the unkno wn quantity is determined.

The zero-power water l evel or inventory is also determined.

B/B-UFSAR D.32-1 REVISION 7 - DECEMBER 1998 D.32 CRAFT2 - Loads Version CRAFT2 is a thermal-hydraulic code that tracks transient pressures and flows due to system pertur bations. The results are processed into for cing functions. T he code is used to produce the forces due to pipe breaks in pre ssurized systems.

CRAFT2 is the Framat ome Technologies, In c., version of the original NRC-approved CR AFT code. It was reprogrammed to make the inputs and outpu ts compatible wi th other codes.

B/B-UFSAR D.33-1 REVISION 7 - DECEMBER 1998 D.33 COMPAR2 COMPAR2 calculates bui lding compartment pressu res resulting from mass and energy input. The code is typically used in asymmetric cavity pressure calculat ions due to high-energy pipe breaks.

These pressures are processed into c ompartment forcing functions. COMPAR2 is t he Framatome Technol ogies, Inc., version of the NRC-approved COMP AR-MOD1 code (NUREG-06 09), which was the original Los Alamos code version.

It was reprogrammed to make the inputs and outpu ts compatible wi th other codes.

B/B-UFSAR D.34-1 REVISION 7 - DECEMBER 1998 D.34 REFERENCES

1. Portland Cement Association, "Notes on ACI 318-71 Building Code Requirements with Design Applications," pp. 1-14, July 1972.

2. E. L. Wilson, "A Compute r Program for th e Dynamic Stress Analysis of Underground Struct ures," Report to U.S. Army Engineering Waterways Experiment Station, January 1965.

3. Newmark, Nathan and Rosenblueth, Emi lio. Fundamentals of Earthquake Engineering , Prentice-Hall, Engle wood Cliffs, N. J., p. 15, 1971.

4. J. Biggs, Introduction to Structural Dynamics, McGraw-Hill, New York, p. 266, 1964.

5. S. Ghosh and E. Wilson, "D ynamic Stress Analysis of Axisymmetric Structu res Under Arbitrary Loading," Report No. EERC 69-10 , University of California , Berkeley, Sept ember 1969.

6. S. Timoshenko and S.

Woinowsky-Krieger, Theory of Plates and Shells , McGraw-Hill, New York, pp. 553-554, 1959.

7. S. Timoshenko an d J. Goodier, Theory of Elasticity , McGraw-Hill, N ew York, 1970.

8. B. Budiansky and P. Radkowski, "Nu merical Analysis of Unsymmetric Bending of Shell of Revolution," Journal of the American Institute of Aeronautics and Astronautics , August 1963.

9. H. Reismann and J.

Padlog, "Forced, Axisymmetric Motions of Cylindrical Shel ls," Journal of the Franklin Institute , Vol. 284, No. 5, pp. 308-319, November 1967.

10. S. Klein, "A Study of the Matrix Displa cement Method as Applied to Shells of R evolution," Proceedings , Conference on Matrix Methods in Stru ctural Mechanics, Wright-Patterson Air Force Base, Ohio, 1965.

11. J. F. Abel, P. P.

Cole, D. P. Billi ngton, "Maximum Seismic Response of Cooling Towers," Report No. 73-SM-1 , Department of Civil and Geological Engineering Research, Princ eton University, March 1, 1973.

12. J. M. Doyle and S. L. Chu, "Liner Plate Buckling and Behavior of Stud and Rip Type Anchors," Proceedings , First International Conference on St ructural Mechanics in Reactor Technology, Berlin, Ge rmany, Volume 4, P art H, September 1972.

13. A. G. Young and L. A. Tate, "Design of Liners for Reactor Vessels," Proceedings , Conference on P restressed Concrete Pressure Vessels, Institute of C ivil Engineers, London, 1967, Paper J57.

B/B-UFSAR D.34-2 REVISION 7 - DECEMBER 1998

14. "Nelson Stud Welding Ap plications in Po wer Generating Plants," Nelson Stud Welding Company, Lorain, Ohio.

15. S. H. Bush, "Pr obability of Damage to Nuclear Components Due to Turbine Missi les," Nuclear Safety , 14(3): 187-201 (May-June 1973).

16. D. H. Shaffer, S.

C. Chay, D. K. McLain , and B. A. Powell, "Analysis of the Probability of the Generation a nd Strike of Missiles from a Nuclear Turbine," West inghouse Electric Corporation, March 1974.

17. Sargent & Lundy , "Turbine Missile S tudy," Appendix C.O, Byron/Braidwood FSAR , Amendment 17, No vember 1978.

18. S. N Semanderes, "Methods of Determinin g the Probability of a Turbine Missile Hitting a Particular P lant Region," Westinghouse Ele ctric Corporation, February 1972.

19. C. K. Wang and C.

G. Salmon, Reinforced Concrete Design, Second Edition, Intext Educational Publi shers, New York and London, 1973, pp. 436-438.

20. Portland Cement Association, Notes on ACI 318-71 Building Code Requirements with Design Applications, 1972, pp. 9-25 through 9-27.

21. ASME Boiler and Pressure Ve ssel Code, Sec tion III, 1977, Winter 1979.

22. J. S. Kinne y, Indeterminate Structural Analysis, Addison-Wesley Publishing Company, Reading, Massachusetts, 1957, p. 377. 23. "Sample Analysis of a P iping System Class 1 Nuclear," prepared by Working Group on Pip ing of the Design Subgroup of the Nuclear Power Committee of t he ASME Boiler and Pressure Vessel Committee, the American Society of Me chanical Engineers, New York, 1972.

24. ICES DYNAL User

's Manual, McDonnell Dou glas Automation Co., September 1971.

25. NASTRAN Theoret ical Manual, NASA SP

-221, September 1970.

26. NASTRAN Use r's Manual, NASA SP-22 2, September 1970.

27. Y. K. Cheung and J. D.

Davies, "Analysis of Rectangular Tanks," CONCRETE , London, England, Vol.

1, pp. 169-174, May 1967.

B/B-UFSAR D.34-3 REVISION 7 - DECEMBER 1998

28. O. Zienkiwicz and Y. Cheung, "The Finit e Element Method for Analysis of Elastic Isotropic and Orthotropic Slabs," Proceedings of the Institute of Civil Engineering, London, England, pp. 471-487 , August 1964.

29. P. B. Schnabel et al., "SHAKE: A Computer Program for Earthquake Response An alysis of Horizontally Layered Sites," Report No. EERC 72-12 , Earthquake Engine ering Resear ch Center, University of California, Berkeley, December 1972.

30. I. M. Idriss and H. B. Seed, "Seismic Res ponse by Variable Damping Finite Eleme nts," Journal of the Geotechnical Engineering Division , ASCE, Vol. 100, No.

GT1, Proc. Paper 10284, pp. 1-13, January 1974.

31. H. B. Seed and I. M. Idriss, "Soil Moduli and Damping Factors for Dynamic Resp onse Analyses," Report No. EERC 70-10 , Earthquake Engineeri ng Research Center, University of California, Berkeley , December 1970.

32. "ICES SLOPE - Slope Stabi lity Analysis Sy stem," McDonnell Douglas Automation Company, 1974.

33. E. L. Wilson, " SAP-A General Struct ural Analysis Program," SESM Report 70-20, Dept. of Civil Engineering, U niversity of California, Be rkeley, 1970.

34. S. Timoshenko a nd J. Gere, Mechanics of Materials , Van Nostrand Reinhold Company, N ew York, pp.99-100, 1972.

35. S. Timoshenko and S. Woinowski-Krieger, Theory of Plates and Shells , McGraw-Hill, New Y ork, p. 118, 1959.

36. K. J. Bathe, E.

L. Wilson and F. E.

Peterson, "SAPIV, A Structural Analysis Pr ogram for Static and D ynamic Response of Linear Systems," Earthquake Engi neering Research Center, Report No. EERC 73-11 , June 1973.

37. "ADL Pipe Stati c-Thermal-Dynamic Pipe Stress Analysis," Arthur D. Little, Inc., Cambridge, Massachus etts, January 1971.

38. "Construction I ndustry Programs, PIPDYN

Dynamic Analysis of Piping Systems," Co mputer Sciences Corpor ation, Los Angeles, California.

39. H. Reismann and J. Padlog, "Forced, Axi symmetric Motions of Cylindrical Shel ls," Journal of the Franklin Institute , Vol. 284, No. 5, Nov., 1967.

40. "A Program to P erform Stress Anal ysis of Shells of Revolution," Knolls At omic Power Laboratory, Schenectady, New York, September 1963.

B/B-UFSAR D.34-4 REVISION 7 - DECEMBER 1998

41. J. H. Percy, D.

R. Navaratna, S. Klein, "Stress and Bending Analysis for Shells of Revolution III," ASRL TR 121-7, MIT Aeroelastic and Structures Laboratory.

42. Manual of Steel Construction , Seventh Edi tion, American Institute of Steel Const ruction, New York, N. Y.

43. R. D. Logcher et al., "ICES STRUDL II, The Structural Design Language Engineer ing User's Manual," De partment of Civil Engineering, M.I.T., 1st ed., November 1968.

44. "ICES STRUDL Im provements," McDonnell Douglas Automation Company, February 1973.

45. "ICES Applicati on Brief," UNIVA C Marketing Supp ort, Sperry Rand Corporation, 1972.

46. R. L. Taylor and C. B. Brow n, "Darcy's Flow Solutions with a Free Surface," Journal of the Hydraulics Division , ASCE, Vol.

93, No. HY2, March 1967, pp. 25-33.

47. M. E. Harr, Groundwater and Seepage , McGraw-Hill Book Company, New York 1962.

48. V. T. Chow, Handbook of Applied Hydrology , McGraw-Hill Book Company, New York, 1964.

49. ACI 318-77 Building Code Requirements f or Reinforced Concrete Section 9.3, page 29.

50. ASME Boiler and Pressure Ve ssel Code, Sec tion III Nuclear Power Plant Components, Division 2, Tables C C-3421-1, CC-3431-1, 80, page 170.

51. Bush, S. H., "Probability of Damage to Nuclear Components Due to Turbine Missiles," Nuclear Safety , 14(3): 187-201 (May-June 1973).

52. Shaffer, D. H., Chay, S. C., McLain, D.

K. and Powell, B.

A., "Analysis of the Probability of the Generation and Strike of Missiles from a Nuclear Turbine," West inghouse Electric Corporation, March, 1974.

53. Sargent & Lundy , "Turbine Missile S tudy," Appendix C.0, Byron/Braidwood PSAR, Am endment 12, May, 1975.

54. Semanderes, S. N., "Methods of Determining the Probability of a Turbine Missile Hitting a Particular Plant Region," Westinghouse Electri c Corporation, F ebruary, 1972.

55. Sheron, Brian W. (NRC) to Cloud, Robert L. (Rob ert L. Cloud

& Associates, Inc.), letter, subject: To pical Report Review of RLCA Report, "A Topical Report on the Me thodology, Verification and Applications of Computer Program GAPPIPE," RLCA/P94/04-94/009, June 1, 1994

," dated April 11, 1995.

B/B-UFSAR

D.T-1 TABLE D-1 SPAN 1 CHARACT ERISTICS AND DESIGN RESULTS LEFT SIDE MIDDLE RIGHT SIDE Clear span (ft) 23.0 Section (in.) 24.0 x 36.0 Design moment 1130.70 650.00 1204.70 M u (kip-ft)

Design shear 345.40 134.10 230.70 V u (kip)

Required area (in

2) CBEAM 8.62 4.57 9.31 Hand 8.58 4.72 9.36 Calcs.

Required bars CBEAM 2 - #10 3 - #11 2 - #10 4 - #11 5 - #11

Hand 2 - #10 3 - #11 2 - #10 Calcs. 4 - #10 5 - #11

Provided steel CBEAM 8.78 4.68 10.34

Hand 8.78 4.68 10.34 Calcs.

Stirrups CBEAM #5 - @ 7.0 in.* #4 - @ 14.0 in.**#4 - @ 4.0 in.**

Hand #5 - @ 7.0 in.* #4 - @ 14.0 in.**#4 - @ 4.0 in.** Calcs.

____________________

• Type 2 Stirrups:

• • Type 1 Stirrups:

B/B-UFSAR

D.T-2 TABLE D-2 SPAN 2 CHARACT ERISTICS AND DESIGN RESULTS LEFT SIDE MIDDLE RIGHT SIDE Clear span (ft) 15.5 Section (in.) 24.0 x 27.0 Design moment 627.40 484.30 543.90 M u (kip-ft)

Design shear

V u (kip) 132.90 70.40 103.60 Required area (in

2) CBEAM 6.51 4.77 5.42 Hand 6.69 4.73 5.45 Calcs.

Required bars CBEAM 2 - #10 4 - #11 6 - #10 5 - #11

Hand 2 - #10 4 - #11 6 - #10 Calcs. 5 - #11

Provided steel CBEAM 10.34 6.24 7.62 Hand 10.34 6.24 7.62 Calcs.

Type 1 stirrups CBEAM #4 - @ 6.0 in. #4 - @ 12.0 in. #4 - @ 12.0 in.

Hand #4 - @ 6.0 in. #4 - @ 12.0 in. #4 - @ 12.0 in. Calcs.

B/B-UFSAR

D.T-3 TABLE D-3 SPAN 3 CHARACT ERISTICS AND DESIGN RESULTS LEFT SIDE MIDDLE RIGHT SIDE Clear span (ft) 15.5 Section (in.) 2.24 x 27.0 Design moment 586.30 503.10 490.40 M u (kip-ft)

Design shear 111.80 67.60 112.80 V u (kip)

Required area (in

2) CBEAM 5.88 4.97 4.84 Hand Calc. 5.86 4.98 4.86

Required bars CBEAM 6 - #10 4 - #11 4 - #10 Hand 6 - #10 4 - #11 4 - #10 Calcs.

Provided steel CBEAM 7.62 6.24 5.08

Hand 7.62 6.24 5.08 Calcs.

Type 1 stirrups CBEAM #4 - @ 10.0 in. #4 - @ 12.0 in. #4 - @ 9.0 in.

Hand #4 - @ 10.0 in. #4 - @ 12.0 in. #4 - @ 9.0 in. Calcs.

B/B-UFSAR

D.T-4 TABLE D-4 RESULTS FOR 28-D AY STRENGTH

Number of Samples Collected - - -46 Mean Observed Strength - - -3456.1Allow. Design Str. - 2955.1Spec. Design Str. - 2500.0

Observed Standard Deviation - - -373.0C.O.V. % - - - 10.8Expected C.O.V.

% - 15.0 Within Test Std. Deviation - - -.0C.O.V. % - - - .0Expected C.O.V.

% - 5.0 Mean Observed Range - - - - -.0

Total Number of Bad Samples - Average Strength 0 Number of Times Inefficient Testing Observed 0 CONTROL ACCORDING TO ACI MANUAL Number of Samples Falling Below FC - - - - - - - - - - 0 Percent of Samples Collected - .00 Number of Samples Falling Below FC-500 - - - - - - - - 0 Percent of Samples C ollected - .00 Number of Times Moving Avg. Fell Below FC - - - - - - 0 Percent of Samples Collected - .00

B/B-UFSAR

D.T-5 TABLE D-5 STRUCTURAL FREQUENCIES STRUCTURAL FREQUENCY

MODE (cps) NUMBER BIGGS DYNAS 1 1.00 1.00 2 2.18 2.18

3 3.18 3.18

B/B-UFSAR

D.T-6 TABLE D-6 PROBABLE MAXIMUM STO RY DISPLACEMENTS PROBABLE MAXIMUM STORY DISPLACEMENT (inches) MODE NUMBER BIGGS DYNAS 1 1.50 1.51 2 3.22 3.20

3 4.86 4.68

B/B-UFSAR

D.T-7 TABLE D-7 ABSOLUTE MAXIMUM STORY SHEARS ABSOLUTE MAXIMUM STO RY SHEAR (kips) MODE NUMBER BIGGS DYNAS 1 3020 3010 2 2080 2068 3 1345 1353 B/B-UFSAR

D.T-8 TABLE D-8 PROBABLE MAXIMUM STORY SHEARS

PROBABLE MAXIMUM STORY SHEARS (kips) MODE NUMBER BIGGS DYNAS 1 2550 2262 2 1740 1757 3 895 902

B/B-UFSAR

D.T-9 TABLE D-9 NATURAL PERIODS FOR THE EIGHT LOWEST FLEXURAL MODES PERIODS (seconds) MODE NUMBER SAPIV DYNAS 1 525.7900 525.69 2 85.36800 85.369 3 30.9650 30.964

4 16.0590 16.060

5 9.9006 9.9010

6 6.8276 6.8279

7 5.1865 5.1866 8 4.3777 4.3778

B/B-UFSAR

D.T-10 TABLE D-10 COMPUTER OUTPUT DISPLACEMENTS LOCATION VALUE (inches)

U l .059492

U 2 .045083

U 3 .033292

U 4 .023913 U 5 .016642

U 6 .011246

U 7 .007491

U 8 .004830 U 9 .002874

U 10 .001338

f l 16.293 kips Post-Buckling Load P = 21.978 kips

B/B-UFSAR

D.T-11 REVISION 1 - DECEMBER 1989 TABLE D-11 COMPUTER OUTPUT ANCHOR FORCES

LOCATION VALUE (kips) f 1 16.270

f 2 15.430

f 3 14.149 f 4 12.338

f 5 10.935

f 6 9.531

f 7 6.348 f 8 4.093

f 9 2.436

f 10 1.134

B/B-UFSAR

D.T-12 TABLE D-12 COMPARISON OF P 2 VALUES FROM MIS LODS AND SEMANDERES MISSILE INITIAL VELOCITY RANGE MISSILE TARGET A1 TARGET A2 TARGET A3 (ft/sec) LOCATION MISLODS SEMANDERES MISLODS SEMANDERES MISLODS SEMANDERES Interior 3.5E-3* 1.8E-3 1.3E-4 8.7E-5 1.3E-4 7.7E-5 270-330 End 4.6E-4 4.8E-3 5.3E-5 4.1E-5 5.3E-5 3.5E-5

Interior 8.4E-4 2.7E-4 8.2E-6** 4.5E-6 8.2E-6 4.1E-6 540-660 End 1.1E-4 5.9E-5 3.2E-6 2.0E-6 3.3E-6 3.9E-5

• The notat ion "3.5E-3" means 3.5 x 10

-3 or 0.0035.

• • Hand calculation of t his value is 8.17E-6.

B/B-UFSAR

D.T-13 TABLE D-13 COMPARISON OF MOMENTS FOR SELECTED MEMBERS MOMENTS FROM MOMENTS FROM REFERENCE 22 PIPSYS (kip-ft) (kip-ft) M AB 106.0 102.8 M BA 72.0 72.5 M BC 133.0 131.8 M CB 133.0 131.8 M CD -133.0 -131.8 M DC -133.0 -131.8 M DE 133.0 131.8 M ED 86.0 84.2 M BE -158.0 -156.6 M EB -158.0 -156.6 M FE 106.0 102.8 M EF 72.0 72.5

B/B-UFSAR

D.T-14 REVISION 1 - DECEMBER 1989 TABLE D-14

SUMMARY

OF LOAD SETS AT GIRTH BUTT-WELD WITH CHANGE IN MATERIAL AND WALL THICKNESS, LOCATION 19

LOAD NO. OF T a T b SET NO. LOAD SET DESCRIPTION TRANSIENTS P M x M y M z T 1 (VALVE) (PIPE) T 2 1 Zero 0 0.0 0.0 0.0 0.0 70 70 0.0 ) 5 2 Cold Hydro Test 3590 0.0 0.0 0.0 0.0 70 70 0.0 3 Hot Hydro Test, Up 2200 251.7 141.6 -7.1 2.4 400 400 0.3 ) 40 4 Hot Hydro Test, Down 0 0.0 0.0 0.0 -2.4 70 94 -0.3 5 Plant Startup 2200 337.2 184.9 -936.0 0.0 70 70 0.0 ) 100 6 Plant Shutdown 0 0.0 0.0 0.0 0.0 70 70 0.0 7 Plant Loading 2200 381.6 204.4 -1169.6 0.0 70 70 0.0 ) 18300 8 Plant Unloading 2200 337.2 184.9 -936.0 0.0 70 70 0.0 9 Loss of Load, 4.1 2515 384.2 204.4 -1183.4 0.0 70 70 0.0 ) 80 10 Loss of Load, 4.2 1500 345.7 186.4 -1011.4 0.0 70 70 0.0 11 N.O. + Earthquake 2200 408.6 463.3 -1134.1 0.0 70 70 0.0 ) 50 12 N.O. - Earthquake 2200 265.8 -93.5 -737.9 0.0 70 70 0.0

B/B-UFSAR

D.T-15 TABLE D-15 SIX HIGHEST VALUES OF STRESS INTENSITY, GIRTH BUTT WELD WITH CHANGE IN MATERIAL AND WALL THICKNESS

VALUES FROM REFERENCE 23 PIPSYS PROGRAM LOAD SET PAIR S n Eq. (12)Eq. (13)K e S n Eq. (12)Eq. (13)K e 3 4 52549 (*) (*) 1.000 52600 (*) (*) 1.000 3 9 49883 (*) (*) 1.000 49900 (*) (*) 1.000 3 10 49620 (*) (*) 1.000 49600 (*) (*) 1.000 3 6 48013 (*) (*) 1.000 48000 (*) (*) 1.000 1 3 48013 (*) (*) 1.000 48000 (*) (*) 1.000 3 11 47728 (*) (*) 1.000 47700 (*) (*) 1.000

(*)Because S n , calculated by Equ ation (10), is less than 3S m , Equations (12) and (13) are satisfied.

B/B-UFSAR

D.T-16 TABLE D-16

SUMMARY

OF CALCU LATIONS OF CUMUL ATIVE USAGE FACTOR, GIRTH BUTT WELD WITH CHANGE IN MATERIAL AND WALL THICKNESS

VALUES BASED ON LOAD SET PAIR REFERENCE 23 VALUES FROM PIPS YS PROGRAM S p K e S p K e USAGE USAGE i j 2 FACTOR 2 FACTOR 3 9 40338 0.0050 40300 0.005 4 9 34400 0.0029 34400 0.003 1 11 29806 0.0002 29800 0.000 6 11 29806 0.0020 29800 0.002 6 7 29163 0.0023 29200 0.002 2 10 26254 0.0002 26300 0.000 10 12 93170 0.0000 93200 0.000

Cumulative Usage Factor 0.0126 0.0124

B/B-UFSAR

D.T-17 TABLE D-17 MODAL FREQUENCIES (cycle/sec)

MODE NO. PIPSYS NASTRAN DYNAL 1 6.07 6.085764 6.0821088 2 10.69 10.94144 10.936468 3 11.48 11.66862 11.666215 4 14.76 15.20947 15.204282 5 20.12 22.25613 22.135260 6 23.87 28.53255 28.505264 7 25.32 30.58105 30.530972 8 28.80 31.22073 31.190062 9 30.00 32.27319 32.199679 10 42.39 43.14653 43.135100 11 42.95 43.50436 43.497053 12 58.02 58.19336 57.991710 13 77.78 76.62025 71.996751 14 90.74 93.69710 92.12974 15 91.8 96.04482 95.167976 16 93.39 97.81956 97.410131 17 96.96 99.40727 98.209594 18 101.42 104.6169 101.64513 19 102.14 105.4910 103.80206 20 103.03 107.7136 107.52304

B/B-UFSAR

D.T-18 TABLE D-18 ALLOWABLE SHEAR, MOMENT AND SPAN OF CABLE TRAY HAND SHEAR, SPAN, OR MOMENT SEISHANG CALCULATION Vertical shear, static (kip) 16.05 16.05 Positive bending moment, static (k-in.) 50.64 50.83 Negative bending moment, static (k-in.) 57.62 57.64 Vertical shear, seismic (kip) 20.84 20.81 Horizontal shear, seismic (kip) 12.84 12.83 Positive bending moment, seismic (k-in.) 67.51 67.61 Negative bending moment, seismic (k-in.) 76.83 76.82 Horizontal bending moment, seismic (k-in.) 153.61 153.59 Span (ft) 20.78 20.75

B/B-UFSAR

D.T-19 REVISION 3 - DECEMBER 1991 TABLE D-19 RESPONSE OF THE CEIL ING-MOUNTED SUPPORT SEISHANG DYNAS Horizontal period (sec) 0.1742 0.1765 Vertical period (sec) 0.0092 0.0093 Forces and moments due to horizontal seismic Vertical element (No. 1) axial (lb) 1600 1607 shear (lb) 770 772 bending (lb-in.)17100 17208 Horizontal element (No. 9) axial (lb) 25 26 shear (lb) 302 304 bending (lb-in.)10900 10944 Forces and moments due to vertical seismic Vertical element (No. 1) axial (lb) 383 340 shear (lb) 0 0 bending (lb-in.)30 24

Forces and moments due to dead load Vertical element (No. 1) axial (lb) 776 774 shear (lb) 0 0 bending (lb-in.)30 0

B/B-UFSAR

D.T-20 TABLE D-20 RESPONSE OF THE WALL-MOUNTED SUPPORT SEISHANG DYNAS Horizontal period (sec) 0.0067 0.0067 Vertical period (sec) 0.1065 0.1080 Forces and moments due to horizontal seismic Vertical element (No. 6) axial (lb) 0 1 shear (lb) 2 2 bending (lb-in.)35 48 Horizontal element (No. 11) axial (lb) 101 105 shear (lb) 2 2 bending (lb-in.)23 24 Forces and moments due to vertical seismic Vertical element (No. 6) axial (lb) 39 0 shear (lb) 131 128 bending (lb-in.)2700 2676

Forces and moments due to dead load Vertical element (No. 1) axial (lb) 717 702 shear (lb) 303 329 bending (lb-in.)4910 5208

B/B-UFSAR

D.T-21 TABLE D-21 INTERACTION COEFFICIENTS OF THE CEILING-MOUNTED SUPPORT INTERACTION COEFFICIENT SEISHANG PIPSYS Vertical element (No. 2) 0.617 0.620 (No. 5) 0.520 0.516

Horizontal element (No. 6) 0.683 0.678 Brace element (No. 3) 0.569 0.553

B/B-UFSAR

D.T-22 TABLE D-22 APPLIED LOADS FOR SL SAP PIPE NETWORK DIRECTION LOADING TYPE X Y Z Concentrated:

At Node 3 1000.0

At Node 4 -200.0 At Node 8 3000.0 1000.0 2000.0

Distributed weight -6284.0

Total 3000.0 -4484.0 2000.0

B/B-UFSAR

D.T-23 TABLE D-23 FORCE EQUILIBRIUM REACTIONS SLSAPIV SAPIV ADLPIPE NODE FX FY FZ FX FY FZ FX FY FZ 9 5643.5 - - 5643.51 - - 5659.0- - 11 - -4044.7 - - -4044.59 - - -4052.0 - 12 2350.1 4023.1 -4960.9 2350.08 4023.01 -4960.702361.04026.0 -4966.0 13 -10993.5 4505.6 2960.6 -10993.59 4505.61 2960.70-11021.04509.0 2966.0

TOTAL -2999.9 4484.0 -2000.3 -3000.00 4484.03 -2000.00-3001.04483.0 -2000.0

B/B-UFSAR

D.T-24 TABLE D-24 PERIODS OF PLANE FRAME PERIOD PERIOD MODE SLSAPIV SAPIV NUMBER (sec) (sec) 1 8.182 8.183 2 2.673 2.673 3 1.543 1.543

B/B-UFSAR

D.T-25 TABLE D-25 COMPARISON OF MOMENT (SLSAPIV AND PIPDYN)

MOMENT MZ (kip/in) IN ELEMENT LO CAL COORDINATES ELEMENT (AT ELEMENT END I) NUMBER SLSAPIV SAPIV PIPDYN 1 376.9 376.9 377.0 2 30.66 30.67 30.68 3 152.9 152.9 152.9 4 100.6 100.6 100.6 5 83.27 83.27 83.27 6 46.17 46.17 46.19 7 1.081 1.081 1.082 8 21.59 21.59 21.81 9 7.052 7.052 7.038 10 7.537 7.537 7.571 11 160.3 160.3 160.4 12 78.07 78.07 78.09 13 26.08 26.08 25.80

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D.T-26 TABLE D-26 CANTILEVER BEAM ANALYSIS -

NATURAL PERIODS FOR THE EIGHT LOWEST FLEXURAL MODES

PERIOD PERIOD MODE SLSAPIV SAPIV NUMBER (sec) (sec) 1 525.8 525.79 2 85.37 85.368 3 30.96 30.965 4 16.06 16.059 5 9.901 9.9006 6 6.828 6.8276 7 5.186 5.1865 8 4.378 4.3777

B/B-UFSAR

D.T-27 TABLE D-27 CYLINDRICAL TUBE ANALYSIS:

SELECTED NATURAL PERIODS

PERIOD PERIOD MODE SLSAPIV SAPIV NUMBER (sec x 10

-3) (sec x 10

-3) 1 1.279 1.2788 5 0.6214 0.62140 10 0.3298 0.32983 15 0.1746 0.17463 20 0.1150 0.11497

B/B-UFSAR

D.T-28 TABLE D-28 ROLLED BEAM DESIGN PROBLEM MAXIMUM SECTION MOMENTS SECTION MODULUS (kip-ft) SELECTED (in

3) AISC 125. W16x40 64.6

STAND 125.58 W18x40 68.4

B/B-UFSAR

D.T-29 TABLE D-29 COMPOSITE BEAM DESIGN PROBLEM BENDING MOMENTS (kip-ft) MAXIMUM NUMBER OF CONSTRUCTION DESIGN SHEAR STEEL SHEAR LOAD LOAD (kips) SECTION CONNECTORS AISC 71.3 237.2 26.4 W21x44 42 STAND 71.3 236.5 26.3 W21x44 42

B/B-UFSAR

D.T-30 TABLE D-30 COLUMN DESIGN PROBLEM AISC AISC AISC ITEMS EXAMPLE 1 EXAMPLE 2 EXAMPLE 5 670kips 540kips 600kips 100 kip-ft Column Design Parameters

190 kip-ft

670kips 540kips 600kips AISC W12X161 W12X99 W14x142 SOLUTION

STAND W12x161 W12x99 W14x142 SOLUTION

B/B-UFSAR

D.T-31 TABLE D-31 PLATE GIRDER D ESIGN PROBLEM RESULTS AISC STAND Maximum bending moment (kip-ft) 2054 2045

Maximum vertical shear (kips) 142 141.3

Web section 1 plate, 70x5/16 1 plate, 70x5/16

Flange section 2 plates, 18x3/4 2 plates, 18x3/4 Stiffener end spacing (ft) 3.4 3.56 Stiffener intermediate spacing (ft) 6.75 6.72

Area of

• stiffeners

furnished (in

2) 2.0 1.88

• Required area is 1.78 in

2.

B/B-UFSAR

D.T-32 TABLE D-32 SECTION AND MATE RIAL PROPERTIES SECTION AND PROBLEM NUMBER MATERIAL PROPERTIES 1 2 3 Thickness (in.) 42.00 30.00 42.00 Width (in.) 12.00 12.00 12.00

Area of first st eel layer (in

2) 6.25 2.25 3.12 Distance of first steel layer (in.) 3.00 3.00 3.00 Area of second s teel layer (in

2) 6.25 4.00 3.12 Distance of second steel layer (in.) 37.00 25.00 37.00 Concrete unit weight (lb/ft

3) 150.00 150.00 150.00 Concrete compressive strength (lb/in

2) 4000.00 4000.00 4000.00 Concrete coeff. of the rmal expansion (in/

°F) 5.56 x 10-6 5.56 x 10-6 5.56 x 10

-6 Steel yield stre ngth (kips/in

2) 45.00 45.00 45.00 Steel modulus of ela sticity (kips/in

2) 29000.00 29000.00 29000.00 Material properties Nonlinear Nonlinear Linear Applied axial force (kips) -38.25 76.53 34.65 Applied bending moment (ft-kips) 129.75 -9.49 206.25 Inside temperature (°F) 82.50 67.50 247.50 Outside temperature (°F) 52.50 0.00 115.50

B/B-UFSAR

D.T-33 TABLE D-33 RESULTS OF TEMCO PROBLEMS PROBLEM NUMBER RESULTS 1 2 3 Equilibrating axial force given by TEMCO program (kips) -38.25 76.53 34.65 Equilibrating axial force

computed by hand (kips) -38.253 76.53 34.65 Equilibrating bending moment given by TEMCO program (ft-kips) 129.75 -9.49 206.26 Equilibrating bending moment computed by hand (ft-kips) 129.752 -9.493 206.25 Thermal moment given by TEMCO program (ft-kips) -54.58 -21.07 -137.75 Thermal moment computed by hand (ft-kips) -54.585 -21.071 -137.757

B/B-UFSAR

D.T-34 TABLE D-34 INPUT FOR TENSILE FORCE AND BIAXIAL BENDING PROBLEM

SECTION AND MATERIAL PROPERTIES PROBLEM 4 Thickness (in.) 42.0 Width (in.) 12.0

Area of each s teel bar (in

2) 1.25 Number of steel bars 10.0

Concrete unit weight (lb/ft

3) 150.0 Concrete compressive strength (lb/in

2) 4000.0 Steel yield stre ngth (kips/in

2) 45.0 Steel modulus of ela sticity (kips/in

2) 29000.0 Material properties Nonlinear

Applied axial force (kips) 21.0 Applied x bending moment (ft-kips) 125.0 Applied y bending moment (ft-kips) 125.0

B/B-UFSAR

`D.T-35 TABLE D-35 RESULTS FROM TEN SILE FORCE AND BIAXIAL BENDING PROBLEM

RESULTS PROBLEM 4 Equilibrating axial force given by TEMCO (kips) 20.999

Equilibrating axial force computed by hand (kips) 22.733

Equilibrating x bending moment given by TEMCO (ft-kips) 125.000

Equilibrating x bending moment computed by hand (ft-kips) 124.630

Equilibrating y bending moment given by TEMCO (ft-kips) 125.000

Equilibrating y bending moment computed by hand (ft-kips) 123.753

B/B-UFSAR

D.T-36 TABLE D-36 PARAMETERS FOR COLID RECTANGULAR SECTION STRESS FACTOR EXAMPLE

B = 12.0 in.

T = 72.0 in.

X 1 = 10.41 in.

A S1 = 1.56 in 2 X 2 = 69.04 in.

A S2 = 1.56 in 2

F y = 60.0 ksi 'c F = 4.5 ksi STRESS FACTORS CONCRETE CONCRETE STEEL BENDING MEMBRANE Primary and Secondary 0.9 0.850 0.765 Primary 0.4 0.600 0.300

B/B-UFSAR

D.T-37 TABLE D-37 COMPARISON OF COLID RESU LTS AND HAND CALCULATIONS FOR RECTANGULAR SECTION STRESS FACTOR EXAMPLE

HAND CALCULATIONS COLID Axial Load Moment Axial Load Moment POINT P u (kips) M u (ft-kips) P u (kips) M u (ft-kips) 1 -168.5 -53.3 -168.5 -52.3 2 3084.0* - - - 3091.0 0.0 3 967.8 2340.0 968.1 2345.0 4 1058.0 -2395.0 1051.0 -2396.0 5 -74.9 -23.65 -74.9 -23.24 6 1197.0* - - - 1201.0 0.0 7 404.0 1048.0 404.1 1056.0 8 446.5 -1050.0 413.4 -1053.0

• Maximum Membrane Forces B/B-UFSAR

D.T-38 TABLE D-38 PARAMETERS FOR C OLID RECTANGULAR SECTION ULTIMATE CAPACITY AND ACI ULTIMATE CAPACITY OPTIONS

B = 12.0 in.

T = 48.0 in.

X 1 = 6.0 in.

A S1 = 1.5 in 2 X 2 = 44.0 in.

A S2 = 2.0 in 2 F y = 60.0 ksi 'c F = 4.0 ksi

B/B-UFSAR

D.T-39 TABLE D-39 COMPARISON OF COLID RESU LTS AND HAND CALCULATIONS FOR RECTANGULAR SECTION ULTIMATE CAPACITY AND ACI ULTIMATE C APACITY OPTIONS

HAND CALCULATIONS COLID M u P u M u P u (ft-kips) (kips) (ft-kips) (kips) Ultimate 1209.0 775.1 1211.0 775.4 ACI Ultimate 846.2 543.3 847.4 542.8

B/B-UFSAR

D.T-40 TABLE D-40 PARAMETERS FOR COLID SOL ID CIRCULAR COLUMN TEST Outer 36.0 in.

Diameter of Reinforcement 29.76 in.

Area of Steel 56 in 2 F y 60.0 ksi

'c F 5.0 ksi B/B-UFSAR

D.T-41 TABLE D-41 COMPARISON OF COLID RESU LTS AND HAND CALCULATIONS FOR SOLID CIRCULAR COLUMN BALANCE POINT PURE COMPRESSION POINT M u P u M u P u (ft-kips) (kips) (ft-kips) (kips) Hand Calculation 2427 1320 0 4170 COLID 2425 1318 0 4170

B/B-UFSAR

D.T-42 TABLE D-42 PARAMETERS FOR COLID HOL LOW CIRCULAR COLUMN EXAMPLE Outer Diameter 36.0 in.

Inner Diameter 24.0 in.

Diameter of Reinforcement 29.76 in.

Area of Steel 64.0 in 2 F y 6.0 ksi 'c F 5.0 ksi B/B-UFSAR

D.T-43 TABLE D-43 COMPARISON OF COLID RESU LTS AND HAND CALCULATIONS FOR HOLLOW CIRCULAR COLUMN

BALANCE POINT PURE COMPRESSION POINT M u P u M u P u (ft-kips) (kips) (ft-kips) (kips) Hand Calculation 2351 898 0 3340 COLID 2351 898 0 3340

B/B-UFSAR

D.T-44 TABLE D-44 COMPARISON OF COLID RESULTS FOR METRIC AND B RITISH UNITS ENGLISH CONVERTED INTO METRIC METRIC M u P u M u P u M u P u (ft-kips) (kips) (kg-m) (kg) (kg-m) (kg) 1211.0 775.4 170.0 x 10 4 351.7 x 10 3 167.3 x 10 3 351.5 x 10 3

B/B-UFSAR

D.T-45 TABLE D-45 ALLOWABLE SLENDERNESS RATIOS MAXIMUM SLENDERNESS MEMBER RATIO TYPE (kl/r)

Compression members (verticals, 200 diagonals and longitudinal braces) in floor and wall mounted supports (i.e., compression system supports)

Compression members (verticals, 300 diagonals and longitudinal braces) in ceiling mounted supports (i.e., tension system supports)

2'0 12 2'n"7" M=4KIP-SEC 2/IN*3 1'\3=500 1'\1 PS I IN. KIP-SEC 2/IN.1'\2=1000 KIPS/IN.MI=8 KIPS-S'f.(;'lf i N.KI=1500 KIPS/IN.BYRON/BRAIDWOOD STATIONS UPDATED fiNAL SAFETY ANALYSIS REPORT FIGURE 0*1 THREE-STORY SHEAR BUILDING I D 1.0 1,,4 0 A g 100.0 In!11I30.'0',b./I,,2 P':lLOlbo**e 2/In 4i'$i.t L CONCENTRATED MASSIb SiC 2/1ft 80t 50'!l 400'---------=1 (a)NODE AND BEAM NUMBER ASSIGNMENTS FOR THE CANT!LEVER MODEL 10 T.IME (aee)(I))GROUND ACCELERATION APPLiED AT NODEBYRON/BRAIDWOOD STATIONS UPDATED FINAL SAFETY ANALYSIS REPORT FIGURE 0-2 RESPONSE HISTORY ANALYSIS OF CANTILEVER BEAM FOR DYNAS PROGRAM 60E+7 SAPlV+DYBAS 50 i I V)40 CO..J-30 au:E 20 (,!)z o10 lD o o MOMENT AT NODE 1 (FIXED END OF CANTILEVER)

BYRON/BRAIDWOOD STATIONS UPDATED FINAL SAFETY ANAlVSIS REPORT FIGURE 0*3 CANTILEVER RESPONSE "6£ PSI 11=0.161 RADIUS=90 IN.BYRON/BRAIDWOOD STATIONS UPDATED FINAL SAFETY ANALYSIS REPORT FIGURE D-4 SHALLOW SPHERICAL SHELL N-2.0 o 10@DYNAX<=Timoshenko a Woinowsky-Krieger BYRON/BRAIDWOOD STATIONS UPDATED FINAL SAFETY ANALYSIS REPORT FIGURE 0-5 AXIAL DISPLACEMENT SHALLOW SPHERICAL SHELL

.20 10".z 0 em""'-Z"'" fIi d F=10 2: w:I 0c=J=20 r<z Q 0.-IS d!=30@DYNAX=Tlmoshenko a Woinowsky-Krieger 10"'" 40+=====r=======v===='"4F====='

@BYRON/BRAIDWOOD STATIONS UPDATED FINAL SAFETY ANALYSIS REPORT FIGURE 0-6 MERIDIONAL MOMENT SHALLOW SPHERICAL SHELL a:: w o Z...I)-Uo cfI)(<4: z z.JJ 61)It)0 0$J l!" fi8-Co-C\!__'-t BYRON/BRAIDWOOD STATIONS UPDATED FINAL SAFETY ANALYSIS REPORT FIGURE 0-7 FINITE ELEMENT IDEALIZATION OF THICK-WALLED CYLINDER

-2.5z v-1.5 I-z I.&JW u_I.<<(-l Q..!!!o-.5=25[=900 PSI.V=O.49 (;)DYNAX TIMOSHENKO AND GOODIER-5 55 80I5 130 RADIUS=INCHES BYRON/BRAIDWOOD STATIONS UPDATED fiNAL SAFETY ANALYSIS REPORT FIGURE D-8 STRESSES AND DISPLACEMENTS IN THICK*WALLED CYLINDERS T 50 To: SHELL THICKNESS:

lIN.I LB:--IN./IN.

£=gl.LS/IN2'\1=.3 N=FOURIER HARMONIC NU*MBER e BYRON/BRAIDWOOD STATIONS UPDATED FINAL SAFETY ANAL VSIS REPORT FIGURE 0-9 CYLINDER UNDER HARMONIC LOADS

=1.=1.0=.a=.+ MERIDIONAL MOMENT Qh.IN/IN')

Xc>I..DYNAXBUDIANSKY AND RADKOWSKI N:;:(2 MERIDIONAL MOMENT (lb.IN.liN)X=i o DVNAX'=BUDIAtJSK'.

AND UR (IN.)RADKOWSKI'0 10.50 AXIAL DISTANC,r:

BYRON/BRAIDWOOD STATIONS UPDATED FINAL SAFETY ANAL VSIS REPORT FIGURE 0*10 MERIDIONAL MOMENTS AND DEFLECTIONS OF CYLINDER N=O AND N=2

=BUDIANSKY ANDDVNAX RADKOWSKI MERIDIONAL MOMENT{'b-IN.I'N.)o Q2b.-=p="i""""'====""'f====v====Y====lI 0.0 5 10 20 30 40:)0 AXIAL DISTANCE (IN.)-1.0-0.8-0.6-0.*-0.2[RIDIONAL MOMENT (lb=IN.!IN.)

x=aJ

=BUDIANSKY AND RADKOWSKI-0.6-1.0-0.2 o O.2

-0.4 5 10 20 30 40 AXIAL DISTANCE (IN.)BYRON/BRAIDWOOD STATIONS UPDATED FINAL SAFETY ANALYSIS REPORT FIGURE D*11 MERIDIONAL MOMENTS AND DEFLECTIONS OF CYLINDER N...5AND N=20 u r'T-...000&StOp*TIME HISTORY LOADING L, IN.P='500lh.R:3IN.'"0.3 IN.[:.10XI0'MASS DENSITY

\):;;0.3 TIME STtPI:i:.000005 SEe.

BYRON/BRAIDWOOD STATIONS UPDATED FINAL SAFETY ANAL VSIS REPORT FIGURE 0-12 SUDDENL V APPLIED RING LINE LOAD 8 8 ij 6 i i U 9 6 F 0 Z.WC)&Ai 90:z.JJ Q.0 c f!)XZ=>F<tU w z cJ.-=...J Z x<<(t\\LL<[<<(=>W:2 0 If')w J.c C/):z<<........, IJJ>-Q;:U 0::: 0 VI=>0B=t=(J)BYRON/BRAIDWOOD STATIONS UPDATED fiNAL SAFETY ANALYSIS REPORT FIGURE 0-13 RADIAL DISPLACEMENT VS.TIME o 60 8<!)i=9 z C IIIJ: 0 a l: z.,J.(z Z z 0<<-:E0-!!1rl.w III 0: t::<:)61I: w)(ii Ii 2 w I:te II CbI=0 II G=VI I I I i BYRON/BRAIDWOOD STATIONS UPDA TED FINAL SAFETY ANALYSIS REPORT FIGURE 0-14 BENDING MOMENT VS.TIME SUODENL Y APPLIED RING (LINE)LOAD N.D STATIONS ANALYSIS REPORT UPDATED FINAL SAFE FIGURE 0-15 SPHERICAL CAP

=.020DYNAX-===-KLEIN-.016=.012 Q: W...Z-.004 w U B=-e<.000 Z w STATICw DISPLACEMENT UoJ.004 (g.Cf)0..J-<.008-x<<.012 0.0.25.75 TIME X 10 SEC.1.0 BYRON/BRAIDWOOD STATIONS UPDATED FINAL SAFETY ANALYSIS REPORT FIGURE 0*16 AXIAL DISPLACEMENT OF SPHERICAL CAP UNDER DYNAMIC LOAD

<:>lOYNAX MOMENY.50 3.15'fIME X 10 SEC..25-1000 z Q In Z W!="i.

Z o olAJ

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o BYRON/BRAIDWOOD STATIONS UPDATED FINAL SAFETY ANALYSIS REPORT FIGURE D-17 MERIDIONAL TENSION OF SPHERICAL CAP UNDER DYNAMIC LOAD

=J-THICKNVARIES FA.OH GiN.TO" E.3.+'S x 10.17 f

$er,/1I1f:t 3--Til Ie I(NESS VARIES FROM ,B@30;&;J.BYRON/BRAIDWOOD STATIONS UPDATED FINAL SAFETY ANALYSIS REPORT FIGURE 0-18 HYPERBOLIC COOLING TOWER BYRON/BRAIDWOOD STATIONS UPDATED FINAL SAFETV ANALYSIS REPORT FIGURE 0*19 SPECTRUM OF DESIGN EARTHQUAKE t==k.'" t=<<0 a:-100:J: t=0M.w-150 U DVNAX Z 0 ABEL, et at.<4(t=lfj 0 0 d=200<<{0 U 0 t=t:lC 00 0 0<<)BYRON/BRAIDWOOD STATIONS UPDATED FINAL SAFETY ANALYSIS REPORT FIGURE 0-20 COOLING TOWER MERIDIONAL FORCE

+u+U+U I:u-U)-k (02-U3)l:u l-U 2)-k(02-01)r-k(U n-U n+1)o n-l n 0-Fa-e-n Cl>--0 G-oS-I-F F-F 0 F 0 0 0-f-f 1-f 2 n Node-1 Node-2 Node-n a c: m"'Cl>0 cCooN--f mm mm 00 0-<-!: ,"":lCl Zo-0 S;o zz):Do-"m r;-m or":llll<0 G>0>->">0-c ,""0 r>J]m::E-Z m°0 Ii'0-0'" ,.0 OJ]-A Zen Z.-oiJJ]>'>0 OZ-<-lJ cn_rom m O rr:mJZ mOO s::-<men 00"'Cl-i 0 m s:::lCl-lJ U n f n U 6 Us U 4 U 3 U 2 r line of symmetry U 2 Ikf 2 Buckled Panel

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/lillV Ui" UI'Il!URV 6 I IS.i£7'V.O.112.2'S*100SY a II S.D."'10 001.006.96C>i oun v oUIS X oUU 1012.2 1012.2 1051.2 BYRON/BRAIDWOOD STATIONS UPDATED FINAL SAFETY ANALYSIS REPORT FIGURE 0-23 DESIGN OF TIED COLUMN TENSION CONTROLS VALIDAVION NO.3 0 OESIGN 0'&VIED DUIGN or vln COLUMN NO.0'IIIU, Q qZ (OVER a.iDO 1.5DO l.iDO LOAD APpLIEil volters CUI AI>Af'll!IHly U,," Ul'1l1 UIllY UP/tiP I I33D.

D.1626.966*o.loU3 2 BUo.o.3l.:u IClo 00 6\U.8.64>6IUD.uu.

'III.loOQQ Ilnu&eVU@1Q CONUOL POlllY!I iiiEQUUT[D P1/1'8 C111!11 oUI!I 3062.9 983.0 116)'.Q V oUIS 3062.9 81.7.'1..1/0.1.5 30,2.9 9",.)'96J)'.Q BYRON/BRAIDWOOD STATIONS UPDATED FINAL SAFETY ANAL VSIS REPORT FIGURE 0-24 DESIGN OF TIED COLUMN BIAXIAL BENDING 12'_0".35K'I=9000 in 4..:.:t" s::..;Co 0::0 0 0 8 0 Itc"\*I't"\I!\ll\1\or-'""'" 1-/r-I B E I=4000 ins::..;..0 0 0 r::{8 0 I 0-I't"\t<"\l!'I 0.-.IJl" 1\/-oj r-I F20'=0"E=30000 ksi BYRON/BRAIDWOOD STATIONS UPDATED FINAL SAFETY ANAL VSIS REPORT FIGURE 0*25 EXAMPLE FRAME FOR PIPSYS STATIC ANALYSIS BYRON/BRAIDWOOD STATIONS UPDATED FINAL SAFETY ANALYSIS REPORT FIGURE 0-26 PIPING SYSTEM FOR COMBINED STRESS ANALYSIS (PIPSYS)

LUMPED MASS z v x BYRON/BRAIDWOOD STATIONS UPDATED FINAL SAFETY ANAL vsrs REPORT FIGURE 0-27 STRUCTURAL MODEL OF PIPING SYSTEM (PIPSYS)

JOINTS 19, 21, 32 zz 24 20-;:;;18.e--Lo.J U 0:: 16 0 u..JO I NTS 15, 11 14 12 10 JOINT 25 8 6 4 2.04.08.12.16.20.24.28.32.36 TIME (sec)BYRON/BRAIDWOOD STATIONS UPDATED FINAL SAFETY ANALYSIS REPORT FIGURE 0*28 LOAD TIME HISTORY (PIPSYS)

.18.16.14.12.10.08.04.08.12.16.20..24.28.32 TiME (Sec).36 BYRON/BRAIDWOOD STATIONS UPDATED FINAL SAFETY ANALYSIS REPORT FIGURE 0-29 FORCE VS.TIME JOINT8Z DIRECTION (PIPSYS)

LOADS (WALLS)FOraeE.F'IIBSSUI2It DIlIDJII]]]

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F LooQ LOAOS I i FILL.EO WITH I'l'A"i'EIt

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N£Q&DO.ES>.:lS' FLOO/'l TMICI(I\lE$$a o.1)00'BYRON/BRAIDWOOD STATIONS UPDATED FINAl..SAFETY ANAl..YSIS REPORT FIGURE 0-30 RECTANGULAR TANK FILLED WITH WATER BYRON/BRAIDWOOD STATIONS UPDATED FINAL SAFETV ANAl..YSIS REPORT FIGURE 0-31 MOMENT OF My AT HORIZONTAL CROSS SECTION OF WALLS

-IfCO;:tNEI(o PI-poEM-CH£U,1/(;, t DAVIES BYRON/BRAIDWOOD STATIONS UPDATED FINAL SAFETY ANALYSIS REPORT FIGURE 0-32 MOMENT My AT TOP OF WALL 20 to-10-40-50 TOP OF" WALL 0PLF"E:.M-CHE.UNGii It OAVI£>.S BYRON/BRAIDWOOD STATIONS UPDATED FINAL SAFETV ANALYSIS REPORT FIGURE 0-33 MOMENT M)(ALONG CROSS SECTION OF LONG WALL j j*IjjBYRON/BRAIDWOOD STATIONS UPDATED FINAL SAFETY ANALYSIS REPORT FIGURE 0-34 PLATE WITH CIRCULAR HOLE UNDER UNIFORM TENSION U')CJ)UJ 0::CJ) 2..00 CD Plf'EM-TIMOSHENI(O AND GOODIER DISTANCE FROM EDGE OF HOLE (IN,)BYRON/BRAIDWOOD STATIONS UPDATED FINAL SAFETY ANALYSIS REPORT FIGURE 0*35 STRESSES IN PLATE WITH CIRCULAR HOLE UNDER UNIFORM TENSION

i-})I.C'i'\<C l'i'\-In@)l.0'lit 11)!:::e(9ll"\t----0_II I!'\t-: e e@@%'"()It\0-G G G Q It'\<r'St tr N--1_4pL"',@V BYRON/BRAIDWOOD STATIONS UPDATED fiNAL SAFETY ANALYSIS REPORT FIGURE D-36 SQUARE PLATE WITH RECTANGULAR HOLE SUBJECTED TO TEMPERATURE VARIATION HZ HRENNEKOFF MODEL*120-I-100 Ll..........l-Ll..I 80'-" N fD{)c::: o At>x:E: 20 M X HRENNEKOFF MODEL*oM X PLFEM.8 M Z PLFEM 10 15;to JOINT NO, M X AND M Z ALONG THE 2-20 LINE HRENNEKOFF MODEL*M X HRENNEKOFF MODEL*<:)<:)M PLFEMM X PLFEM Z 120 N GO40:x20-.t rOO

-;:::

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Ll..80 I'-" 1.4 ItO 17 18 JO I NT NO.M X AND M Z ALONG THE 14-18 LINE*HRENNEKOFF MODEL BASED ON A FRAMEWORK ELEMENT 0.875'SQUARE BYRON/BRAIDWOOD STATIONS UPDATED FINAL SAFETY ANALYSIS REPORT FIGURE 0-37 MOMENTS IN PLATE DUE TO TEMPERATURE VARIATION Vs=ySO SINn T ACCELERATION TIME HISTORV o RSG BIGGS DAMP I NG BIts)=0.2f\,/dk.cl....)/0/"I o o 0.5 1.0 1.5 20 2.5 3.0 GJ/f\.3<i...JI e RESPONSE SPECTRUM BYRON/BRAIDWOOD STATIONS UPDATED FINAL SAFETY ANALYSIS REPORT FIGURE 0-38 VALIDATION FOR A ONE-DEGREE-OF*FREEDOM DAMPED SYSTEM (RSG) 0.105" 93" III E!=-L o oo 293" s 1.250" 0.951 0.2 a Ft'0 (/.N'lr 0 0,j22*t ,..-..-_.1 IiJ Il Ft'ti)!!2ci i'-0"'" i u I1i 0<qII-q;-It)<ij'II))(I a

$,.u t ei f*Ft'0.293"<>I I (j'l N 1'.414" c;j 1-=:-0 vertical seismic design0 1 0 5g horizontal seismic design load a 4059 BYRON/BRAIDWOOD STATIONS UPDATED FINAL SAFETV ANALVSIS REPORT FIGURE 0*39 CABLE TRAY MODEL FOR SEISHANG PROGRAM I=2.22C>*:2 A=2.7':l l.n Ii./-a.'-til 1/5" IS".I.J-f_0" j 1'-0"1

'-c" B YRON/BRAIDWOOD STATIONS UPDATED FINAL SAFETY ANALYSIS REPORT FIGURE D-40 CEILING MOUNTED SUPPORT MODEL FOR SEISHANG PROGRAM A= in 2 I=1.24 inI q'(r-0---_.__.._.---...;=-._--I i 2'-(:/'I I6'q i'-6 Ii I ,_'" If'-**----t---*:1

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OW),I BYRON/BRAIDWOOD STATIONS UPDATED FINAL SAFETY ANALYSIS REPORT FIGURE 0-41 WALL MOUNTED SUPPORT MODEL FOR SEISHANG PROGRAM IIIII o'.!..:l-3:>V.HtnS MO'38 l=I.ld30 I o Q BYRON/BRAIDWOOD STATIONS UPDATED FINAL SAFETV ANALYSIS REPORT FIGURE 0-42 SOIL PROFILE AND LAYERED REPRESENTATION USED FOR SAMPLE PROBLEM MAXIMUM SHEAR STRtSS-PSf 00.40080 1200 1600 2000 2400.30G PUBUSHE:O SOLUTION DENSE SAND 10 o VALUES OBTAINED IN VALIDA TION RUN 20 40 50 60 70 80 90 100 BYRON/BRAIDWOOD STATIONS UPDATED FINAl.SAFETY ANAL VSIS REPORT FIGURE 0-43 COMPARISON OF SHEAR STRESSES AND ACCELERATIONS 2.0 SPE:CTRAl.

DAMPING=O.OS 0.3 PERIOD-SECONDS 0.1 Ollo------I"-....&.-....I...--='0.03

" 1.6 I:z oa:I.

L&J UBLISHED SOLUTIONPOINTS OBT AINE:DI IN VALIDATION RUN...J<<0.8 0::U W 0..ifI BYRON/BRAIDWOOD STATIONS UPDATED FINAL SAFETY ANALYSIS REPORT FIGURE 0*44 COMPARISON OF SPECTRAL VALUES FOR SURFACE MOTIONS r R=50 it!100 RSF 4

/lI777777777l7777?711777777777111111111777dllm NOBEC/717 n'71 nn rrrr trn 1717 1m rrn nn rm HT7 SL SAP E=593141.8 kips/ft 2\I=0.205 D=0.15 kips sec 2/ft 4 BYRON/BRAIDWOOD STATIONS UPDATED fiNAL SAFETY ANALYSIS REPORT FIGURE 0-45 CIRCULAR PLATE ON A RIGID FOUNDATION FOR SLSAP AND NOBEC BYRON/BRAIDWOOD STATIONS UPDATED fiNAL SAFETY ANALYSIS REPORT FIGURE 0-46 COMPARISON OF DISPLACEMENT AND MOMENT VARIATION OF CIRCULAR PLATE FROM SLSAP AND NOBEC 1000 Ibs ,CONSTANT BYRON/BRAIDWOOD STATIONS UPDATED FINAL SAFETV ANALYSIS REPORT FIGURE 0-47 MODEL OF PIPE NETWORK FOR SLSAP AND SAPIV (SLSAP VALIDATION PROBLEM 1)

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-+------..-----"--'-1-""-+-+....L__+-;....._..__c.l_BYRON/BRAIDWOOD STATIONS UPDATED fiNAL SAFETY ANALYSIS REPORT FIGURE 0-48 COMPARISON OF SURFACE STRESSES IN A CLAMPED SPHERICAL SHELL UNDER EXTERNAL PRESSURE FOR SLSAP AND SAPIV (SLSAP VALIDATION PROBLEM 2)

AT (J'II 200'-------={

9 i Ii/if//'////III'//1 III///'1//'117'117/TTTTTl (a)ELEVATION OF FRAME DATA: YOUNG'S MODULUS:: 432000, MASS DENSITY=1.0 FOR ALL BEAMS AND COLUMNS A,=3.0, II=I...==1.0 UNITS: FT 9 KIPS (b)BEAM ELEMENT'DEFINITION S,,5 2 AND 53=BEAM LOCAL AXES 1 111 1 2 AND I!=FLEXURAL INERTIA ABOUT SIDS20AND$3 A, g AREA ASSOCIATED WITH BYRON/BRAIDWOOD STATIONS UPDATED FINAL SAFETY ANAL VSIS REPORT FIGURE D-49 MODEL OF PLANE FRAME FOR SLSAP AND SAPIV (SLSAP VALIDATION PROBLEM 3)

-1I ,/" I 12 I BYRON/BRAIDWOOD STATIONS UPDATED FINAL SAFETY ANALYSIS REPORT FIGURE 0*50 MODEL OF PIPE ASSEMBLAGE FOR SLSAP AND SAPIV (SLSAP VALIDATION PROBLEM 4)

L=101;)B=--+V D::: i'E:;: 30)(103 KS1 (0)p\=0', p=10 KIPS SLSAP\:: 2 1>=0pa 10 KIPS TIMOSHENKO a GERE=2;p::o o,"-,,"-"&"-'""-"-9"-'0"-"-<\"-"" 20 40 80 100 60 o 2 4 10 (b)BYRON/BRAIDWOOD STATIONS UPDATED FINAL SAFETY ANALYSIS REPORT FIGURE 0-51 BENDING MOMENTS IN A CANTILEVER BEAM B 5.5.A S.S.SS....5.5.x" A=B'=IO v=0.3 E=30X 10 3 KSI I, T=I=1.0 KSI M)1)(MyY'5 4 3 2/J TIMOSHENKO a WOINOWSKY-KRIEGER---Mn/V=O;M)(l(/x:o SLSAP RESULTS o MyY/V=O;Myy/X=O

)(Myy/V::O;Mn::/X=O.IA.2A.3A.4A.5A BYRON/BRAIDWOOD STATIONS UPDATED FINAL SAFETY ANALYSIS REPORT FIGURE 0-52 BENDING MOMENTS IN A SIMPLY SUPPORTED PLATE x:: 1.0 in 4 n A=100.0 in 2 6E:: 30xl0 Ib$/In p:: 1.0 Ib-sec 2/ln 4 I41ZQ i f-w*[!].3**m*[!]*ill Q%II)69(;2/In I>;D----8 at 50':: 400'(0)NODE AND BEAM NUMBER ASSIGNMENTS FOR THE CANTILEVER MODEL 1000 in/sGc 2---(b)GROUND ACCELERATION APPLIED AT NODE i BYRON/BRAIDWOOD STATIONS UPDATED FINAL SAFETY ANALYSIS REPORT FIGURE 0-53 MODEL FOR RESPONSE HISTORY ANALYSIS FOR SLSAP AND SAPIV (SLSAP VALIDATION PROBLEM 7)

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GO E+i'50 SAP IV-X SLSAPI C/)40 m..J-30 z UJ020 (!)z 0 z 10 w m 0 0 18 BYRON/BRAIDWOOD S1 AllONS UPDATED fiNAL SAFETY ANALYSIS REPORT FIGURE 0-55 COMPARISON OF SLSAP AND SAPIV BENDING MOMENTS OF THE CANTILEVER BEAM (SLSAP VALIDATION PROBLEM 7) 1000 Ibs/ln p E g 30 ltl0 6 Ibs/in 2'il g O.3 p=3.663 I02 ,bs 81c 2/ln 4CYLINDRICAL TUBE P Ibs/ln 1000 r--====--===

VIMF b)TIME VARIATION OF LOAD BYRON/BRAIDWOOD STATIONS UPDATED fiNAL SAFETY ANALYSIS REPORT FIGURE 0-56 CYLINDRICAL TUBE AND LOAD HISTORY FOR SLSAP AND SAPIV MODE SUPERPOSITION AND DIRECT INTEGRATION ANAL VSES (SLSAP VALIDATION PROBLEM 8) 1-.--1]I SLSAP x_

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,'.12-6 CROSS SECTION MATERIAL PROfERTI£:

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.....'vl'.......".......R Radial Distance from Well R Ft.I, Ft.110 10 9 8 1 6 53 2 I o 10 20 40 60 200 250....1

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-.L..1...1 1 Numbers indicate the nodal identification Circled numbers indicate alement identification BYRON/BRAIDWOOD STATIONS UPDATED FINAL SAFETY ANALYSIS REPORT FIGURE D-65 FINITE ELEMENT MESH FOR AXISYMMETRIC FLOW PROBLEM k T===;>1 CHARACTERISTICS B=Width of Section T=Thickness of Section Xl=Location of Reinforcing Layer 1 A Sl=Area of Steel in Layer 1 X 2=Location of Reinforcing Layer 2 A s2=Area of Steel in Layer 2 F y=Steel Yield Strength=Concrete Strength c BYRON/BRAIDWOOD STATIONS UPDA TED FINAL SAFETY ANALYSIS REPORT FIGURE 0-66 COllO RECTANGULAR SECTION PARAMETERS AND SIGN CONVENTION o o o o o.o o.o N ('t')I o o.o lD-o q IN o o.oI OO'OB OO*j i OO'OB-l\:j I7_c....c....Oz*...0 l:c o c.N I o Co)o o o o oII U'-o o C"'l o OO'09tNI U o00 LnO CDCi')*0 00 II II U(I')U o IIlI:l CD r0-o o II N-U"l Z U"lll::ZZo 0U"l00 U"l**00 a: 0.".**lD NN 11-1'%UIIII>-.&....10....X oo'OOt BYRON/BRAIDWOOD STATIONS UPDATED FINAL SAFETY ANAL VSIS REPORT FIGURE 0-67 COLID INTERACTION DIAGRAM FOR RECTANGULAR SECTION STRESS FACTOR PROBLEM