RS-16-248, Byron/Braidwood Nuclear Stations, Revision 16 to Updated Final Safety Analysis Report, Appendix D - Computer Programs
Text
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 beams. 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 forcing 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 whose 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 solution obtained by Biggs (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 static 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 analysis 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 applied 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 compared 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 deformation, 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 121 (1) f + )U - U - U (2 a EA = O n1+n1-nn (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.7-1 D.7 PCAUC PCAUC (Portland Cement Association 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, documented 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.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 acceleration 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 subjected 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 combined 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 displacement 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 restraints, element property 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 plotting 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. Results of the SOR-III analysis 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, space trusses and frames, 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 material 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 internal 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 variety 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 compare 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-specified 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 factor, 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.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-1970s. 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 computation 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 obtained, it was found that the secondary saturation conditions were inconsistent 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 outputs compatible with 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 outputs compatible with other codes.
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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
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lIN.I LB:--IN./IN.
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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.)
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\):;;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
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=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
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LUMPED MASS z v x BYRON/BRAIDWOOD STATIONS UPDATED FINAL SAFETY ANAL vsrs REPORT FIGURE 0-27 STRUCTURAL MODEL OF PIPING SYSTEM (PIPSYS)
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.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)
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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
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-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--====--===
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©.N I"0 IBYRON/BRAIDWOOD STATIONS UPDATED FINAL SAFETY ANALYSIS REPORT FIGURE 0-61 RADIAL SHEAR COMPARISON FOR SABOR-III ANOSCR-III 10 KIPS 3KIPS/ri.10 KIPS 142 KIPS 142 KIPS
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d=60'-1 y'0 13 26 156 169 III@8 12 125 I 5 168 H=60'2 15 145 158 I CD@@14 Numbers indicate nodal identification Circled numbers indicate element identification 144 157 BYRON/BRAIDWOOD STATIONS UPDATED FINAL SAFETY ANALYSIS REPORT FIGURE D-63 PLANE FLOW PROBLEM AND THE FINITE ELEMENT MESH v PermeabiHty values K)(S fey!!::3 (10-4)ft:/sac.g 3 x 10-4 ft.lsec.Steadystate-freesurface Initial trial free surfgce H=60'Analytical method SEEPAGE BYRONIBRAIDWOOD STATIONS UPDATED FINAL SAFETY ANALYSIS REPORT e=IGURE D-64 COMPARISON OF FREE SURFACES OBTAINED FROM SEEPAGE AND ANAL VTICAL METHOD c.GroundII r f of..ell Permeability
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