ML20028D523

Buckling of Steel Containment Shells.Task 1b:Buckling of Washington Public Power Supply Systems Plant No. 2 Containment Vessel

ML20028D523
Person / Time
Site:	Columbia
Issue date:	12/31/1982
From:	Bushnell D, Meller E LOCKHEED PALO ALTO RESEARCH LABORATORY
To:	Office of Nuclear Reactor Regulation
References
CON-FIN-B-6568 LMSC-D812950, NUREG-CR-2836, NUREG-CR-2836-V01-P2, NUREG-CR-2836-V1-P2, NUDOCS 8301190224
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NUREG/CR-2836 LMSC D812950 i Vol.1, Part 2 l l

Buckling of Steel Containment Shells .

Task 1b: Buckling of Washington Public Power Supply Systems' Plant No. 2 Containment Vessel Prepared by E. Meller, D. Bushnell Lockheed Palo Alto Research Laboratory Prepared for U.S. Nuclear Regulatory Commission i

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NOTICE This report was prepared as an account of work sponsored by an agency of the United States I

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( product or process disclosed in this report, or represents that its use by such third party would not infringe privately owned rights.

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NUREG/CR-2836 LMSC D812950 Vol.1, Part 2 Buckling of Steel Containment Shells Task 1b: Buckling of Washington Public Power Supply Systems' Plant No. 2 Containment Vessel Manuscript Completed: September 1982 Date Published: December 1982 Prepared by E. Meller, D. Bushnell Lockheed Palo Alto Research Laboratory 3251 Hanover Street Palo Alto, CA 94304 Prepared for Division of Engineering Office of Nuclear Reactor Regulation U.S. Nuclear Regulatory Commission Washington, D.C. 20666 NRC FIN B6668 1

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NUREG/CR2836 l LMSC D812950 Vol. 1, Part 2 )

BUCKLING OF STEEL CONTAINMENT SHELLS TASK lb: BUCKLING OF WASHINGTON PUBLIC POWER SUPPLY SYSTEMS' PLANT NO. 2 CONTAINMENT VESSEL Final Report 25 August, 1980 - 30 September, 1982 Eli Meller and David Bushnell Lockheed Palo Alto Research Laboratory Prepared for U. S. Nuclear Regulatory Commission

ABSTRACT Static buckling analyses of the steel containment vessel of the Washington Public Power Supply Systems' (WPPSS) plant no. 2 were conducted with use of several computer programs developed at the Lockheed Missiles and Space Company (LMSC) . These ana-lyses were conducted as part of Task 1, " Evaluation of Two Steel Containment Designs".

The report is divided into two main sections. The first gives results from analyses of the containment as if it were ax-isymmetric (computerized models with use of BOSOR4, BOSOR5, and PANDA), and the second gives results from a STAGSC-1 model in which the largest penetration is included.

Good agreement is obtained from analyses with BOSOR5 and STAGSC-1 for a case in which both of these computer programs were applied to the same configuration and loading. It is im-portant to include nonlinear material behavior (plasticity) in the computerized models for collapse.

Predictions of collapse from STAGSC-1 indicate that the largest penetration of the WPPSS-2 containment vessel is rein-forced such that there is no decrease in load carrying capabili-ty below that indicated from models in which this penetration is neglected. A collapse load factor of 3.6 times the loads postu-lated by Pittsburgh Des Moines Steel (PDM) is indicated. The buckling mode is axisymmetric collapse. Bifurcation buckling involving nonaxisymmetric modes occurs at higher load factors than 3.6.

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TABLE OF CONTENTS Ili Abstract List of Figures Vii List of Tables x XIii Preface and Acknowledgments

1.0 INTRODUCTION

I AXISYMMETRIC MODELS WITH BOSOR4, BOSORS and PANDA 3 2.0 3

2.1 BOSOR4 and BOSORS Models 4

2.2 Analysis with PANDA 2.3 Plastic Strains from BOSOR5 Model 5 2.4 BOSORS Model of a Portion of the WPPSS-2 Vessel 5 2.5 Buckling of the Drywell Head under Internal 6 Pressure 3.0 STAGSC-1 MODELS OF THE WPPSS-2 7 CONTAINMENT VESSEL 7

3.1 Axisymmetric Model 3.2 Model Including Largest Penetration 8

4.0 CONCLUSION

S 11

5.0 REFERENCES

13 6.0 APPENDICES 15 6.1 Short Descriptions of 15 STAGSC-1, BOSOR4, BOSOR5, and PANDA 6.2 Input Data for BOSOR5 Overall Model 25 6.3 Input Data for STAGSC-1 Axisymmetric Model 59 6.4 User-written subroutine WALL for STAGSC-1 63 Model 6.5 Input Data for STAGSC-1 Model with 66 Penetration v

l LIST OF FIGURES 89 Fig. 1.1 WPPSS-2 containment vessel: Overall view Fig. 1.2 Rollout of WPPSS-2 containment vessel. Area mo-deled with STAGSC-1 is outlined. 90 Fig. 2.1 BOSOR4 and BOSOR5 discretized, segmented model of 91 the entire WPPSS-2 steel containment vessel Fig. 2.2 Line loads and moments applied at many meridional stations in order to simulate the equivalent static loading 92 specified by PDM it its final stress report.

Fig. 2.3 Meridional locations of discrete rings, many of which are " phony", their purpose being to provide a station at 93 which to " hang" a line load and moment.

Fig. 2.4 Axisymmetric deformations due to external pres-sure component only of the loading, predicted by BOSOR4 94 Fig. 2.5 Axisymmetric prebuckling deformations due to i external pressure plus the line loads shown in Fig. 2.2. ,

values of the line loads are listed in the Appendix, which gives 95 the BOSORS input file for the VAX 11/780 version of BOSOR5 Fig. 2.6 Axisymmetric prebuckling displacement and meridi-i onal rotation distributions due to total load (pressure + line 96

{ loads)

Fig. 2.7 Axisymmetric prebuckling stress resultants and meridional moment due to pressure + line loads 97 Fig. 2.8 Buckling mode predicted by BOSOR4 corresponding to N = 18 circumferential waves. "E.V.", meaning "eigenvalue",

is the load factor required to cause buckling with the assump-98 tion that the material remain elastic.

Fig. 2.9 Buckling mode predicted by BOSOR4 corresponding 99 to N = 16 circumferential waves.

Fig. 2.10 Buckling mode predicted by BOSOR4 corresponding to N = 12 circumferential waves. This is the critical (lowest) 100 buckling mode obtained in the elastic analysis.  ;

l Fig. 2.11 Interaction curves for the suppression chamber I corresponding to four types of failure, yielding ("S"), local buckling ("L"), general instability ("G"), and panel i

I (inter-ring, smeared stringers) instability ("SS").

101 Imperfections and plasticity neglected.

Fig. 2.12 Interaction curves for the suppression chamber with plasticity and imperfections included according to ASME vii i

code case N-284 (modified) 102 Fig. 2.13 Critical interaction curves for the perfect and imperfect suppression chamber, with stress point predicted by BOSOR4 superposed 103 Fig. 2.14 Interaction curves for the lowest part of the drywell cone corresponding to three types of failure, yielding

("S") , general instability ("G") , and local (between stringers) buckling ("L"). Imperfections'and plasticity neglected in buck-ling analyses. 104 Fig. 2.15 Interaction curves for the lowest end of the drywell cone with plasticity and imperfections included in the buckling analyses 105 Fig. 2.16 Critical interaction curves for the perfect and imperfect lowest part of the drywell cone, with stress-point predicted by BOSOR4 superposed. 106 Fig. 2.17 Discretized BOSOR5 modal of a portion (Segments 3-9 in Fig. 2*l) of the WPPSS-2 containment vessel. 107 Fig. 2.18 Line loads and Moments applied to the model in order to simulate the equivalent static load specified in the PDM stress report. Moments are required to " move" the line loads from the reference surface, which is the shell inner sur face, to the middle surface. 108 Fig. 2.19 Axisymmetric deformations at a load factor of 3.6, which corresponds to BOSOR5's prediction of axisymmetric collapse. Collapse occurs because of the large stress concen tration between segments 2 and 4. 109 Fig. 2.20 Critical buckling mode. Load factor of 4.52 is not meaningful because nonsymmetric bifurcation buckling is pre-ceeded by axisymmetric collapse at a load factor of 3.6. 110 Fig. 2.21 Discretized meridian of upper head of WPPSS con-tainment for BOSOR5 analysis of elastic-plastic buckling under internal pressure 111 Fig. 2.22 Axisymmetric deformations under an internal pressure. Plastic flow initiates in the knuckle region at a pressure of about 1.5

• 45 psi. Compressive hoop stresses exist in the knuckle region where the meridian moves toward the axis I of revolution. These compressive hoop stresses could cause buckling, and the purpose of this analysis is to prove that they do not. 112 Fig. 2.23 Axisymmetric deformations caused by an internal pressure of 3.0

• 45 psi. For internal pressure higher than this, the hoop compression diminishes. Nonsymmetric bifurcation buckling does not occur in the head at any internal pressure. 113 viii

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Fig. 2.24 Buckling mode predicted by BOSOR5. The eigenva- I lue, about 4, corresponds to an internal pressure of about 12*45 l psi, at which pressure the stresses are everywhere positive and 114 buckling is therefore impossible.

Fig. 3.1 Normal deflection of BOSORS and STAGSC-1 axi-symmetric models due to a load factor of unity, i.e., the load 115 level obtained from the PDM stress report.

Fig. 3.2 Normal deflections of STAGSC-1 axisymmetric model (units 1,2, and 3 of the model shown in Fig. 3.4) at elevation

= 5588 in, with a uniform circumferential spacing of 2.5 deg.,

5 deg., and uniform spacing within segments; 2.5 deg. along '

theta = 0 to theta = 15 deg. and 5 deg. along theta = 15 deg.

i 115 to theta = 35 deg.

Fig. 3.3 Normal deflections of STAGSC-1 (portion of the model shown in Fig. 3.4 between elevations 5588 in. to 6496.5 in. and theta = 30 deg. to theta = 35 deg.) and BOSORS axi-116 symmetric models at collapse.

Fig. 3.4 STAGSC-1 finite element model for collapse analy-sis of the portion of the WPPSS-2 containment which contains the 117 largest opening.

Fig. 3.5 Collapse mode of the STAGSC-1 model with pene-tration. Deflections are multiplied by a scale factor of 40 for 118 visual effects.

Fig. 3.6 Contours of normal deflections for shell unit 4 at collapse. The actual deflection in inches is W=0.0623 times 119 the designated number along the contour.

Fig. 3.7 Contours of normal deflections for shell unit 5 at collapse. The actual deflection in inches is W=0.0492 times 120 the designated number along the contour.

Fig. 3.8 Contours of normal deflections for shell unit 11 at collapse. The actual deflection in inches is W=0.0534 times 121 the designated number along the contour.

Fig. 3.9 Variation of nonlinear portion of normal defor-mation (at elevation = 5960.806 in. and theta = 20 deg.) Load with load factor for the STAGSC-1 model with penetration. fac-tor of unity here imply the actual load level obtained from the 122 PDM stress report.

Fig. 3.10 Normal deflections along a meridian for the axi-symmetric BOSORS model, and along the meridian at thetafactor = 35 deg. for the STAGSC-1 model with penetration, at a load 123 of 3.6.

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f LIST OF TABLES I Table 2.1 Maximum plastic strain predicted by B0 SORS. ,

81 Table 2.2 Maximum plastic strain predicted by SOS 0RS. 84 I

Table 3.1 Materials, thicknesses, and longitudinal stiffeners in the STAGSC-1 model of the WPPSS-2 containment (Fig. 3.4).

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PREFACE AND ACKNOWLEDGMENTS This volume represents the second part of the first in a series of volumes reporting work performed under Contract NRC-03-80-103. The effort in the contract is divided into 5 tasks, as follows:

1. Investigation of buckling of two steel containments

a. Offshore Power Systems' (OPS) Floating Nuclear Plant Containment (Ice Condenser)

b. Washington Public Power Supply Systems' (WPPSS)

Mark II Containment for the WPPSS-2 Power Plant;

2. Prediction of buckling of six ring stiffened cylindrical shells under nonuniform axial compression, the specimens fabri-cated and tested by Los Alamos National Laboratory under a sep-arate contract with NRC;

3. Conduct of parameter studies for buckling of steel con-tainment shells, including the effects of random imperfections, stif feners, nonuniform axial compression, and fabrication (weld-ing) effects;

4. Modification and delivery to NRC of a computer program (PANDA) for calculation of buckling loads, including imperfec-tions and plasticity, for unstiffened or stiffened cylindrical shells under combined in-plane loading, this program suitable for use in preliminary design;

5. Modification as needed and delivery to NRC of all other computer programs (BOSOR4, BOSORS, and STAGSC-1) used for execu-tion of this contract.

Documentation of Task 1 is contained in two volumes, one i for each containment shell. Documentation of Tasks 2, 3, and 4 is contained in Volumes 2, 3, and 4. Documentation of Task 5 is contained in the user's manuals and theory manuals for the com-puter programs PANDA, BOSOR4, BOSOR5, and STAGSC-1. All of these programs are in the public domain.

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The authors are most grateful for the cooperation of Washington Public Power Supply System (WPPSS), Pittsburgh-Des Moines Corpo-ration (PDM), and Burns and Roe (BR) during Task Ib. All data were provided to LMSC in a timely manner by E. Fredenberg, R.

M. Nelson, D. L. Whitcomb, and M. K. Chakravorty of WPPSS; M. Offineer of PDM; and A. J. Lageraan, P. Hsueh, and J.

J. Verderber of BR.

We would also like to express our thanks to Charles Rankin and Frank Brogan of Lockheed for their prompt assistance with any problems encountered with STAGSC-1 and with any programming needs, such as the generation of postprocessors, file manipula-tion, conversion from one computer to another, etc.. Without their skill and willingness to cooperate this task could not have been performed. We are grateful also for many fruitful technical discussions with Bo Almroth and Jorgen Skogh.

Mr. Sang Bo Kim of the U. S. Nuclear Regulatory Commis-sion (NRC) was technical monitor. We would like to express our appreciation for his aid in setting up meetings with personnel at WPPSS, PDM, and BR and for his and Mr. Franz Schauer's en-couragement throughout the course of this work.

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BUCKLING OF STEEL CONTAINMENT SHELLS TASK lb: BUCKLING OF WASHINGTON PUBLIC POWER SUPPLY SYSTEMS' PLANT NO. 2 CONTAINMENT VESSEL

1.0 INTRODUCTION

Confiauration 2f the Containment Vessel Figure 1.1 shows the overall elevation of the WPPSS-2 con-tainment vessel. The BOSOR4 and BOSORS overall models include the meridian from elevation (EL.) 446'-0" to 598'-8". A partial BOSOR5 model and the STAGSC-1 models include a segment of the vessel around the transition region from cone to cylinder (EL.

about 490').

Figure 1.2 is a rolled-out plan of the containment. The STAGSC-1 model including the largest penetration covers the re-gion outlined by a heavy line.

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2.0 AXISYMMETRIC MODELS WITH BOSOR4, BOSOR4, AND PANDA 2.1 BOSOR4 and BOSOR5 Models 2.10, Figs.

Results obtained are shown in Figs. 2.1 - ,

2.17 - 2.24, and Tables 2.1 and 2.2. Input for the BOSORS pre-processor (VAX version) is listed in Appendix 6.1.

Figure 2.1 shows the discretized meridian (every third nodal point is indicated), which consists of 23 shell segments. The The same model was used for both BOSOR4 and BOSOR5 runs.

loading is indicated in Fig. 2.2 (external pressure not shown).

In order to simulate the prebuckling state of axial compression

, which varies along the meridian, it is necessary in the BOSOR4 and BOSOR5 models to introduce line axial loads, radial loads, and meridional moments at many meridional stations. The posi-tions of these loads appears in Fig. 2.2. Their values are derived from data in the PDM stress report (Ref. 1) . These va-lues, plus the distribution of external pressure, can be obta-ined by inspection of the list of input data contained in Appen-dix 6.1.

Figure 2.3 shows the positions of discrete rings in the BOSOR model. Not all of these rings are structural; many of them are " phony" rings required in the BOSOR input at stations where line loads are applied.

Figure 2.4 shows the axisymmetrically deformed vessel under external pressure only. The pressure is 2 psi over shell seg-ments 21-23, 4 psi over shell segments 3-20 (upper part of Seg.

3), and 19 psi over the lower part of Seg. 3 and Segs. 1 and 2 (suppression chamber). Figure 2.5 shows the axisymmetric defor-mations under external pressure plus the line loads shown in Fig. 2.2. Note that in Fig. 2.5 the deformations are plotted to a different scale than they are in Fig. 2.4; that is why the deformations due to the pressure component of the loading do not show up clearly in Fig. 2.5.

Figures 2.6 and 2.1 give the prebuckled state of the con-tainment vessel as loaded axisymmetrically by external pressure and by the line loads and moments shown in Fig. 2.2. In these plots the arc length is the accumulated meridional distance from the beginning of the first segment. All segments are plotted continuously on the abcissa, which leads to the discontinuities that appear near arc length s = 500, s = 1000, and s = 1400 inches. The several other discontinuities in the meridional and radial re-sultant, N10, arise from the application of axial line loads at the stations shown in Fig. 2.2.

Figures 2.8 - 2.10 display buckling modes predicted by BOSOR4 for circumferential wave numbers 18, 16, and 12, respec-tively. The quantity "E.V." is the eigenvalue, or buckling load factor in each case. The eigenvalue signifies the following:

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e If you were to multiply the loads applied to the containment by 1

this factor, and if the material were to remain elastic, the containment would buckle-in the mode displayed for each wave number. Thus the critical buckling load corresponds to 4.894 times the applied load system and buckling first occurs in the drywell cone, primarily in Segment 14, with twelve circumferen-tial waves. At a slightly higher load factor, 5.322, buckling would occur just above the transition region (Seg. 6), in Seg-ment 9, and the buckling mode would contain 16 circumferential waves. Almost simultaneously, buckling would occur in the upper i

part of the cylindrical portion of the vessel in a mode with 18 circumferential waves. ,

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j Since the load factors for these three buckling modes are about' the same, it appears that the WPPSS-2 containment is con-sistently designed with respect to buckling in the regions spanned by Segments 4-14. '

The BOSOR4 analysis does not account for plasticity or im-perfections.

2.2 Analysis with PANDA Figures 2.11 - 2.16 show interaction curves for buckling or yielding in two regions of the containment: Figs 2.11 - 2.13 pertain to the suppression chamber, Segments 1,2, and part of 3; and Figs. 2.14 - 2.16 pertain to the lower part of the drywell cone (Seg. 9, analyzed here as an equivalent cylinder). The PANDA computer program was used to obtain these results. PANDA is described in Vol. 4 of this report.

Figure 2.11 shows interaction curves for possible failure modes of the suppression chamber (the region stiffened by both stringers and large rings). Imperfections and plasticity are neglected. The critical mode, by far, is represented by the small ellipse at the center of the figure. This is simply the l

. Von Mises yield criterion. The next most critical mode of fai-lure is represented by the curve labelled "L", which stands for '

local buckling between adjacent rings and adjacent stringers.

The next curve out from the origin in loading space is lebelled "G" for general instability. This curve is crossed by one la-belled "SS" for " smeared stringers". The "SS" curve signifies buckling of skin and stringers together between adjacent rings, what many researchers call " panel buckling". The arrangement of these interaction' curves demonstrates that the suppression chamber is so strongly built that it will not fail until most of its material is stressed beyond the yield point.

i Figure 2.12 shows interaction curves in which plasticity as well as imperfections are included in the buckling analysis.

, Knockdown factors for imperfections and plasticity reduction i

factors are taken from ASME ccde case N-284 (with minor modifi-cations). Note that the curves tend to cluster around the von Mises yield ellipse, which indicates that all the types of fai-lure are essentially caused by yielding of the material; the l

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buckling analysis of the suppression chamber is not very inter-esting because the chamber is very much overdesigned with regard to buckling. Hence we will not pursue such analyses with use of the STAGSC-1 computer program for this portion of the WPPSS con-

! tainment vessel. )

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Figure 2.13 displays two interaction curves, the critical curve for the perfect shell and that for the imperfect shell.

Also shown in Fig. 2.13 is a stress point representing the state of compression at the bottom of the suppression chamber (beginning of Seg. 1) . Again, it is clear that buckling of the suppression chamber is not a problem.

Figures 2.14 - 2.16 provide the same type of information for the lowest part of the drywell cone (Segment 9 in Fig.

1) .

Figure 2.14 shows interaction curves for von("G"), Mises and yielding ("S"

" stress"), for general instability for local for buckling between stringers ("L"). (There are noneglected rings in this region). Plasticity and imperfections are in the buckling curves "G" and "L". In Fig. 2.15 the effects of plas-ticity and imperfections have been included in the generation of the curves labelled "G" and "L". Figure 2.16 shows the critical interaction curves for the perfect elastic and imperfect plastic j cases, with the stress point from the BOSOR4 run superposed.

the margin appears to be adequate.

This region is of Again, with more interest than the suppression chamber and is modelled STAGSC-1. The largest cutout is of course included in the l

STAGSC-1 model.

2.3 Plastic Strains from BOSORS Models The model shown in Fig. 2.1 has also been run on BOSOR5.

j Table 2.1 shows how the plastic strain grows with load. (In BOSORS the load is increased by increasing a pseudo time and specifying that the load increase in proportion with time.) The factors t = 2.0, t = 2.2, etc. nearest the right-hand-margin are time steps, which are equal in this case to load factors.

Axisymmetric collapse is predicted to occur at a load factor of 3.0 to 3.2. This prediction is consistent with plastic collapse occurring in the suppression chamber (See Fig. 2.13. If the stress state indicated by the point is multiplied by a factor of 3.2, the point is brought very near to the von Mises yield el-lipse. ) Particularly large plastic strains are predicted at 7

the clamped boundary, as might be expected. (See third page of t

Table 2.1, Seg. 1, point 1.)

2.4 BOSOR5 Model gi A Portion Li thg WPPSS-2 Vessel Figures 2.17 - 2.19 depict a portion of the WPPSS contain-ment represented by segments 3 through 9 in Fig. 2.1. At the lower and upper extremities of the model meridional rotation was prevented. Figure 2.17 shows the discretization and segment numbering scheme; Fig. 2.18 shows the applied line loads and moments. Note that moments are applied because the reference surface is the inner surface of the shell and the centroids of l l

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I. . . --.- -. - - - _ . _--.

the " phony" rings are on the reference surface. Line loads are assumed to be applied at ring centroids. Therefore, in order to represent a load applied at the middle surface, it is necessary to move it from the ring centroid on the inner surface (refer-ence surface) by expressing it as a line load plus meridional moment, where the meridional moment is equal to the axial load V times one-half the wall thickness. The (axial load, meridional moment) combination applied at the ring centroid (shell inner surface) is equivalent to the same axial load applied by itself at the shell wall middle surface. Note that the loading due to uniform external pressure of 4.0 psi is not shown in Fig. 2.18.

Figure 2.19 shows the wall deformations at axisymmetric collapse, which occurs at a load factor (time) of 3.6. Collapse occurs bacause of large discontinuity stresses at the junction between segments 2 and 4, where there is a discontinuity in mer-idional curvature. Table 2.2 lists the growth of plastic strain as the load factor (time) is increased.

! Figure 2.20 displays the critical buckling mode for the

! partial model. The predicted load factor, 4.52, is not meaning-l ful because axisymmetric collapse occurs at 3.6. The buckling mode agrees with that shown for the full BOSOR4 model in Fig.

2.8, except that there is a hinge between Segments 2 and 4 which develops because of local prebuckling plastic flow.

2.5 Buckling of the Drywell Head under Internal Pressure Figures 2.21 - 2.24 show the BOSOR5 model of the top head of the WPPSS containment vessel (Fig. 2.21), axisymmetric de-formations due to internal pressure (Figs. 2.22 and 2.23), and

, a buckling mode (Fig. 2.24) . Although buckling load factors l

and nonaxisymmetric mode shapes can be calculated for this head with use of BOSOR5, in actual fact such buckling cannot occur for such a thick (small r/t) head. At the load factors for which nonsymmetric (bifurcation) buckling is predicted to occur, the circumferential resultant in the knuckle region, which causes buckling in thinner heads, is positive.

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3.0 STAGSC-1 MODELS OF THE WPPSS-2 CONTAINMENT VESSEL 3.1 Axisymmetric Models Before embarking on the construction of a complicated fin-ite element model of the WPPSS containment vessel including the

! largest penetration, we felt it prudent to start with some ati-symmetric models. We wished to compare the results from STAGSC-1 to those from BOSORS for models which both of those 4

codes can treat rigorously. With the use of axisymmetric models

' one can verify STAGSC-1 input data such as geometry, thickness, stiffener properties, loading, refinment of grid, etc. without a large expenditure of computer time and manhours. In STAGSC-1 conditions of axisymmetry are imposed by specification of symme-try conditions along the meridional edges.

Three axisymmetric STAGSC-1 models were set up:

(a) an initial simple elastic model to compare with BOSOR5 results at a load factor of unity; (b) a slightly more complex model spanning 35 degrees in order to determine the effect of varying the grid spacing in the circumferential direction; (c) a final simple elastic-plastic model spanning 5 degrees in order to compare the plastic collapse load with that predict-ed by BOSOR5 and to ensure that the model with the penetration included spans enough of the circumference such that the same collapse load /(length of circumference) would have been predict-ed even if a wider model had been analyzed.

First axisymmetric model: This STAGSC-1 model spans 5 de-grees in the circumferential direction and extends between ele-

vation 5588 inches and elevation 6184 inches. It is similar to j the BOSOR5 model described in section 2.4. Figure 3.1 displays normal deflections predicted by both BOSORS and STAGSC-1 for a load factor of unity. The loads that the load factor in multi-plied by are listed in the input data file for BOSOR5 given in Appendix 6.2. The slight difference between the STAGSC-1 and j

BOSORS results is probably due to the small difference in the i lowest elevation to which the two models were extended (BOSOR5' l 5514 inches; STAGSC-1 = 5588 inches) and to the different

manner in which the catwalk (Shell seg. no. 3 in Fig. 2.17) is modelled. (In BOSORS it is a shell branch with a ring on the end [See Fig. 2.19], whereas in STAGSC-1 it is treated as a discrete ring with a non- deformable cross section.)

Second Axisymmetric Model-Spanning li Degrees: In the past

, certcin difficulties have resulted from STAGSC-1 models in which the grid spacing varies in the circumferential direction. Since it was originally planned in the analysis of the vessel includ-ing the penetration to use a circumferentially varying grid, we 7

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i felt it advisable to check the results first on a simple case without any penetration. Thirty-five degrees of circumference

, were included in this model because it was planned to use the same for the model with the penetration. The axial extent of

! the model is from EL. 5588 to EL. 5867.

Results from two models are displayed in Fig. 3.2. In the model with uniform grid spacing in the circumferential direc-tion, two spacings were used: 2.5 deg. and 5.0 deg. In the model with nonuniform spacing, the spacing was 2.5 deg. for'15 degrees and 5.0 deg. for the remaining 20 deg. Loading is uni-form axial compression.

These results clearly indicate that the nonuniform grid spacing in the circumferential direction is not suitable for the collapse analysis, since it causes the model to deform signifi-i cantly nonsymmetrically even though the structure and loading

, are axisymmetric. Therefore, only uniform grid spacing in the circumferential direction is used for the model with the pene-tration.

l Third STAasc-1 Arisymmetric Model: The final axisymmetric model for an elastic-perfectly plastic collapse analysis was se-

' lected after the complete finite element model with the penetra-tion was designed. Therefore this axisymmetric model comprises the segment of the large model between elevations 5588 in, to 6496.5 in, and theta =30 deg. to theta =35 degrees (see Figure 3.4 for the complete model). Collapse of this model was reached at a load factor of 3.6, which is the same as that obtained with the use of the BOSOR5 computer code and discussed in section 2.4.

The input data for STAGSC-1 for this model are listed in Appendix 6.3. Figure 3.3 shows the normal deflections from STAGSC-1 and from BOSORS at the collapse loads predicted by each of these programs (load factor 3.6 for BOSOR5 and 3.75 for STAGSC-1) .

3.2 Model Including Largest Penetration Figure 1.2 shows a " rollout" of the WPPSS-2 containment vessel. The region chosen for analysis with STAGSC-1 is out-lined with a heavy line. STAGSC-1 data are listed in Appendices 6.4 and 6.5.

The STAGSC-1 finite element model of the portion of the WPPSS-2 containment which contains the largest opening (indicat-ed in Fig. 1. 2) is shown in Fig. 3.4. Boundary conditions im-posed on the model are symmetry along the meridians at theta =0 and theta =35 degrees, axial deformation and edge meridional ro-tation restrained at the lower end (elevation =5588 in.) and un-restrained (other than by a very large ring) at the upper end (elevation = 6496.5 in.).

In the STAGSC-1 model the material behavior is assumed to 8

t be elastic-perfectly plastic, with yield strengths depending on the type of material, which varies from shell unit to shell unit as listed in Table 3.1.

As with the BOSOR4 and BOSOR5 models, the loading (meridi-onal compression combined with external pressure) was derived from data in the PDM stress report. (Actually, for the STAGSC-1 models it was derived from the load data listed in Appendix 6.2, the BOSORS input data.) In the' collapse (load-deflection) ana-lysis, the combined loading is increased in steps until a maxi-mum load is reached or until iterations no longer converge.

The STAGSC-1 finite element model consists of 11 shell units and 1 element unit. (The terminology "shell unit" and

" element unit" are STAGSC-1 jargon; both kinds of units repre-sent thin shells. "Shell units" are sections of structure the discretization of which is handled by automatic mesh generation

[ cylinders, cones, plates, etc.). " Element unit" refers to a structural branch in which the entire grid must be specified by the user.)

In using STAGSC-1 the analyst can choose any of several mo-dels to describe the geometry. For example, shell units 1,2, and 3 in Fig. 3.4 could have been modeled as a single shell unit. However, in that case it would have been necessary to in-troduce the wall thickness variation via a user-written subrou-tine, WALL, since the thickness would not have been constant within the shell unit. Also, refinement of the mesh in local areas is accomplished more easily by splitting these areas into individual shell units.

Since the area adjacent to the cutout is of particular con-cern in this analysis, it is discretized with a more refined mesh than is the rest of the structure.

The most complicated shell unit in this WPPSS-2 model is Unit 5. It is a cone with a cutout between elevations 5998.5 in, and 6148.5 in. and between meridians at theta = 0 and i

theta = 10 degrees. There are three different thicknesses, two different materials, and discrete longitudinal stiffeners. The element unit consists of the hatch construction and the transi-tion portion between the hatch and Unit 5.

Table 3.1 displays the unit thicknesses, materials, types of longitudinal stiffeners, and spacings of longitudinal stif-feners. In this model the longitudinal stiffeners are spaced at 5 degrees increments. This requires modification in stiffener properties to account for the difference in spacing between the actual structure and the finite element model. That is, in this

. model, the longitudinal stiffeners can be considered as smeared out for all practical purposes.

Appendix 6.4 lists the user-written subroutine WALL, which i

is used to introduce materials and thicknesses for shell units 5, 6, 10, and 11. Appendix 6.5 lists the input data for the en-9 i'

tire STAGSC-1 model.

Results: Collapse is predicted to occur at a load factor of 3.75, that is, at a load level which is 3.75 times the as-sumed loading configuration described previously. The collapse mode superimposed on the undeformed geometry is shown in Fig.

3.5. The displacements in Figure 3.5 are multiplied by a factor of 40 for visual effects. Figures 3.6 to 3.8 display contours of the normal (radial) displacement for shell units 4, 5, and

11. The actual displacements (in inches) can be obtained by multiplication of the factors 0.0623, 0.0492, and 0.053 4 by the contour callouts for units 4, 5, and 11, respectively.

t Figure 3.9 displays the variation with load factor of the I nonlinear portion of the radial displacement at an elevation of 5960.806 inches and theta =20 degrees. The nonlinear portion of the displacement is obtained by subtracting the displacement that would have been obtained from a linear analysis from the total displacement printed out in the STAGSC-1 output.

Figure 3.10 displays the radial displacement along the mer-idian at theta =35 degrees for the STAGSC-1 model with the pene-tration and for the BOSORS model. Both curves correspond to a l load factor of 3.6.

The collapse analysis for the WPPSS-2 model described here

, indicates that the penetration does not affect the collapse load of a mcdel in which the cutout and associated reinforcements have been neglected, i

I i

l 10

l

4.0 CONCLUSION

S l

The PANDA, BOSOR4, BOSOR5, and STAGSC-1 computer programs were 1 used to perform buckling analyses of the Washington Public Power )

Supply System's (WPPSS) plant No. 2 containment vessel. This report illustrates methods of analysis for buckling problems that we feel are reasonably efficient. Steps in any buckling analysis might be as follows:  ;

1. First use PANDA to obtain approximate buckling loads for a wide variety of loading conditions (interaction curves, such as plotted in Figs. 2.11-2.16) and a wide variety of de-sign parameters. This program is based on a " classical" type of buckling approach, and runs very fast on the computer. Cases are easy to set up because the data are called for in an inter-active, " conversational" mode. Information obtained with regard to buckling load estimates and mode shapes is very useful for

, subsequent runs with more elaborate programs such as BOSOR4, BOSOR5, and STAGSC-1. For example, the waviness of the buckling pattern is a guide for sizing the finite element grid in a STAGSC-1 model.

2. Next, set up models with BOSOR4 and BOSOR5. BOSOR4 does both modal vibration analysis and buckling analysis for shells of revolution with elastic material and BOSOR5 does buck-ling analysis only but includes elastic-plastic material behavi-or. These programs are more difficult to run than PANDA, but they are easier to run than STAGSC-1 because the discretization is one dimensional rather than two dimensional. Therefore, they run fast. One does not have to worry too much about convergence due to discretization error because one can afford to have closely spaced nodal points. An entire structure or a very large portion of it can be modelled as one case, again because of the one dimensional discretization. The BOSOR programs yield additional information to that provided by PANDA: They will handle any meridional shape (not just flat or cylindrical as is the case with PANDA) , and buckling loads obtained with discrete rings are more accurate than those obtained from the approximate l formulas used in PANDA. The BOSOR programs can handle a shell

! with variable thickness, such as is the case in the discretized model shown in Fig. 2.1, where the thicknesses of the many courses are different. With PANDA, each course must be analysed separately.

3. Based on the results obtained so far (with PANDA and the BOSOR programs), set up small models of critical areas with l use of STAGSC-1, performing convergence studies with respect to grid refinement. The converged results obtained with these small models should agree very well with converged results from BOSOR4 and BOSOR5, since these small models should be for areas I of the shell away from penetrations, etc. that destroy symme-l try. Small models such as these are inexpensive to run on the t computer and yield valuable information about how dense the fin-l l 11

ite element grid should be in order to obtain accuracy within a given amount. They provide guidance for the larger, more expen-sive models to follow.

4. Finally, choose a critical area and construct STAGSC-1 models of various types, such as shown in Figs. 3.4 and 3.5.

Having performed analyses 1 - 3, you will have a very good idea of what the buckling load and mode shape should be. If you ob-tain a very different answer from that expected, you will be in a much better position to determine whether the anomaly is a real physical effect, an error in your model, or a bug in the program.

i l

12

REFERENCE

1. Pittsburgh Des Moines Corp. Stress Report:

B and R file no. 213A-00-0058 B and R file no. 213 026 8 (Section IV-9)

B and R file no. 213 0280 (Section II-6)

B and R file no. 213 0260 (Section II-8)

B and R file no. 213 0455 (Section IV-10)

B and R file no. 213 1545 (Section IV-2)

B and R file no. 213 (Section IV-1) (pages extracted by Mr. Offineer and supplied to LMSC at Feb. 1982 meeting at WPPSS-2) e l

13

I 1

l l

l APPENDIX 6.1 Summaries of characteristics of STAGSC-1 BOSOR4 BOSORS PANDA 15

d l

STAGSC1 at a Glance Keywords: general shells, stress, buckling, vibration, transient response, nonlinear, elastic, plastic, stiffeners, penetrations, cutouts, composites, finite elements, imperfections.

Purpose:

To perform stress, buckling, modal vibration, and transient response analyses of general shells with stiffeners, elastically and plastica 11y. Complex wall construction permitted.

Date: 1970, most recent version 1982 Developers: Bo Almroth, Frank Brogan Lockheed Missiles & Space Co. , Inc.

, 3251 Hanover Street

Palo Alto, CA 94304 Telephone: (415) 858-4027

! Method: Discrete variational analysis. Local two-dimensional power representations of the displacement components. Modified Newton method for solution of the nonlinear algebraic equations.

Automatic correction of load or time steps. Restart capability.

Restrictions: 30 shell branches, 20 layers in shell wall. No bifurcation i with plastic prebuckling. 10 point stress-strain curve definition.

Language: FORTRAN IV or FORTRAN V (FORTRAN 77)

Documentation: User's Manual: Vol. I, Theory; Vol. II, User Instructions; Vol. III, Example Cases. Journal articles. Reports.

Input: Free-field input,11 standard geometries defined by their dimensions or data cards, non-standard geometries in user-written subroutines.

No element or node numbering required for standard geometries.

Automatic mesh generation for geometries defined analytically in user-written subroutines. Loads are defined on data cards, or if varying with location on shell, are defined in user-written subroutines. Loads can be forces or displacements. Data preparation j and postprocessing possible by GIFTS. J Output: Displacements, stress resultants, stresses, strains, equilibrium I forces, eigenvalues, eigenvectors; lists and plots.

Hardware: UNIVAC 1108, CDC 6600 OR 7600, CDC 205, VAX, IBM, CALCOMP, SC4020,

)

PRINTRONIX, TEKTRONIX.

Usage: About 40 institutions use STAGS.

RiiiTTime: Varies with type of structure. Typical examole, stiffened cylinder, 966 00F, run on CDC 6600: Bifurcation, 2 modes: 34 CPA seconds.

Availability: CDC and UNIVAC versions available from the developers. Price  !

for tape and documentation: $2500. Updating, maintenance, and consultation available to members of the STAGS User's Group at a

$2500 annual fee.

STAGS References Almroth, B.0. , and Felippa, C. A. , " Structural Stability," Proceedings of International Symposium on Structural Mechanics Software, U. of MarylanE College Park, Maryland, Uiine 1974, pp. 499-540.

16

i STAGSC-1 (concluded)

Almroth, B.0. , and Brogan, F. A. , " Automated Choice of Procedures in Computerized Structural Analysis", Presented at 2nd National Symposium on Computerized Structural Analysis and Design, Washington, D.C., 29-31 March 1976.

Ericsson, L.E. , Almroth, B.0. , Bailie, J. A. , Brogan, F. A. , and Stanley, G.M. ,

" Hypersonic Aeroelastic Analysis", Lockheed Report LMSC-D056746, Sept. 1975.

Almroth, B.O. , and Holmes, A.M.C. , " Shells with Cutouts, Experiment and Analysis", International Journal of Solids & Structures, Vol. 8,1972, pp.

1057-1071.

Almroth, B.O. , Brogan, F. A. . and Marlowe, M.B. , " Stability Analysis of Cylinders with Circular Cutouts", AIAA jb,, Vol. 11, 1973, pp. 1582-1584.

Stephens, W.B. , Starnes, J.H. , Jr. , and Almroth, B.O. , " Collapse of Long Cylindrical Shells under Combined Bending and Pressure loads", AIAA J., Vol.

13, 1975, pp. 20-25.

Stein, M., and Starnes, J.H. , Jr. , " Numerical Analysis of Stiffened Shear Webs in the Post-Buckling Range, Numerical Solution of Nonlinear Structural Problems", AMD-Vol. 6, ASME,1973, pp. 211-223.

Almroth, B.O. , Brogan, F. A. , and Marlowe, M.B. , " Collapse Analysis for Elliptic Cones", AIAA J. , Vol. 9,1971, pp. 32-37.

Marlowe, M.B., and Brogan, F. A., " Collapse of Elliptic Cylinders under Uniform External Pressure", AI AA Jb , Vol. 9,1971, pp. 2264-2266.

Skogh, J. , Stern, P. , and Brogan, F. A. , " Instability Analysis of Skylab Structure", Computers and Structures, Vol. 3,1973, pp.1219-1240.

Skogh, J. , and Stern, P. , "Postbuckling Behavior of a Section Representative of the B-1 Aft Intermediate Fuselage", AFFDL TR-73-63, Wright-Patterson AFB, Ohio, Pby 1973.

Skogh, J. , Meller, E., and Brogan, F. A. , "The Buckling and the Thereaf ter of the D-1T Stub Adapter", Lockheed Report LMSC-D358099, January 1974.

Skogh, J., " Stress Analysis of the LIMCO Electrolyte Heat Exchanger" (Analysis for certification by Bureau of Shps), Lockheed Report LMSC-D676427, Feb.1979.

Skogh, J., "Shell Structure Collapse Study using the STAGSC-1 Computer Program" (Evaluation of STAGSC-1 for NSRDC), Lockheed Report LMSC-D676588, June 1979.

17

B050R4 at a Glance Keywords: shells, stress, buckling, vibration, nonlinear, elastic, shells of revolution, ring-stiffened, branched, composites, discrete model

Purpose:

To perform stress, buckling, and modal vibration analyses of ring-stiffened, branched shells of revolution loaded either axisymmetrically or nonsymmetrically. Complex wall construction permitted.

Date: 1972; most recent update 1982 Developer: David Rushnell, 52-33/255 Lockheed Missiles & Space Company, Inc. ,

3251 Hanover Street l Palo Alto, CA 94304 Telephone: (415) 858-4037 Method: Finite difference energy minimization; Fourier superposition in circumferential variable; fkwton method for solution of nonlinear axisymmetric problem; inverse power iteration with spectral shifts for eigenvalue extraction; Lagrange multipliers for constraint conditions; thin shell theory.

Restriction: 1500 degrees of freedom (d.o.f.) in nonaxisymmetric problems; 1000 d.o.f. in axisymmetric prebuckling stress analysis; maximum of 20 Fourier harmonics per case; knockdown factors for imperfections not included; radius / thickness should be greater than about 10.

Language: FORTRAN V Extended Documentation: BOSOR4 User's Manual [1] and 10 journal articles with numerous examples (References [2] - [11]); VAX version has interactive prompts.

" Help" file available with VAX version.

Input: Free-field input. Required for input are shell segment geometries, ring geometries, number of mesh points, ranges and increnents of circumferential wave numbers, load and temperature distributions, shell wall construction details, and constraint conditions. VAX version is interactive.

Output: Displacements and stress resultants or extreme fiber stresses, buckling loads, vibration frequencies; list and plots.

Ha rdwa re: UNIVAC 1108 or 1110, CDC 6600 or 7600, IBM 360 or 370, VAX; SC4020 and CALCOMP plotters.

Usage: About 150 institutions have obtained B0SOR4. It is currently being used on a daily basis by many of them.

Run Time: Typically a job will require 1-5 minutes of computer time on main-frame; 5-15 minutes on VAX.

Availability: VAX, CDC, and UNIVAC versions available from developer (see above); IBM version from Professor Victor Weingarten, Dept. of Civil Eng. , Univ. of Southern California, University Park, Los Angeles, CA 90007. Price: $1000. B050R4 may be run through the following data centers and networks:

McDonnell- Douglas Automation, Huntington Beach, Ca.

Control Data Corp. , Rockville, Md.

Westinghouse Electric, Pittsburgh, Pa.

Information System Design, Oakland, Ca.

Boeing Computer Service, Seattle, Wa.

United Computing Systems (United Information System)

University Computing Company 18

l B050R4 (concluded)

Det Norske Veritas (Norway)

CNES (France)

CERN (Switzerland)

Aeronautical Res. Inst. of Sweden (FFA) (Sweden)

CTR (Italy)

Matematischer Beratungs and Programmierungsdienst (West Germany)

BOSOR4 References by D. Bushnell, et al

[1] "B050R4--Program for Stress, Buckling and Vibration of Complex Shells of Revolution", Structural Mechanics Software Series, vol.1, edited by N.

Perrone and W. Pilkey, University Press of Virginia, Charlottesville, pp.11-143, 1977.

[2] " Thin Shells"--STRUCTURAL MECHANICS COMPUTER PROGRAMS, Surveys, Assessments, and Availability, edited by W. Pilkey, K. Saczalski, and H.

Schaeffer, Univ. of Virginia Press, Charlottesville, Va. , pp. 277-358, 1974.

[3] " Finite Difference Energy Models Versus Finite Element Models: Two Variational Approaches in One Computer Program", Nunerical and Computer Methods in Structural Mechanics, (edited by Fenves, PerroneDobinson and SchnobriBi), Academic Press, New York, pp. 291-336, 1973.

[4] " Evaluation of Various Analytical Models for Buckling and Vibration of Sti ffened Shells", AI AA J. , Vol . 11, No. 9, pp. 1283-1291,1973.

[5] "Nonsymmetric Buckling of Cylinders with Axisymmetric Thermal Di scontinuities", AI AA J. , Vol. 11, No. 9, pp.1292-1295,1973.

[6] " Stress, Stability, and Vibration of Complex, Branched Shells of Revolution", Computers &_ Structures, Vol. 4, pp. 399-435,1974.

[7] " Local and General Buckling of Axially Compressed, Semi-Sandwich, Corrugated, Ring-Stiffened Cylinder", J. Spacecraft and Rockets, Vol. 9, No. 5, pp. 357-363, May 1972

[8] " Stress and Buckling of Nonuniformly Heated Cylindrical and Conical Shells", (with S. Smith), AIAA J. , Vol. 9, No. 12, pp. 2314-2321, Dec.

1971.

[9] " Stress Buckling and Vibration of Prismatic Shells", AIAA J. , Vol. 9, pp.

2004-2013, 1971.

[10] " Analysis of Ring-Stiffened Shells of Revolution Under Combined Thermal and Mechanical Loading", AIAA J_., Vol. 9, pp. 401-410, March 1971.

[11] " Analysis of Buckling and Vibration of Ring-Stiffened, Segnented Shells of Revolution", Intern. J. Solids and Structures, Vol. 6, pp.157-181, Feb. 1970.

19

---

l

B050R5 at a Glance Keywords: shells, stress, buckling, nonlinear, plasticity, creep, shells of revolution, ring-stiffened, branched, discrete model Pu rpose: To perform stress and buckling analyses of ring-stiffened, branched shells of revolution loaded axisymmetrically. Layered walls with different elastic-plastic-creep properties in each layer. Prebuckling deformations are axisymmetric; buckling may be either axisymmetric or non-axisymmetric. Does not supersede BOSOP4. (See "B050R4 at a Glance".)

Date: 1974; most recent update in 1982 .

Developer: David Bushnell, 52-33/255 l Lockheed Missiles & Space Company, Inc.

3251 Hanover Street Palo Alto, CA. 94304 Telephone: (415) 858-4037 Method: Finite difference energy minimization; trigonometric variation in circumferential direction; Newton method for solution of nonlinear axisymmetric problem; inverse power iteration with spectral shifts for eigenvalue extraction for bifurcation buckling; Lagrange multipliers for constraint conditions; thin shell theory; isotropic strain hardening; subincremental method for evaluation of plastic and creep strains.

Restrictions: 1000 degrees of freedom (d.o.f.) in ax1synmetric prebuckling stress analysis; 1500 d.o.f. in non-axisymmetric bifurcation buckling analysis; knockdown f actors for imperfections not included; radius thickness should be greater than about 10.

Language: FORTRAN V Extended Documentation: B0S0R5 Use:s Manual [1] and 8 journal articles with numerous examples (References [2]-[9]). VAX version has interactive prompts.

" Help" file available with VAX version.

Input: Required for input are shell segment geometries, ring geometries, number of mesh points, ranges and increments of circumferential wave numbers, load and temperature distributions, shell wall construction details including stress-strain curves for materials, and constraint conditions. B050R5 is divided into three executable modules, a preprocessor for which most of the input data is prepared, a main processor with restart capability, and a post-processor. VAX version is interactive.

Output: Displacements and stress resultants; stresses and strains through the thickness at each nodal point for user-selected load or time steps; i buckling modes; list and plots.

Hardware: UNIVAC 1108 or 1110, CDC 6600 or 7600, IBM 360 or 370; SC4020 and CALCOMP plotters.

Usage: About 70 institutions have obtained B0SOR5. It is currently being used on a daily basis by many of them.

Run Time: Typically a job will require 1-10 minutes of computer time on mainf rame, 5-30 minutes on VAX.

Availability: VAX, CDC, and UNIVAC versions available from developer (see above); IBM version from Professor Victor Weingarten, Department of Civil Engineering, University of Southern California, University Park, Los Angeles, CA 90007; Price: $1000. BOS0R5 nay be run through the

, following data centers and networks:

20

r l

l BOS0R5 (concluded)

McDonnell-Douglas Automation, Huntington Beach, California Control Data Corporation, Rockville, Maryland Westinghouse Electric, Pittsburgh, Pennsylvania Information Systens Design, Oakland, California Boeing Computer Service, Seattle, Washington Det Norske Veritas (Norway)

CERN (Switzerland)

Aeronautical Research Institute of Sweden (FFA) (Bromma, Sweden)

BOS0R5 REFERENCES by D. Bushnell, et al.

[1] Bushnell, D., "B0 SORS--A Computer Program for Buckling of Elastic-Plastic Complex Shells of Revolution Including Large Deflections and Creep", Vol.

I: User's Manual, Input Data, LMSC-D407166; Vol. II: User's Manual, Test cases, LMSc-D4U7T67; Vol. -III: Theory a7iiiTomparisons with Tests, H5T-D407168; Lockheed Missiles TTpace Co. , Sunnyvale, CA. , Dec. ,1974.

[2] "BOS0RS--Program for Buckling of Elastic-Plastic Complex Shells of Revolution Including large Deflections and Creep", Computers and Structures, Vol. 6, pp. 221-239, 1976.

[3] "A Strategy for the Solution of Problems Involving Large Deflections, Plasticity and Creep", International Journal for Numerical Methods in Engineering, Vol. 11, 683-708, 1977. ---

[4] " Bifurcation Buckling of Shells of Revolution Including large Deflections, Plasticity and Creep", Int. J. of Solids & Structures, Vol.

10, pp. 1287-1305, 1974.

-- ~~- --

[5] " Comparisons of Test and Theory for Nonsymmetric Elastic-Plastic Buckling of Shells of Revolution" (with G. D. Galletly, University of Liverpool, England), Int. J. of Solids & Structures, Vol.10, pp.1271-1286,1974.

[6] " Buckling of Elastic-Plastic Shells of Revolution with Discrete Elastic-Plastic Ring Stiffeners", Int. J. Solids and Structures, Vol.12, pp. 51-66, 1976.

[7] Nonsymmetric Buckling of Internally Pressurized Ellipsoidal and Torispherical Elastic-Plastic Pressure Vessel Heads", Journal of Pressure Vessel Technology, Vol. 99, pp. 54-63,1977. -~

[8] " Stress and Buckling of Internally Pressurized Elastic-Plastic Torispherical Vessel Heads - Comparisons of Test and Theory", (with G. D.

Galletly), Journal of Pressure Vessel Technoloay, Vol. 99, pp. 39-53, 1977.

[9] " Elastic-Plastic Buckling of Internally Pressurized Torispherical Vessel Heads", (with G. Lagae, Univ. of Ghent), Nuclear Engineering and Design, Vol. 48, pp. 405-414, 1978.

21

PANDA at a Glance i

Keywords: panels, cylinders, buckling, optimization, composite, stiffened, elastic-plastic

Purpose:

To optimize, with respect to weight, cylindrical panels or complete cylindrical shells with discrete or smeared stringers and/or rings subjected to simultaneous in-plane axial compression, hoop compression and shear. Shell wall can be layered composite material. Plasticity included in isotropic layers and in stiffeners. General and local buckling loads as well as maximum effective stress or maximum strain

! components are constraints on the design. Local buckling modes include  ;

skin buckling between stiffeners and local buckling of parts of the l stiffeners, such as web crippling. Stiffener rolling modes included '

l also. Can use PANDA to calculate buckling loads and interaction curves for known designs. Empirically derived knockdown factors (ASME Code Case .

N-284, modified) included in this branch. ,

Date: 1982 Developer: David Bushnell, 52-33/255 Lockheed Missiles & Space Company, Inc.

l 3251 Hanover Street Palo Alto, California 94304 Telephone: (415) 858-4037 l

Method: Buckling modes assumed to follow simple sin mx sin ny pattern for both general and local buckling. For buckling under shear loading and unbalanced laminates the pattern sin ny sin m(x - cy) is used. Other simple analytical expressions are used to describe buckling modes for parts of the stiffeners or rolling, crippling, and wide column buckling of stringers and rings. Optimization is by method of feasible l

directions. The optimizer (CONMIN) was written by Vanderplaats. Donnell equations used, with suitable correction factors applied for low wave numbers.

Restriction: Panel is simply supported; prebuckling stress resultants uniform in the panel. Thickness and stringer and ring spacing uniform. All stringers are identical; all rings are identical; stringers may be L

different from rings, panel must be cylindrical or flat. Plasticity in I isotropic material only. No postbuckled skin.

l Language: FORTRAN V Extended Documentation: References 1 and 3 and program itself.

Input: The interactive PANDA system consists of three independently executed nodules that share the same data base. In the first module an initial design concept with rough -(not necessarily feasible or accurate) i dimensions are provided by the user in a " conversational" mode. In the second module the user decides which of the design parameters of the concept are to be treated by PANDA as decision variables-in the optimization phase. In the third module the optimization calculations are carried out.

l Output: PANDA supplies current panel weight, dimensions, and buckling modes.

Hardware: VAX, CDC Cyber 175, System NOS.

Run Time: Typically an optimum design can be obtained with an hour at the terminal and about half a minute of computer time. Cost for the computer time is negligible, i Availability: VAX and CDC versions from developer for $1000.

22

PANDA (concluded)

References

[1] Bushnell D., " Panel optimization with integrated software (POIS)", Volume 1: " PANDA--Interactive program for preliminary minimum weight design",

Report No. AFWAL-TR-81-3073, Flight Dynamics Laboratory, Air Force Wright Aeronautical Laboratories, Wright Patterson AFB, Ohio (July,1981).

[2] Bushnell, D., " PANDA--Interactive program for minimum weight design of stiffened cylindrical panels and shells" to appear in Computers and Structures, 1982.

[3] Bushnell, D., " PANDA--Interactive computer program for preliinary minimum weight design of composite or elastic-plastic, stiffened cylindrical panels and shells under combined in-plane loads", Proc. International Symposium on Optimum Structural Design, Oct. 19-22, 1981, Univ. of Arizona (to be published by John Wiley).

I 23 i

I APPENDIX 6.2 Input data file for BOSOR5 Model shown in Fig. 2.1 l

25 I

WPP99-2 BOSOR5 CVERALL MODEL 23 $ NSEQ = number of shell segments (less than 25) 11

• NMESH=no. of node points (5= min.s98= max.) SEGMENT NO.( 1) 3 $ NTYPEH= control integer (1 or 2 or 3) for nodal point spacing 2 $ NSHAPE= indicator (1,2 or 4) for geometry of meridian 508.8940 $ R1 = radius at beginning of segment (see p. P7)

! 5352.000 $ Z1 = axial coordinate at beginning of segment 514. 5000 $ R2 = radius at end of segment 5396. 500 $ Z2 = axial coordinate at end of segment 336. 6250 $ RC = radius from axis of rev. to center of curvature 5396. 500 $ ZC = axial coordinate of center of curvature

-1 $ SROT= indicator for direction of increasing arc (-1. or +1.)

O $ IMP = indicator for imperfection (O=none, !=some) 3 $ NTYPEZ= control (1 or 3) for reference surface location 7.930000 $ ZVAL = distance from leftmost surf. to reference surf.

N $ Do you want to print out r(s), r '( s ), etc. for this segment?

2 $ NRINGS= number (max =20) of discrete rings in this segment 2 $ NTYPE = control for identification of ring location (2=r, 3=r) 5372 $ Z(I) = axial coordinate of Ith ring, z( 1)

! 5396. 500 $ Z(I) = axial coordinate of Ith ring, z( 2) i 1 $ NTYPER= type (O or 1 ) of discrete ring no.( 1)

O $ NTYPER= type (O or 1 ) of discrete ring no.( 2) 2 $ NPARTS = number of segments in discrete ring no.( 1) 1 $ NCEOM = geometry type of ring segment no.( 1)-

1 $ NTEMP = type of temperature distribution in ring seg.( 1)

, 1 $ NMATL = type of material for ring segment no.( 1) 5 $'INTEQ = number of integration points for ring seg.( 1)

O $ NCREEP = control for creep of ring segment no.( 1)

O $ NUMBT = number of temperature distributions in seg.( 1)

N $ Are D1 D2, PHI.T FL for this ring seg, same as for a previous?

O $ D1 = radial distance to beginning of ring segment ( 1)

O $ D2 = axial distance to beginning of ring segment ( 1) 180 $ PHI = angle in degrees of ring segment ( 1) 1.437500 $ T = thickness of ring segment ( 1) 20 $ FL = length of ring segment ( 1)

N $ Are TEMP 1. TEMP 2, TEMP 3 identical to those of a previous seg.?

N

• Is this ring mat'l same as a previous 1g specified ring mat'17 0.2790000E+08 $ E = elastic modulus of ring segment no.( 1)

O $ ALPHA = thermal expansion coef. of ring , segment no.( 1)

Y $ Can the material of this ring segment go plastic?

3 $ NPOINT = no. of points used for s-s curve of ring seg.( 1)

O $ EPSILON = strain coord. of the s-s curve. EPS( 1) 0.1319350E-02 $ EPSILON = strain coord. of the s-s curve. EPS( 2) 1 $ EPSILON = strain coord, of the s-s curve. EPS( 3)

O $ SIGMA = stress coord. of the s-s curve. SIQ( 1) 36810 $ SIGMA = stress coord, of the s-s curve. SIQ( 2) 36810 $ SIGMA = stress coord. of the s-s curve. SIQ( 3) 2 $ NGEDM = geometry type of ring segment no.( 2) ,

1 $ NTEMP = type of temperature distribution in ring seg.( 2) 1 $ NMATL = type of material for ring segment no.( 2) 5 $ INTEQ = number of integration points for ring seg.( 2)

O $ NCREEP = control for creep of ring segment no.( 2)

O $ NUMBT = number of temperature distributions in seg.( 2)

N $ Are D1.D2. PHI.T.FL for this ring seg, same as for a previous?

-20 $ D1 = radial distance to beginning of ring segment ( 2)

-9 $ D2 = axial distance to beginning of ring segment ( 2)  :

90 $ PHI = angle in degrees of ring segment ( 2) 1.437500 $ T = thickness of ring segment ( 2) 18 $ FL = length of ring segment ( 2)

Y $ Are TEMP 1, TEMP 2, TEMP 3 identical to those of a previous seg.?

Y $ Is this ring mat'l same as a previous 1g specified ring mat'17 26

-20 $ XS = radial coordinate of shear center, ring no.( 1)

O $ YS = axial coordinate of shear center, ring no.( 1)

N $ Do you want general information on loading?

O $ NTSTAT = number of temperature callout points along meridian 1 l 1 $ NPSTAT = number of meridional callouts for pressure {

j -19.00000 $ PN = normal pressure, positive as shown on p. P41.  !

O $ PT = meridional traction, positive along increasing e. l 1 $ ISTEP = control integer for time variation of pressure  ;

N $ Do you want to print out distributed loads along meridian?

1 $ LINTYP = control for line loads (0 = nones 1 = some)

Y $ Are there any axial line loads in this segment?

O $ V(K) = axial line load / length of cire. at ring no.( 1) 493.5500 $ V(K) = axial line load / length of circ. at ring no.( 2) 1 $ ISTEP1 = pointer to time function associated with V( 1) I 1 $ ISTEP1 = pointer to time function associated with V( 2)

N $ Are there any radial line loads in this segment?

N $ Are there any applied meridional moments in this segment?

Y $ Do you want to include smeared stiffeners?

Y $ Do you want information about smeared stiffeners?

Y $ Do you want to include smeared stringers (axial stiff.)?

Y $ Are the stringers internal (on the left side of the shell)?

2 $ Indicate type of stringer cross section (1 or 2 or 3)

N $ Do you want to include smeared rings?

Y $ Do you want more information on smeared stringer modeling?

3 $ LAYERS = number of layers (max. = 6)

Y $ Are all the layers of constant thickness?

2 $ MATL = type of material for shell wall lager no.( 1) 3 $ MATL = type of material for shell wall layer no.( 2) 1

• MATL = type of matarial for shell wall layer no.( 3) 0.4280000 $ T(i) = thickness of ith layer (i=1 = leftmost), T( 1)

7. 502000 $ T(i) = thickness of ith layer (i=1 = leftmost), T( 2) 1.437500 $ T(i) = thickness of ith layer (i=1 = leftmost), T( 3)

O $ O(i) = shear modulus of ith layer, Q( 1)

O $ Q(i) = shear modulus of itn lager, G( 2) 0.1073100E+08 $ G(i) = shear modulus of ith lager, Q( 3) 4828000.

• EX(i)= modulus in meridional direction, EX( 1) 206446.0 $ EX(i)= modulus in meridional direction, EX( 2)

0. 2790000E+08 $ EX(i)= modulus in meridional direction, EX( 3)

O $ EY(i)= modulus in circumferential direction. EY( 1)

O $ EY(i)= modulus in circumferential direction, EY( 2) 0.2790000E+08 $ EY(i)= modulus in circumferential direction, EY( 3)

O $ UXY(1)= Poisson's ratio (EY*UXY = EX*UYX). UXY( 1)

O $ UXY(i)= Poisson's ratio (EV*UXY = EX*UYX). UXY( 2) l 0.3000000 $ UXY(i)= Poisson's ratio (EY*UXY = EX*UYX). UXY( 3)

O $ ALPHA 1(i)=coef. thermal exp. in merid, direction, ALPHA 1( 1)

O $ ALPHA 1(i)=coef, thermal exp. in merid. direction, ALPHA 1( 2)

O $ ALPHA 1(i)=coef. thermal exp. in merid, direction, ALPHA 1( 3)

O $ ALPHA 2(i)=coef. thermal esp. in cire, direction, ALPHA 2( 1)

O $ ALPHA 2(i)=coef. thermal exp. in cire, direction, ALPHA 2( 2)

O $ ALPHA 2(i)=coef. thermal exp. in circ. direction, ALPHA 2( 3)

Y $ Do you wish to include plasticity in this segment?

N $ Do you wish to include creep in this segment?

Y $ Is this a new shell well material?

3 $ NPOINT = number of points in s.s. curve, layer no.( 1) 3 $ NITEG=no. integration pts. thru thickness, layer no.( 1)

N $ Do you want to use power law for stress-strain curve?

O $ EPS(i)= strain coordinates of s-s curve, EPS( 1) 0.1319350E-02 $ EPSti)= strain coordinates of s-s curve, EPS( 2) 1 $ EPS(i)= strain coordinates of s-s curve, EPS( 3)

O $ SIO(i)= stress coordinates of s-s curve, SIC ( 1) 6035.000 $ SIQ(i)= stress coordinates of s-s curve. SIG( 2) 27

. _ _ -- - _ -_._~.- . - - - _ - - - - _ _ , __ _- -_-

_ - - - =

6035.000 $ SIQ(i)= stress coordinates of s-s curve, SIQ( 3)

Y $ Is this a new shell well material?

3 $ NPOINT = number of points in s.s. curve, lager no.( 2) 3 s NITEG=no. integration pts. thru thickness, layer no.( 2)

N $ Do you want to use power law for stress-strain curve?

O $ EPS(i)= strain coordinates of s-s curve, EPS( 1) 0.1319350E-02 4 EPS(i)= strain coordinates of s-s curve, EPS( 2) 1 $ EPS(i)= strain coordinates of s-s curve, EPS( 3)

O $ SIQ(i)= stress coordinates of s-s curve, SIQ( 1) 250.0000 $ SIG(i)= stress coordinates of s-s curve, SIQ( 2) 258.0000 $ SIQ(i)= stress coordinates of s-s curve, SIO( 3)

Y $ Is this a new shell wall material?

3 $ NPOINT = number of points in s.s. curve, lager no.( 3) 5 $ NITEQ=no. integration pts. thru thickness, layer no.( 3)

N $ Do you want to use power law for stress-strain curve?

O $ EPS(i)= strain coordinates of s-s curve, EPS( 1) 0.1319350E-02 $ EPS(i)= strain coordinates of s-s curve, EPS( 2) 1.000000

$ EPS(i)= strain coordinates of s-s curve, EPS( 3)

O $ SIQ(1)= stress coordinates of s-s curve, SIG( 1) 36910.00 $ SIQ(i)= stress coordinates of s-s curve, SIQ( 2) 36810.00 $ SIQ(i)= stress coordinates of s-s curve, SIQ( 3)

Y $ Do you want to have C(1,J) printed for this segment?

19 $ NMESH=no. of node points (5= min.:98= max.)SEOMENT NO.( 2) 3 $ NTYPEH= control integer (1 or 2 or 3) for nodal point spacing 1

$ NSHAPE= indicator (1.2 or 4) for geometry of meridian 514.5000 $ R1 = radius at beginning of segment (see p. P7) 5396.500 $ Z1 = axial coordinate at beginning of segment 510.5000 $ R2 = radius at end of segment 5514.201 $ Z2 = axial coordinate at end of segment O $ IMP = indicator for imperfection (O=none, 1=some) 3 7.930000 $ NTYPEZ= control (1 or 3) for reference surface location N

$ ZVAL = distance from leftmost surf, to reference surf.  !

4

$ Do you want to print out f(s), c'(s), etc. for this segment? l

$ NRINGS= number (max =20) of discrete rings in this segment 5406 2 $ NTYPE = control for identification of ring location (2=r, 3=r)

• Z(I) = axial coordinate of Ith ring, z( 1) 5442

• Z(I) = axial coordinate of Ith ring, z( 2) 5478 $ Z(I) = axial coordinate of Ith ring, r( 3) 5514.281

• Z(I) = axial coordinate of Ith ring, z( 4) 1

$ NTYPER= type (O or 1 ) of discrete ring no.( 1) 1

$ NTYPER= type (O or 1 ) of discrete ring no.( 2) 1

$ NTYPER= type (O or 1 ) of discrete ring r.t ( 3)

'2 1

$ NTYPER= type (O or 1 ) of discrete ring (c.( 4)

$ NPARTS = number of segments in discrete ring no.( 1) 1 $ NCEOM = geometry type of ring segment no.( 1) i 1

$ NTEMP = type of temperature distribution in ring seg.( 1)

$ NMATL = type of material Por ring segment no.( 1) 1 5

• INTEQ = number of integration points for ring seg.( 1) 0 $ NCREEP = control for creep of ring segment no.( 1) ,

O $ NUMBT = number of temperature' distributions in seg.( 1)

Y l

i Y

$ Are D1.D2, PHI.T FL for this ring seg. same as for a previous? -

Y

$ Are TEMP 1, TEMP 2, TEMP 3 identical to those of a previous seg.?

2

$ Is this ring mat'l same as a previous 1g specified ring mat'1?

$ NGEDM =. geometry type of ring segment no.( 2) 1

• NTEMP = type of temperature distribution in ring seg.( 2) l 1 $ NMATL = type of material for ring segment no.( 2) 5 $ INTEQ = number of integration points for ring seg.( 2)

O $ NCREEP = control for creep of ring segment no.( 2)

O $ NUMBT = number of temperature distributions in seg.( 2)

Y $ Are D1,D2, PHI,T,FL for this ring seg. same as for a previous?

Y

$ Are TEMP 1. TEMP 2 TEMP 3 identical to those of a previous seg.?

28

Y $ Is this ring mat'l same as a previous 1g specified ring mat'1?

-20 $ XS = radial coordinate of shear center, ring no.( 1)

O $ YS = axial coordinate of shear center, ring no.( 1) 2 $ NPARTS = number of segments in discrete ring no.( 2) 1 $ NCEDM = geometry type of ring segment no.( 1) 1 $ NTEMP = type of temperature distribution in ring seg.( 1) 1 $ NMATL = type of material for ring segment no.( 1) 5 $ INTEC = number of integration points for ring seg.( 1)

O $ NCREEP = control for creep of ring segment no.( 1)

O $ NUMBT = number of temperature distributions in seg.( 1)

Y $ Are D1.D2. PHI T,FL for this ring seg. sama as for a previous?

Y $ Are TEMP 1 TEMP 2, TEMP 3 identical to those of a previous seg.?

Y $ Is this ring mat'l same as a previous 1g specified ring mat'1?

2 $ NOEDM = geometry type of ring segment no.( 2) 1 $ NTEMP = type of temperature distribution in ring seg.( 2) 1 $ NMATL = type of material for ring segment no.( 2) 5 $ INTEC = number of integration points for ring seg.( 2)

O $ NCREEP = control for creep of ring segment no.( 2)

O $ NUMBT = number of temperature distributions in seg.( 2)

Y $ Are D1,D2, PHI,T FL for this ring seg, same as for a previous?

Y $ Are TEMP 1, TEMP 2. TEMP 3 identical to those of a previous seg.?

Y $ Is this ring mat'l same as a previousig specified ring mat'17

-20 $ XS = radial coordinate of shear center, ring no.( 2)

O $ YS = axial coordinate of shear center, ring no.( 2) 2 $ NPARTS = number of segments in discrete ring no.( 3) 1 $ NGEDM = geometry type of ring segment no.( 1) 1 $ NTEMP = type of temperature distribution in ring seg.( 1) 1 $ NMATL = type of material for ring segment no.( 1) 5 $ INTEQ = number of integration points for ring seg.( 1)

O $ NCREEP = control for creep of ring segment no.( 1)

O $ NUMBT = number of temperature distributions in seg.( 1)

Y $ Are D1.D2, PHI,T.FL for this ring seg, same as for a previous?

Y $ Are TEMP 1. TEMP 2, TEMP 3 identical to those of a previous seg.?

Y $ Is this ring mat'l same as a previousig specified ring mat'17 2 $ NCEDM = geometry type of ring segment no.( 2) 1 $ NTEMP = type of temperature distribution in ring seg.('2) 1 $ NMATL = type of material for ring segment no.( 2) 5 $ INTEQ = number of integration points for ring seg.( 2)

O $ NCREEP = control for creep of ring segment no.( 2)

O $ NUMBT = number of temperature distributions in seg.( 2)

Y $ Are D1 D2. PHI.T,FL for this ring seg. same as for a previous?

Y $ Are TEMP 1, TEMP 2, TEMP 3 identical to those of a previous seg.?

Y $ Is this ring mat'l same as a previous 1g specified ring mat'1?

-20 $ XS = radial coordinate of shear center, ring no.( 3)

O $ YS = axial coordinate of shear center, ring no.( 3) 2 $ NPARTS = number of segments in discrete ring no.( 4) 1 $ NGEDM = geometry type of ring segment no.( 1) 1 $ NTEMP = type of temperature distribution in ring seg.( 1) 1

• NMATL = type of material for ring segment no.( 1) 5 $ INTEQ = number of integration points for ring seg.( 1)

O $ NCREEP = control for creep of ring segment no.( 1)

O $ NUMBT = number of temperature distributions in seg.( 1)

Y $ Are D1.D2. PHI.T.FL for this ring seg. same as for a previous?

Y $ Are TEMP 1, TEMP 2, TEMP 3 identical to those of a previous seg.?

Y $ Is this ring mat'l same as a previous 1g specified ring mat'17 2 $ NOECM = geometry type of ring segment no.( 2) 1 $ NTEMP = type of temperature distribution in ring seg.( 2) 1 $ NMATL = type of material for ring segment no.( 2) 5 $ INTEC = number of integration points for ring seg.( 2.$

0 $ NCREEP = control for creep of ring segment no.( 2)

O $ NUMBT = number of temperatere distributions in seg.( 2) 29

Y Y

$ Are D1 D2. PHI,T FL for this ring seg. same as for a previous?

i Y

$ Are TEMP 1, TEMP 2, TEMP 3 identical to those uf a previous seg.?

$ Is this ring mat'l same as a previously specified ring mat'17

-20 $ XS = radial coordinate of shear center, ring no.( 4)

N O $ Y8 = axial coordinate of shear center, ring no.( 4)

O

$ Do you want general information on loading?

$ NTSTAT = number of temperature callout points along meridian i

~19 1

$ NPSTAT = number of meridional callouts for pressure O

$ PN = normal pressure, positive as shown on p. P41.

$ PT = meridional traction, positive along increasing s.

N 1

$ ISTEP = control integer for time variation of pressure O

$ Do you want to print out distributed loads along meridian?

$ LINTYP = control for line loads (0 = nones 1 = some)

Y $ Do you want to include smeared stiffeners?

Y $ Do you want information about smeared stiffeners?

Y $ Do you want to include smeared stringers (axial stiff.)?

Y 2

$ Are the stringers internal (on the left side of the shell)?

N

$ Indicate type of stringer cross section (1 or 2 or 3)

$ Do you want to include smeared rings?

Y 3

$ Do you want more information on smeered stringer modeling?

$ LAYERS = number of layers (max. = 6)

Y $ Are all the layers of constant thickness?

2 $ MATL = type of material for shell wall lager no.( 1) 3 $ MATL = type of material for shell wall lager no.( 2) 0.4280000 1

$ MATL = type of material for shell wall layer no.( 3)

$ T(i) =

thickness of ith lager (i=1 = leftmost). T( 1) 7.502000 $ T(i) =

thickness of ith layer (i=1 = leftmost), T( 2) 1.437500 $ T(i) =

thickness of ith lager (i=1 = leftmost). T( 3) 0 $ Q(i) = shear modulus of ith layer, O( 1)

O $ Q(i) =

shear modulus of ith lager, Q( 2) 0.1073100E+08 8 Q(i) =

shear modulus of ith lager, Q( 3) 4:28000. 9 EX(i)= modulus in meridional direction, EX( 1) 206446.0 $ EX(i)= modulus in meridional direction, EX( 2) 0.2790000E+0G $ EX(1)= modulus in meridional direction, EX( 3)

O $ EY(1)= modulus in circumferential direction, EY( 1)

O

$ EY(1)= modulus in circumferential direction. EY( 2)

0. 2790000E+08 $ EY(1)= modulus in circumf erential direction, EY( 3)

O O

$ UXYC1)= Poisson's ratio (EY*UXY = EX*UYX). UXY( 1)

O.3000000 $ UXY(i)= Poisson's ratio (EY*UXY = EX*UYX). UXY( 2) i 0

$ UXY(i)= Poisson's ratio (EY*UXY = EX*UYX). UXY( 3) l O

$ ALPHA 1(i)=coef. thermal exp. in merid. direction. ALPHA 1( 1)

O

$ ALPHA 1(1)=coef. thermal esp. in merid, direction, ALPHA 1( 2)

O

$ ALPHA 1(1)=coef. thermal exp. in merid. direction, ALPHA 1( 3) 0

$ ALPHA 2(i)=coef. thermal exp. in cire. direction, ALPHA 2( 1) l O

$ ALPHA 2(i)=ccef. thermal exp. in cire, direction. ALPHA 2( 2) j Y

$ ALPHA 2(i!=coef, thermal exp. in circ. direction, ALPHA 2( 3)

N

$ Do you wish to include plasticity ir. this segment?

N

$ Do you wish to include creep in this segment?

N

$ Is this a new shell wall material?

N

$ Is this a new shell wall material?

N

$ Is this a new shell wall material?

19

$ Do you want to have C(i,J) printed for this segment?

$ NMESH=no. of node points (5= min.s98= max.) SEGMENT NO.( 3) i 3 $ NTYPEH= control integer (1 or 2 or 3) for nodal point spacing l 1

4 NSHAPE= indicator (1.2 or 4) for geometry of meridian '

514.5000 $ R1 = radius at beginning of segment (see p. P7) 5514.281 9 21 = axial coordinate at beginning of segment 514.5000 $ R2 = radius at end of segment 5632.063 $ Z2 = axial coordinate at end of segment O $ IMP = indicator for imperfection (O=none, 1=some) 3

$ NTYPEZ= control (1 or 3) for reference surface location 30

7.930000 $ ZVAL = distance from leftmost surf. to reference surf.

N

• Do you want to print out f(s), v'(s), etc. for this segment?

3 $ NRINGS= number (max =20) of discrete rings in this segment 2 $ NTYPE = control for identification of ring location (2=z, 3=r) 5514.281 $ Z(I) = axial coordinate of Ith ring, z( 1) 5550 $ Z(I) = axial coordinate of Ith ring, z( 2) 5588 **Z(I) = axial coordinate of Ith ring, z( 3)

O $ NTYPER= type (O or 1 ) of discrete ring no.( 1)

$ NTYPER= type (O or 1 ) of discrete ring no.( 2) l 1

1 $ NTYPER= type (O or 1 ) of discrete ring no.( 3. l 2 $ NPARTS = number of segments in discrete ring no.( 2) l 1 $ NGEOM = geometry type of ring segment no.( 1) l 1 $ NTEMP = type of temperature distribution in rina seg.( 1) 1 $ NHATL = type of material for ring segment no.( 1) <

5 $ INTEQ = number of integration points for ring seg.( 1)

O $ NCREEP = control for creep of ring segment no.( 1)

O $ NUMBT = number of temperature distributions in seg.( 1)

Y $ Are D1 D2,FHI T,FL for this ring seg, same as for a previous?

Y $ Are TEMP 1, TEMP 2, TEMP 3 identical to those'of a previous seg.?

Y $ Is this ring mat'l samu as a previously specified ring mat'1?

2 $ NGEDM = geometry type of ring segment no.( 2) 1 $ NTEMP = type of temperature distribution in ring seg.( 2) 1 $ NMATL = type of F *" ial for ring segment no.( 2) 5 $ INTEQ = number at ..itegration points for ring seg.( 2)

O $ NCREEP = control for creep of ring segment no.( 2)

O $ NUMBT = number of temperature distributions in seg.( 2)

Y $ Are D1,D2, PHI,T,FL for this ring seg, same as for a previous?

Y $ Are TEMP 1, TEMP 2. TEMP 3 identical to those of a previous seg.?

Y $ Is this ring mat'l same as a previous 1g specified ring mat'17

-20 $ XS = radial coordinate of shear center, ring no.( 2)

O $ YS = axial coordinate of shear center, ring no.( 2) 2 $ NPARTS = number of segments in discrete ring no.( 3) 1 $ NGEOM = geometry. type of ring segment no.( 1) 1 $ NTEMP = type of temperature distribution in ring seg.( 1) 1 $ NMATL = type of material for ring segment no.( 1) 5 $ INTEQ = number of integration points for ring seg.( 1)

O $ NCREEP = control for creep of ring segment no.( 1)

O $ NUMBT = number of temperature distributions in seg.( 1) '

Y $ Are D1,D2, PHI.T,FL for this ring seg. same as for a previous?

Y $ Are TEMP 1, TEMP 2, TEMP 3 identical to those of a previous seg.?

Y $ Is this ring mat'l same as a previously sot.4fied ring mat'17 2 $ NGEOM = geometry type of ring segment no.( 2) 1 $ NTEMP = type of temperature distribution in ring seg.( 2) 1

• NMATL = type of material for ring segment no.( 2) i 5 $ INTEQ = number of integration points for ring seg.( 2)

O $ NCREEP = control for creep of ring segment no.( 2)

O $ NUMBT = number of temperature distributions in seg.( 2)

Y $ Are D1.D2. PHI,T.FL for this ring seg, same as for a previous?

Y $ Are TEMP 1, TEMP 2, TEMP 3 identical to those of a previous seg.?

Y $ Is this ring mat'l same as a previously specified ring mat'1?

-20 $ XS = radial coordinate of shear center, ring no.( 3)

O $ YS = axial coordinate of shear center, ring no.( 3)

N $ Do you want general information on loading?

O $ NTSTAT = number of temperature callout points along meridian 4 $ NPSTAT = number of meridional callouts for pressure 2 $ NTYPE = control for meaning of loading callout (2=2, 3=r) 5514.281 $ Z(I) = axial coordinate of Ith loading callout, z( 1) 5596.750 $ Z(I) = axial coordinate of Ith loading callout, z( 2) 5600 $ Z(I) = axial coordinate of Ith loading callout, z( 3) 5632.063 $ Z(I) = axial coordinate of Ith loading callout, z( 4)

-19 $ PN(J)= normal pressure at meridional callout pt. no.( 1)

! 31

l 1

-19 $ PN(J)= normal pressure at meridional callout pt, no.( 2)

-4 $ PN(J)= normal pressure at meridional callout pt. no.( 3)

-4 $ PN(J)= normal pressure at meridional callout pt. no.( 4)

O $ PT(J)= meridional traction at callout peint no.( 1)

O $ PT(J)= meridional traction at callout point no.( 2)

O $ PT(J)= meridional traction at callout point no.( 3)

O $ PT(J)= meridional traction at callout point no.( 4) 1 4 ISTEP = control integer for time variation of pressure Y $ Do you want to print out distributed loads along meridian?

1

$ LINTYP = control for line loads (0 = nones 1 = some)

Y $ Are there any axial line loads in this segment?

1400. 500 $ V(K) =

axial line load / length of circ. at ring no.( 1)

O $ V(K) =

axial line load / length of cire. at ring no.( 2)

O $ V(K) =

axial line load / length of cire. at ring no.( 3) 1 $ ISTEP1 = pointer to time function associated with V( 1) 1 $ ISTEP1 = pointer to time function associated with V( 2) 1 $ ISTEP1 = pointer to time function associated with V( 3)

N $ Are there any radial line loads in this segment?

Y 156.2400

$ Are there any applied meridional moments in this segment?

$ FM(K) = meridional moment / length of cire. at ring no.( 1)

0. OOOOOOOE+00 $ FM(K) = meridional moment / length of circ. at ring no.( 2)

0. 0000000E+00 $ FH(K) = meridional moment / length of cire. at ring no.( 3) 1 $ ISTEP3 = pointer to the F(time) associated with FM( 1) 1

• ISTEP3 = pointer to the F(time) associated with FM( 2) 1 $ ISTEP3 = pointer to the F(time) associated with FM( 3) i Y $ Do you want to include smeared stiffeners?

l Y $ Do you want information about smeared stiffeners?

Y $ Do you want to include smeared stringers (axial stiff.)?

{ Y 2

$ Are the stringers internal (on the left side of the shell)?

l

$ Indicate type of stringer cross section (1 or 2 or 3)

N $ Do you want to include smeared rings?

Y 3

$ Do you want more information on smeared stringer modeling?

$ LAYERS = number of layers (max. = 6)

Y $ Are all the layers os constant thickness?

2 $ MATL = type of material for shell wall lager no.( 1) 3 $ MATL = type of material for shell wall layer no.( 2) 0.4280000 1

$ MATL = type of material for shell wall layer no.( 3)

$ T(i) r thickness of ith layer (i=1 = leftmoss), T( 1)

7. 502000 $ T(i) = thickness of ith layer (i=1 = leftmost). T( 2) 1.312500 $ T(i) = thickness of ith layer (i=1 = leftmost), T( 3)

O $ Q(i) = shear modulus of ith layer, C( 1)

O $ O(i) = shear modulus of ith layer, G( 2) 0.1073100F+08 9 Q(i) = shear modulus of ith layer, G( 3) 4B28000. $ EX(i)= modulus in meridional direction, EX( 1) 206446.0 $ EX(i)= modulus in meridional direction, EX( 2) 0.2790000E+08 $ EX<i)= modulus in meridional direction, EX( 3)

O $ EY(i)= modulus in circumferential direction, EY( 1)

O $ EY(1)= modulus in circumferential direction, EY( 2)

0. 2790000E+08 $ EY( i )= modulus in circumferential direction, EY( 3)

O O

$ UXY(i)= Poisson's ratio (EY*UXY = EX*UYX). UXY( 1) 0.3000000 $ UXY(i)= Poisson's ratio (EYeUXY = EX*UYX). UXY( 2)

O

$ UXY(1)= Poisson's ratio (EY*UXY = EX*UYX). UXY( 3)

O

$ ALPHA 1(i)=coef. thermal exp. in merid. direction. ALPHA 1( 1)

O

$ ALPHA 1(i)=coef. thermal exp. in merid. direction, ALPHA 1( 2)

$ ALPHA 1(i)=coef. thermal exp. in merid. direction, ALPHA 1( 3) l O $ ALPHA 2(i)=coef. thermal exp. in cire. direction, ALPHA 2( 1)

O $ ALPHA 2(i)=coef. thermal esp. in cire. direction, ALPHA 2( 2)

Y O $ ALPHA 2(i)=coef. thermal exp. in cire. direction, ALPHA 2( 3)

N

$ Do you wish to include plasticity in this segment?

N

$ Do you wish to include creep in this segment?

t

$ Is this a new shell wall material?

32

a l

N $ Is this a new shell wall material?

N $ Is this a new shell wall material?

N $ Do you want to have C(1,J) printed for this segment?

19 $ NMESH=no. of node points (5= min.s98= max.)SECMENT NO.( 4) 3 $ NTYPEH= control integer (1 or 2 or 3) for nodal point spacing 1

• NSHAPE= indicator (1,2 or 4) for geometry of meridian 514. 5000 $ R1 = radius at beginning of segment (see p. P7) 5632.063 $ 21 = axial coordinate at beginning of segment 514. 5000 $ R2 = radius at end of segment 5867. 605 $ Z2 = axial coordinate at end of segment O $ IMP = indicator for imper?ection (O=none, 1=some) l 3 $ NTYPEZ= control (1 or 3) for reference surface location 7.930000 $ ZVAL = distance from leftmost surf. to reference surf.

N $ Do you want to prin't out r(s), r'(s), etc. for this segment?

! 3 $ NRINGS= number (max =20) of discrete rings in this segment 2 $ NTYPE = control for identification of ring location (2=r, 3=r) 5632. 063 $ Z(I) = axial coordinate of Ith ring, z( 1) 5749. 844 $ Z(I) = axial coordinate of Ith ring, z( 2) 5867.625 $ Z(I) = a:ial coordinate of Ith ring, z( 3)

O $ NTYPER= type (O or 1 ) of discrete ring no.( 1)

O $ NTYPER= type (O or 1 ) of discrete ring no.( 2)

O $ NTYPER= type (O or 1 ) of discrete ring no.( 3)

N $ Do you want general information on loading?

O $ NTSTAT = number of temperature callout points along meridian 1 $ NPSTAT = number of meridional callouts for pressure

-4 $ PN = normal pressure, positive as shown on p. P41.

O $ PT = meridional traction, positive along increasing s.

1 $ ISTEP = control integer for time variation of pressure N $ Do you want to print out distributed loads along meridian?

1 $ LINTYP = control for line loads (0 = none; 1 = some)

Y $ Are there any axial line loads in this segment?

1818. 140 $ V(K) = axial line load / length of circ. at ring no.( 1) 1536.200 $ V(K) = axial line load / length of circ. at ring no.( 2) 1823.700 $ V(K) = axial line load / length of cire. at ring no.( 3) 1 $ ISTEP1 = pointer to time function associated with V( 1) 1 $ ISTEP1 = pointer to time function associated with V( 2) 1 $ ISTEP1 = pointer to time function associated with V( 3)

N $ Are there any radial line loads in this segment?

Y $ Are there any applied meridional moments in this segment?

103. 0000 $ FM(K) = meridional moment / length of cire. at ring no.( 1) 0.OOOOOOOE+00 $ FM(K) = meridional moment / length of cire. at ring no.( 2) 103.0000 $ FM(K) = meridional moment / length of circ. at ring no.( 3) 1 $ ISTEP3 = pointer to the F(time) associated with FM( 1) 1 $ ISTEP3 = pointer to the F(time) associated with FM( 2) 1 $ ISTEP3 = pointer to the F(time) associated with FM( 3)

Y $ Do you want to include s6aeare d stiffeners?

Y $ Do you want information about smeared stiffeners?

Y $ Do you want to include smeared stringers (axial stiff.)?

Y $ Are the stringers internal (on the left side of the shell)?

2 $ Indicate type of stringer cross section (1 or 2 or 3)

N $ Do you want to include smeared rings?

Y $ Do you want more information on smeared stringer modeling?

3 $ LAYERS = number of layers (max. = 6)

N $ Are all the layers of constant thickness?

2 $ MATL = type of material for shell wall layer no.( 1) 3 $ MATL = type of material for shell wall layer no.( 2) 1 $ MATL = type of material for shell wall layer no.( 3)

O $ C(i) = shear modulus of ith layer, G( 1)

O $ G(i) = shear modulus of ith layer, Q( 2) 0.1073100E+08 $ G(i) = shear modulus of ith layer, C( 3) 4828000 $ EX(i)= modulus in meridional direction, EX( 1) 33

1 206446 $ EX(i)= modulus in meridional direction. EX( 2)

0. 2790000E+08 $ EX ( 1 ) = modulus in meridional direction, EX( 3)

O

$ EY(i)= modulus in circumferential direction. EY( 1)

O $ EY(i)= modulus in circumferential direction, EY( 2)

0. 2790000E+08 4 EY(i)= modulus in circumferential direction, EY( 3)

O O

$ UXY(i)= Poisson's ratio (EYeUXY = EX*UYX). UXY( 1) 0.3000000 $ UXY(i)= Poisson's ratio (EY*UXY = EX*UYX). UXY( 2) 1 0

$ UXY(i)= Poisson's ratio (EY*UXY = EX*UYX). UXY( 3)

O

$ ALPHAlft)=coef. thermal exp. in merid. direction. ALPHA 1( 1)

O

$ ALPHA 1(1)=coef. thermal exp. in merid. direction, ALPHA 1( 2)

O

$ ALPHA 1(i)=coef. thermal exp. in merid. direction. ALPHA 1( 3)

O

$ ALPHA 2(1)=coef. thermal exp. in cire. directisn, ALPHA 2( 1)

O

$ ALPHA 2(i)=coef. thermal exp. in circ. direction. ALPHA 2( 2)

Y

$ ALPHA 2(i)=coef, thereal exp. in cire, direction, ALPHA 2( 3)

N

$ Do you wish to include plasticity in this segment?

N

$ Do you wish to include creep in this segment?

N

$ Is this a new shell wall material?

N

$ Is this a new shell wall material?

4

$ Is this a new shell wall materialt 2 $ NTIN = number of meridional :allouts for variable thickness

$ NTYPE = control for meaning of thickness callout (2=z, 3=r)

C632.063 $ Z(I) = axial coordinate of Ith thickness callout,

( 1) 5749.844

• Z(I) = axial coordinate of Ith thickness callout, z( 2) 3750 $ Z(I) = axial coordinate of Ith thickness callout, 5867.625 ( 3)

• Z(1) = axial coordinate of Ith thickness callout, r( 4) 0.4280000 $ TIN (i) = thickness at Ith callout, TIN ( 1) 0.4280000 $ TIN (1) = thickness at Ith callout, f!N( 2) j' O.4280000 $ TIN (1) = thickness at Ith callout. TIN ( 'J )

O.4280000 $ TIN (i) = thickness at Ith callout, TIN ( 4) 7.502000 $ TIN (i) = thickness at Ith callout, TIN ( 1) l 7.502000 $ TIN (i) = thickness ?t Ith callout. TIN ( 2) 2 7.502000 $ TIN (i) = thickness at Ith callout, TIN ( 3) 7.502000 $ TIN (1) = thickness at Ith callout, TIN ( 4) 1.250000 $ TIN (1) = thickness at Ith callout, TIN ( 1) 1.250000 $ TIN (i) = thickness at Ith callout, TIN ( 2) 1.312500 $ TIN (1) = thickness at Ith callout, TIN ( 3) 1.31250. $ TIN (i) = thickness at Ith ca? lout. TIN ( 4)

N 7

$ Do you want to have C(i,J) printed for this segment?

• NMESH=no. of node points (5= min.,98= max.)SEOMENT NO ( 5) 3

$ NTYPEH= control integer (1 or 2 or 3; for nodal poli.' spacing 514. 5000 1

$ NSHAPE= indicator (1,2 or 4) for geometry of meridian

$ R1 = radius at beginning of segment (see p. P7) 5841. 451 $ Z1 = axial coordinate at beginning of segment 465.5000 $ R2 = radius at end of segment 5841. 51

• Z2 = axial coordinate at end of segment

! O $ IMP = indicator for imperfection (O=none, 1=some) t 3

l 0.1250000 $ NTYPEZ= control (1 or 3) for reference surface location N $ ZVAL = distance from leftmost surf. to reference surf.

$ Do you want to print out r(s), c'(s),

1 etc. for thi. segment?

3

$ NRINOS= number (man =20) of discrete rings in this segment 465.5000

$ NTYPE = control for identification of ring location (2=r, 3=r)

$ R(I) l = radial coordinate of Ith ring, r( 1) 1 3

$ NTYPER= type (O or 1 ) of discrete ring no.( 1) 3

$ NPARTS = number of segments in discrete ring no.( 1) t

$ NCEOM = geometry type of ring segment no.( 1) 1

$ NTEMP = type of temperature di(tribution in ring seg.( 1) 1 5

$ NMATL = type of material for ring segment no.( 1)

O

$ INTEC = number of integration points for ring seg.( 1)

O

$ NCREEP = control for creep of ring segment no.( .t )

N $ NUMBT = number of temperature distributions in seg.( 1)

$ Are D1,D2, PHI,T,FL for this ring seg, same as for a previous?

34

am

-1.000000 $ D1 = radial distance to beginning of ring segment ( 1)

-0.2750000 $ D2 = axial distance to beginning of ring segment ( 1)

O $ PHI = angle in degrees of ring segment ( 1) 0.3200000 $ T = thickness of ring segment ( 1) 1.650000 $ FL = length of ring segment ( 1)

Y $ Are T6MP1, TEMP 2. TEMP 3 identical to those of a previous seg.?

Y $ Is this ring mat'l same as a previously specified ring mat'1?

4 $ NCEOM = geometry type of ring segment no.( 2) 1 $ NTEMP = type of temperature distribution in ring seg.( 2) 1 $ NMATL = type of material for ring segment no.( 2) 5 $ INTEQ = number of integration points for ring seg.( 2)

O $ NCREEP = control for creep of ring segment no.( 2)

O $ NUMBT = number of temperature distributions in seg.( 2)

N $ Are D1,D2 PHI T.FL for this ring seg. same as for a previous?

-1 $ Di = raJial distance to beginning of ring segment ( 2)

-0.2750000 $ D2 = axial distance to beginning of ring segment ( 2)

~90 $ PHI = angle in degrees of ring segment ( 2) 0.1900000 $ T = thickness of ring segment ( 2) 5

• FL = length of ring segment ( 2)

Y $ Are TEMP 1. TEMP 2, TEMP 3 identical to those of a previous seg.?

Y $ Is this ring mat'l same es a previously specified ring mat'17 5 $ NGEOM = geometry type of ring segment no.( 3) 1 $ NTEMP = type of temperature distribution in ring seg.( 3) 1 $ NMATL = type of material for ring segment no.( 3) 5 $ INTEG = number of integration points for ring seg.( 3)

O $ NCREEP = control for creep of ring segment no.( 3)

O $ NUMBT = number of temperature distributions in seg.( 3)

N $ Are D1.D2, PHI T,FL for this ring seg. same as for a previous?

-1 $ D1 = radial distance to beginning of ring segment ( 3)

-3.275000 $ D2 = axial distance to beginning of ring segment ( 3)

O $ PHI = angle in degrees of ring segment ( 3) 0.3200000 $ T = thickness of ring segment ( 3) 1.650000 $ FL = length of ring segment ( 3)

Y $ Are TEMP 1. TEMP 2, TEMP 3 identical to those of a previous seg.?

Y $ Is this ring mat'l same as a previous 1g specified ring mat'17

-1 $ XS = radial coordinate of shear center, ring no.( 1)

-2.500000 $ YS = axial coordinate of shear center, ring no.( 1)

N $ Do you want general information on loading?

O $ NTSTAT = number of temperature callout points along meridian O $ NPSTAT = number of meridional callouts for pressure O $ LINTYP = control for line loads (0 = nones 1 = some)

N $ Do you want to include smeared stiffeners?

1 $ LAYERS a number of layers (max. = 6)

Y $ Are al: the layers of constant thickness?

1 $ MATL = type of material for shell wall layer no.( 1) 0.2500000 $ T(i) = thickness of ith layer (i=1 = leftmost), T( 1) 0.1073100E+08 $ G(i) = shear modulus of ith layer, G( 1) 0.2790000E+08 $ EX(i)= modulus in meridional direction, EX( 1)

0. 2790000E+08 $ EY(i)= modulus in circumferential direction, EY( 1) 0.3000000 $ UXY(i)= Poisson's ratio (EY*UXY = EX*UYX). UXY( 1)

O $ ALPHA 1(i)=coef. thermal exp. in merid. direction, ALPHA 1( 1)

O $ ALPHA 2(i)=coef. thermal exp. in circ. direction, ALPHA 2( 1)

I Y $ Do you wish to include plasticity in this segment?

N $ Do you wish to include creep in this segment?

l N $ Is this a new shell wall material?

N $ Do you want to have C(i j) printed for this segment?

13 $ NMESH=no. of node points (5= min.;98= max.) SEGMENT NO.( 6) 3 $ NTYPEH= control integer (1 or 2 or 3) for nodal point spacing 2 $ NSHAPE= indicator (1.2 or 4) for geometry of meridian 514. 5000 $ R1 = radius at beginning of segment (see p. P7) 5867.625 $ Z1 = axial coordinate at beginning of segment 35 1 l

l 1

s 501.5665 $ R2 = radius at end of segment 5960.806 $ Z2 = axial coordinate at end of segment 174.0630 $ RC = radius from axis of rev. to center of curvature 5267.625 $ ZC = axial coordinate of center of curvature

-1 O

$ SROT= indicator for direction of increasing arc (-1. or +1.)

$ IMP = indicator for imperfection (O=none, !=some) 3 0.130000 $ NTYPEZ= control (1 or 3) for reference surface location N- $ ZVAL = distance from leftmost surf. to reference surf.

2

• Do you want to print out r(s), c'(s), etc. for this segment?

$ NRINGS= number (max =20) of discrete rings in this segment 5921.000 2 $ NTYPE = control for identification of ring location (2=z, 3=r)

$ Z(I) = axial coord.i.nate of Ith ring, r( 1) 5960.906 $ Z(I) = axial coordinate of Ith ring, z( 2) 1

$ NTYPER= type (O or 1 ) of discrete ring no.( 1)

O $ NTYPER= type (O or 1 ) of discrete ring no.( 2) 2 $ NPARTS = number of segments in discrete ring no.( 1) 6 $ NGEOM = geometry type of ring segment no.( 1) 1

$ NTEMP = type of temperature distribution in ring seg.( 1) 1

$ NMATL = type of material for ring segment no.( 1) 5 $ INTEG = number of integration points for ring seg.( 1) ,

0 $ NCREEP = control for creep of ring segment no.( 1) l i

O $ NUMBT = number of temperature distributions in seg.( 1)  !

N $ Are D1 D2, PHI,T,FL for this ring seg. same as for a previous?

O $ D1 = radial distance to beginning of ring segment ( 1) 100 O $ D2 = axial distance to beginning of ring segment ( 1)

$ PHI = angle in degrees of ring segment ( 1) 0.9375000 $ T = thickness of ring segment ( 1) 11.51600 $ FL = length of ring segment ( 1)

Y Y

$ Are TEMP 1, TEMP 2, TEMP 3 identical to those of a previous seg.?

7

$ Is this ring mat'l same as a previously specified ring mat'17

$ NGEOM = geometry type of ring segment no.( 2) 1

$ NTEMP = type of temperature distribution in ring seg.( 2) 1

$ NMATL = type of material for ring segment no.( 2) 5 $ INTEC = number of integration poants for ring seg.( 2)

O $ NCREEP = control for creep of ring segment no.( 2)

O $ NUMBT = number of temperature distributions in seg.( 2)

N $ Are Di,D2, PHI T.FL for this ring seg. same as for a previous?

-11.51600 $ D1 = radial distance to beginning of rin2 segment ( 2) 270 O $ D2 = axial distance to beginning of ring segment ( 2)

$ PHI = angle in degrees of ring segment ( 2) 0.0750000 $ T = thickness of ring segment ( 2) 0.562500 $ FL = length of ring segment ( 2)

Y Y

$ Are TEMP 1. TEMP 2, TEMP 3 identical to those of a previous seg.?

$ Is this ring mat'l same as a previous 1g specified ring mat'1?

-11.51600 $ XS = radial coordinate of shear center, ring no.( 1)

N O $ YS = axial coordinate of shear center, ring no.( 1)

O

$ Do you want general information on loading?

$ NTSTAT = number of temperature callout points along meridian

-4 1

$ NPSTAT = number of meridional callouts for pressure O

$ PN = normal pressure, positive as shown on p. P41.

$ PT = meridional traction, positive along increasing s.

N 1

$ ISTEP = control integer for time variation of pressure

$ Do you want to print out distributed loads along meridian?

Y 1

$ LINTYP = control for line loads (O = nones 1 = some)

$ Are there any axial line loads in this segment?

320.4800 O $ V(K) = axial line load / length of cire. at ring no.( 1)

$ V(K) = axial line load / length of circ. at ring no.( 2) 1

$ ISTEP1 = pointer to time function associated with V( 1)

Y 1

$ ISTEP1 = pointer to time function associated with V( 2)

$ Are there any radial line loads in this segment?

O $ HF(K) = radial line load / length of cire. at ring no.( 1) 36

91.19000 $ HF(K) = radial line load / length of circ. at ring no.( 2) 1 $ ISTEP2 = pointer to the F(time) associated with HF( 1) 1

• ISTEP2 = pointer to the F(time) associated with HF( 2)

N $ Are there any applied meridional moments in this segment?

s Y $ Do you want to include smeared stiffeners?

Y $ Do you want information about smeared stiffeners?

Y $ Do you want to include smeared stringers (axial stiff.)?

Y $ Are the stringers internal (on the left side of the shell)? l 2 $ Indicate type of. stringer cross section (1 or 2 or 3) '

I N $ Do you want to include smeared rings?

Y $ Do you want more information on smeared stringer modeling?

3 $ LAYERS = number of layers (max. = 6)

Y $ Are all the layers of constant thickness?

4 $ MATL = type of material for shell wall lager no.(.1) 5 $ MATL = type of material for shell wall lager no.( 2) 1 $ MATL = type of material for shell wall lager no.( 3) 0.6280000 $ T(i) = thickness of ith lager (i=1 = leftmost), T( 1) 7.502000 $ T(i) = thickness of ith lager (i=1 = leftmost). TC 2) 1.250000 $ T(i) = thickness of ith lager (i=1 = leftmost), T( 3)

O $ Q(i) = shear modulus of ith lager. Q( 1)

O $ Q(i) = shear modulus of ith lager, Q( 2) 0.1073100E+08 $ Q(i) = shear modulus of ith lager. Q( 3) 6349000. $ EX(i)= modulus in meridional direction, EX( 1) 341000.0 $ EX(i)= modulus in meridional direction, EX( 2) 0.2790000E+08 $ EX(i)= modulus in meridional direction, EX( 3)

O $ EY(i)= modulus in circumferential direction, EY( 1)

O $ EY(i)= modulus in circumferential direction, EY( 2) 0.2790000E+08 $ EY(i)= modulus in circumferential direction, EY( 3)

O $ UXY(i)= Poisson's ratio (EY*UXY = EX*UYX). UXY( 1)

O $ UXY(i)= Poisson's ratio (EY*UXY = EX*UYX). UXY( 2) 0.3000000 $ UXY(i)= Poisson's ratio (EY*UXY = EX*UYX). UXY( 3)

O $ ALPHA 1(i)=coef. thermal exp. in merid, direction, ALPHA 1( 1) 4 0 $ ALPHA 1(i)=coef, thermal exp. in merid. direction. ALPHA 1( 2)

O $ ALPHA 1(i)=coef. thermal exp. in merid, direction, ALPHA 1( 3)

O $ ALPHA 2(i)=coef. thermal exp. in cire. direction, ALPHA 2( 1)

O $ ALPHA 2(i)=coef. thermal exp. in cire. direction, ALPHA 2( 2)

O $ ALPHA 2(i)=coef. thermal exp. in circ. direction. ALPHA 2( 3)

Y $ Do you wish to include plasticity in this segment?

N $ Do you wish to include creep in this segment?

Y $ Is this a new shell wall material?

3 $ NPOINT = number of points in s.s. curve, lager no.( 1) 3 $ NITEQ=no, integration pts, thru thickness, layer no.( 1)

N $ Do you want to use power law for stress-strain curve?

O $ EPS(i)= strain coordinates of s-s curve, EPS( 1) 0.1319350E-02

• EPS(i)= strain coordinates of s-s curve. EPS( 2) 1 $ EP8(i)= strain coordinates of s-s curve, EPS( 3)

O $ SIQ(i)= stress coordinates of s-s curve. 910( 1) 7937.000 $ SIQ(i)= stress coordinates of s-s curve, SIQ( 2) 7937.000 $ SIQ(i)= stress coordinates of s-s curve, SIQ( 3)

Y $ Is this a new shell wall material?

3 $ NPOINT = number of points in s.s. curve, lager no.( 2)

[ 3 $ NITEQ=no. integration pts. thru thickness, layer no.( 2) l N $ Do you want to use power law for stress-strain curve?

l 0 $ EPS(i)= strain coordinates of s-s curve, EPS( 1)

O.1319350E-02 $ EPS(i)= strain coordinates of s-s curve, EPS( 2) 1 $ EPS(i)= strain coordinates of s-s curve, EPS( 3)

O $ SIQ(i)= stress coordinates of s-s curve, SIQ( 1) 426.0000 $ SIQ(i)= stress coordinates of s-s curve, SIQ( 2) 426.0000 $ SIQ(i)= stress coordinates of s-s curve, SIQ( 3)

N $ Is this a new shell wall material?

N $ Do you want to have C(i,J) printed for this segment?

37

21 $ NMESH=no. of node points (5= min.s99= max.)SE0 MENT NO.( 7) 3 $ NTYPEH= control integer (1 or 2 or 3) for nodal point spacing ,

1 $ NSHAPF' indicator (1,2 or 4) for geometry of meridian 501.5665 $ R1 = radius at beginning of segment (see p. P7) 5960.806 $ Z1 = axial coordinate at beginning of segment 490.8662 $ R2 = radius at end of segment 5998.000 $ Z2 = axial coordinate at end of segment O $ IMP = indicator for imperfection (O=none, !=some) 3 O

$ NTYPEZ= control (1 or 3) for reference surface location I N $ ZVAL = distance from leftmost surf. to reference surf.

$ Do you want to print out r(s), t'(s), etc. for this segment?

O $ NRINGS= number (max =20) of discrete rings in this segment N $ Do you want general information on loading?

O $ NTSTAT = number of temperature callout points along meridian 1

$ NPSTAT = number of meridional callouts for pressure

-4 $ PN = normal pressure, positive as shown on p. P41.

O $ PT = meridional traction, positive along increasing s.

l N

1

• ISTEP = control integer for time variation of pressure i

0

$ Do you want to print out distributed loads along meridian?

l N

$ LINTYP = control for line loads (0 = nones 1 = some)

( $ Do you want to include smeared stiffeners?

T 1 $ LAYERS = number of layers (max. = 6) l N $ Are all the lagers of constant thickness?

1 $ MATL = type of material for shell wall lager no.( 1) 0.1073100E+08 $ Q(i) = shear modulus of ith lager, Q( 1) 0.2790000E+08 $ EX(i)= modulus in meridional direction, EX( 1) 0.2790000E+08 $ EY(i)= modulus in circumferential direction, EY( 1) 0.3000000 $ UXY(i)= Poisson's ratio (EY*UXY = EX*UYX). UXY( 1) i 0 $ ALPHA 1(i)=coef, thermal exp. in merid. direction, ALPHA 1( 1)

O $ ALPHA 2(i)=coef. thermal exp. in cire. direction, ALPHA 2( 1)

Y N

$ Do you wish to include plasticity in this segment?

$ Do you wish to include creep in this segment?

N 4

$ Is this a new shell wall material?

$ NTIN = number of meridional callouts for variable thickness 2 $ NTYPE = control for meaning of thickness callout (2=2, 3=r) 5960.806 $ Z(I) = axial coordinate of Ith thickness callout, r( 1) 5961.767 $ Z(I) = axial coordinate of Ith thickness callout, ( 2) 5966.632 $ Z(I) = axial coordinate of Ith thickness callout, ( 3) 5998.000 $ Z(I) = axial coordinate of Ith thickness callout, ( 4) 1.250000 $ TIN (i) = thickness at Ith callout, TIN ( 1) 1.250000 $ TIN (i) = thickness at Ith callout. TIN ( 2) 2.937500 $ TIN (i) = thickness at Ith callout, TIN ( 3) 2.937500 $ TIN (i) = thickness at Ith callout. TIN ( 4)

N $ Do you want to have C(1,J) printed for this segment?

l 5 $ NMESH=no, of node points (5= min.s98= max.) SEGMENT NO.( 8) 3 $ NTYPEH= control integer (1 or 2 or 3) for nodal point spacing 1 $ NSHAPE= indicator (1,2 or 4) for geometry of meridian 490.8662 $ R1 = radius at beginning of segment (see p. P7) 5998.000 $ Z1 = axial coordinate at beginning of segment 488. 0340 $ R2 = radius at end of segment 6008.280 $ Z2 = axial coordinate at end of segment O $ IMP = indicator for imperfection (O=none, 1=some) 3 $ NTYPEZ= control (1 or 3) for reference surface location 7.930000 $ ZVAL = distance from leftmost surf. to reference surf.

N $ Do you want to print out r(s), r'(s), etc. Por this segment?

O $ NRINGS= number (man =20) of discrete rings in this segment N $ Do you want general information on loading?

O $ NTSTAT = number of temperature callout points along meridian 1 $ NPSTAT = number of meridional callouts for pressere

-4 $ PN = normal pressure, positive as shown on p. P41.

l 0 $ PT = meridional traction, positive along increasing s.

38

1 $ ISTEP = control integer for time variation of pressure N $ Do you want to print out distributed loads along meridian?

O $ LINTYP = control for line loads (O = nones 1 = some)

Y $ Do you want to include smeared stiffeners?

N $ Do you want information about smeared stiffeners?

Y $ Do you want to include smeared stringers (axial stiff.)?

N $ Are the stringers internal (on the left side of the s5 ell)?

2 $ Indicate type of stringer cross section (1 or 2 or 3)

N $ Do you want to include smeared rings?

N $ Do you want more information on smeared stringer modeling?

3 $ LAYERS = number of layers (max. = 6)

N $ Are all the layers of constant thickness?

2 $ MATL = type of material for shell wall lager no.( 1) 3 $ MATL = type of material for shell wall layer no.( 2) 1 $ MATL = type of material for shell wall lager no.( 3)

O $ C(i) = shear modulus of ith layer, G( 1)

O $ C(i) = shear modulus of ith lager, G( 2) 0.1073100E+08 $ G(i) = shear modulus of ith lager, Q( 3) 4828000.

• EX(i)= modulus in meridional direction, EX( 1) 206446.0 $ EX(i)= modulus in meridional direction. EX( 2) 0.2790000E+08 $ EX(i)= modulus in meridional direction, EX( 3)

O $ EY(i)= modulus in circumferential direction, EY( 1)

O $ EY(i)= modulus in circumferential direction, EY( 2) 0.2790000E+08 $ EY(i)= modulus in circumferential direction. EY( 3)

O $ UXY(i)= Poisson's ratio (EY*UXY = EX*UYX). UXY( 1)

O $ UXY(i)= Poisson's ratio (EY*UXY = EX*UYX). UXY( 2) 0.3000000 $ UXY(i)= Poisson's ratio (EY*UXY = EX*UYX). UXY( 3)

O $ ALPHA 1(i)=coef. thermal exp. in merid. direction. ALPHA 1( 1)

O $ ALPHA 1(i)=coef. thermal exp. in merid. direction, ALPHA 1( 2)

O $ ALPHA 1(i)=coef. thermal exp. in merid. direction. ALPHA 1( 3)

O $ ALPHA 2(i)=coef. thermal exp. in cire. direction. ALPHA 2( 1)

I O $ ALPHA 2(i)=coef. thermal exp. in cire. direction. ALPHA 2( 2)

! O $ ALPHA 2(i)=coef. thermal exp. in cire. direction, ALPHA 2( 3)

Y $ Do you wish to include plasticity in this segment?

N $ Do you wish to include creep in this segment?

N $ Is this a new shell wall material?

N $ Is this a new shell wall material?

N $ Is this a new shell wall material?

l 3 $ NTIN = number of meridional callouts for variable thickness 2 $ NTYPE = control for meaning of thickness callout (2=r, 3=r) 5998.000 $ Z(I) = axial coordinate of Ith thickness callout, z( 1) 6003.415 $ Z(I) = axial coordinate of Ith thickness callout, 2( 2) 6008.200 $ Z(I) = axial coordinate of Ith thickness callout, z( 3) 0.4280000 $ TIN (i) = thickness at Ith callout, TIN ( 1) 0.4280000 $ TIN (i) = thickness at Ith callout, TIN ( 2) 0.4280000 $ TIN (i) = thickness at Ith callout, TIN ( 3) 7.502000 $ TIN (i) = thickness at Ith callout, TIN ( 1) 7.502000 $ TIN (i) = thickness at Ith callout, TIN ( 2) 7.502000 $ TIN (i) = thickness at Ith callout, TIN ( 3) 2.937500 $ TIN (i) = thickness at Ith callout, TIN ( 1) 2.937500 $ TIN (i) = thickness at Ith callout, TIN ( 2) 1.250000 $ TIN (i) = thickness at Ith callout, TIN ( 3)

N $ Do you want to have C(i,J) printed for this segment?

37 $ NMESH=no, of node points (5= min.s98= max.) SEGMENT NO.( 9) 3 $ NTYPEH= control integer (1 or 2 or 3) for nodal point spacing 1 $ NSHAPE= indicator (1.2 or 4) for geometry of meridian 488. 0340 $ R1 = radius at beginning of segment (see p. P7) 6000.280 $ 21 = axial coordinate at beginning of segment 437.1914 $ R2 = radius at end of segment 6184.000 $ 22 = axial coordinate at end of segment

, O $ IMP = indicator for imperfection (O=none, 1=some)  ;

39

3 $ NTYPEZ= control (1 or 3) for reference surface location 7.930000 $ ZVAL = distae:e from leftmost surf. to reference surf.

N 2

$ Do you want to print out r(s), v'(s), etc. for this segment?

$ NRINOS= number (max =20) of discrete rings in this segment 2 $ NTYPE = control for identification of ring location (2= , 3=r) 6122.590 $ Z(I) = axial coordinate of Ith ring, :( 1) 61C4.000 $ Z(I) = axial coordinate of Ith ring, z( 2)

O $ NTYPER= type (O or 1 ) of discrete ring no.( 1)

O $ NTYPER= type (O or 1 ) of discrete ring no.( 2)

N $ Do you want general information on loading?

O $ NTSTAT = number of temperature callout points along meridian 1 $ NPSTAT = number of meridional callouts for pressure

-4 $ PN = normal pressure, positive as shown on p. P41.

O ' $ PT = meridional traction, positive along increasing s.

N 1 $ ISTEP = control integer for time variation of pressure

$ Do you want to print out distributed loads along meridian?

1

$ LINTYP = control for line loads (0 = nones 1 = some)

Y $ Are there any axial line loads in this segment?

1053.070 $ V(K) = axial line load / length of cire. at ring no.( 1) 1630. 550 $ V(K) = axial line load / length of circ. at ring no.( 2)  !

1 $ ISTEP1 = pointer to time function associated with V( 1) 1 4 ISTEP1 = pointer to time function associated with V( 2)

Y $ Are there any radial line loads in this segment?

304.6900 $ HF(K) = radial line load / length of cire, at ring no.( 1) 471.7800 $ HF(K) = radial line load / length of circ, at ring no.( 2) 1 $ ISTEP2 = pointer to the F(time) associated with HF( 1) 1 4 ISTEP2 = pointer to the F(time) associated with HF( 2)

N $ Are there any applied meridional moments in this segment?

Y $ Do you want to include smeared stiffeners?

N $ Do you want information about smeared stiffeners?

, Y $ Do you want to include smeared stringers (axial stiff.)?

Y $ Are the stringers internal (on the left side of the shell)?

2

• Indicate type of stringer cross section (1 or 2 or 3)

N $ Do you want to include smeared rings?

N $ Do you want more information on smeared stringer modeling?

i 3 $ LAYERS = number of layers (max. = 6) i N $ Are all the layers of constant thickness?

2 $ MATL = type of material for shell wall layer no.( 1) 3 $ MATL = type of material for shell wall layer no.( 2)

O 1

• MATL = type of material for shell wall layer no.( 3)

$ Q(i) = shear modulus of ith layer, Q( 1)

O $ Q(i) = shear modulus of ith lager, O( 2) 0.1073100E+08 8 Q(i) = shear modulus of ith lager. Q( 3)

, 4829000.

• EX(i)= modulus in meridional direction, EX( 1) 206446.0

$ EX(1)= modulus in meridional direction, EX( 2) l 0. 2790000E+08 $ EX(i)= modulus in meridional direction, EX( 3)

O $ EY(i)= modulus in circumferential direction, EY( 1)

O $ EY(i)= modulus in circumferential direction, EY( 2) l 0.2790000E+08 $ EY(1)= modulus in circumferential direction, EY( 3)

! O $ UXY(i)= Poisson's ratio (EYeUXY = EX*UYX). UXY( 1) t O $ UXY(i)= Poisson's ratio (EYeUXY = EXeUYX). UXY( 2) 0.3000000 $ UXY(1)= Poisson's ratio (EY*UXY = EX*UYX). UXY( 3) l 0 $ ALPHA 1(i)=coef. thermal esp. in merid. direction, ALPHA 1( 1) i 0 $ ALPHA 1(1)=coef. thermal exp. in merid. direction, ALPHA 1( 2)

O $ ALPHA 1(i)=coef. thermal exp. in merid. direction, ALPHA 1( 3)

O $ ALPHA 2( i )cc oe f, thermal exp. in cire. direction, ALPHA 2( 1)

O $ ALPHA 2(1)=coef. thermal exp. in cire. direction, ALPHA 2( 2)

O $ ALPHA 2(i)=coef. thermal esp. in cire. direction, ALPHA 2( 3)

Y $ Do you wish to include plasticity in this segment?

N $ Do you wish to include creep in this segment?

N $ Is this a new shell wall material?

40

N $ Is this a new shell wall material?

N $ Is this a new shell wall material?

4 $ NTIN = number of meridional callouts for variable thickness 2 $ NTYPE = control for meaning of thickness callout (2=r, 3=r) 6008.280 $ Z(I) = axial coordinate of Ith thickness callout, z( 1) 6122.590 $ Z(I) = axial coordinate of Ith thickness callout, x( 2) 6123.000 $ Z(I) = axial coordinate of Ith thickness callout, z( 3) 6184.000 $ Z(I) = axial coordinate of Ith thickness callout, z( 4) 0.4280000 $ TIN (i) = thickness at Ith callout, TIN ( 1) 0.4280000 $ TIN (i) = thickness at Ith callout, TIN ( 2) 0.4280000 $ TIN (i) = thickness at Ith callout, TIN ( 3) 0.4280000 $ TIN (i) = thickness at Ith callout, TIN ( 4) 7.502000 $ TIN (i) = thickness at Ith callout, TIN ( 1) 7.502000 $ TIN (i) = thickness at Ith callout, TIN ( 2) 7.502000 $ TIN (i) = thickness at Ith callout, TIN ( 3) 7.502000 $ TIN (i) = thickness at Ith callout, TIN ( 4) 1.250000 $ TIN (i) = thickness at Ith callout, TIN ( 1) 1.250000 $ TIN (i) = thickness at Ith callout, TIN ( 2) 1.437500 $ TIN (i) = thickness at Ith callout, TIN ( 3) 1.437500 $ TIN (i) = thickness at Ith callout, TIN ( 4)

N $ Do you want to have C(i,J) printed for this segment?

7 $ NMESH=no. of node points (5=m4n.s98= max.)SEQMENT NO.(10) 3 $ NTYPEH= control integer (1 or 2 or 3) for nodal point spacing 1 $ NSHAPE= indicator (1,2 or 4) for geometry of meridian i 437.1914 $ R1 = radius at beginning of segment (see p. P7) 6184.000 $ Z1 = axial coordinate at beginning of segment J

429.5667 $ R2 = radius at end of segment 6210. 500 $ Z2 = axial coordinate at end of segment O $ IMP = indicator for imperfection (O=none, 1=some) 3 $ NTYPEZ= control (1 or 3) for reference surface location O $ ZVAL = distance from leftmost surf. to reference surf.

N $ Do you want to print out r(s), r'(s), etc. for this segment?

O $ NRINGS= number (max =20) of discrete rings in this segment N $ Do you want general information on loading?

O $ NTSTAT = number of temperature callout points along meridian 1 $ NPSTAT = number of meridional callouts for pressure i

-4.000000 $ PN = normal pressure, positive as shown on p. P41.

O $ PT = meridional traction, positive along increasing s.

1 $ ISTEP = control integer for time variation of pressure N $ Do you want to print out distributed loads along meridian?

O $ LINTYP = control for line loads (O = nones 1 = some)

N $ Do you want to include smeared stiffeners?

1 $ LAYF9S = number of layers (max. = 6)

Y $ Are all the layers of constant thickness?

q 1 $ MATL = type of material for shell wall lager no.( 1) 1.437500 $ T(i) = thickness of ith layer (i=1 = leftmost), T( 1) 0.1073100E+08 $ C(i) = shear modulus of ith lager. Q( 1) 0.2790000E+08 $ EX(i)= modulus in meridional direction, EX( 1) 0.2790000E+08 $ EY(i)= modulus in circumferential direction, EY( 1) 0.3000000 $ UXY(i)= Poisson's ratio (EY*UXY = EX*UYX). UXY( 1)

O $ ALPHA 1(i)=coef. thermal exp. in merid, direction, ALPHA 1( 1)

0 $ ALPHA 2(i)=coef. thermal exp. in circ. direction. ALPHA 2( 1)

! Y $ Do you wish to include plasticity in this segment?

N $ Do you wish to include creep in this segment?

N $ Is this a new shell wall material?

. N $ Do you want to have C(1,J) printed for this segment?

5 $ NMESH=no. of node points (5= min.s98= max.)SEQMENT NO.(11) 3 $ NTYPEH= control integer (1 or 2 or 3) for nodal point spacing 1 $ NSHAPE= indicator (1.2 or 4) for geometry of meridiaa 437.1914 $ R1 = radius at beginning of segment (see p. P7) 6184.000 $ 21 = axial coordinate at beginning of segment 41 4

- - - - , - . . - . - - - . . , . . - - - - - - - ~ , - . , - - - - - - - - - - - - - - - - . - - - , - - - - - . - - - - - - - - - - - - - , - -

410.5969 $ R2 = radius at end of segment 6184.000 $ Z2 = axial coordinate at end of segment O $ IMP = indicator for imperfection (O=none, 1=some) 3 $ NTYPEZ= control (1 or 3) for reference surfar.e location 0.7L_, ) $ ZVAL = distance from leftmost surf. to reference surf.

N $ Do you want to print out r(s), r '( s ), etc. for this segment?

O $ NRINGS= number (max =20) of discrete rings in this segment N $ Do you want general information on loading?

O $ NTSTAT = number of temperature callout points along meridian O $ NPSTAT = number of meridional callouts for pressure O $ LINTYP = control for line loads (0 = nones 1 = rome)

N 4 Do you want to include smeared stiffeners?

1 $ LAYERS = number of layers (max. = 6)

Y $ Are all the layers of constant thickness?

1

• MATL = type of material for shall wall lager no.( 1) 1.500000 $ T(i) = thickness of i.Sh lager (i=1 = leftmost), T( 1) t 0.1073100E+08 $ Q(i) = shear modulus of ith laver, O( 1)

0. 2790000E+08 $ EX ( i )= mo d ulu s in meridional direction, EX( 1) 0.2790000E+08 $ EY(i)= modulus in circumferential direction, EY( 1) 0.3000000 $ UXY(i)= Poisson's ratio (EY+UXY = EX*UYX). UXY( 1)

O $ ALPHA 1(i)=coef. whermal exp. in merid. direction, ALPHA 1( 1)

O $ ALPHA 2(i)=coef. thermal exp. in circ. direction, ALPHA 2( 1)

Y $ Do you wish to include plasticity in this segment?

N $ Do you wish to include creep in this segment?

N $ Is this a new shell wall material?

N

• Do you want to have C(ieJ) printed for this segment?

5 $ NMESH=no. of node points (5= min. s 98= max. )SEOMENT NO. (12) 3 $ NTYPEH= control integer (1 or 2 or 3) for nodal point spacing 1 $ NSHAPE= indicator (1,2 or 4) for geometry of meridian 410.5069 $ R1 = radius at beginning of segment (see p. P7) 6184.000 $ Z1 = axial coordinate at beginning of segment 410.5069 $ R2 = radius at end of segment 6210. 500 $ Z2 = axial coordinate at end of segment O $ IMP = indicator for imperfection (O=none, i=some) 3 $ NTYPEZ= control (1 or 3) for reference surface location 1.250000 $ IVAL = distance from leftmost surf. to reference surf.

N $ Do you want to print out f(s), c '( s ), etc. for this segment?

O $ NRINGS= number (max =20) of discrete rings in this segment i

N $ Do you want general information on loading?

O $ NTSTAT = number of temperature callout points along meridian O $ NPSTAT = number of meridional callouts for pressure O $ LINTYP = control for line loads (0 = nones 1 = some)

N $ Do you want to include smeared stiffeners?

1 $ LAYERS = number of layers (max. = 6)

Y $ Are all the layers of constant thickness? i i $ MATL = type of material for shell wall layer no.( 1) 1.500000 $ T(i) = thickness of ith lager (i=1 = leftmost). T( 1)

0.1073100E+08 $ Q(i) = shear modulus of ith layer, Q( 1) 0.2790000E+08 $ EX(i)= modulus in meridional direction, EX( 1) 0.2790000E+08 4 EY(i)= modulus in circumferential direction, EY( 1) 0.3000000 $ UXY(i)= Poisson's ratio (EY*UXY = EX*UYX). UXY( 1)

O $ ALPHA 1(1)=coef, thermal exp. in merid. direction, ALPHA 1( 1)

)1 0 $ ALPHA 2(i)=coef. thermal exp. in cire. direction, ALPHA 2( 1)

Y $ Do you wish to include plasticity in this segment?

N $ Do you wish to include creep in this segment?

N $ Is this a nek shell wall material?

. N $ Do you want to have C(i,J) printed for this segment?

5 $ NMEBH=no, of node points (5= min.s98= max.)SEOMENT NO.(13)

. 3 $ NTYPEH= control integer (1 or 2 or 3) for nodal point spacing l 1 $ NSHAPE= indicator (1.2 or 4) for geometry of meridian j 410.5069 $ R1 = radius at beginning of segment (see p. P7) 42 l

1

\ __

6210.500 $ 21 = axial coordinate at beginning of segment 429. 5667 $ R2 = radius at end of segment 6210.500 $ 22 = axial coordinate at end of segment O $ IMF = indicator for imperfection (O=none, 1=some) 3 $ NTYPEZ= control (1 or 3) for reference surface location 0.7500000 $ ZVAL = distance frcm leftmost surf. to reference surf.

N $ Do you want to print out r(s), c'(s), etc. for this segment?

O $ NRINGS= number (max =20) of' discrete rings in this segment N $ Do you want general information on loading?

O w NTSTAT = number of temperature callout points along meridian O $ NPSTAT = number of meridional callouts for pressure O $ LINTYP = control for line loads (0 = nones 1 = some)

N $ Do you want to include smeared stiffeners?

1 $ LAYERS = number of layers (max. = 6)

Y $ Are all the layers of constant thickness?

1 $ MATL = type of material for shell wall layer no.( 1) 1.500000 $ T(i) = thickness of ith layer (i=1 = leftmost), T( 1) 0.1073100E+08 $ C ( i ) = shear modulus of ith layer, Q( 1)

0. 2790000E+08 $ EX(i )= modulus in meridional direction, EX( 1)

0. 2790000E+08 $ EY(i)= modulus in circumferential direction, EY( 1) 0.3000000 $ UXY(i)= Poisson's ratio (EY*UXY = EX*UYX). UXY( 1)

O $ ALPHA 1(i)=coef. thermal exp. in merid. direction. ALPHA 1( 1)

O $ ALPHA 2(i)=coef. thermal e x p. in cire. direction. ALPHA 2( 1)

Y $ Do you wish to include plasticity in this segment?

N $ Do you wish to include creep in this segment?

N $ Is this a new shell wall material?

N $ Do you want to have C(i,J) printed for this segment?

37 $ NMESH=no. of node points (5= min.:98= max.)SEOMENT NO.(14) 3 $ NTYPEH= control integer (1 or 2 or 3) for nodal point spacing 1 $ NSHAPE= indicator (1 2 or 4) for geometry of meridian 429. 5667 $ R1 = radius at beginning of segment (see p. P7) 6210. 500 $ Z1 = axial coordinate at beginning of segment 347.4955 $ R2 = radius at end of segment 6496.500 $ Z2 = axial coordinate at end of segment O $ IMP = indicator for imperfection (O=none, !=some) 3 $ NTYPEZ= control (1 or 3) for reference surface location O $ ZVAL = distance from leftmost surf. to reference surf.

N $ Do you wart to print out r(s), c'(s), etc. for this segment?

4 $ NRINGS= number (max =20) of discrete rings in this segment 2 $ NTYPE = control for identification of ring location (2=r, 3=r) 6236.840 $ Z(I) = axial coordinate of Ith ring, z( 1) 6343.905 $ Z(I) = axial coordinate of Ith ring, z( 2) 6450.970 $ Z(I) = axial coordinate of Ith ring, z( 3) 6496.500 $ Z(I) = axial coordinate of Ith ring, z( 4)

O $ NTYPER= type (O or 1 ) of discrete ring no.( 1)

O $ NTYPER= type (O or 1 ) of discrete ring no.( 2)

O $ NTYPER= type (O or 1 ) of discrete ring no.( 3)

O $ NTYPER= type (O or 1 ) of discrete ring no.( 4)

N $ Do you want general information on loading?

O $ NTSTAT = number of temperature callout points along meridian 1 $ NPSTAT = number of meridional callouts for pressure

-4.000000 $ PN = normal pressure, positive as shown on p. P41.

O $ PT = meridional traction, positive along increasing s.

. 1 $ ISTEP = control integer for time variation of pressure N $ Do you want to print out distributed loads along meridian?

1 $ LINTYP = control for line loads (0 = nones 1 = some)

Y $ Are there any axial line loads in this segment?

1172.000 $ V(K) = axial line load / length of circ. at ring no.( 1) 1105.860 $ V(K) = axial line load / length of cire. at ring no.( 2) 961. 4600 $ V(K) = axial line load / length of circ. at ring no.( 3) 1586.100 $ V(K) = axial line load / length of cire. at ring no.( 4) 43 l

I

1 4 ISTEP1 = pointer to time function associated with V( 1) 1 $ ISTEP1 = pointer to time function associated with V( 2) 1 $ ISTEP1 = pointer to time function associated with V( 3) 1 $ ISTEP1 = pointer to time function associated with V( 4)

Y $ Are there any radial line loads in this segment?

,l 336.3200 $ HF(K) = radial line load / length of cire. at ring no.( 1) 317.3400 $ HF(K) = radial line load / length of circ. at ring no.( 2) 275.9000 $ HF(K) = radial line load / length of cire. at ring no.( 3) 455.1500 $ HF(K) = radial line load / length of cire. at ring no.( 4) 1 $ ISTEP2 = pointer to the F(time) associated with HF( 1) 1

• ISTEP2 = pointer to the F(time) associated with HF( 2) 1

• ISTEP2 = pointer to the F(time) associated with HF( 3) 1

• ISTEP2 = pointer to the F(time) associated with HF( 4)

Y $ Are there any applied meridional moments in this segment?

876. 370C $ FM(K) = meridional moment / length of circ. at ring no.( 1) 755.0100 $ FM(K) = meridional moment / length of circ. at ring no.( 2) 627.6800 $ FM(K) = meridional moment / length of circ. at ring no.( 3) 1186.000 t FM(K) = meridional moment / length of cire. at ring no.( 4) 1 $ ISTEP3 = pointer to the F(time) associated with FM( 1) 1 $ ISTEP3 = pointer to the F(time) associated with FM( 2) 1 $ ISTEP3 = pointer to the F(time) associated with FM( 3) l 1 $ ISTEP3 = pointer to the F(time) associated with FM( 4) '

i N $ Do you want to include smeared stiffeners?

1 $ LAYERS = number of layers (max. = 6)

N $ Are all the layers of constant thickness?

1 $ MATL = type of material for shell wall lager no.( 1) 0.1073100E+08 $ G(i) = shear modulus of ith lager, C( 1) 0.2770000E+08 $ EX(i)= modulus in meridional direction, EX( 1) 0.2790000E+08 $ EY(i)= modulus in circumferential direction, EY( 1) 0.3000000 $ UXY(1)= Poisson's ratio (EY*UXY = EX*UYX). UXY( 1)

O $ ALPHA 1(i)=coef. thermal exp. in merid. direction, ALPHA 1( 1)

O $ ALPHA 2(i)=coef. thermal exp. in cire, direction, ALPHA 2( 1)

Y $ Do you wish to include plasticity in this segment?

N $ Do you wish to include creep in this segment?

N $ Is this a new shell wall material?

8 2

• NTIN = number of meridional callouts for variable thickness

$ NTYPE = control for meaning of thickness callout (2=z, 3=r) 6210.500 $ Z(I) = axial coordinate of Ith thickness callout, z( 1) 6236.000 $ Z(I) = axial coordinate of Ith thickness callout, z( 2) 6237.000 $ Z(I) = axial coordinate of Ith thickness callout, z( 3) 6343.000 $ Z(I) = axial coordinate of Ith thickness callout, z( 4) 6304.000 $ Z(I) = axial coordinate of Ith thickness callout, z( 5) 6C50.000 $ Z(I) = axial coordinate of Ith thickness callout, z( 6) 6451'.000 $ Z(I) = axial coordinate of Ith thickness callout, z( 7) 6496. 500 $ Z(I) = axial coordinate of Ith thickness callout, z( 8) 1.437500 $ TIN (i) = thickness at Ith callout. TIN ( 1) 1.437500 $ TIN (i) = thickness at Ith callout. TIN ( 2) 1.375000 $ TIN (i) = thickness at Ith callout. TIN ( 3) 1.375000 $ TIN (i) = thickness at Ith callout. TIN ( 4) 1.312500 $ TIN (i) = thickness at Ith callout. TIN ( 5) 1.312500 $ TIN (i) = thickness at Ith callout, TIN ( 6) 1.437500 $ TIN (i) = thickness at Ith callout, TIN ( 7) 1.437500 $ TIN (i) = thickness at Ith callout, TIN ( 8)

N $ Do you want to have C(1,J) printed for this segment?

5 $ NMESH=no, of node points (5= min.s98= max.) SEGMENT NO.(15) 3 $ NTYPEH= control integer (1 or 2 or 3) for nodal point spacing 1 $ NSHAPE= indicator (1,2 or 4) for geometry of meridian 347.4955 $ R1 = radius at beginning of segment (see p. P7) 6496.500 $ Z1 = axial coordinate at beginning of segment 339.0000 $ R2 = radius at end of segment 6526.000 $ Z2 = axial coordinate at end of segment 44

O $ IMP = indicator for imperfection (O=none, !=some) 3 $ NTYPEZ= control (1 or 3) for reference surface location O $ ZVAL = distance from leftmost surf. to reference surf.

N $ Do you want to print out r(s), c'(s), etc. for this segment?

O t NRINGS= number (max =20) of discrete rings in this segment N e Do you want general information on loading?

O $ NTSTAT = number of temperature callout points along meridian 1 $ NPSTAT = number of meridional callouts for pressure

-4. 000000 $ PN = normal pressure, positive as shown on p. P41.

O $ PT = meridional traction, positive along increasing s.

1 $ ISTEP = control integer for time variation of pressure N $ Do you want to print out distributed loads along meridian?

O $ LINTYP = control for line loads (0 = nones 1 = some)

N $ Do you want to include smeared stiffeners?

1 $ LAYERS = number of layers (max. = 6)

Y $ Are all the layers of constant thickness?

1 $ MATL = type of material for shell wall layer no.( 1) 1.437500 $ T(i) = thickness of ith lager (i=1 = leftmost), TC 1) 0.1073100E+08 $ Q(i) = shear modulus of ith layer, Q( 1) 0.2790000E+08 $ EX(i)= modulus in meridional direction, EX( 1) 0.2790000E+08 $ EY(i)= modulus in circus.ferential direction, EY( 1)

O.3000000 $ UXY(i)= Poisson's ratio (EY*UXY = EX*UYX). UXY( 1)

O $ ALPHA 1(i)=coef. thermal exp. in merid. direction, ALPHA 1( 1)

O $ ALPHA 2(i)=coef. thermal exp. in cire, direction. ALPHA 2( 1)

Y $ Do you wish to include plasticity in this sognent?

' N $ Do you wish to include creep in this segment?

N $ Is this a new shell wall material?

N $ Do you want to have C(1,J) printed for this segment?

5 $ NMESH=no. of node points (5= min. s 98= max. )SEOMENT NO. (16) 3 $ NTYPEH= control integer (1 or 2 or 3) for nodal point spacing

'1 $ NSHAPE= indicator (1,2 or 4) for geometry of meridian 347.4955 $ R1 = radius at beginning of segment (see p. P7) 6496.500 $ Z1 = axial coordinate at beginning of segment 325.2500 $ R2 = radius at end of segment 6496. 500 $ Z2 = axial coordinate at end of segment O $ IMP = indicator for imperfection (O=none, 1=some) 3 $ NTYPEZ= control (1 or 3) for reference surface location 0.7500000 $ ZVAL = distance from leftmost surf. to reference surf.

N $ Do you want to print out r(s), c'(s), etc. for this segment?

O $ NRINGS= number (max =20) of discrete rings in this segment

, N $ Do you want general information on loading?

l 0 $ NTSTAT = number of temperature callout points along meridian O $ NPSTAT = number of meridional callouts for pressure O $ LINTYP = control for line loads (0 = nones 1 = some)

N $ Do you want to include smeared stiffeners?

1 $ LAYERS = number of layers (max. = 6)

Y $ Are all the layers of constant thickness?

1 $ MATL = type of material for shell wall lager no.( 1) 1.500000 $ T(i) = thickness of ith layer (i=1 = leftmost), TC 1) 0.1073100E+08 $ Q(i) = shear modulus of ith layer, C( 1) 0.2790000E+08 $ EX(i)= modulus in meridional direction, EX( 1) 0.2790000E+08 $ EY(i)= modulus in circumferential direction, EY( 1) 0.3000000 $ UXY(1)= Poisson's ratio (EY*UXY = EX*UYX). UXY( 1)

O $ ALPHA 1(i)=coef. thermal exp. in merid. direction. ALPHA 1( 1)

O $ ALPHA 2(i)=coef. thermal esp. in circ. direction. ALPHA 2( 1)

Y $ Do you wish to include plasticity in this segment?

N $ Do you wish to include creep in this segment?

N $ Is this a new shell wall material?

N $ Do you want to have C(i,J) printed for this segment?

5 $ NMESH=no. of node points (5= min.s98= max.)SEOMENT NO.(17) 3 $ NTYPEH= control integer (1 or 2 or 3) for nodal point spacing i

j 45

4 1 $ NSHAPE= indicator (1,2 or 4) for geometry of meridian 325.2500 $ R1 = radius at beginning of segment (see p. P7) 6096. 500 $ Z1 = axial coordinate at beginning of segment l 3RS.2500 $ R2 = radius at end of segment ,

6526.000 $ Z2 = axial coordinate at end of segment

! O $ IMP = indicator for imperfection (O=none, 1=some) i 3 $ NTYPEZ= control (1 or 3) for reference surface location 1.250000 $ ZVAL = distance from leftmost surf. to reference surf.

N $ Do you want to print out r(s), v'(s), etc. for this segment?

O $ NRINGS= number ( .,a n =20 ) of discrete rings in this segment N $ Do you want general information on loading?

!. O $ NTSTAT = number of temperature callout points along meridian O $ NPSTAT = number of meridional callouts for pressure O $ LINTYP = control for line loads (0 = nones 1 = some)

N $ Do you want to include smeared stiffeners?

1 $ LAYERS = number of layers (max. = 6)

Y $ Are all the layers of constant thickness?

( 1 $ MATL = type of material for shell wall lager no.( 1)

2. 500000 $ T(i) = thickness of ith layer (i=1 = leftmost). T( 1) 0.1073100E+08 $ Q(i) = shear modulus of ith layer, Q( 1)

! O. 2790000E+08 $ EX ( i ) = mod ulus in meridional direction, EX( 1) i' O. 2790000E+08 $ EV(i)= modulus in circumferential direction. EY( 1) 0.3000000 $ UXY(i)= Poisson's ratio (EY*UXY = EX*UYX). UXY( 1) 0 $ ALPHA 1(i)=coef. thermal exp. in merid. direction, ALPHA 1( i)

( 0 $ ALPHA 2(i)=coef. thermal exp. in cire. direction, ALPHA 2( 1)

Y $ Do you wish to include plasticity in this segment?

N $ Do you wish to include creep in this segment?

N $ Is this a new shell wall material?

N $ Do you want to have C(i,J) printed for this segment?

I l

5 $ NMESH=no. of node points (5= min.s98= max.) SEGMENT NO.(18) 3 $ NTYPEH= control integer (1 or 2 or 3) for nodal point spacing l 1 $ NSHAPE= indicator (1,2 or 4) for geometry of meridian 325.2500 $ R1 = radius at beginning of segment (see p. P7) 6526.000 $ Z1 = axial coordinate at beginning of segment 339.0000 $ R2 = radius at end of segment 6526.000 $ Z2 = axial coordinate at end of segment O $ IMP = indicator for imperfection (O=none, 1=some) 3 $ NTYPEZ= control (1 or 3) for reference surface location 0.7500000 N

$ ZVAL = distance from leftmost surf. to reference surf.

$ Do you want to print out r(s), r'(s), etc. for this segment?

O $ NRINOB= number (max =20) of discrete rings in this segment N $ Do you want general information on loading?

O $ NTSTAT = number of temperature callout points along meridian O $ NPSTAT = number of meridional callouts for pressure O $ LINTYP = control for line loads (0 = nones 1 = some)

N $ Do you want to include smeared stiffeners?

1 $ LAYERS = number of layers (max. = 6)

Y $ Are all the layers of constant thickness?

1 $ MATL = type of material for shell wall layer no.( 1) l

1. 500000 $ T(i) = thickness of ith lager (i=1 = leftmost). T( 1) l O.1073100E+08 $ Q(i) = shear modulus of ith layer, Q( 1)

0. 2790000E+00 $ EX ( i )= modulus in meridional direction. EX( 1) 0.2790000E+08 $ EY(i)= modulus in circumferential direction. EY( 1)

0. 3000000 $ UXY(i)= Poisson's ratio (EY*UXY = EX*UYX). UXY( 1)

O $ ALPHA 1(i)=coef. thermal exp. in merid. direction, ALPHA 1( 1)

O $ ALPHA 2(i)=coef. thermal exp. in cire, direction, ALPHA 2( 1)

Y $ Do you wish to include plasticity in this segment?

N $ Do you wish to include creep in this segment?

N $ Is this a new shell wall material?

N $ Do you want to have C(i,J) printed for this segment?

l 37 $ NMESH=no. of node points (5= min. s 98=ma x. ) SEGMENT NO. (19) l l 46 ,

i l

3 $ NTYPEH= control integer (1 or 2 or 3) for nodal point spacing 1 $ NSHAPE= indicator (1.2 or 4) for geometry of meridian 339.0000 $ R1 = radius at beginning of segment (see p. P7) 6526.000 $ 21 = axial coordinate at beginning of segment 237.2500 $ R2 = radius at end of segment 6879.250 $ 22 = axial coordinate at end of segment O $ IMP = indicator for imperfection (O=none, i=some) 3 $ NTYPEZ= control (1 or 3) for reference surface location O $ ZVAL = distance from leftmost surf. to reference surf.

N $ Do you want to print out r(s), v'(s), etc. for this segment?

5 $ NRINGS= number (max =20) of discrete rings in this segment 2 $ NTYPE = control for identification of ring location (2=z, 3=r) 6558.000 $ Z(I) = axial coordinate of Ith ring, z( 1) 6665.063 $ Z(I) = axial coordinate of Ith ring, z( 2) 6696.000 $ Z(I) = axial ccordinate of Ith ring, z( 3) 6778.000 $ Z(I) = axial coordinate of Ith ring, z( 4) 6879.250 $ Z(I) = axial coordinate of Ith ring, z( 5) l 0 $ NTYPER= type (O or 1 ) of discrete ring no.( 1) i O $ NTYPER= type (O or 1 ) of discrete ring no.( 2) 1 $ NTYPER= type (O or 1 ) of discrete ring no.( 3)

O $ NTYPER= type (O or 1 ) of discrete ring no.( 4) 1 $ NTYPER= type (O or 1 ) of discrete ring no.( 5) 2 $ NPARTS = number of segments in discrete ring no.( 3) 8 $ NGEOM = geometry type of ring segment no.( 1) 1 $ NTEMP = type of temperature distribution in ring seg.( 1) 1 $ NMATL = type of material for ring segment no.( 1) 5 $ INTEG = number of integration points for ring seg.( 1)

O $ NCREEP = control for creep of ring segment no.( 1)

O $ NUMBT = number of temperature distributions in seg.( 1)

N $ Are D1,D2, PHI.T,FL for this ring seg. same as for a previous?

O $ D1 = radial distance to beginning of ring segment ( 1)

O $ D2 = axial distance to beginning of ring segment ( 1) 180 $ PHI = angle in degrees of ring segment ( 1) 0.4990000 $ T = thickness of ring segment ( 1) 10.17200 $ FL = length of ring segment ( 1)

Y $ Are TEMP 1. TEMP 2, TEMP 3 identical to those of a previous seg.?

Y $ Is this ring mat'l same as a previous 1g specified ring mat'17 9 $ NGEOM = geometry type of ring segment no.( 2) 1 $ NTEMP = type of temperature distribe+ ion in ring seg.( 2) 1 $ NMATL = type of material for ring segment no.( 2) 5 $ INTEG = number of integration points for ring seg.( 2)

O $ NCREEP = control for creep of ring segment no.( 2)

O $ NUMBT = number of temperature distributions in seg.( 2)

N $ Are D1.D2. PHI T FL for this ring seg, same as for a previous?

-10.17200 $ D1 = radial distance to beginning of ring segment ( 2)

-4.481000 $ D2 = axial distance to beginning of ring segment ( 2) 90 $ PHI = angle in degrees of ring segment ( 2) 1 0.7950000 $ T = thickness of ring segment ( 2) 8.962000 $ FL = length of ring segment ( 2)

Y $ Are TEMP 1. TEMP 2 TEMP 3 identical to those of a previous seg.?

Y $ Is this ring mat'l same as a previously specified ring mat'17

-10.17200 $ XS = radial coordinate of shear center, ring no.( 3) l O $ YS = axial coordinate of shear center, ring no.( 3) 2 $ NPARTS = number of segments in discrete ring no.( 5) 10 $ NGEOM = geometry type of ring segment no.( 1) 1 $ NTEMP = type of temperature distribution in ring seg.( 1) 1 $ NMATL = type of material for ring segment no.( 1) 5 $ INTEG = number of integration points for ring seg.( 1) l 0 $ NCREEP = control for creep of ring segment no.( 1) l 0 $ NUMBT = number of temperature distributions in sog.( 1) l N $ Are D1 D2. PHI,T,FL for this ring seg. same as for a previous?

47

l O $ D1 = radial distance to beginning of ring segment ( 1) l 0 $ D2 = axial distance to beginning of ring segment ( 1) l 100 $ PHI = angle in degrees of ring segment ( i) l 0.3080000 $ T = thickness of ring segment ( 1) t 10.56100 $ FL = length of ring segment ( 1)

Y $ Are TEMP 1 TEMP 2 TEMP 3 identical to those of a previous seg.?

Y $ Is this ring mat'l same as a previous 1g specified ring mat'17 11 $ NGEOM = geometry type of ring segment no.( 2) 1 $ NTEMP = type of temperature distribution in ring seg.( 2) 1 $ NMATL = type of material for ring segment no.( 2) 5 $ INTEQ = number of integration points for ring seg ( 2)

O $ NCREEP = control for creep of ring segment no.( 2)

O $ NUMBT = number of temperature distributions in seg.( 2) i N $ Are D1.D2. PHI T,FL for this ring seg. same as for a previous?

-10.56100 $ D1 = radial distance to beginning of ring segment ( 2)

-3.250000 $ D2 = axial distance to beginning of ring segment ( 2) 90 $ PHI = angle in degrees of ring segment ( 2)

( O.4510000 $ T = thickness of ring segment ( 2) 6.500000 $ FL = length of ring segment ( 2)

Y $ Are TEMP 1, TEMP 2, TEMP 3 identical to those of a previous seg.?

Y $ Is this ring mat'l same as a previous 1g specified ring mat'17

-10.56100 $ XS = radial coordinate of shear center, ring no.( 5) l O $ YS = axial coordinate of shear center, ring nos ( 5) l N $ Do you want general information on loading?

)

O $ NTSTAT = number of temperature callout points along meridian

1 $ NPSTAT = number of meridional callouts for pressure I

-4

• PN = normal pressure, positive as shown on p. P41.

O $ PT = meridional traction, positive along increasing s.

1

• ISTEP = control integer for time variation of prossure N $ Do you want to print out distributed loads along meridian?

1 $ LINTYP = control for line loads (0 = nones 1 = some)

Y $ Are there any axial line loads in this segment?

1174.600 $ V(K) = axial line load / length of cire, at ring no.( 1) 1357.500 $ V(K) = axial line load / length of circ. at ring no.( 2)

O $ V(K) = axial line load / length of circ. at ring no.( 3)

C75.9000 $ V(K) = axial line load / length of circ. at ring no.( 4)

O $ V(K) = axial line load / length of circ. at ring no.( 5) 1

• ISTEP1 = pointer to time function associated with V( 1) 1 $ ISTEP1 = pointer to time function associated with V( 2) 1 $ ISTEP1 = pointer to time function associated with V( 3)

, 1 $ ISTEP1 = pointer to time function associated with V( 4) i 1

• ISTEP1 = pointer to time function associated with V( 5) l Y $ Are there any radial line loads in this segment?

338.3500 $ HF(K) = radial line load /langth of cire. at ring no.( 1) 391. 0350 $ HF(K) = radial l ir.e load / length of cire, at ring no.( 2)

O $ HF(K) = radial line load / length of cire, at ring no.( 3) 252.3100 $ HF(K) = radial line~1oad/ length of cire. at ring no.( 4)

O $ HF(K) = radial line load / length of cire. at ring no.( 5)

1 $ ISTEP2 = pointer to the F(time) associated with HF( 1)

! 1 $ ISTEP2 = pointer to the F(time) associated with HF( 2) 1 $ ISTEP2 = pointer to the F(time) associated with HF( 3)

,! 1 $ ISTEP2 = pointer to the F(time) associated with HF( 4) l 1 $ ISTEP2 = pointer to the F(time) assocasted with HF( 5)

Y $ Are there any applied meridional moments in this segment?

) 078. 5700 $ FM(K) = meridional moment / length of circ. at ring no.( 1) 662.2000 $ FM(K) = meridional moment / length of cire. at ring no.( 2)

O $ FM(K) = meridional moment / length of circ. at ring no.( 3) 427.2700 $ FM(K) = meridional moment / length of cire. at ring no.( 4)

O $ FM(K) = meridional moment / length of circ. at ring no.( 5) 1

• ISTEP3 = pointer to the F(time) associated with FM( 1) 1 $ ISTEP3 = pointer to the F(time) associated with FM( 2) 48 l

l

. - - - - _ _ _ - _ _ _ _ \

1 $ ISTEP3 = pointer to the F(time) associated with FM( 3) 1 $ ISTEP3 = pointer to the F(time) associated with FM( 4) 1 $ ISTEP3 = pointer to the F(time) associated with FM( 5)

N $ Do you want to include smeared stiffeners?

1 $ LAYERS = number of layers (max. = 6)

N $ Are all the layers of constant thickness?

1 $ MATL = type of material for shell wall layer no.( 1) j O.1073100E+08 $ G(i) = shear modulus of ith lager, G( 1) l

0. 2790000E+08 $ EX(i)= modulus in meridional direction. EX( 1)

0. 2790000E+08 $ EY(i)= modulus in circumferential dzrection. EY( 1) 0.3000000 $ UXY(i)= Poisson's ratio (EY*UXY = EX*UYX). UXY( 1) i O $ ALPHA 1(i)=coef. thermal exp. in merid. direction, ALPHA 1( 1)

O $ ALPHA 2(i)=coef. thermal exp. in circ. direction, ALPHA 2( 1)

Y $ Do you wish to include plasticity in this segment?

N $ Do you wish to include creep in this segment?

N $ Is this a new shell wall material?

6 $ NTIN = number of meridional callouts for variable thickness l

2 $ NTYPE = control for meaning of thickness callout (2=r, 3=r)

( 6526.000 6558.000

$ Z(I) = axial coordinate of Ith thickness callout, z( 1)

$ Z(1) = axial coordinate of Ith thickness callout, z( 2) 6559.000 $ Z(I) = axial coordinate of Ith thickness callout, z( 3)#

6778.000 $ Z(I) = axial coordinate of Ith thickness callout, 2( 4) 6779.000 $ Z(I) = axial coordinate of Ith thickness callout, z( 5) 6879.250 $ Z(I) = axial coordinate of Ith thickness callout, z( 6) 1.437500 $ TIN (i) = thickness at Ith callout, TIN ( 1) 1.437500 $ TIN (i) = thickness at Ith callout, TIN ( 2) 0.9375000 $ TIN (i) = thickness at Ith callout, TIN ( 3) 0.9375000 $ TIN (i) = thickness at Ith callout, TIN ( 4) 0.7500000 $ TIN (i) = thickness at Ith callout, TIN ( 5) 0.7500000 $ TIN (i) = thickness at Ith callout, TIN ( 6)

N $ Do you want to have C(1,j) printed for this segment?

21 $ NMESH=no, of node points (5= min.s98= max.) SEGMENT NO.(20) 3 $ NTYPEH= control integer (1 or 2 or 3) for nodal point spacing 1 $ NSHAPE= indicator (1,2 or 4) for geometry of meridian 237.2500 $ R1 = radius at beginning of segment (see p. P7) 6879.250 $ Z1 = axial coordinate at beginning of segment 190. 0000 $ R2 = radius at end of segment 6961.250 $ Z2 = axial coordinate at end of segment O $ IMP = indicator for imperfection (O=none, 1=some) 3 $ NTYPEZ= control (1 or 3) for reference surface location O $ ZVAL = distance from leftmost surf. to reference surf.

N $ Do you want to print out r(s), c'(s), etc. for this segment?

2 $ NRINGS= number (max =20) of discrete rings in this segment 2 $ NTYPE = control for identification of ring location (2=z, 3=r) 6879.250 $ Z(I) = axial coordinate of Ith ring, 2( 1) 6961.250 $ Z(I) = axial coordinate of Ith ring, z( 2)

O $ NTYPER= type (O or 1 ) of discrete ring no.( 1)

O $ NTYPER= type (O or 1 ) of discrete ring no.( 2)

N $ Do you want generc' information on loading?

O $ NTSTAT = number oP temperature callout points along meridian 1 $ NPSTAT = number of meridional callouts for pressure

-4 $ PN = normal pressure, positive as shown on p. P41.

O $ PT = meridional traction, positive along increasing s.

1 $ ISTEP = control integer for time variation of pressure N $ Do you want to print out distributed loads along meridian?

1 $ LINTYP = control for line loads (0 = nones 1 = some)

Y $ Are there any axial line loads in this segment?

481. 0000 $ V(K) = axial line load / length of cire. at ring no.( 1) 1592.000 $ V(K) = axial line load / length of cire. at ring no.( 2) 1 $ ISTEP1 = pointer to time function associated with V( 1) 1 $ ISTEP1 = pointer to time function associated with V( 2) 49

4 Y $ Are there any radial line loads in this segment?

138.5500 $ HF(K) = radial line load / length of circ. at ring no.( 1) 917.3300 $ HF(K) = radial line load / length of cire. at ring no.( 2) 1 $ ISTEP2 = pointer to the F(time) associated with HF( 1) 1 $ ISTEP2 = pointer to the F(time) associated with HF( 2)

Y $ Are there any applied meridional moments in this segmentJ 107.7100 $ FM(K) = meridional moment / length of circ. at ring no.( 1) 744.4300 $ FM(K) = meridional moment / length of circ. at ring no.( 2) 1 $ ISTEP3 = pointer to the F(time) associated with FM( 1) 1 $ ISTEP3 = pointer to the F(time) associated with FM( 2)

N $ Do you want to include smeared stiffeners?

1 $ LAYERS = number of layers (max. = 6)

Y $ Are all the layers of constant thickness?

1 $ MATL = type of material for shell wall lager no.( 1)

O.0125000 $ T(i) = thickness of ith lager (i=1 = leftmost), TC 1)

O.1073100E+08 $ Q(i) = shear modulus of ith layer, O( 1)

0. 2790000E+08 $ EX(i)= modulus in meridional direction, EX( 1)

0. 2790000E+08 $ EY( i )= modulus in circumferential direction. EY( 1) 0.3000000 $ UXY(i)= Poisson's ratio (EY*UXY = EX*UYX). UXY( 1)

O $ ALPHA 1(i)=coef. thermal exp. in merid. direction, ALPHA 1( 1)

O $ ALPHA 2(i)=coef, thermal exp. in cire. direction, ALPHA 2( 1)

Y $ Do you wish to include plasticity in this segment?

N $ Do you wish to include creep in this segment?

N $ Is this a new shell wall material?

N $ Do you want to have C(i,J) printed for this segment? l 11 t NMESH=no. of node points (5= min.s98= max.)SEOMENT NO.(21) 3 $ NTYPEH= control integer (1 or 2 or 3) for nodal point spacing 1 $ NSHAPE= indicator (1,2 or 4) for geometry of meridian 190.0000 $ R1 = radius at beginning of segment (see p. P7) 6961.250 $ Z1 = axial coordinate at beginning of segment 190. 0000 $ R2 = radius at end of segment 7089.250 $ Z2 = axial coordinate at end of segment O $ IMP - = indicator for imperfection (O=none, 1=some) 3 $ NTYPEZ= control (1 or 3) for reference surface location O $ ZVAL = distance from leftmost surf. to reference surf.

N $ Do you want to print out r(s), c'(s), etc. for this segment?

2 $ NRINGS= number (man =20) of discrete rings in this segment 2 $ NTYPE = control for identification of ring location (2= , 3=r) 6961. 250 $ Z(I) = axial coordinate of Ith ring, :( 1) 6997.250 $ Z(I) = a:ial coordinate of Ith ring, z( 2) '

1 $ NTYPER= type (O or 1 ) of discrete ring no.( 1) 1 $ NTYPER= type (O or 1 ) of discrete ring no.( 2)

' 1 $ NPARTS = number of segments in discrete ring no.( 1) 12 $ NCEDM = geometry type of ring segment no.( 1) 1 $ NTEMP = type of temperature distribution in ring seg.( 1) 1 $ NMATL = type of material for ring segment no.( 1) 5 $ INTEQ = number of integration points for ring seg.( 1)

O $ NCREEP = control for creep of ring segment no.( 1)

O $ NUMBT = number of temperature distributions in seg.( 1)

N $ Are D1,D2, PHI,T,FL for this ring seg. same as for a previous?

O $ D1 = radial distance to beginning of ring segment ( 1)

O $ D2 = axial distance to beginning of ring segment ( 1)

O $ PHI = angle in degrees of ring segment (-1)

2 $ T = thickness of ring segment ( 1) l 15.5C000 $ FL = length ef ring segment ( 1)

{ Y $ Are TEMP 1, TEMP 2, TEMP 3 identical to those of a previous seg.?

i Y $ Is this ring mat'l same as a previously specified ring mat'1?

7.75C000 $ XS = radial coordinate of shear center, ring no.( 1)

I O $ YS = axial coordinate of shear center, ring no.( 1) 1 $ NPARTS = number of segments in discrete ring no.( 2) 13 $ NCEOM = geometry type of ring segment no.( 1) i 50

1 $ NTEMP = type of temperature distribution in ring seg.( 1) 1 $ NMATL = type of material for ring segment no.( 1) 5

• INTEC = number of integration points for ring seg.( 1)

O $ NCREEP = control for creep of ring segment no.( 1)

O $ NUMBT = number of temperature distributions in seg.( 1)

N $ Are D1,D2, PHI,T,FL for this ring seg, same as for a previous?

O $ D1 = radial distance to beginning of ring segment ( 1)

O $ D2 = axial distance to beginning of ring segment ( 1)

O $ PHI = angle in degrees of ring segment ( 1) 6.250000 $ T = thickness of ring segment ( 1) 10 $ FL = length of ring segment ( 1)

Y $ Are TEMP 1, TEMP 2, TEMP 3 identical to those of a previous seg.?

Y $ Is this ring mat'l same as a previous 1g specified ring mat'1?

3.125000 $ XS = radial coordinate of shear center, ring no.( 2)

O $ YS = axial coordinate of shear center, ring no.( 2)

N $ Do you want general information on loading?

O $ NTSTAT = number of temperature callout points along meridian 1 $ NPSTAT = number of meridional callouts for pressure

-2 $ PN = normal pressure, positive as shown on p. P41.

O $ PT = meridional traction, positive along increasing s.

1 $ ISTEP = control integer for time variation of pressure N $ Do you want to print out distributed loads along meridian?

O $ LINTYP = control for line loads (0 = nones 1 = some)

N $ Do you want to include smeared stiffeners?

1 $ LAYERS = number of layers ( ma i . = 6)

Y $ Are all the layers of constant thickness? ,

1 $ MATL = type of material for shell wall lager no.( 1) 0.6875000 $ T(i) = thickness of ith lager (i=1 = leftmost), T( 1) 0.1073100E+08 $ Q(i) = shear modulus of ith layer, Q( 1) 0.2790000E+08 $ EX(i)= modulus in meridional direction, EX( 1) 0.2790000E+08 $ EY(i)= modulus in circumferential direction. EY( 1) 0.3000000 $ UXY(i)= Poisson's ratio (EYeUXY = EX*UYX). UXY( 1)

O $ ALPHA 1(i)=coef. thermal exp. in merid, direction. ALPHA 1( 1)

O $ ALPHA 2(i)=coef. thermal exp. in circ. direction. ALPHA 2( 1)

Y $ Do ocu wish to include plasticity in this segment?

N $ De you wish to include creep in this segment?

N $ Is this a new shell wall material?

N $ Do you want to have C(i,J) printed for this segment?

15 $ NMESH=no. of node points ( 5= min. s 98=ma x. )SEOMENT NO. (22) 3 $ NTYPEH= control integer (1 or 2 or 3) for nodal point spacing 2 $ NSHAPE= indicator (1,2 or 4) for geometry of meridian 190.0000 $ R1 = radius at beginning of segment (see p. P7) 7089.250 $ Z1 = axial coordinate at beginning of segment 153.9647 $ R2 = radius at end of segment 7147.594 $ Z2 = axial coordinate at end of segment 124.7500 $ RC = radius from axis of rev. to center of curvature 7089.250 $ ZC = axial coordinate of center of curvature

-1 $ SROT= indicator for direction of increasing arc (-1. or +1.)

O $ IMP = indicator for imperfection (O=none, 1=some) 3 $ NTYPEZ= control (1 or 3) for reference surface location O $ ZVAL = distance from leftmost surf. to reference surf.

t N $ Do you want to print out r(s), r'(s), etc. for this segment?

! O $ NRINGS= number (max =20) of discrete rings in this segment N $ Do you want general information on loading?

O $ NTSTAT = number of temperature callout points along meridian 1 $ NPSTAT = number of meridional callouts for pressure

-2 $ PN = normal pressure, positive as shown on p. P41.

l 0 $ PT = meridional traction, positive along increasing s.

1 $ ISTEP = control integer for time variation of pressure N $ Do you want to print out distributed loads along meridian?

O $ LINTYP = control for line loads (0 = nones 1 = some) 51

N $ Do you want to include smeared stiffeners?

1 $ LAYERS = number of layers (max. = 6)

Y $ Are all the layers of constant thickness?

1 $ MATL = type of material for shell wall lager no.( 1) 0.0750000 $ T(i) = thickness of ith layer (i=1 = leftmost). T( 1) 0.1073100E+08 $ C(i) = shear modulus of ith layer, G( 1)

0. 2790000E+08 $ EX ( i ) = modulus in meridional direction, EX( 1) 0.2790000E+08 $ EY(i)= modulus in circumferential direction, EY( 1) 0.3000000 $ UXY(i)= Poisson's ratio (EY*UXY = EX*UYX). UXY( 1)

O $ ALPHA 1(i)=coef. thermal exp. in merid. direction, ALPHA 1( 1)

O $ ALPHA 2(i)=coef. thermal exp. in cire. direction, ALPHA 2( 1)

Y $ Do you with to include plasticity in this segment?

N $ Do you wish to include creep in this segment?

N $ Is this a new shell wall material?

N $ Do you want to have C(i,J) printed for this segment?

15 $ NMESH=no. of node points (5= min.s98= max.) SEGMENT NO.(23) 3 $ NTYPEH= control integer (1 or 2 or 3) for nodal point spacing 2 $ NSHAPE= indicator (1,2 or 4) for geometry of meridian 153.9647 $ R1 = radius at beginning of segment (see p. P7) 7147.594 $ Z1 = axial coordinate at beginning of segment O $ R2 = radius at end of segment 7184.000 $ Z2 = axial coordinate at end of segment O $ RC = radius from axis of rev. to center of curvature 6840.125 $ ZC = axial coordinate of center of curvature

-1 $ SROT= indicator for direction of increasing arc (-1. or +1.)

O $ IMP = indicator for imperfection (O=none, 1=some) 3 $ NTYPEZ= control (1 or 3) for reference surface location O $ ZVAL = distance from leftmost surf. to reference surf.

N $ Do you want to print out r(s), r'(s), etc. for this segment?

O $ NRINGS= number (max =20) of discrete rings in this segment N $ Do you want general information on loading?

O $ NTSTAT = number of temperature callout points along meridian 1 $ NPSTAT = number of meridional callouts for pressure

-2 $ PN = normal pressure, positive as shown on p. P41.

O $ PT = meridional traction, positive along increciing s.

1 $ ISTEP = control integer for time variation of pressure H $ Do you want to print out distributed loads along meridian?

O $ LINTYP = control for line loads (0 = nones 1 = some)

N $ Do you want to include smeared stiffeners?

1 $ LAYERS = number of lagers (max. = 6)

Y $ Are all the layers of constant thickness?

1

• MATL = type of material For shell wall layer no.( 1) 0.8750000 $ T(i) = thickness of ith lager (i=1 = leftmost), T( 1) 0.1073100E+08 $ C(i) = shear modulus of ith lager, G( 1) 0.2790000E+0B $ EX(i)= modulus in meridional direction, EX( 1) 0.2790000E+08 $ EY(i)= modulus in circumferential direction, EY( 1)

0. 3000000 $ UXY(i)= Poisson's ratio (EY*UXY = EX*UYX). UXY( 1)

O $ ALPHA 1(i)=coef. thermal exp. in merid, direction, ALPHA 1( 1)

O $ ALPHA 2(i)=coef. thermal exp. in circ. direction, ALPHA 2( 1)

Y $ Do you wish to include plasticity in this segment?

N $ Do you wish to include creep in this segment?

N $ Is this a new shell wall material?

N $ Do you want to have C(i,J) printed for this segment?

N $ Do you want information on time functions for loading?

1 $ IUTIME = control for time increment (O or 1). IUTIME 1 $ DTIME = time increment 1000000. $ TMAX = maximum time to be encountered during this case 1 4 NFTIME= number of different furictions of time 2 $ NPOINT=no. of points j for ith load factor F(i,J). 1"( 1)

O $ T(i,J)=Jth time callout for ith time function, J =( 1) 1000000.

• T(i,J)=Jth time callout for ith time function. J =( 2) 52 1

O $ F(i,J)=Jth value for ith load factor. J =( 1) 1000000. $ F(i,J)=Jth value for ith load factor. J =( 2)

N $ Do you want general information on constraint conditions?

O $ Number of poles (places where r=0) in SEOMENT( 1) 1 $ At how many stations is this segment constrained to ground?

1

• INODE = nodal point number of constraint to ground, INODE( 1) 1 $ IUSTAR= axial displacement (O= free, i= constrained) 1 $ IVSTAR= circumferential displacement (O= free, 1= constrained)

O $ IWSTAR= radial displacement (O= free, 1= constrained) 1 $ ICHI = meridional rotation (O= free,  != constrained)

0. OOOOOOOE+00 $ D1 = radial component of offset of ground support O. OOOOOOOE+00 $ D2 = axial component of offset of ground support N $ Is this constraint the same for both prebuckling and buckling?

1 $ IUSTARB= axial displacement for buckling or vibration phase 1 $ IVSTARB= circ. displacement for buckling or vibration phase 1

• IWSTARB= radial displacement for buckling or vibration 1 $ ICHIB = meridional rotation for buckling or vibration N $ In this segment Joined to ang lower-numb'ered segments?

O $ Number of poles (places where r=O) in SEGMENT ( 2)

O $ At how many stations is this mes.r.:nt cer9 trained to ground?

Y $ Is this segment Joined to ang lower-numbereo segments?

1 $ At how mag stations is this segment joined to previous segt.?

1 $ INODE = node in current segment (ISEG) of Junction, INODE( 1) 1 $ JSEO = segment no. of previous segment involved in Junction 11 $ JNODE = node in previous sogent (JSEG) of Junction 1 $ IUSTAR= axial displacesent (O=not slaved. 1= slaved) 1 $ IVSTAR= circumferential displacement (O=not slaved, 1= slaved) 1 $ IWSTAR= radial displacement (O=not slaved. 1= slaved) 1 $ ICHI = meridional rotation (O=not slaved, 1= slaved)

O $ D1 = radial component of Juncture gap O $ D2 = axial component of Juncture gap Y $ Is this constraint the same for both prebuckling and buckling?

O $ Number of poles (places where r=O) in SEGMENT ( 3)

O $ At how many stations is this segment constrained to ground?

Y $ Is this segment joined to ang lower-numbered segments?

1 $ At how may stations is this segment Joined to previous segs.?

1 $ INODE = node in current segment (ISEC) of Junction. INODE( 1) 2 $ JSEQ = segment no. of previous segment involved in Junction 19 $ JNODE = node in previous segant (JBEO) of junction 1

• IUSTAR= axial displacement (O=not slaved. 1= slaved) 1 $ IVSTAR= circumferential displacement (O=not slaved. 1= slaved) 1 $ IWSTAR= radial displacement (O=not slaved, 1= slaved) 1 $ ICHI = meridional rotation (O=not slaved. 1=s14ved) 1 0 $ D1 = radial component of juncture gap 3

0 $ D2 = axial component of juncture gap Y $ Is this constraint the same for both prebuckling and buckling? '

O $ Number of poles (places where r=O) in SEGMENT ( 4)

O $ At how many stations is this segment constrained to ground?

. Y $ Is this segment Joined to ang lower-numbered segments?

1 $ At how may stations is this segment Joined to previous segs.?

1 $ INODE = node in current segment (ISEG) of Junction, INODE( 1) 3 $ JSEQ = segment no. of previous segment involved in Junction 19 $ JNODE = node in previous segent (JSEG) of Junction 1 $ IUSTAR= axial displacement (O=not slaved. 1= slaved) 1 $ IVSTAR= circumferential displacement (O=not slaved, != slaved) 1 $ IWSTAR= radial displacement (O=not slaved, 1= slaved) 1 $ ICHI = meridional rotation (O=not slaved, 1= slaved)  :

j O $ D1 = radial component of juncture gap l 0 $ D2 = axial component of Juncture gap ,

l Y $ Is this constraint the same for both prebuckling and buckling?

l 0 $ Number of poles (places where r=0) in SEGMENT ( 5) l 53

O $ At how many stations is this segment constrained to ground?

Y $ Is this segment joined to any lower-numbared segments?

1 $ At how may stations is this segment joined to previous segs.?

1 $ INODE = node in current segment (ISEG) of Junction, INODE( 1) 4 $ JSEG = segment no. of previous segment involved in Junction 17 $ JNODE = node in previous segmnt (JSEG) of junction 1 $ IUSTAR= axial displacement (O=not slaved, 1= slaved) 1 $ IVSTAR= circumferential displacement (O=not slaved, != slaved) 1 $ IWSTAR= radial displacement (O=not slaved, 1= slaved) 1 $ ICHI = meridional rotation (O=not slaved, 1= slaved) 0.OOOOOOOE+00 $ D1 = radial component of juncture gap O.OOOOOOOE+00 $ D2 = axial component of juncture gap Y $ Is this constraint-the same for both prebuckling and buckling?

O $ Number of poles (places where r=0) in SEGMENT ( 6)

O $ At how many stations is this segment constreined to ground?

Y $ Is this segment Joined to any lower-numbered segments?

1 $ At how may stations is this segment joined to previous segs.?

1 $ INODE = node in current segment (ISEG) of Junction, INODE( 1) 4 $ JSEC = segmgnt no. of previous segment involved in Junction 19 $ JNODE = node in previous segmnt (JSEG) of Junction 1 $ IUSTAR= axial displacement (O=not slaved, 1= slaved) 1 $ IVSTAR= circumferential displacement (O=not slaved. 1= slaved) 1 $ IWSTAR= radial displacement (O=not slaved, i= slaved) 1 $ ICHI = meridional rotation (O=not slaved. 1= slaved)

O $ D1 = radial component of Juncture gap O $ D2 = axial component of Juncture gap l Y $ Is this constraint the same for both prebuckling and buckling? -

0 $ Number of poles (places where r=O) in SEGMENT ( 7)

O $ At how many stations is this segment constrained to ground?

Y $ Is this segment Joined to any lawsc-numbered segments?

1 $ At how may stations is this segment joined to previous segs.?

1 $ INODE = node in current segment (ISEG) of junction, INODE( 1) 6 $ JSEO = segment no. of previous segment involved in Junction ,

13 $ JNODE = node in previous segmnt (JSEG) of Junction  !

1 $ IUSTAR= axial displacement (O=not slaved, 1= slaved) )

1 $ IVSTAR= circumferential displacement (O=not slaved, 1= slaved) l 1 $ IWSTAR= radial displacement (O=not slaved, 1= slaved) I 1 $ ICHI = meridional rotation (O=not slaved, 1= slaved)

O $ D1 = radial component of Juncture gap O $ D2 = axial component of J urec tur e gap Y $ Is this constraint the same for both prebuckling and buckling?

O $ Number of poles (places where r=0) in SEGMENT ( 8)

O $ At how many stations is this segment constrained to ground?

Y $ Is this segment joined to any lower-numbered segments?

1 $ At how may stations is this segment joined to previous segs.?

1 $ INODE = node in current segment (ISEG) of junction, INODE( 1)  !

7 $ JSEG = segment no. of previous segment involved in Junction ,

21 $ JNODE = node in previous segmnt (JSEG) of junction I 1 $ IUSTAR= axial displacement (O=not slaved, 1= slaved)  ;

1 $ IVSTAR= circumferential displacement (O=not slaved, 1= slaved) 1 1 $ IWSTAR= radial displacement (O=not slaved, i= slaved) 1 1 $ ICHI = meridional rotation (O=not slaved, 1= slaved) I O $ D1 = radial component of juncture gap l 0 $ D2 = axial component of Juncture gap Y

)

$ Is this constraint the same for both prebuckling and buckling? l 0 $ Number of poles (places where v=O) in SEGMENT ( 9) i 0 $ At how many stations is this segment constrained to ground? .

Y $ Is this segment joined to any lower-numbered segments? I 1 $ At how may stations is this segment joined to previous segs.?

1 $ INODE = node in current segment (ISEG) of Junction, INODE( 1) 8 $ JSEG = segment no. of previous segment involved in Junction 54 I

5 $ JNODE = node in previous segant (JSEG) of junction 1 $ IUSTAR= axial displacement (O=not slaved, 1= slaved) 1 $ IVSTAR= circumferential displacement (O=not slaved, 1= slaved) 1 $ IWSTf.R= radial displacement (O=not slaved, 1= slaved) 1 $ ICHI = meridional rotation (O=not slaved. 1= slaved)

O $ Di = radial component of Juncture gap O $ D2 = axial component of Juncture gap Y $ Is this constraint the same for both prebuckling and buckling?

O $ Number of poles (places where r=O) in SEGMENT (10)

O $ At how many stations is this segment constrained to ground?

Y $ Is this segment joined to ang lower-numbered segments?

1 $ At how may stations is this segment joined to previous segs.?

1 $ INODE = node in current segment (ISEG) of Junction, INODE( 1) 9 $ JSEG = segment no. of previous segment involved in Junction 37 $ JNODE = node in previous begent (JSEG) of Junction 1 4 IUSTAR= axial displacement (O=not slaved, 1= slaved) 1

• IVSTAR= circumferential displacement (O=not slaved, 1= slaved) i 1 $ IWSTAR= radial displacement (O=not slaved. 1= slaved) l 1 $ ICHI = meridional rotation (O=not slaved, 1= slaved)

O $ D1 = radial component of Juncture gap

! O $ D2 = axial component of juncture gap Y $ Is this constraint the same for both prebuckling and buckling?

O $ Number of poles (places where r=0) in SEGMENT (11)

O $ At how many stations is this segment constrained to ground?

Y $ Is this segment joined to ang lower-numbered segments?

1 $ At how may stations is this segment Joined to previous segs.?

1 $ INODE = node in current segment (ISEC) of junction. INODE( 1) 9 $ JSEQ = segment no. of previous segment involved in Junction 37 $ JNODE = node in previous segmnt (JSEC) of Junction 1 $ IUSTAR= axial displacement (O=not slaved, 1= slaved) 1 3 IVSTAR= circumferential displacement (O=not slaved. 1= slaved) 1

• IWSTAR= radial displacement (O=not slaved, != slaved) 1 $ ICHI = meridional rotation (O=not slaved, 1= slaved)

O $ D1 = radial component of Juncture gap 4

0 $ D2 = axial component of Juncture gap 1

Y $ Is this constraint the same for both prebuckling and buckling?

O $ Number of poles (places where r=O) in SEGMENT (12)

O $ At how many stations is this segment constrained to ground?

Y $ Is this segment Joined to any lower-numbered segments?

1 $ At how may stations is this segment joined to previous segs.?

1 $ INODE = node in current segment (ISEC) of Junction, INODE( 1) 11 $ JSEQ = segment no. of previous segment involved in Junction 5 $ JNODE = node in previous segant (JSEG) of Junction 1 $ IUSTAR= axial displacement (O=not slaved. 1= slaved) i 1 $ IVSTAR= circumferential displacement (O=not slaved, 1= slaved) 1 $ IWSTAR= radial displacement (O=not slaved, i= slaved) 1 $ ICHI = meridional rotation (O=not slaved, i= slaved)

O $ D1 = radial component of Juncture gap

O $ D2 = axial component of Juncture gap

! Y $ Is this constraint the same for both prebuckling and buckling?

O $ Number of poles (places where r=0) in SEGMENT (13) i 0 $ At how many stations is this segment constrained to ground?

l Y $ Is this segment joined to ang lower-numbered segments?

2 $ At how may stations is this segment joined to previous segs.?

1 $ INODE = node in current segment (IBEG) of Junction. INODE( 1) 12 $ JSEQ = segment no. of previous segment involved in Junction 5 $ JNODE = node in previous segmnt (JSEG) of Junction i 1 $ IUSTAR= axial displacement (Oenot slaved, 1= slaved) 1 $ IVSTAR= circumferential displacement (O=not slaved. 1= slaved) 1 $ IWSTAR= radial displacement (O=not slaved, 1= slaved) 1 $ ICHI = meridional rotation (O=not slaved, i= slaved) l 55 r

r ___ _. _ _ . _ _ _ _ _ _ . _ . . _ ., . - _ _ _.

O $ D1 = radial component of Juncture gap O $ D2 = axial component of Juncture gap Y $ Is this constraint the same for both prebuckling and buckling?

5 9 IMODE = node in current segment (ISEG) of Junction. INODE( 2) 10 $ JSEO = segment no. of previous segment involved in Junction 7 $ JNDDE = node in previous sogant (JSEG) of Junction 1 $ IUSTAR= axial displacement (O=not slaved, 1= slaved) 1 $ IVSTAR= circumferential displacement (O=not slaved, 1= slaved) 1 8 IWSTAR= radial displacement'(O=not slaved, != slaved) 1 4 ICHI = meridional rotation (O=not slaved. 1= slaved)

O $ D1 = radial component of Juncture gap O $ D2 = axial component of Juncture gap Y $ Is this constraint the same for both probuckling and buckling?

O $ Number of poles (places where r=O) in BECMENT(14)

O $ At how many stations is this segment constrained to ground?

Y $ Is this segment Joined to any lower-numbered segments?

1 $ At how may stations is this segment Joined to previous segs. ?

1 $ INODE = node in current segment (ISEG) of Junction, INODE( 1) 10 $ JSEO = segment no. of previous segment involved in Junction 7 $ JNODE = node in previous segs.nt (JSEG) of Junction 1 $ IUSTAR= axial displacement (O=not slaved, 1= slaved) 1 $ IVSTAR= circumferential displacement (O=not slavet, != slaved) 1 $ IWSTAR= radial displacement (O=not slaved, 1= slaved) 1 $ ICHI = meridional rotation (O=not slaved, 1= slaved) i O $ D1 = radial component of juncture gao O $ D2 = axial component of Juncture gap Y $ Is this constraint the same for both prebuckling and buckling?

O $ Number of poles (places where r=O) in SEOMENT(15)

O $ At how many stations is this segment constrained to ground?

Y $ Is this segment joined to ang lower-numbered segments?

1

• At how may stations is this segment Joined to previous segs.?

1 $ INODE = node in current segment (ISEG) of Junction, INODE( 1) 14 $ JSEO = segment no. of previous segment involved in Junction i 37 $ JNODE = node in previous segent (JSEC) of junction l 1 $ IUSTAR= axial displacement (O=not slaved, != slaved) -

1 $ IVSTAR= circumferential displacement (O=not slaved, 1= slaved) i 1 8 IWSTAR= radial displacement (O=not slaved, 1= slaved) 1 4 ICHI = meridional rotation (O=not slaved, 1= slaved)

O $ D1 = radial component of juncture gap O $ D2 = axial component of Juncture gap Y $ Is this constraint the same for both prebuckling and buckling?

O $ Number of poles (places where r=O) in SEGMENT (16)

O $ At how many stations is this segment constrained to ground?

Y $ Is this segment joined to ang lower-numbered segments?

1 $ At how may stations is this segment joined to previous segs.?

1 $ INODE = node in current segment (ISEG) of Junction, INODE( 1)

, 14 4 JSEQ = segment no. of previous segment involved in Junction l 37 $ JNODE = node in previous sogant (JSEC) of Junction 1 $ IUSTAR= axial displacement (O=not slaved. 1= slaved) 1 $ IVSTAR= circumferential displacement (O=not slaved, 1= slaved) i 1 $ IWSTAR= radial displacement (O=not slaved. 1= slaved) 1 $ ICHI = meridional rotation (O=not slaved, 1= slaved)

O $ D1 = radial component of juncture gap O $ D2 = axial component of Juncture gap

Y $ Is this constraint the same for both prebuckling and buckling?

i O $ Number of poles (placss where r=O) in SEQMENT(17)

O $ At how many stations i this segment constrained to ground?

, Y $ Is this segment joined to ar.g lower-numbered segments?

1 $ At how may stations is this segment Joined to previous segs.?

1 $ INODE = node in current segment (ISEG) of Junction. INODE( 1) 16 $ JSEO = segment no. of previous segment involved in Junction 56

5 $ JNODE = node in previous segent (JSEC) of Junction 1 $ IUSTAR= axial displacement (O=not slaved, 1= slaved) 1 $ IVSTAR= circumferential displacement (O=not slaved, 1= slaved) 1 $ IWSTAR= radial displacement (O=not slaved. 1= slaved) 1 $ ICHI = meridional rotation (O=not slaved, i= slaved)

O $ D1 = radial component of Juncture gap O $ D2 = axial component of Juncture gap Y $ Is this constraint the same for both prebuckling and buckling?

O $ Number of poles (places where r=O) in SECMENT(18)

O $ At how many stations is this segment constrained to ground?

Y $ Is this segment Joined to ang lower-numbered segments?

2 $ At how may stations is this segment Joined to previous segs.?

1 $ INODE = node in current segment (ISEG) of Junction, INODE( 1) 17 $ JSEC = segment no. of previous segment involved.in Junction 5 $ JNODE = node in previous segent (JSEG) of Junction 1 $ IUSTAR= axial displacement (O=not slaved, 1= slaved) 1 $ IVSTAR= circumferential displacement (O=not slaved, 1= slaved) 1 $ IWSTAR= radial displacement (O=not slaved, 1= slaved) 1 4 ICHI = meridional rotation (O=not slaved. 1= slaved)

O $ D1 = radial component of Juncture gap O $ G2 = axial component of Juncture gap Y $ Is this constraint the same for both prebuckling and buckling?

5 $ INODE = node in current segment (ISEG) of Junction, INODE( 2) 15 $ JSEC = segment no. of previous segment involved in Junction 5

• JNODE = node in previous sogent (JSEG) of Junction 1 $ IUSTAR= axial displacement (O=not slaved, 1= slaved) 1 $ IVSTAR= circumferential displacement (O=not slaved, != slaved) 1 $ IWSTAR= radial displacement (O=not slaved. 1= slaved) 1 $ ICHI = meridional rotation (O=not slaved, 1= slaved)

O $ D1 = radial component of Juncture gap O $ D2 = axial component of juncture gap Y $ Is this constraint the same for both prebuckling and buckling?

O $ Number of poles (places where r=O) in SEGMENT (19) i 1 $ At how many stations is this segment constrained to ground?

30 $ INODE = nodal point number of constraint to ground. INODE( 1) j O $ IUSTAR= axial displacement (O= free, != constrained)

O $ IVSTAR= circumferential displacement (O= free, 1= constrained)

O $ IWSTAR= radial displacement (O= free, i= constrained)

O $ ICHI = mtridional rotation (O= free, 1= constrained) i O.OOOOOOCE+00 $ D1 = radial component of offset of ground support O.OOOOOOOE+00 $ D2 = axial ' component of offset of ground support d $ Is this constraint ~the same for both prebuckling and buckling?

O $ IUSTARB= axial displacement for buckling or vibration phase 1

• IVSTARB= circ. displacement for buckling or vibration phase O $ IWSTARB= radial displacement for buckling or vibration O $ ICHIB = meridional rotation for buckling or vibration Y $ Is this segment joined to ang lower-numbered segments?

1 $ At how may stations is this segment joined to previous segs.?

1 $ INODE = node in current segment (ISEG) of Junction, INODE( 1) 15 $ JSEC = segment no. of previous segment involved in Junction 5 $ JNODE = node in previous sogent (JSEG) of junction 1 $ IUSTAR= axial displacement (O=not slaved. 1= slaved) 1 $ IVSTAR= circumferential displacement (O=not slaved, != slaved) 1 $ IWSTAR= radial displacement (O=not slaved, 1= slaved) ,

1 $ ICHI = meridional rotation (O=not slaved, 1= slaved)

O $ D1 = radial component of Juncture gap O $ D2 = axial component of juncture gap Y $ Is this constraint the same for both prebuckling and buckling?

O $ Number of poles (places where r=O) in SEGMENT (20)

O $ At how many stations is this segment constrained to ground?

Y $ Is this segment joined to ang lower-numbered sagments?

57

1 $ At how may stations is this s*gment Joined to previous segs.?

1 $ INODE = node in current segment (ISEG) of Junction, INODE( 1) 19 $ JBEQ = segment no. of previous segment involved in Junction l

37 $ JNODE = node in previous sogant (JSEG) of Junction 1 4 IUSTAR= axial displacement (O=not slaved, != slaved) 1 $ IVSTAR= circumferential displacement (O=not slaved, 1= slaved) 1 $ IWSTAd= radial displacement (O=not slaved. 1= slaved) 1 $ ICHI = meridional rotation (O=not slaved, 1= slaved) l 0 $ D1 = radial component of Juncture gap

! O $ D2 = axial component of juncture gap Y $ Is this constraint the same for both prebuckling and buckling?

O $ Number of poles (places where r=O) in SEQMENT(21)

O $ At how many stations is this segment constrained to ground?

Y $ Is this segment Joined to ang lower-numbered segments?

l I 1 $ At how may stations is this segment joined to previous segs.?

1 $ INODE = node in currsnt segment (ISEG) of junction, INODE( 1) 20 $ JSEQ = segment no. of previous segment involved in Junction 21 $ JNODE = node in previous segmnt (JBEG) of Junction 1 $ IUSTAR= axial displacement (O=not slaved, 1= slaved) 1 $ IVSTAR= circumferential displacement (O=not slaved, 1= slaved) l l

1 $ IWSTAR= radial displacement (O=not slaved, 1= slaved) 1 $ ICHI = meridional rotation (O=not slaved, 1= slaved)

O $ D1 = radial component of Juncture gap 4 0 $ D2 = axial component of Juncture gap Y $ Is this constraint the same for both prebuckling and buckling?

O $ Number of poles (places where r=O) in SEGMENT (22)

O $ At how many stations is this segment constrained to ground?

Y $ Is this segment joined to any lower-numbered segments?

1 $ At how may stations is this segment joined to previous segs.?

1 $ INODE = node in current segment (ISEG) of Junction, INODE( 1) 21 $ JSEQ = segment no. of previous segment involved in Junction 11 $ JNODE = node in previous sogant (JSEG) of Junction 1 $ IUSTAR= axial displacement (O=not slaved, 1= slaved) 1 $ IVSTAR= circumferential displacement (O=not slaved, 1= slaved) 1 $ IWSTAR= radial displacement (O=not slaved. 1= slaved) i 1 $ ICHI = meridional rotation (O=not slaved, 1= slaved)

O $ D1 = radial component of Juncture gap O $ D2 = axial component of Juncture gap Y $ Is this constraint the same for both prebuckling and buckling?

, 1 $ Number of poles (places where r=0) in SEQMENT(23) 15 $ IPDLE = nodal point number of pole, IPDLE( 1)

O $ At how many stations is this segment constrained to ground?

Y $ Is this segment Joined to ang lower-numbered segments?

1 $ At how may stations is this segment joined to previous segs.?

1 $ INODE = node in current segment (ISEG) of Junction, INODE( 1) 22 4 JSEQ = segment no. of previous segment involved in Junction 15 4 JNODE = node in previous sogant (JSEG) of Junction 1 $ IUSTAR= axial displacement (O=not slaved, 1= slaved) i l 1

• IVSTAR= circumferential displacement (O=not slaved, 1= slaved) ,

l 1 $ IWSTAR= radial displacement (O=not slaved, 1= slaved) 1 $ ICHI = meridional rotation (O=not slaved, 1= slaved)

O $ D1 = radial component of Juncture gap O $ D2 = axial component of juncture gap j Y $ Is this constraint the same for both prebuckling and buckling?

N $ Given existing constraints, are rigid body modes possible?

f 3

58  !

APPENDIX 6.3 One of the Axisyneetric STAGSC-1 Models of WPPSS-2 59

WPP88-2 COLLAPSE MODEL (SYM) 31 1 1OO1 11 0 6 11 669

3. .1 4.

5 35900 2 5 33 63 63 53 18 3 33 33 33 33 33 93 102/202/312/402/502/11 1 /

1321/2331/3341/4351/5361/5373/

6393/63101/7181/8391/10311 1/

1 1 / 27.9E6 .3 0. .29 / 1.31935E-3 36810.

21 / 27.9E6 .3 O. . 29 / 1.91488E-3 53425.

31 / 27.9E6 .3 O. .29 / 1.25018E-3 34880.

41/ 13.95E6 .3 O. .29 / 1.25018E-3 17440.

51/ 15.486E6 .3 O. .29 / 1.25018E-3 10358.4 61 / 20.144E6 .3 O. .29 / 1.25018E-3 25183.4 1 3 5 5 .25 / .1495 .1495 -2.501 0.

.1495 .1495 -5.002 -2.501

.1495 .1495 -7.502 -5.002

-3.496 O. -7.93 -7.502 O. -3.496 -7.93 -7.502 2365.72/ .19.19-2.5O.

.19 19 -5.0 -2.5

.19 .19 -7.5 -5.

-3.5365 O. -0.13 -7.5 O. 3.5365 -8.13 -7.5 331 1 64. / -3.8125 3.8125 -1.46875 1.46875 41 1 1 11950. / 133. 6028. 18409.

51 1 1 .06 / 14.22 3471.63 17.77 6 3 4 5 .25 / .1495 .1495 -2.501 O.

.1495 .1495 -5.002 -2.501

.1495 .1495 -7.502 -5.002

-3.496 O. -7.93 -7.502

0. -3.496 -7.93 -7.502 1 1 1 5/1 1.3125 O. 1 21 1 5/1 1.25 O. 1 31 1 5/1 1. 5 O. 1 41 1 5 / 1 2.5 O. 1 51 1 5 / 1 2.9375 O. 1 61 1 5 / 1 2.4375 O. 1 71 1 / 1 2.9375 O. 1 81 1 / 1 1.3125 O. 1 91 1 / 1 1.1875 O. 1 C UNIT 1 (CYL) 5 / 5588. 5632.0625 30. 35. 514.5 1 O O. .65625 0 1 0/ 1 / 411 2 1 1 123

10. O. O. O1 / 1 13 1 O. O. O. O1 /313 0464/011 100 1/ 1 1 / -4. 53 1 O O O 1 20 C UNIT 2 (CYL) 5 / 5632.0625 5749.84375 30. 35. 514.5 2 O O. .625 0 1 0/ 1 / 411 5 1 1 123

10. O. O. O1/1 16 1 O. O. O. O1/316 6464 1/1 5 / -4. 53

-40815.97 1 1 1 1 60

r

-40815.97 1 1 1 3

-34488.41 116 1

-34488.41 1 16 3 1OOO10 C UNIT 3 (CYL) 5 / 5749.84375 5867.625 30. 35. 514.5 1 O O. .65625 0 1 0/1 / 411 5 1 1 123 5 O. .36 -27.8 / O 1 3 5841.451

10. O. O. O1 /1 16

10. O. O. O1 /316 6464 1 / 1 3 / -4. 53

-40940.78 1 16 1

-40940.78 1 163 1OOO10 C UNIT 4 (TRANS) 8 / 90. 105.885127 30. 35. 174.0625 340.4375 2 O O. .625 0 1 0

4 / 321 1 1 1 12122 321 1 1231322 321 1 1 131 122 411 3 2 2 1 3 2 2 O. O. O. O1/1 15 2 O. O. O. O1/315 6464 1/1 1 / -4. 53 1OOO10 C UNIT S (CONE) 6 / 5960.806 6184. 30. 35. 501.5665 438.050649 0

411 3 / 37.694 150. 35.5 / 4 11 2 1 O. O. O. O1 / 1 5 18

10. O. O. O 1 / 3 5 18 6464 1 / 1 7 / -4. 53

-3646. 1 1 1 1

-7292. 1 1 12

-3646. 1 1 13

-10894. 5 1 1 14 1

-21789. 1 1 14 2

-10894.5 1 1 14 3 1OOO10 C UNIT 6 (CONE-BOX) 6 / 6184. 6210.5 30. 35. 43E. 050649 430. 50936 0

411 6464 1/1 4 / -4. 53

-16222. 1 1 1 1

-32444. 1 1 1 2

-16222. 1 1 13 1OOO1O C UNIT 7 (PLATE-LOX) 4 / 410. 5069 438.050649 30. 35.

300. .7501 411 6464 0

1OOO10 61

C UNIT 8 (CYL-BOX) 5 / 6184. 6210.5 30. 35. 410.5069 400. 1.25 0 1 411 6464 ,f 0 <

1OOO10 C UNIT 9 (PLATE-BOX) 4 / 410. 5069 430.50936 30. 35.

300. .75 0 1 411 6464 0

1OOO10 C UNIT 10 (CONE) 6 / 6210.5 6236.84 30. 35. 430.50936 423.013607 0

0 4 / 411 121 122 321 1 1213122 321 11332322 321 11313322 6464 1/ 1 1 / -4. 53 1OOO10 C UNIT 11 (CONE) 6 / 6236.84 6496.5 30. 35. 423.013607 349.120375 0

03/ 107.065 107.065 45.53 / 3 3 2 /

1/41181 1 1P3

40. 14.75 -16. /913 6 4 0 4 / 111 111 1 /1 17 / -4. 53

-100295.7 1 19 1 l -100295.7 1 193

-72007.5 1 5 9 1

-72087.5 1 593

-15802.8 1 17 1

-15802.8 1 173

-10370.5 1 57 1

-10370.5 1 5 7 3

-19705.6 1 14 1

-19705.6 1 143

-13547.6 1 54 1

-13547.6 1 543

-22505. 1 1 1 1

-22505. 1 1 13

-16175.6 1 5 1 1

-16175.6 1 513 1OOO1O l

1 62

. _ . - _ _ .____ . - _ - - - - . _ - _ -_ _ _ _ _ ___. = _ _ ._

APPENDIX 6.4 i

User-writtan subroutine for STAGSC-1 Models 63

l i

USER WRITTEN SUBROUTINE WALL FOR STAGSC-1 MODEL SUBROUTINE WALL ( IUNIT, KUNIT, X, Y, Z U, ZETA, ECZ , ILIN, I PLAS)

COMMON /WALLX/ JWALL,KWALL,NLAY,NLIP,NSMRS COMMON /WALLl/ MATL(30) ,TL(30) ,ZETL(30) ,LSO(30)

COMMON /WACO/ IPRCO,ITYME,NETO DATA IT1,IT2,IT3,IT4,ITS,IT6,IT7,IT8,IT9,IT10,IT11 / 11*0 /

ZETA =0.

ILIN=0 IPLAS=1 JWALL=0 KWALL=1 NLAY=1 NLIP=5 NSMRS=0 MATL(1)=1 IF (IUNIT .EQ. 6) GO TO 100 IF (IUNIT .EQ.10) GO TO 200

' IF (IUNIT .EQ. 11) GO TO 300 ECZ=1.46 875 TL(1)=2.*ECZ IF (X .LT. 6 008.26 .AND. ITl .LT. 1) ITYME=0 IF (X .LT. 6008.26) IT1=IT1+1 IF (X .LT. 6008.26) RETU RN ECZ = .7187 5 IF (X .GT. 6122. .AND. Y .GT. 10.) MATL(1) =2 IF(X.GT.6122. . AND.Y.GT.10. . AND. IT2,LT.1) ITYME=0 IF (X .GT. 6122. .AND. Y .GT. 10.) IT2=IT2+1 IF (Y .LT.10.) ECZ=1.21875 IF (Y.LT.10. .AND. IT3 .LT. 1) ITYME=0 IF (Y .LT.10.) IT3 =IT3 +1 TL (1) =2. *ECZ IF ( X.LT.6122. . AND. Y. GT.10. . AND. IT10.LT.1) ITYME=0 IF (X .LT. 6122. .AND. Y .GT. 10. ) IT10 =IT10+1 RETURN 100 CONTINUE IF (Y .GT. 10.) GO TO 50 ECZ=1.21875 TL (1) =2 . *ECZ IF (IT4 .LT. 1) ITYME=0 IT4=IT4+1 RETU RN 50 MATL(1)=2 -

ECZ = .7187 5 TL(1)=2.*ECZ IF (ITS .LT. 1) ITYME=0 IT5=IT5+1 RETURN i 200 CONTINUE IF (Y .GT. 10.) GO TO 150 64

ECZ=1,2187S TL (1) =2.

• ECZ IF (IT6 .LT. 1) ITYME=0 IT6=IT6+1 RETU RN 150 MATL (1) =2 ECZ = .7187 5 TL ( 1) =2 .

• ECZ IF (IT7 .LT. 1) ITYME=0 IT7 =IT7 +1 RETU RN 300 CONTINUE ECZ = .6 87 5 IF (X .LT. 6343. .AND. ITll .LT. 1) ITYME=0 IF (X .LT. 6343.) ITll=ITll+1 IF (X .GT. 6343.) ECZ=.65625 IF (X .GT. 6343. .AND. IT8 .LT. 1) ITYME=0 IF (X .GT. 6343.) IT8=IT8+1 IF (X .GT. 6450.) ECZ = .7187 5 IF (X .GT. 6450. .AND. IT9 .LT. 1) ITYME=0

. IF (X .GT. 6450.) IT9=IT9+1 I

TL (1) =2.

• ECZ RETU RN END 65

APPENDIX 6.5 Input data for STAGSC-1 model of WPPSS-2, including penetration 66

INPUT DATA FOR STAGSC-1 MODEL WITH PENETRATION WPPSS-2 COLLAPSE MODEL 3111001 11 1 6 11 899

1. 1. 3 .

0 35900 1 10 9 19 3 19 6 19 6 19 5 19 18 19 3 19 3 19 3 19 3 19 3 19 108/208/318/408/508/111/

1321/2331/3341/4351/5361/5373/

6393/63101/7181/8391/103111/

920197338 1 1 / 27.9E6 .3 0. .2 9 / 1.3193 5E-3 36 810.

2 1 / 27.9E6 .3 0. .29 / 1.91488E-3 53425.

3 1 / 27.9E6 .3 0. .29 / 1.25018E-3 3 4880.

4 1 / 31.E6 .3 0. .29 / 1.25018E-3 3 87 52.

5 1 / 15.5E6 .3 0. .29 / 1.25018E-3 19376.

6 1 / 40.29E6 .3 0. .29 / 1.25018E-3 50366.

7 1 / 20.145E6 .3 0. .2 9 / 1.25018E-3 25183.

8 1 / 13.95E6 .3 0. .2 9 / 1.25018E-30.17 4 40.

1345 .25 / .1495 .1495 -2.501

.1495 .1495 -5.002 -2.501 ,

.1495 .1495 -7.502 -5.002

-3.496 0. -7.93 -7.502

0. -3.496 -7.93 -7.502 ,

2 3 5 5 .25 / .1495 .1495 -2.501 0.

.1495 .1495 -5.002 -2.501

.1495 .1495 -7.502 -5.002

-3.496 0. -7.93 -7.502

0. -3.496 -7 .93 -7.502 3365 .72 / .19 .19 -2.5 0.

.19 .19 -5.0 -2.5

.19 .19 -7.5 -5.

-3.5365 0. -8.13 -7.5

0. 3.5365 -8.13 -7.5 4375.72/ .19 .19 -2.5 0.

.19 .19 -5.0 -2.5

.19 .19 -7.5 -5.

-3.5365 0. -8.13 -7.5

0. 3.5365 -8.13 -7.5 5335 .25 / .1495 .1495 -2.501 0.

.1495 .1495 -5.002 -2.501

.1495 .1495 -7.502 -5.002

-3.496 0. -7.93 -7.502

0. -3.496 -7.93 -7.502 6385 .25 / .1495 .1495 -2.501 0.

.1495 .1495 -5.002 -2.501 67

.1495 .1495 -7.502 -5.002

-3.496 0. -7.93 -7.502

0. -3.496 -7.93 -7.502 7 3 1 1 64. / -3.8125 3.8125 -1.46875 1.46875 8 1 1 1 11950. / 133. 6028. 18409.

9111 .06 / 14.22 3471.63 17.77 1 1 1 5 / 1 1.3125 0. 1 2 1 1 5 / 1 1.25 0. 1 3 1 1 5 / 1 1.5 0. 1 4 1 1 5 / 1 2.5 0. 1 5 1 1 5 / 1 2.9375 0. 1 6 1 1 5 / 1 2.4375 0. 1 711/12.93750.1 8 1 1 / 1 1.3125 0. 1 911/11.18750.1 C UNIT 1 (CYL) 5 / 5588. 5632.0625 0. 35. 514.5 100, .65625 0 1 002/10.25./810 2 / 411 2 2 1 1 2 5 0 0 0 4 411 2 5 1 9 2 11 0 0 0 2 2 0. O. O. 0 1 / 1 1 3 1 0. O. O. 0 1 / 5 1 3

10. O. O. 01/ 913 10.O.O.01/1113 1 0. O. O. 0 1 / 13 1 3 10.O.O.01/1513 1 0. O. O. 0 1 / 17 1 3 20.O.O.01/1913 4464 1 / 1 1 / -4. 5 3 1 20 0 0 1 20 C UNIT 2 (CYL) 5 / 5632.0625 5749.84375 0. 35. 514.5 200. .625 0 1 0 0 2 / 10. 25. / 8 10 2 / 411 5 2 1 1 2 5 0 0 0 4 411 5 5 1 9 2 11 0 0 0 2 2 0. O. O. 01/ 1 16 1 0. O. O. 0 1 / 5 1 6

10. O. O. 01/ 916 10.O.O.01/1116 1 0. O. O. 0 1 / 13 1 6 1 0. O. O. 0 1 / 15 1 6 1 0. O. O. 0 1 / 17 1 6

' 20.O.O.01/1916 6464 1 / 1 17 / -4. 53

-40815.97 1 1 1 1

-81631.93 1 1 1 5

-81631.93 1 1 1 9

-81631.93 1 1 1 11

-81631.93 1 1 1 13

-81631.93 1 1 1 15

-81631.93 1 1 1 17 68

l l

l l

-40815.97 1 1 1 19

-34488.41 1 1 6 1

-68976.81 1 1 6 5

-68976.81 1 1 6 9

-68976.81 1 1 6 11

-68976.81 1 1 6 13

-68976.81 1 1 6 15s

-68976.81 1 1 6 17

-34488.41 1 1 6 19 1 20 0 0 1 20 C UNIT 3 (CYL) 5 / 5749.84375 5867.625 0. 35. 514.5 1 0 0. .65625 0 1 0 2 2 / 91.60725 26.17 / 4 1 / 10. 25. / 8 10 2 / 411 5 2 1 1 2 5 0 0 0 4 411 5 5 1 9 2 11 0 0 0 2 9 0. .36 -27.8 / 0 1 19 5841.451 2 0. O. O. 01/ 1 16 1 0. O. O. 0 1 / 5 1 6

10. O. O. 01/ 916 10.O.O.01/1116 1 0. O. O. 0 1 / 13 1 6 10.O.O.01/1516 1 0. O. O. 0 1 / 17 1 6 20.O.O.01/1916 6464 1/19/-4.53

-40940.78 1 1 6 1

-81881.57 1 1 6 5

-81881.57 1 1 6 9

-81881.57 1 1 6 11

-81881.57 1 1 6 13

-81881.57 1 1 6 15

-81881.57 1 1 6 17

-40940.78 1 1 6 19 1 20 0 0 1 20 C UNIT 4 (TRANS) 8 / 90. 105.885127 0. 35. 174.0625 340.4375 200. .625 0 1 002/10.25./810 8 / 321 1 2 1 1 2 3 1 5 0 4 321 1 2 1 1 2 1 2 3 0 4 321 1 2 1 5 2 3 2 5 0 4 411 3 4 2 1 3 3 0 0 0 2 321 1 5 1 9 2 10 1 11 0 2 321 1 5 1 9 2 9 2 10 0 2 321 1 5 1 11 2 10 2 11 0 2 411 3 10 2 9 3 10 4 0. O. O. 0 1 / 1 1 5 3 0. O. O. 01/ 515 3 0. O. O. 01/ 915 30.O.O.01/1115 3 0. O. O. 0 1 / 13 1 5 30.O.O.01/1515 3 0. 0. O. 0 1 / 17 1 5 69

40.O.O.01/1915 6464 1 / 1 1 / -4. 5 3 1 20 0 0 1 20 C UNIT 5 (CONE) 6 / 5960.806 6184. O. 35. 501.5665 438.050649 0

0 3 2 / 37.694 150. 35.5 / 4 11 2 / 10. 25. / 8 10 9 / 321 1 4 1 1 2 2 1 3 0 2 321 1 4 1 1 2 1 2 2 0 2 321 1 4 1 3 2 2 2 3 0 2 411 3 8 2 1 3 2 411 1 8 16 1 17 2 3211417218118302 321 1 4 17 1 18 1 17 2 0 2 321 1 4 17 3 17 2 18 3 0 2 411 17 10 1 9 2 10 6 0. O. O. 0 1 / 1 16 18 5 0. O. O. 0 1 / 5 16 18 5 0. O. O. 0 1 / 9518 5 0. O. O. 0 1 / 11 5 18 5 0. O. O. 0 1 / 13 5 18 50.O.O.01/15518 5 0. O. O. 0 1 / 17 5 18 60.O.O.01/19518 6464 1 / 1 27 / -4. 53

-3646. 1 1 1 1

-7292. 1 1 1 3

-7292. 1 1 1 5

-7292. 1 1 1 7

-7292. 1 1 1 9

-7292. 1 1 1 10 1 -7292. 1 1 1 11

-7292. 1 1 1 12

-7292. 1 1 1 13

-7292. 1 1 1 14 l

-7292. 1 1 1 15 l -7292. 1 1 1 16

-7292. 1 1 1 17

-7292. 1 1 1 18

-3646. 1 1 1 19

-29052. 1 1 14 9 I

-29052. 1 1 14 10 t

-29052. 1 1 14 11

-29052. 1 1 14 12

-29052. 1 1 14 13

-29052. 1 1 14 14

-29052. 1 1 14 15

-29052. 1 1 14 16

-29052. 1 1 14 17

-29052. 1 1 14 18

-14584. 1 1 14 19 1 20 0 0 1 20 C UNIT 6 (CONE-BOX) 70

6 / 6184. 6210.5 0. 35. 438.050649 430.50936 0

002/10.25./810 2 / 411 2 4 1 1 2 3 0 0 0 2 411 2 10 1 9 2 10 6464 1 / 1 16 / -4. 5 3

-16222. 1 1 1 1

-32444. 1 1 1 3

-32444. 1 1 1 5

-32444. 1 1 1 7

-32444. 1 1 1 9

-32444. 1 1 1 10

-32444. 1 1 1 11

-32444. 1 1 1 12

-32444. 1 1 1 13

-32444. 1 1 1 14

-32444. 1 1 1 15

-32444. 1 1 1 16

-32444. 1 1 1 17

-32444. 1 1 1 18

-16222. 1 1 1 19 1 20 0 0 1 20 C UNIT 7 ( PL ATE-BOX) 4 / 410.5069 438.050649 0. 35.

300. .7501 002/10.25./810 2 / 411 2 4 1 1 2 3 0 0 0 2 411 2 10 1 9 2 10 6464 0

1 20 0 0 1 20 C UNIT 8 ( CYL-BOX) 5 / 6184. 6210.5 0. 35. 410.5069 4 0 0. 1.25 0 1 002/10.25./810 2 / 411 2 4 1 1 2 3 0 0 0 2 411 2 10 1 9 2 10 6464 0

1 20 0 0 1 20 C UNIT 9 (PLATE-BOX) 4 / 410.5069 430.50936 0. 35.

3 0 0. .7501 002/10.25./810 2 / 411 2 4 1 1 2 3 0 0 0 2 411 2 10 1 9 2 10 6464 0

1 20 0 0 1 20 C UNIT 10 (CONE) 6 / 6210.5 6236.84 0. 35. 430.50936 423.013607 0

002/10.25./810 8/ 411 1 4 1 1 2 3 0 0 0 2 71

321 1 2 2 3 3 1 3 5 0 4 321 1 2 2 1 3 1 2 3 0 4 321 1 2 2 5 2 3 3 5 0 4 411 1 10 1 9 2 10 321 1 5 2 10 3 9 3 11 0 2 321 1 5 3 9 2 10 2 9 0 2 321 1 5 2 11 2 10 3 11 0 2 6464 1 / 1 1 / -4. 5 3 1 20 0 0 1 20 C UNIT 11 (CONE) 6 / 6236.84 6496.5 0. 35. 423.013607 349.120375 0

0 3 2 / 107.065 107.065 45.53 / 3 3 2 / 10. 25. / 8 10 2 / 411 8 2 1 1 2 5 0 0 0 4 411 8 5 1 9 2 11 0 0 0 2 8 0. 14.75 -16. / 9 1 19 6404/111111 1 / 1 65 / -4. 5 3

-100295.7 1 1 9 1

-200591.4 1 1 9 5

-200591.4 1 1 9 9

-200591.4 1 1 9 11

-200591.4 1 1 9 13

-200591.4 1 1 9 15

-200591.4 1 1 9 17

-100295.7 1 1 9 19

-72087.5 1 5 9 1

-144175. 1 5 9 5

-144175. 1 5 9 9

-144175. 1 5 9 11

-144175. 1 5 9 13

-144175. 1 5 9 15

-144175. 1 5 9 17

-72087.5 1 5 9 19

-15802.8 1 1 7 1

-31605.6 1 1 7 5

-31605.6 1 1 7 9

-31605.6 1 1 7 11

-31605.6 1 1 7 13

-31605.6 1 1 7 15

-31605.6 1 1 7 17

-15802.8 1 1 7 19

-10370.6 1 5 7 1

-20741.2 1 5 7 5

-20741.2 1 5 7 9

-20741.2 1 5 7 11

-20741.2 1 5 7 13

-20741.2 1 5 7 15

-20741.2 1 5 7 17

-10370.6 1 5 7 19

-19705.7 1 1 4 1

-39411.3 1 1 4 5

-39411.3 1 1 4 9

-39411.3 1 1 4 11 72

-39411.3 1 1 4 13

-39411.3 1 1 4 15

-39411.3 1 1 4 17

-19705.7 1 1 4 19

-13547.6 1 5 4 1

-27095.1 1 5 4 5

-27095.1 1 5 4 9

-27095.1 1 5 4 11

-27095.1 1 5 4 13

-27095.1 1 5 4 15

-27095.1 1 5 4 17

-13547.6 1 5 4 19

-22505. 1 1 1 1

-45010. 1 1 1 5

-45010. 1 1 1 9

-45010. 1 1 1 11

-45010. 1 1 1 13

-45010. I 1 1 15

-45010. 1 1 1 17

-22505. 1 1 1 19

-16175.5 1 5 1 1

-32351. 1 5 1 5

-32351. 1 5 1 9

-32351. 1 5 1 11

-32351. 1 5 1 13

< -32351. 1 5 1 15

-32351. 1 5 1 17

-16175.5 1 5 1 19 1 20 0 0 1 20 C ELEMENT UNIT C NODES 15 51 25 52 35 53 45 54 55 55 65 56 7 0 0 0 424.13 52.992 483.6 111 111 8 0 0 0 424.13 63.535 482.53 111 111 9 0 0 0 424.13 74.048 481.03 111 111 10 0 0 0 437.77 73.45 477.14 111 111 11 5 79 12 5 89 13 5 99 14 5 10 9 15 5 11 9 16 5 12 9 175139 18 5 14 9 19 0 0 0 533.22 69.261 449.93 111 111 20 0 0 0 546.86 68.663 446.04 111 111 21 0 0 0 546.86 58.915 447.44 111 111 22 5 16 7 23 5 16 6 24 5 16 5 73

~ -

25 5 16 4 26 5 16 3 27 5 16 2 28 5 16 1 29 0 0 0 413.60738 21.36470 489.33211 111 111 30 0 0 0 417.64957 31.95809 487.58621 111 111 31 0 0 0 423.66002 42.43603 485.04604 111 111 32 0 0 0 428.73659 49.01954 482.95327 111 111 33 0 0 0 437.77273 57.85419 479.34968 111 111 34 0 0 0 451.40909 66.80427 474.21289 111 111 35 0 0 0 465.04546 72.15686 469.44910 111 111 36 0 0 0 478.68182 74.68944 465.06977 111 111 37 0 0 0 492.31818 74.68944 461.08585 111 111 38 0 0 0 505.95455 72.15685 457.50767 111 111 39 0 0 0 519.59091 66.80427 454.34482 111 111 40 0 0 0 533.22728 57.85419 451.60602 111 111 41 0 0 0 546.86364 43.12196 449.29904 111 111 42 0 0 0 552.04266 34.59876 448.53743 111 111 43 0 0 0 554.50744 29.37640 448.19728 111 111 44 0 0 0 557.90737 19.54926 447.75176 111 111 45 0 0 0 410.50000 0.00000 507.80500 101 010 i 46 0 0 0 410.50000 10.70455 507.80500 111 111 47 0 0 0 413.60738 21.36470 507.80500 111 111 48 0 0 0 417.64957 31.95809 507.80500 111 111 49 0 0 0 423.66002 42.43603 507.80500 111 111 50 0 0 0 428.73659 49.01954 507.80500 111 111 51 0 0 0 437.77273 57.85419 507.80500 111 111 52 0 0 0 451.40909 66.80427 507.80500 111 111 53 0 0 0 465.04546 72.15686 507.80500 111 111 54 0 0 0 478.68182 74.689'44 507.80500 111 111 55 0 0 0 492.31818 74.68944 507.80500 111 111 56 0 0 0 505.95455 72.15686 507.80500 111 111 57 0 0 0 519.59091 66.80427 507.80500 111 111 58 0 0 0 533.22728 57.85419 507.80500 111 111 59 0 0 0 546.96364 43.12196 507.80500 111 111 60 0 0 0 552.04266 34.59876 507.80500 111 111 i

61 0 0 0 554.50744 29.37640 507.80500 111 111 62 0 0 0 557.90737 19.54926 507.80500 111 111 63 0 0 0 560.50000 9.76065 507.80500 111 111 64 0 0 0 560.50000 0.00000 507.80500 101 010 65 5 57 66 5 58 67 5 59 I

68 5 6 9 69 5 15 9 i 705169 71 5 16 8 l 72 0 0 0 410.50000 0.00000 577.00000 101 010 73 0 0 0 410.50000 10.70455 577.00000 111 111 74 0 0 0 413.60738 21.36470 577.00000 111 111 75 0 0 0 417.64957 31.95809 577.00000 111 111 76 0 0 0 423.66002 42.43603 577.00000 111 111 l 77 0 0 0 428.73659 49.01954 577.00000 111 111 1

78 0 0 0 437.77273 57.85419 577.00000 111 111 79 0 0 0 451.40909 66.80427 577.00000 111 111 74 ,

i l

80 0 0 0 465.04546 72.15686 577.00000 111 111 81 0 0 0 478.68182 74.68944 577.00000 111 111 82 0 0 0 492.31818 74.68944 577.00000 111 111 83 0 0 0 505.95455 72.15686 577.00000 111 111 1 I

84 0 0 0 519.59091 66.80427 577.00000 111 111 I 85 0 0 0 533.22728 57.85419 577.00000 111 111 86 0 0 0 546.86364 43.12196 577.00000 111 111 87 0 0 0 552.04266 34.59876 577.00000 111 111 88 0 0 0 554.50744 29.37640 577.00000 111 111 89 0 0 0 557.90737 19.54926 577.00000 111 111 90 0 0 0 560.50000 9.76065 577.00000 111 111 91 0 0 0 560.50000 0.00000 577.00000 101 010 92 0 0 0 485.50000 0.00000 592.84000 101 010 C BEAMS 1 2 45 211 3 0. 3.8125 -1.46875 2 29 46 211 3 0. 3.8125 -1.46875 29 30 47 211 3 0. 3.8125 -1.46875 30 31 48 211 3 0. 3.8125 -1.46875 31 32 49 211 3 0, 3.8125 -1.46375

, 32 33 50 211 3 0. 3.8125 -1.4t875 l 33 34 51 211 3 0. 3.8125 -1.46875 34 35 52 211 3 0. 3.8125 -1.46875 35 36 53 211 3 0. 3.8125 -1.46875 36 37 54 211 3 0, 3.8125 -1.46875 37 38 55 211 3 0. 3.8125 -1.46875 38 39 56 211 3 0. 3.8125 -1.46875 39 40 57 211 3 0. 3.8125 -1.46875 40 41 58 211 3 0. 3.8125 -1.46875 41 42 59 211 3 0. 3.8125 -1.46875 42 43 60 211 3 0. 3.8125 -1.46875 43 44 61 211 3 0. 3.8125 -1.46875 44 27 62 211 3 0. 3.8125 -1.46875 27 28 63 211 3 0. 3.8125 -1.46875 C PLATES 29 3 2 321 5 0. 1.46875 0 1 3 29 4 321 5 0. 1.46875 0 1 30 4 29 321 5 0. 1.46875 0 1 4 30 5 321 5 0. 1.46875 0 1 31 5 30 321 5 0. 1.46875 0 1 5 31 6 321 5 0. 1.46875 0 1 7 6 31 321 5 0. 1.46875 0 1 6 7 8 321 5 0. 1.46875 0 1 8 65 6 321 5 0. 1.46875 0 1 65 8 66 321 5 0. 1.46875 0 1 9 66 8 321 5 0. 1.46875 0 1 66 9 68 321 5 0. 1.46875 0 1 68 67 66 321 5 0. 1.46875 0 1 32 7 31 321 6 0. 1.21875 0 1 7 32 33 321 6 0. 1.21875 0 1 7 33 8 321 6 0. 1.21875 0 1 8 33 9 321 6 0. 1.21875 0 1 10 9 33 321 6 0. 1.21875 0 1 9 10 11 321 6 0. 1.21875 0 1 11 68 9 321 6 0. 1.21875 0 1 33 34 10 321 6 0. 1.21875 0 1 75

w

/

10 34 12 321 6 0. 1.21875 0 1 12 11 10 321 6 0. 1.21875 0 1 34 35 12 321 6 0. 1.21875 0 1 13 12 35 321 6 0. 1.21875 0 1 35 36 13 321 6 0, 1.21875 0 1 14 13 36 321 6 0. 1.21875 0 1 36 37 14 321 6 0. 1.21875 0 1 15 14 37 321 6 0. 1.21875 0 1 37 38 16 321 6 0. 1.21875 0 1 16 15 37 3 21 6 0. 1.2187 5 ~0 1 38 39 17 321 6 0. 1.21875 0 1 17 16 38 321 6 0. 1.21875 0 1 19 39 40 321 6 0. 1.21875 0 1 39 19 17 321 6 0. 1.21875 0 1 18 17 19 321 6 0. 1.21875 0 1 21 40 41 321 6 0. 1.21875 0 1 40 21 20 321 6 0. 1.21875 0 1 20 19 40 321 6 0. 1.21875 0 1 19 20 18 321 6 0. 1.21875 0 1 69 18 20 321 6 0. 1.21875 0 1 70 69 71 321 6 0. 1.21875 0 1 20 71 69 321 6 0, 1.21875 0 1 71 20 21 321 6 0. 1.21875 0 1 21 22 71 321 6 0. 1.21875 0 1 22 21 23 321 6 0. 1.21875 0 1 23 21 41 321 6 0. 1.21875 0 1 23 41 24 321 6 0. 1.21875 0 1 42 24 41 321 6 0. 1.21875 0 1 24 42 43 321 6 0. 1.21875 0 1 43 25 24 321 6 0. 1.21875 0 1 25 43 44 321 6 0. 1.21875 0 1 44 26 25 321 6 0. 1.21875 0 1 26 44 27 321 6 0. 1.21875 0 1 73 72 92 321 9 0. .59375 74739232190. .59375 75 74 92 321 9 0. .59375 76 75 92 321 9 0. .59375 77769232190. .59375 78779232190. .59375 79789232190. .59375 80799232190. .59375 81 80 92 321 9 0. .59375 82 81 92 321 9 0. .59375 83 82 92 321 9 0. .59375 84 83 92 321 9 0. .59375 85 84 92 321 9 0. .59375 86 85 92 321 9 0. .59375 87869232190. .59375 88879232190. .59375 89 88 92 321 9 0. .59375 90899232190. .59375 91909232190. .59375 1 45 46 2 411 7 0. 1.46875 2 46 47 29 411 7 0. 1.46875 29 47 48 30 411 7 0. 1.46875 76

l l

30 48 49 31 411 7 0. 1.46875 1 31 49 50 32 411 7 0. 1.46875 32 50 51 33 411 7 0. 1.46875 33 51 52 34 411 7 0. 1.46875 34 52 53 35 411 7 0. 1.46875 35 53 54 36 411 7 0. 1.46875 36 54 55 37 411 7 0. 1.46875 37 55 56 38 411 7 0. 1.46875 38 56 57 39 411 7 0. 1.46875 39 57 58 40 411 7 0. 1.46875 40 58 59 41 411 7 0. 1.46875 41 59 60 42 411 7 0. 1.46875 42 60 61 43 411 7 0. 1.46875 43 61 62 44 411 7 0. 1.46875 44 62 63 27 411 7 0. 1.46875 27 63 64 28 411 7 0. 1.46875 4572734641180. .65625 4673744741180. .65625 l 4774754841180. .65625 4875764941180, .65625 49 76 77 50 411 8 0. .65625 5077785141180. .65625 5178795241180. .65625 5279805341180. .65625 5380815441180. .65625 54 81 82 55 411 8 0. .65625 55 82 83 56 411 8 0. .65625 56 83 84 57 411 8 0. .65625 5784855841180. .65625 58 85 86 59 411 8 0. .65625 5986876041180. .65625 60 87 88 61 411 8 0. .65625 61 88 89 62 411 8 0. .65625 62 89 90 63 411 8 0. .65625 6390916441180. .65625 1/102 1 20 0 0 1 20 77

W 9

TABLES 1

79

Table 2.1 Maximum plastic strain predicted by B0SOR5. Model is shown in Fig. 2.1.

PLASTIC STRAINING OCCURS AT THE FOLLOUING STATIONS...

SHELL NERIDIDHAL MERIDIDHAL CIRCUMFERENTIAL SEGMENT STATION MAX. PLASTIC MAX. PLASTIC STRAIH(%) STRA!H(%)

!= 1 1.8614E+00 2.3498E-02 1 2 1.2050E+00 1.6037E-02 1 8 -1.5012E-01 0.0000E+00 t = 2.0 1 9 -5.6550E-01 0.0000E+00 1 10 -6.0002E-01 0.0000E+00 1 11 -2.7533E-01 0.0000E+00 ABSOLUTE _ VALUES OF THE NAXIMUN PLASTIC STRA!HS IH % =

NERIDIDHAL CONPONENT = 1.8614E+00, CIRC. COMPONENT = 2.3498E-02 l SHELL NERIDIDHAL MERIDIDHAL CIRCUMFERENTIAL i SEGMENT STATION MAX. PLASTIC MAX. PLASTIC

! STRAIH(x) STRAIH(x) 1 1 3.6744E+00 3.0022E-02 1 2 1.7104E+00 2.3427E-02 1 0 -3.1627E-01 0.0000E+00 1 9 -0.0992E-01 9.3251E-03 1 10 -8.1312E-01 9.2663E-03 t = 2. 2 1 11 -3.2185E-01 0.0000E+00 4 20 -1.6965E-02 0.0000E+00 4 21 -5.6890E-02 0.0000E+00 7 1 -0.7631E-03 4.8061E-03 7 2 -6.3822E-03 3.5509E-03 ABSOLUTE VALUES OF THE MAXIMUM PLASTIC STRAlHS IN % =

MERIDIGNAL CONPONENT = 3.6744E+00, CIRC. COMP 0HEHT = 3.0022E-02 PLASTIC STRAINING OCCURS AT THE FOLLOUIHG STATIONS...

SHELL MERIDIDHAL MERIDIDHAL CIRCUMFERENTIAL SEGMENT STATIDH MAX. PLASTIC MAX. PLASTIC STRA!H(%) STRA IH (%)

1 1 4.7475E+00 3.0522E-02 1 2 2.4067E+00 2.8306E-02 1 8 -4.0880E-01 1.2501E-03 1 9 -1.2764E+00 2.7671E-02 1 10 -1.1238E+00 2.3606E-02 t = 2.4 1 11 -3.2185E-01 0.0000E+00 4 20 -9.8875E-02 0.0000E+00 4 21 -2.9168E-01 0.0000E+00 7 1 -2.2705E-02 1.2245E-02 7 2 -2.0042E-02 1.0958E-02 ABSOLUTE VALUES OF THE MAXIMUM PLASTIC STRAINS IH % =

MERIDIONAL COMPOHEHT = 4.7475E+00, CIRC. COMPONENT = 3.0522E-02 81

Table 2.1 (continued)

PLASTIC STRAINING OCCURS AT THE FOLLOWING STATIONS...

SHELL MERIDIDHAL NERIDIONAL CIRCUMFERENTIAL SEGMENT STATIDH MAX. PLASTIC MAX. PLASTIC STRAIH(x) STRAIH(X) 1 1 5.9151E+00 3.0662E-02 1 2 3.2349E+00 3.0134E-02 1 0 -4.6426E-01 9.8189E-03 1 9 -1.9604E+00 4.8552E-02 1 10 -1.4597E+00 3.8300E-02 t = 2.6 1 11 -3.2185E-01 4.9335E-03 4 20 -2.3255E-01 0.0000E+00 4 21 -4.4835E-01 0.0000E+00 7 1 -3.8220E-02 2.0193E-02 7 2 -3.3096E-02 1.7785E-02 A8 SOLUTE VALUES OF THE NAXIMUN PLASTIC STRAlHS IN X =

MERIDIDHAL COMPONENT = 5.9151E+00, CIRC. COMP 0HEHT = 4.8552E-02 PLASTIC STRAINING OCCURS AT THE FOLLOUING STATIONS...

SHELL NERIDIONAL MERIDIDHAL CIRCUMFERENTIAL SEGMENT STATIDH MAX. PLASTIC MAX. PLASTIC STRAIHCx) STRAIN (x) 1 1 1.0691E+01 3.0926E-02 1 2 4.0557E+00 3.0735E-02 1 8 -7.1296E-01 2.8154E-02 1 9 -2.80llE400 6.5913E-02 1 la -1.6375E+00 4.8094E-02 1 11 -3.2185E-al 1.4416E-02 t = 2.8 1 12 -1.3927E-03 0.0000E+00 4 20 -3.6482E-01 0.0000E+00 4 21 -6.4419E-01 7.5879E-03 7 1 -6.5521E-02 3.3009E-02 7 2 -5.9010E-02 3.0385E-02 7 3 -5.6880E-03 3.6577E-03 A8 SOLUTE VALUES OF THE NAXIMUM PLASTIC STRA!HS IN X =

MERIDIDHAL COMPONENT = 1.0691E+01, CIRC. COMPONENT = 6.5913E-O' 82

Table 2.1 (conclusion)

PLASTIC STRAlHING OCCURS AT THE FOLLOU1HG STATIONS...

SHELL MERIDIONAL MERIDIONAL CIRCUMFERENTIAL SEGMENT STATION MAX. PLASTIC MAX. PLASTIC STRAIH(x) STRAlH(x) 1 1 1.4575E+01 3.1141E-02 1 2 5.4325E+00 3.1183E-02 1 3 -7.5081E-03 2.0814E-03 1 4 -1.4012E-03 0.0000E+00 1 5 -1.4394E-03 0.0000E+00 1 6 -1.3916E-02 7.6825E-03 1 7 -4.3408E-02 2.2602E-02 1 8 -1.4206E+00 6.3747E-02 1 9 -3.3665E+00 8.1225E-02 1 10 -2.3965E+00 7.5590E-02 1 11 -3.2185E-01 3.7655E-02 1 12 -6.1793E-02 2.9640E-02 1 13 -5.6680E-02 2.6749E-02 2 1 -4.5912E-02 2.3042E-02 t = 3.0 2 2 -3.8056E-02 1.9087E-02 2 3 -3.6315E-02 1.5436E-02 2 4 -1.8454E-02 7.3376E-03 2 5 -1.0087E-02 3.6029E-03 2 6 -4.8188E-03 1.4928E-03 3 19 -3.0C75E-03 0.0000E+00 3 20 -2.5857E-02 0.0000E+00 3 21 -3.3183E-02 0.0000E+00 4 20 -5.0827E-01 7.3011E-03 4 21 -9.8541E-01 2.3152E-02 7 1 -9.4329E-02 4.5122E-02 7 2 -8.6369E-02 4.2375E-02 7 3 -1.4821E-02 9.4877E-03 19 39 -3.2751E-03 1.8441E-03 ABSOLUTE VALUES OF THE MAX 1 MUM PLASTIC STRAIHS IN x =

MERIDIONAL COMPONENT = 1.4575E+01, CIRC. COMP 0HEHT = 8.1225E-02 83

- -- - . _ _ _ - - - - - _ _ _ )

I Table 2.2 Maximum plastic strain predicted by BOSOR5. Model is shown in Fig. 2.17.

PLASTIC STRAlHING OCCURS AT THE FOLLOUING STATIONS...

4 SHELL NERIDIDHAL NERIDIONAL CIRCUNFERENTIAL SEGMENT STATIDH MAX. PLASTIC MAX. PLASTIC STRAlH(X) STRAIH(X) 1 19 -0.3242E-02 0.0000E+00 1 20 -1.7978E-01 0.0000E+00 i 1 21 -1.9333E-01 0.0000E+00 2 20 -7.0345E-01 2.0052E-02 t = 3.2 2 21 -1.3899E+00 3.9044E-02 5 1 -1.2742E-01 5.7325E-02 5 2 -1.1622E-01 5.3964E-02 5 3 -2.2947E-02 1.4590E-02 1 18 -3.1213E-03 0.0000E+00 1 19 -1.7481E-01 0.0000E+00 1 20 -3.1215E-01 2.6868E-03 1 21 -3.3002E-01 3.0817E-e3  ;

2 20 -9.4503E-01 3.4697E-02 2 21 -1.7776E+30 5.1716E-02 l 4 6 -7.2447E-03 0.0000E+00 t = 3. 4 4 7 -1.9166E-03 0.0000E+00 4 15 -1.2302E-03 0.0000E+00 5 1 -1.6074E-01 6.8047E-02 1

5 2 -1.4673E-01 6.4489E-02 S 3 -3.5363E-02 2.2251E-02 5 4 -7.1220E-03 5.1668E-03 1

i 1 18 -3.1213E-03 0.0000E+00 1 19 -1.7726E-01 1.9415E-03 1 20 -0.0963E-01 1.7698E-02 1 21 -8.9635E-01 1.9515E-02 2 19 -9.5224E-03 6.2896E-03 2 20 -1. 3444E+00 5.3380E-02 2 21 -1.8662E+00 5.7991E-02 4 1 -1.3089E-02 1.0762E-G'2 4 2 -1.2165E-02 1.003?E-02 4 3 -6.3347E-03 5.6470E-03 t = 3.6 4 4 -2.8907E-03 2.6789E-03 4 5 -1.3579E-03 1.2775E-03 4 6 -7.2447E-03 0.0000E+00 4 7 -1.9166E-03 0.0000E+00 4 13 -2.2228E-03 1.7383E-03 4 14 -1.0163E-02 7.1112E-03 4 15 -1.1311E-02 7.8616E-03 5 1 -1.8773E-01 7.5879E-02 5 2 -1.7102E-01 7.2133E-02 5 3 -4.8273E-02 2.9916E-02 5 4 -1.3638E-02 9.8503E-03 84

a I

Table 3.1 Materials, thicknesses, and longitudinal stiffeners in the STAGSC-1 model of the WPPSS-2 containment (Fig.3/t).

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WPPSS-2 PRIMARY CONTAINHENT, DVERALL BOSOR4 INITIAL UNDEFORMED STRUCTURE o INMM N MD G MT 7200. INDIC =1.0 I I I I I I I I 7000. _ @ _

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         -1000-800.-600.-400.-200. 0.0 200. 400. 600. 800. 1000.1200.

R Fig. 2.1 BOSOR4 and BOSORS discretized, segmented model of the entire WPPSS-2 steel containment vessel 91

WPPSS-2 PRIMARY CONTRINMENT, DVERALL BOSOR4 10 INITIAL UNDEFORMED STRUCTURE RINGS HRVE VRRIRBLE LORDS ONLY 7200. INDIC =1.0

                    ,     ,   ,    ,          i      i         i  i  i 7000. _

y *, --

                                              *y+

6800. _

                                                 +m                       -
                                                  ,=                              ,

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                                                         ]p'              -       '

5600. _ - IF 5400. 1 (1w P - 5200. _ - 5000. I I I I I I I I I

           -1000-800.-600.-400.-200. O.0 200. 400. 600. 800. 1000.1200.

R msone Fig. 2.2 Line loads and moments applied at many meridional stations in order to simulate the equivalent static loading specified by PDM it its final stress report.- 92

                                                                         =                 .__ .

WPPSS-2 PRIMARY CONTAINMENT, DVERALL BDSOR4 2. 0 ' DEFORMED STRUCTURE LORD STEP 1. LORD = 0.000E+00 PRESTRESS INDIC =0.0 N l l l l 31 I I I I 7000. _ 6800. _ 6500. _ 6400. _ G , 6200. _ k k f s 6000. _ 5800. _ 5600. _ 5400. _ l - 5200. _ - 5000 I I I l I I I I I I I1000.800.-600.-400.-200. 0!0 200. 400. 600. 800. 1000.1200. R sosaae Fig. 2.3 Meridional locations of discrete rings, many of which are " phony", their purpose being to provide a station at which to " hang" a line load and moment 93

4 WPPSS-2 PRIMARY CONTRINMENT, DVERALL BOSOR4 2. 0 DEFORMED STRUCTURE LORD STEP 1. LDAD = 1.000E+00 PRESTRESS 7200. " * *' I I I I I I I I I 7000. _ _ S800. _ i _ q 4 6600. _ _ external pressure only 6200. _ [ _ 2 - 6000. _. _ 5800. . _ o 5600. _ ll ~ ll l 5400. _ l _ 5200. _ _ 5000. I I I I I I I I I I

            -1000-800.-600.-400.-200. O.0 200. 400. 600. 800. 1000.1200.

R msmu Fig . 2.4 Axisymmetric deformations due to external pressure component only of the loading, predicted by BOSOR4 94

WPPSS-2 BOSOR5 OVERALL MODEL 10 DEFORMED STRUCTURE LORO STEP 1. LORD = 0.000E+00 PRESTRESS 7200. I I I i ~- 1 I i l l 7000. - I 6800. _

                                                       \                          -

, Iq i 6600. - - External pressure + ,

                         'i"* 1 *d" *h "" i" 6400. _                                                                 -

Fig. 2. 2 6200. _ , _ 6000. _ _ 5800. _

                                                                   =

t l 5600. _

                                                                      /

5400. _ [j _ 5200. _ _ 5000. I I I I I I I I I

            -1000:800.-600.-400.-200. O.0 200. 400. 600. 800. 1000.1200.

R sos s Fig. 2.5 Axisymmetric prebuckling def ormations due to exter-nal pressure plus the line loads shown in Fig. 2.1. Values of the line loads are listed in the Appendix, which gives the BOSOR5 input file for the VAX 11/780 version of BOSORS 95

2. 0 "8 WPPSS-2 BOSOR5 OVERALL MODEL 8

E h 0. 150.. Segs. Seg. 21 g Seg.} \@ (fb

 -                      %                              (                _yi     . _ _ _                       _ _ _.

Sog. 8*8* * *8 'E* g -0.20Q.. m . O Segs. Segs. 61 u -0.550 ,  ;  ; . .

  @                  0.00    300.         600.         900.      O.120E+C40.150E+040.180E+040.210E+04 g                                                         RRC LEETH 7 __._ _ _ _ ___..__ _               .
  @-            -0.100..

4 N 3 g -0.275.. N l 3 ' ,'N

                -0.450          .            .            .            .               .           .      t _- - e 0.00    360.         660.         900.      O.120E+040.15DE+ 040.18'0E+040. 210E44 FRC LEh5TH c          0.700E-02.

O u 0.00- _ - _ _ _ _ _ ;- :Y- _ m __ 8 w 3 -0.700E @ , , , , , , t u_;, . . _ _ e 0.00 300. 600. 900. O.120E+040,150E+040.100E+040.210E+04

 %                                  LOR) STEP      1. LOAD =     0.000E4) PRESTESS BOSOR5 Fig. 2.6 Axisymmetric prebuckling displacement and meridion-al  rotation distributions due to total load (pressure + line loads) 96

?                                                      Y                       segs.f&@           l' 3

WPPSS-2)BOSOR5OVERALLMODELj r ~~- 0 - - - - - (~ ~ ~ 't

                                                  ~ ~                                 ---

5a y -0.400E+01_ E u g scontinuities due to application of axial line loads 3 g-0.110E+05. O 3u E -0,180E+05 g. . . . . . - ma 0.00 360. 660. 9do. O.12'0E+040.15DE+040.18'0E+040. 21'0E+04 e E LENGTH o j y O.100E+05_ 1 c b ^ j g 0. m ____l_ __ b ._ , t S -0.100E+05 . . . . . . um ra 0.00 360. 660. 900. O.12DE+040.150E+040.18'0E+040. 21'0E+04 - E LENGTH O.250E+05 . E 85 as ~g S 0.00.. _ A I _ ._'t t _ _ .__- - E7 $$ == ma Y -0.250E45 $ 0.00 360. 660. 960. O.12'E+040.150E+040.10'0E+040,21'E+04 0 0 LOR) STEP 1, LORD = 0.000E+00 PRESTRESS BOSORS Fig. 2.7 Axisymmetric prebuckling stress resultants and mer-idional moment due to pressure + line loads 97

WPPSS-2 PRIMRRY CONTRINMENT, DVERALL 8050R4 51 DEFORMED STRUCTURE BUCKLE MODE 1. N = 18. E.V. = 5.334E+00 7200. " * "I' I I I

                                         ]I               I        I      I    I   i 7000. _

6800. _ l 6600. _ 6400. _ 6200. _ Z 6000. _ ll 5800. _ , _ w(s,9) = w(s) sin 180 7 5600. _ l ' E _ 5400. _ 5200. _ . 5000. I I I I I I I I I I

            -800.-600.-400.-200. 0.0 200. 400. 600. 800. 1000.1200.1400.

R msom Fig . 2.8 Buckling mode predicted by BOSOR4 corresponding to N = 18 circumferential waves. "E.V.", meaning "eigenvalue", is the load factor required to cause buckling with the assumption that the material remain elastic. 98

WPPSS-2 PRIMARY CONTAINMENT, OVERALL DOSOR4 40 DEFORMED STRUCTURE BUCKLE MODE 1. N = 16. E.V. = 5.322E+00 "U* "I' 7200. I I I QI I I I I I 7000. _ ,, _ l 6800. _ _ 6600. _ _ 6400. _ , J _ (L 6200. _ _ w(s,9) - w(s) sin 16e 6000. _ _ I i 5800. _ 5600. _ _ 5400. _ _ 5200. _ l _ 5000. I I I I I I I I I I

         -800.-600.-400.-200. O.0 200. 400. 600. 800. 1000.1200.1400.

R 803 2 . Fig. 2.9 Buckling mode predicted by BOSOR4 corresponding to N = 16 circumferential waves. 99

WPPSS-2 PRIMARY CONTAINMENT, OVERALL BOSOR4 2. 0 DEFORMED STRUCTURE BUCKLE MODE 1. N = 12. E.V. = 4.894E+00 7200. a m =1.o i I i i mi I i I I 7000. _ _ 6800. _ _ 6600. _ _ 6400. _ _ w(8,9) = w(s) sin 129 6200. _ _ Z 6000. _ l( _ 5800. h  % ll 5600. _ ll _

                                             .              ll 5400. _                                                          _

5200. _ _

5000. I I I I I I I I I

             -1000.800.-600.-400.-200. O.0 200. 400. 600. 800. 1000.1200.

R msne Fig. 2.10 Buckling mode predicted by BOSOR4 corresponding to N = 12 circumferential waves. This is the critical (lowest) buck-ling mode obtained in the elastic analysis. l 100 l

NX - NY INTERACTION CURVE (NXCR= 4.822E+05 NYCR= 1. 574 E + 06) 8._ . 8 J x o

   %o zw s ._       .

z S E8 a .. .

                                                   /N   {.

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      "                  '                          >                             i 1.50         -t.00                                       O' 50        1.00        t '. 50 H00           ESUL      NT,     NN Fig. 2.11 Interaction curves for the suppression chamber corresponding to four types of failure, yielding ("S"), local buckling          ("L"),          general   instability           ( "G ") ,  and    panel (inter-ring,              smeared         stringers)           instability       ("SS").

Imperfections and plasticity neglected. 101

I e d-- NX - NY INTERRCTION CURVE (NXCR= tt.822E+05 NYCR= 1.574E+06) _ . = 8 g_ . c a, i X, . zo ! N ._ . I x0 z 1 = l H o Zo C ._ ' p O i i o l w , i to -r i l c.o_ . .t t , l' __j i c jti f x i f l E . j o_ .

     ,                            esS!

7 G o_ .

     ,                               s.e-l. ( S .
       -0.12       -0.08               -0.04       0'.00   0'.04       0'.08      0'.12 l                                 HOOP RESULTANT,         NY/NYCR Fig . 2.12 Interaction curves for           the suppression chamber with plasticity and                 imperfections included according to ASME code case N-284 (modified)

I 102

w g- NX - NY INTERACTION CURVE (NXCR= 4.822E+05 NYCR= 1. 574E+06) t g_ . m g_ . m 6 3 o ' X, > e . Zo .. ..

         = -

z H ' z8

c. s.

po O g . D o o_ . t

                                                          .D. f l

_a i g [] ..[.. . .

 -                                           Wff55 X                     "
                                          ,Lgfress E, CLAM:i g,

o_ .

                                        /

W d_ . f . s d ' '

      ' 0.12
                    -0.08         - 0. 0L1          0'. 0 0      0'. 0 tl         O'.08    0'.12 HOOP RESULT ANT, NY/NYCR Fig . 2.13 Critical interaction curves for                   the perfect     and imperfect       suppression chamber,                 with stress point predicted by BOSOR4 superposed 103

8

- - NX - NY INTERACTION CURVE (NXCR=

NYCR= 9.012E+0u 2.167E+04) o m '

g. .

4

       }_ .                    ,
                                             /                                           '

z.8 g ( . sc, e N

     .                             f,                                                        !
          .                                            6 C o_          .

H' , . _J 4 O ( M 1 (O ^ ^i. tuo T* . f '0 o_ . Jl . E s

                                                !{L x                                                      3 ce q'.      .

N 8

j. .

8 lu '

       ' 2.40
                          -1.60            -O.80       - 3.00 0'.80       l'.60       2'.40 HOOP RESULTlNT, NY/NYCR Fig . 2.14 Interaction curves for the lowest part              of  the drywell cone corresponding to three types of failure,                     yielding

("S"), general instability ("G") , and local (between stringers) buckling ("L"). Imperfections and plasticity neglected in buck-ling analyses. 104

o "g_ . NX - NY INTERACTION CURVE (NXCR= 9.012E+04 NYCR= 2.167E+04) 8._ .

                         ~

E g_ . x ' u x0 /

                                 /

xo o z de Ed,_ . J 4

                                                                                                ,-                                    1, r                       !

,s b l 0 G S UN o y_ . C - t X "S [ d_

                 .                                                                               .L L

6 o, _ . R _ . _. .. 8 ' d ' ' '

      ' 2.40
                         -1.60                                                                                                   -O.80           -O.00          0'.80      l'.60     2'.40 HOOP RESULTANT, NY/NYCR Fig. 2.15 Interaction curves for the lowest end of the drywell cone with plasticity and imperf ections included in the buckling analyses 105

i 8 d-' NX - NY INTERACTION CURVE (NXCR= 9.012E+04 NYCR= 2.167E+04) o to t

    ; y/'

O xa ZN N =_ . X O  : 2

• p_'. o 29 QQ .

e

          ,                                    . , , _ , , __                                                                                  1
    ._J                                                                  :
      >                                                       -   Ne     tilOCO    up% pgywEsd co4E o                                    l*                   5 9' f 3T00        CrohEL 500' % 515 '

[" o_ . (t-li.tc o.srd) . ' g' ' l ig;. 1 (i ( $l= W*) x  : l i- ' 6: 1 7 o w '

                               .         Yl b_ .

I i o d ' ' l ' 1.20

                            -O.70         -O.20                       0'.30             0'.80                 l'.30                             l'.80 l                                   HOOP RESULTANT, NY/NYCR Fig . 2.16 Critical interaction curves for the perfect and imperfect lowest part of                                     the drywell cone, with stress point predicted by BOSOR4 superposed.

I 106 l 1 - ._- _

1.o WPPSS-2 BOSORS SEGMENTS 3 THRU 9 MODEL INITIRL UNDEFORMED STRUCTURE INDICRTES ERCH MESH POINT 6200. I I I y i i i pg f o SA Ye'o n 6100. _

                                                         @ = 5 3.@            E32) _          ,
                                                            \

6000. _ If b ~ L, 5900.'__ 4 2 5E00. l T

• bj !!l ~

ll<[) ll ~ 5700. _ o ll 3, l 5600. _ f _ o 5500, 1 no rdstW Scy *[,E %S i i i 5400. l l I i

0. 0 100. 200. 300. 400. 500. 600. 700. 800.

R sosms Fig . 2.17 Discretized BOSORS modal of a portion (Segments 3-9 in Fig. 21) of the WPPSS-2 containment vessel. 107 , i

WPPSS-2 BDSOR5 SEGMEllTS 3 THRU 9 MODEL 2.o INITIAL UNDEFORMED STRUCTURE RINGS HAVE BOTH FIXED AND VARIABLE LORDS 6200.

                               ,     ,        ,  ,,           i    i 6100.      _

I" - 6000. _ --

                                                      ,w i'_                                    '

5909. _.

                                                     ,,a              -

n. Hi 2 5600. _ - o 5700. _ n u 5600. _ -

                                                  ,   i
                                                  *An 5500. _

{ 5400. I I I I I I I

0. 0 100. 200. 300. 400. 500. 600. 700. 800.

R sosms Fig. 2.18 Line loads and Moments applied to the model in order to simulate the equivalent static load specified in the PDM stress report. Moments are required to " move" the line loads f rom the ref erence surf ace, which is the shell inner sur-face, to the middle surface. 108

                                                                                                   +0 WPPSS-2 80SOR5 SEGMENTS 3 THRU 9 MODEL DEFORMED STRUCTURE LORD STEP 10. LORD =         0.000E+00            PRESTRESS 6200.

I I I I I I I 6100. _ t 6000. _ g

                                                             \

i M 5900. _ i 5, g _ l = 3. 4 2 5600. _

                                 = Lo l b 6                     '

y*hw ' ^ ~b'Y'" _ J e ,c p metria f 5700. _ c " U '['" i4 - Std _ 1 5600. _ t 111 I " 5500. _ 5400. I I I I I I I

0. 0 100. 200. 300. 400. 500. 600. 700. 800.

R sosons Fig. 2.19 Axisymmetric def ormations at a load f actor of 3.6, which corresponds to BOSOR5's prediction of axisymmetric col-lapse. Collapse occurs because of the large stress concentra-tion between segments 2 and 4. 109

WPPSS-2 80SOR5 SEGMENTS 3 THRU 9 MODEL s1 DEFORMED STRUCTURE BUCKLE MODE. N = 18. LORD =

                                                                             #999tM9' % 5~2_

6200. I I I I I I I 6100. _ 6000. _ 5900. _ l N, ". _

                                               'E '
                                                                 }f 2 5600. -                                                             i                     _

i E 5700. _ w(s,e) .- w(s) ssa 18e _ 5600. _ ll 5500. _ 5400. I I I I I I I

0. 0 100. 200. 300. 400. 500. 600. 700. 800.

R sosas Fig. 2.20 Critical buckling mode. Load factor of 4.52 is not meaningful because nonsymmetric bifurcation buckling is pre-ceeded by axisymmetric collapse at a load factor of 3.6. 110

10' TOP HERD OF WPPSS UNDER INT. PRES. BOSORS INITIAL UNDEFORMED STRUCTURE

                                                 *I         ""

7200. I l l I I I I

                                ===== u 7150.   -

{

                                 "~~ ~ d_ep. N                            -

x

                                                                 ,/

7100. _

                                                          '         A i

2 7050. _. l ll_ t 7000. _ lL

                                 ,                                      ll l ',

v ll 6950. _ I I 6900. I I I

         -100.       -50. 0. 0       50.        100.      150.           200.

R sos e Fig. 2.21 Discretized meridian of upper head of WPPSS containment for BOSORS analysis of elastic-plastic buckling under internal pressure 111

TOP HEAD OF WPPSS UNDER INT. PRES. 80 SORS 10 DEFORMED STRUCTURE LORD STEP 5. LOAD = 0.000E+00 PRESTRESS 3 7200. m A. I i I

                                        .- -.-.~ . ...

t s r 7150. L _ t t 7100. h

                                                                          )            \

o

                                      /.

Z 7050. _ ' - g i i 7000. _ I) - 4 6950. - k[ _ 6900. i I I

                     -50.        0. 0          50-       100.      1h0-    200. 250.

R soscas Fig. 2.72 Axisymmetric deformations under an internal pres-sure. Plastic flow initiates in the knuckle region at a pres-sure of about 1.5

• 45 psi. Compressive hoop stresses exist in the knuckle region where the meridian moves toward the axis of revolution. These compressive hoop stresses could cause buck-ling, and the purpose of this analysis is to prove that they do not.

112

s.1 TOP HEAD OF WPPSS UNDER INT. PRES. BOSOR5 DEFORMED STRUCTURE LORO STEP 7. LORD = 0.000E+00 PRESTRESS 7250. I I i l I 7200. __ s

                                                              'Xg 7150. _

s..Nj _ i 7100. _ T _ f ' l 7050. _ l i 7000, _ 1 J 6950. _ I I 6900. I I I I

        -100.     -50.       0. 0          50.        100.        150.      200.         250.

R sos e Fig . 2.23 Axisymmetric deformations caused by an internal pressure of 3.0

• 45 psi. For internal pressure higher than this, the hoop compression diminishes. Nonsymmetric bifurcation buckling does not occur in the head at any internal pressure.

113

TOP HEAD OF WPPSS UNDER INT. PRES. BOSOR5 El DEFORMED STRUCTURE BUCKLE MODE. N = 35. LORD = 0.000E+00 7200.

                      ,        ,         ,        i                       i 7150. _

s -

                                                                                                                                   )

7100. _ I-l 2 7050.t_ - 7000. _ Il 11 6950. _ 6900. I I I I I

       -100.      -50. 0. 0       50.      100.        150.                                                                         200.

R sosons Fig. 2.24 Buckling mode predicted by BOSOR5. The eigenva-lue, about 4, corresponds to an internal pressure of about 12*45 psi, at which pressure the stresses are everywhere positive and buckling is therefore impossible. 114

3 STAGSC-1 m z .1 _ N S \ t \

                           =

2 - E 0 -[ d g s.,-- E

                                 .1 5588                                          6184 ELEVATION AXIAL C0 ORDINATE (in)

Fig. 3.1 l'ormal deflection of B0$0R5 and STAGSC-1 axisymmetric models due to a lead factor of unity, i.e., the load level obtair.ed from the PDM stress rcport, c C 2 g UNIFORM GRID [ 0 -- I m _ _ _ _ _ _ - _ _ _ _ E .02 _ E VARIABLE GRID' d .04 _ a i i N 0 15 30 CIRCUMFERENTIAL COORDINATE (degrees) Fig. 3.2 Normal deflections of STAGSC-1 axisymmetric model (units 1,2, and 3 of the model shown in Fig. 3.4) at elevation = 5588 in. with a uniform circumferential spacing of 2.5 deg. , 5 deg. , and uniform spacing within segments; 2.5 deg. along theta = 0 to theta = 15 deg. and 5 deg. along theta = 15 deg. to theta = 35 deg. 115

II i

                         .6 n

STAGSC-1 '\

                                                \
                     'E                           \
                     }3 5
                                                    \
                                                      \
                                                       \

P 1

y

• i

                     $                                     f Y

g D' / N j' v '

j  % BOSORS

( 1 N/

                        .3                                                         l i

5588 6184 , ELEVATION -AXI AL COORDINATE (in) Fig. 3.3 Normal deflections of STAGSC-1 (portion of the model shown in Fig. 3.4 between elevations 5588 in. to 6496.5 in, and theta = 30 deg. to theta = 35 deg.) and B0 SORS axi-symmetric models at collapse. 116

X 1 l

                  ,,,      ,  ,            --6496.5 1ii illl III1
                /l1                        il III III

/

i;11TJ i 'Gl', ' '

                             'r Ubbb
                                           -yI6 is4  I- 0                      Elem"t usk/

8 5h'II U" __ 7 id ,

W ' '.  : : =,"

.., im -

WM 5 GOT 3 b

1q 7

                                           - 5960.006 4                                    .

N /vx/x/x/x/x/N _ g 8 6 7.C ?_5-

                                                                                                 .)_

3 [Z: ._ b _- _ E 7 4 9. 8 4 4 F_.+

                                                                                          ,     _j_

z g.----

                                             ---- 5 C 3 7 . O C ?                         c-I=

y e_ , b F E88.O e= ar o L s k el\ u w d s (O (N Vi ew gotdieo 60 De . Coswby clockwi R bIcou x - A xis Fig. 3.4 STAGSC-1 finite element model for collapse analysis of the portion of the WPPSS-2 containment which contains the largest opening.

i ei i i i l 1

                                                                                              \
                                                                                      ,1 1              ,

Yw  ;, 72g=_N b

                                       +

I D

                                               -.r N

i kl

                                                                       .     )
                                      = , .   .i.;;.;a                      .

en 5 [f C' j , e i.

                                                       .%              ;p .

n

                                      ;g g en . E=
                                              -=
                                                       =n s :.
                                                                               ;             ll                1 1

_l

                                    ===       c.                                -   --               L i.._-._.___    ..

[

• Z e..e% 4 C, 4 lt"%- ~ y' <

3 - - - . Fig. 3.5 Collapse mode of the STAGSC-1 model with penetration. Deflections are multiplied by a scale factor of 40 for visual effects. l I 118

e a a e m a w u - c.

                                                                  ~

e g 8 s

                     'A     ._

a m l Fig. 3.6 Contou.s of normal deflections for shell unit 4 at collapse. The actual deflection in inches is W=0.0623 times the designated number along the contour. 119

                         . - . _ .            .           .-.       .       -      - - _ . ~ _                  .

I i i 4 4 a a a

                              ~

y n'\J i

                                                   \
                                                                \
                         -10           1 ;

1 7 I I A N8%3 Fig. 3.7 Contours of normal deflections for shell unit 5 at collapse. The l actual deflection in inches is W=0.0492 times the designated number along the contour. i 120

I

)
                                                                           -5
                              ~
                                                                            .g
                             .g                                             -3
                                                                             ~
                             -3 l '1          ~1
                             -2                                j      {

l

                                                                         ,      o
                            -1 1

m I I J g l' o u

M,,\V/)

a laa a a a a a i Fig. 3.8 Contours of normal deflections for shell unit 11 at collapse. The actual deflection in inches is W=0.0534 times the desigrated number along the contour. 121

4 3 - E ti I 2 - 3 S 1 O e L i I

                               .0  .02        .04         .06     .08        .1 NONLINEAR PORTION OF RADIAL DEFORMATION ii = W-W LIN II")

Fig. 3.9 Variation of nonlinear portion of normal deformation (at elevation

          = 5960.806 in. and theta = 20 deg.) with load factor for the STAGSC-1 model with penetration. Load factor of unity here imply the actual load level obtained from the PDM stress report.

2 122 l

A

                                                        /\

l \ I \

                                                               \
                                 .3  -
                                                                 \

C B0SOR5 \

                                                                     \
                            #                                         \
                                          ~

l y l a s) D 0- I E / STAGSC-1 d 5 o i

                                                                          /
                                 .3--

1 I 5588 6184 ELEVATION (in) Fig. 3.10 Normal deflections along a meridian for the axisymmetric BOSOR5 model, and along the meridian at theta = 35 deg. for the STAGSC-1 model with penetration, at a load factor of 3.6. 123

      - --                                       -                                     -                               . - ,            _= .-. .

7C ' ""

• u.s. NucteAn neoutAToRY COMMISeloN BIBLIOGRAPHIC DATA SHEET VO1. 1. Part 2 4 TITLE AND SusTITLE (Add Vo4,me No., af appropr,esel 2. (Leme esmet Buckling of Steel Containment Shells Task lb: Buckling of Washington Public Power Supply Systems' Plant No. 2 3. RECIPIENT S Accession NO.

Containment Vessel

7. AUTHOR (S) 5. DATE REPORT COMPLETED Eli Meller and David Bushnell uONTu lveAR 9 PERFORMING ORGANIZATION N AME AND MAILING ADDRESS (tactue les Com/ OATE REPORT ISSUED

                                                                                                      ~

i Lockheed Palo Alto Research Laboratory De'" ember I"'"1982 De;'. 52-33/ Bldg. 255 8 a ' * * *' 3251 Hanover Street, Palo Alto, CA 94304 s. <te. e w-as I i2. SPONSORING ORGANIZATION NAME AND MAILING A00RESS (tactum I,a Comf p Office of Nuclear Reactor Regulation Division of Engineering ii. riN NO. U. S. Nuclear Regulatory Commission Washington, D. C. 20555 B6568

13. TYPE OF RE PORT PE RIOD COVE ME D (/nclusive daars/

FINAL 25 August, 1980 30 September,1982

15. SUPPLEMENTARY NOTES 14 (Leave ormal

16. ABSTRACT #00 orords or dessJ Static buckling analyses of the steel containment vessel of the Washington Public Power Supply Systems' (WPPSS) plant No. 2 were conducted with use of several computer programs developed at the Lockheed Missiles and Space Company (LMSC). These analyses were conducteil as part of Task 1," Evaluation of Two Steel Containment Designs".

The report is divided into two main sections. The first gives results from analyses of the containment as if it were axisymmetric (computerized models with use of B050R4, B0SOR5, anil PANDA), and the second gives results from a STAGSC-1 model in which the largest penetration is included. J Good agreement is obtained from analyses with BOSOR5 and STAGSC-1 for a case in which both of these computer programs were applied to the same configuration and loading. It is im-portant to include nonlinear material behavior (plasticity) in the computerized models for collapse. Predictions of collapse from STAGSC-1 indicate that the largest penetration of the WPPSS-2 containment vessel is reinforced such that there is no decrease in load carrying capability below that indicated from models in which this penetration is neglected. A collapse load factor of 3.6 times the loads costulated by Pittsburgh Des Moines Steel (PDM) is indicated The buckling mode is axisynmetric collapse. Bifurcation buckling involving nonaxisymmetrii: ii"RMOE%b d6cdVGBeLA9MStactors tnan J.0. ir. oESCRiPTORS BUCKLING FINITE ELEMENTS SHELLS CONTAINMENT STIFFENED STEEL COMPUTER 17b IDENTIFIE RS/ OPE N ENDE D TERMS 18 AV AILABILITY ST ATEMENT 19 SE C T AS .h s report) 21 NO OF PAGES l Unlimited S"U"n'c'1Is's'Ifi58'' s mnC F Omu 335 ein en '

• U.S. GWUvlENT PRluTING OFFICE: 1,82- 381-29782595

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