ML20063B369
| ML20063B369 | |
| Person / Time | |
|---|---|
| Site: | Catawba  |
| Issue date: | 05/27/1982 |
| From: | Harstead G, L A, Morris N HARSTEAD ENGINEERING ASSOCIATES, INC. |
| To: | |
| Shared Package | |
| ML20063B363 | List: |
| References | |
| 8106-2, NUDOCS 8208250358 | |
| Download: ML20063B369 (70) | |
Text
{{#Wiki_filter:_ _ _ _ . _ - . . . _ H ! p v f HARSTEAD ENGINEERING ASSOCIATES
- INC.
169 KINDERKAMACK ROAD, PARK RIDGE, N.J. 07656
- Phone:(201)3912115 l
l CONTAINMENT VESSEL STABILITY ANALYSIS CATAWBA NUCLEAR STATION, UNITS 1 & 2 DUKE POWER COMPANY
, REPORT NO. 8106-2 MAY 27, 1982 Prepared by: .
A. I. Unsal Reviewed by: % . - N. F. Morris Approved by:
.A. Harstead O"
l ENCONTROLLED 8208250358 820819 PDR ADOCK 05000413 A PDR
A VV CONTENTS Chapter 1 Introduction . . . . . . . . . . . . . 1 Chapter 2 Summary and Conclusions . . . . . . . . 4 Chapter 3 Approach and Theory . . . . . . . . . . 7 3.1 Background . . . . . . . . . . . . . . 7 3.2 Basic Approach . . . . . . . . . . . . 10 Chrm er 4 Mathematical Models . . . . . . . . . . 14 4.1 BOSOR4 Model . . . . . . . . . . . . . 14 4.2 NASTRAN Model . . . . . . . . . . . . . 16 4.3 NASYS Model . . . . . . . . . . . . . . 20 4.4 Wilson-Ghosh Model . . . . . . . . . . 20 Chapter 5- Loads Acting on Containment Vessel . . 24 - 5.1 Dead Load . . . . . . . . . . . . . . . 24 5.2 Seismic Loads . . . . . . . . . . . . . 24 5.3 Pressure Loads . . . . . . . . . . . . 24 5.4 LOCA Pressure State . . . . . . . . . . 32 5.5 LOCA Thermal State . . . . . . . . . . 33 Chapter 6 Buckling Analysis . . . . . . . . . . . 39 6.1 Buckling of Cylindrical Shell . . . . . 39 6.1.1 Load Combination 10 . . . . . . . . . . 39 6.1.2 Load Combination 6 and 3 . . . . . . . 56 6.2 Buckling of Spherical Dome . . . . . . 59 References . . . . . . . . . . . . . . . . . . . . 63 Appendix I Glossary . . . . . . . . . . . . . . . 65 Appendix II SHELL 3 Computer Program . . . . . . . 66 i l (h \
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ENCONTROLLED
l N ,l v FIGURES Figure 4.1 BOSOR4 Model 4.2 NASTRAN Model - Node Numbering 4.3 NASTRAN Model - Elements 4.4 ANSYS Model for Thermal Analysis 4.5 Ambient Temperature for Steam and Air During LOCA
~
4.6 Wilson-Ghosh Finite Element Model Figure 5.1 Dead Load - N1 Stress 5.2 Dead Load - N2 Stress 5.3 Horizontal Seismic - N1 Stress 5.4 Horizontal Seismic - N2 Stress 5.5 Horizontal Seismic - N12 Stress
/)/ 5.6 External Pressure - N1 Stress
(~L- 5.7 External Pressure - N2 Stress 5.8 LOCA Transient - N1 Stress 5.9 LOCA Transient - N2 Stress 5.10 LOCA Transient - N12 Stress 5.11 LOCA Temperature Variation at T = 250 seconds. BOSOR4 Input 5.12 LOCA Thermal - N2 Stress Figure 6.1 Load Combination l'O ' - N1 Stress 6.2 Load Combination 10 - N2 Stress l I 6.3 Load Combination 10 - N12 Stress 6.4 Load Combination 10 - Buckling Mode, n = 18 6.5 Load Combination 10 - Buckling Mode, n = 26 6.6 NASTRAN Model - NX Stress Contours l O
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\=/ l Figure 6.7 NASTRAN Model - NY Stress Contours 6.8 NASTRAN Model - NXY Stress Contours 6.9 NASTRAN Model - First Buckling Mode 1
6.10 NASTRAN Model - Second Buckling Mode 6.11 NASTRAN Model - Third Buckling Mode 6.12 NASTRAN Model - Fourth Buckling Mode 6.13 NASTRAN Model - Fifth Buckling Mode 6.14 NASTRAN Model - Sixth Buckling Mode 6.15 Load Combination 6 - N1 Stress 6.16 Load Combination 6 - N2 Stress 6.17 Load Combination 6 - Buckling Mode, n = 60 3 l O' UNCONTROLLED
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CHAPTER 1: INTRODUCTION I The Catawba containment is a freestanding welded steel shell consisting of a vertical cylinder with a hemispherical done and a flat circular base. Since the base of the cylinder is encased in concrete, the structure can be considered as fixed at that support. The cylinder has a diameter of 115 ft.; its thickness is 0.75 in, for most of its length although the thickness increases to 1 in. in the vicinity of the base. The hemisphere's thickness is 0.688 in. Large ring stiffeners are spaced at approximately 10 ft. intervals along the longitudinal axis of the cylinder. In addition, there are longitudinal str-ingers spaced at angles of 3 degrees around the circumference of the cylinder. These stringers are rather small rectangular bars which are not welded to the ring stiffeners. The containment cylinder contains numerous penetrations, ('"} 'A hs the largest pc.ietration is that for the equipment hatch which is 20 ft. in diameter. Reinforcement around the penetrations is designed in accordance with Section III, Subsection NE, of the ASME Doiler and Pressure Vessel Code. The co-tainment vessel must be designed for the following loads:
- a. Dead load
- b. Design basis accident - LOCA
- c. External pressure
- d. Seismic loads The effect of these loads must be combined in accordance with Table 3.8.2-1 of the Catawba FSAR. It is usually possible to carry out stress analyses for each load separately and com-bine the resulting stresses by a simple superposition. There is, however, a problem with the application of these combina-tions in stability analyses. Buckling is basically a nonlinear s 4 ENCONTROLLED 1
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Since the containment shell is stiffened in two directions and the loading is due to nonuniform transient pressures, the ASME formula design approach cannot be used. Code case N-284 of the ASME code specifically deals with buckling of cylindrical and spherical shells which covers the problem under investiga-tion (1). This specification calls for a combination of com-puter aided buckling analyses, analyses formulas, and knockdown factors. Although the code case was used as a basis for the methodology proposed herein, it should be noted that the code case does lack sufficient detail as applied in the investiga-tion of some problems which arise in the analysis, notably the effect cf penetrations, and the investigation of thermal stresses. A stiffened shell such as the Catawba containment shell can buckle in three different ways. First, there can be a. complete buckling of the whole shell including the stiffeners. This failure mode is addressed in section 1712.2 of the code case wherein a procedure for the computation of the buckling stress is presented. The second type of failure which can occur is buckling of the shell between the large circumferential ring stiffeners which are spaced approximately 10 ft. apart, ver-tically, for the cylindrical portion of the containment. This buckling state is called stringer buckling. It is described by the same set of equations in the code case as general buckling but with different definiti6ns of the parameters which enter these equations. The third possible buckling configuration is local buckling of the cylindrical panel contained between the ] small longitudinal stringers and the large circumferential ring stiffeners. The code case procedures for computing the accom-y'"; panying buckling stress are presented in section 1712.1. 3 . UNCONTRO.L. .L. ED, !
l r% N V The procedure adopted herein was to use the code case to compute the local buckling stress and the knockdown factors for all buckling configurations. Stringer buckling and general buckling loads were computed with the aid of two computer pro-grams, BOSOR4 and NASTRAN. The code case equations for both stringer and general buckling were solved by a computer program, SHELL, developed by Harstead Engineering Associates, Inc. (HEA, Inc.). While this program was used to determine the range of the critical buckling modes and stress states, its results are superceded'by those of BOSOR4 and NASTRAN. i l l
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\=/ CHAPTER 2:
SUMMARY
AND CONCLUSIONS The three load combinations which can cause buckling in the cylindrical shell are load combination 6 which includes dead load, seismic load, internal pressure and temperature due to LOCA, load combination 10 which includes dead load, seismic load, and the short transient TMD loads due to LOCA, and load combina-tion 3 which includes dead load, seismic load and operating temperature. The transient response of the containment vessel under TMD loads was provided by Duke Power Company. The results of this analysis were directly used in combination with other stress states. All other stress states were computed at HEA Inc. using the BOSOR4 program. These stress states were then used to compute the local buckling factor, according to the code case equations. The general buckling factors were calculated with the aid of BOSOR4. The effect of the equipment hatch and /T the personnel air lock openings on the buckling stress in load
Jh combination 10 was computed with the aid of NASTRAN. The longer term LOCA effects of load combination 10 do not affect the buckl-ing capability in the region of these operings.
The two load combinations which can cause buckling of the spherical dome are load combination 7 which includes dead load, seismic load, and the external pressure, 1.5 psig, due to the internal vacuum crested by accidental trip of the containment spray system, and load combination 10. Both combinations are due to accident conditions. In addition, a negative external i
~
pressure can only be attained if the containment pressu're con-trol system fails. This system, which meets the single failure i criterion, controls the pressure in the containment vessel so i that no negative pressure can occur. j The results of the analyses described above are presented in Table 2.1. Since load combination 3 is the only normal operating condition, it should, and does, have a large factor l (s
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f% f3 O V (V (U Genera 1 Buck 1ing 1,oca1 Buck 1ing Part of Load Containment Comb. No. Knockdown Factor of Knockdowre Factor of Fa ctor Safety Factor Safety 3 0.80 (CC) 7.04 (BSR) 0.80 (CC) 4.73 (CC) Cylinder 6 0.80 (CC) 2.18 (BSR) 0.80 (CC) 2.33 (CC) 10 0.52 (CC) 3.05 (BSR) 0.52 (CC) 1.97 (NAS) 7 0.124 (CC) 2.23 (CC) O.124 (CC) 2.23 (CC)
-o Dome 10 0.60 (IIEA) 4.01 (IIEA) 0.60 (ilEA) 4.01 (IIEA) 9 n Ma TABLE 2.1
SUMMARY
OF RESULTS Notes: 1 - Shell thickness 0.05" less than nominal, therefore actual factor of safety is - L above 2.00 W 2 - E = 27,000 and 27,700 for T = 200 F and 70 F respectively. 3 - Load Combination 3 = DL + Seismic + Operating Thermal 6 = DL + Seismic + LOCA 7 = DL + Seismic + External Pressure 10 = DL + Seismic + IOCA (TMD) 4 - Analytical Methods Used CC - ASME Code Case N-284 BSR - BOSOR4 . NAS - NASTRAN IIEA - IIEA Computed
i l 1 l (3 E]
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CHAPTER 3: APPROACH AND THEORY
3.1 Background
As stated earlier, a stiffened shell such as the contain-ment shell can undergo several different buckling modes. First, there is the general instability mode for the whole structural system or a portion of it. Since this mode includes the ef-fect of the stringers and ring stiffeners, analyses were carried out to insure that these elements do not fail locally prior to the attainment of the general buckling load. In addition, it was necessary to analyze the small curved panels between the ring stiffeners and stringers to insure that they do not buckle in a local buckling mode at lower loads than either the general or stringer buckling loads. The effect of large penetrations on the local buckling of the shell is an open question among
-w
( ) those investigating containment stability at the present time
% *// (2), (6). It was not appropriate to claim that if reinforce-ment around large penetrations is in accordance with the ASME Code, there will be no reduction in buckling loads. Hence a local buckling analysis for the areas around the large penetra-tions was carried out.
The ASME Pressure Vessel Code states that the buckling stresses for a nuclear containment can be determined by one of the following methods: A. Rigorous nonlinear analyses wherein the analyst can incorporate the effects of gross and local buckling, geometric imperfections, large deformations and inertial forces (if there are dynamic loads). B. Linear buckling analyses reduced by knockdown fac-tors that reflect the difference between theoretical and actual load carrying capabilities. C. Tests of physical models which simulate the restraint, (% ) geometry and loading of the actual containment. ENCONTROLLED l l 7
,f- ~ NJ \"# The last method can be disposed of quite readily. Shell structures are such that correlation between the buckling loads of actual systems and shell models is extremely difficult to achieve. In fact correlation between buckling loads for shell models of the same shell is difficult to achieve (7). Furthermore, the difficulty of modeling the transient pressures required for buckling of this containment shell, renders the method of physical models impractical, if not impossible. If the shell were to be investigated for a single static load, the use of a rigorous nonlinear analysis might be a reasonable approach to employ. This analysis requires a com-putation of the complete load deflection curve for the struc-ture. It utilizes the nonlinear strain displacement equations as well as equilibrium equations formulated with respect to the deformed position of the shell. Therefore, in order to achieve a solution, it is necessary to apply the load in increments, to update the structural stiffness matrix at each load increment, and to solve the nonlinear equations of motion at each load in-crement by iteration. This procedure requires a large amount of computer time for a single load case but this is not the main difficulty involved in a nonlinear analysis. Consider, for example, the analysis of an axisymmetric spherical dome under a symmetrical load. The response would be expected to be symmetrical, which it might be. Nevertheless, there are loads ; at which the shell may bifurcate into a nonsymmetrical deflec-tion shape. Unfortunately, the load at which bifurcation oc- . curs depends upon the nonlinear solution at that load level. Hence, a new eigenvalue problem must be formulated and solved l l at each load level (8). This leads to a very large increase in computer costs over that required for a nonlinear symmetric analysis. If asymmetric imperfections are included in the nonlinear ,y analysis, the situation is much worse because the nonlinear ( "! UNCONTROLLED 8
/ UNCONTROLLED (3/ response is nonsymmetrical from the start. Since symmetry cannot be employed at all, a large nonlinear three dimensional analysis is required. The computer cost for a single run is extremely high (9) because the incremental. load procedure re-quires reformation of a completely new static equilibrium problem at each load level. While the investigation of dynamic buckling is more com-plex than the static investigation described above, the loads which.could cause buckling in the Catawba containment vessel are dynamic lotas. The field of dynamic buckling is a recent development in solid mechanics (11), (12). In order to ob-tain a dynamic buckling load for a shell under a transient pressure load, a nonlinear dynamic analysis must be perforned. Dynamic buckling is characterized by a rapid and significant nonlinear growth in some response parameter. Hence, a single nonlinear dynamic analysis under a specific loading would suf-(a l fice to insure dynamic stability for that load. Unfortunately, the problem of large penetrations and imperfections mentioned in connection with the static analysis still exists. Therefore, it can be questioned whether such an approach is worthwhile. Another problem exists for nonlinear dynamic analyses of shell structures, the results obtained by different programs disagree. The figure reproduced below is taken from (11). It i- . ! :
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\=/ represents a comparison of different nonlinear dynamic response computations for an impulsively loaded truncated cone. As can be seen, there is a great deal of variation in the nonlinear responses even though the linear responses agree closely.
This is due to various assumptions made in the models used, but the results do reveal the pitfall's involved in a nonlinear dynamic analysis. Nonlinear analyses are costly, but they are not cost-effect,ive. Most shells are imperfection-sensitive. That is, their buckling' load is strongly affected by the existence of small imperfections in shell geometry (10). This being the case, unless one has a very accurate knowledge of these imper-fections, a rigorous nonlinear analysis will not yield accur-ate resul'ts. At the present time such knowledge of imperfections does not exist. This difficulty is overcome in practice with rx the aid of knockdown factors. Knockdown factors are applied to ( I x_/ linear bifurcation buckling loads to make the results of this analysis coincide with experimentally determined buckling loads. A Their use in the analyses described herein is presented in Section 3.2 of this report. 3.2 Basic Approach Having eliminated rigorous nonlinear analyses and physical models as practical approaches to stability analyses, only one method remains: linear bifurcation analyses in conjunction with knockdown factors (1), (2). The primary membrane state, either input directly or obtained from a prior linear static analysis is employed in a small deflection eigenvalue analysis. Buckl-ing loads and mode shapes are obtained from such an analysis which is the application of the classical theory of elastic stability to shell structures. It is well known that the actual buckling loads for a shell are usually much smaller than the linear bifurcation buckling load. The reason for this discrep-
/") ancy is the existence of initial imperfections.
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(\s) s/ Knockdown factors are employed in an attempt to bring the loads closer to reality. Formulas for these factors are presented in (1) and (3). Nevertheless, the rationale behind these fac-tors is not fully documented and some care must be exercised j in their use (2). A theoretical derivation of the knockdown factors is also possible using Koiter's theory (10), (13), (14). However, at the present state of the art, the knockdown factors presented in code case N-284 are probably conservative enough for the containment vessel analysis. The instability analysis of the containment vessel was performed with the aid of the BOSOR4 program (15). BOSOR4 is a program written exclusively for axisynmetric shells of revolu-tion. The documentation on the accuracy of BOSOR4 is exten-sive (16), and it reveals a close correlation between the results obtained by this program and experiments on shells.
-~ BOSOR4 had an advantage in the modeling of the Catawba
\s_s containment vessel. It was possible to model the ring stiffness accurately as shell elements in this program. Studies have shown that the assumed behavior of stiffener rings will influ-ence the buckling loads obtained in a shell stability analysis (16); hence they should be modeled as accurately as possible.
Since the shell model utilized in BOSOR4 must be axisymmetric, the longitudinal stringers
- were " smeared" over the shell thick-ness. The procedure is discussed in (15) and, inasmuch as it is commonly used, it caused no difficulty. However, there was one difficulty involved with the use of BOSOR 4: it could not model penetrations in the shell. Since the effect of large penetrations can be quite pronounced, the exclusive use of BOSOR4 in the stability analyses of the Catawba containment vessel was not possible.
The BOSOR4 rodel was used to compute the linear bifurca-tion load of the complete containment under various load com-binations. Although the use of static external pressure and
- i
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dead load was obvious, the choice of loadings to describe the response under LOCA did require some judgement. The output of the transient analyses, provided by Duke Power, was investi-gated to determine what response states might cause buckling as a static loading. The critical state in load combination 10 was input into the BOSOR4 model as a prestress, and the linear bifurcation analysis was then performed. It was originally en-visio- - '5at several different transient stress states due to LOCA __ have to be used in load combination 10 before a buckling value could be chosen. This was one reason for devel-oping the in-house program, SHELL, to check out these possible stress states. However, the critical transient stress states became obvious as the Wilson-Ghosh (LOCA analysis) output was analyzed. The procedure proposed herein has been called the frozen-in-time method (6), an appropriate name because it describes precisely what was done in the analysis. A justifi-b y ,/ cation of the method is presented in (2). v The linear bifurcation loads computed by the frozen-in-time method, as well as those due to static pressures, were reduced by knockdown factors. These factors are the result of imperfections, the effect of large penetrations, and the re-placement of a dynamic state of stress by an equivalent static state of stress. Studies of dynamic buckling are rare (11, 12), but it appears that the knockdown factor for the dynamic effect is unity (2). The effect of imperfections has been dis-cussed above. As stated, the knockdown factors were computed with the aid of code case N-284. A local buckling analysis was performed to ensure that penetrations in the shell do not reduce the buckling loads for I the complete shell below acceptable values. Local buckling analysis requires a three dimensional model of a portion of the shell around the equipment hatch and the personnel air lock. ( (~ The computer program NASTRAN was used to compute the linear N,) l l UNCONTROLLED
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%d bifurcation buckling load for this model. NASTRAN was chosen for this purpose because published results (17) reveal excel-lent agreement between buckling values determined by this pro-gram and experimental values for shells with openings.
The knockdown factors to be used in this bifurcation analysis are somewhat open to judgment. The knockdown values utilized herein were those presented in the code case for stringer and general buckling. These values are extremely con-servative, and a legitimate claim can be made that they should be unity rather than the valves used. The effect of openings in a shell wall dominate over the effect of imperfections so a factor based on imperfections is unrealistic. This conclusion is confirmed by nonlinear analyses of shells with openings (18) wherein it is found that the nonlinear buckling loads exceed the linear bifurcation loads. Nevertheless, the Catawba con-tainment vessel satisfies the more stringent requirement that knockdown factors less than unity are applied to the.bifurca-tion loads obtained from the NASTRAN model. u X UNCONTROLLED
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CHAPTER 4: MATHEMATICAL MODELS The results obtained herein are based on analyses of four mathematical models of the centainment shell or some portion thureof. The BOSOR4 model was utilized in the stress analysis j of the containment shell under the following static loadings: dead load, external pressure, horizontal seismic load, and temperature load. In addition, the BOSOR4 model was used to l compu'te the linear buckling loads for load combinations 6 and 10, which are the only two wherein buckling is a real possi-bility. The NASTRAN model was used to compute the effect of tne large equipment hatch and the personnel air lock penetra-tions on.the buckling loads found for load combination 10. Transient and steady state thermal analyses of a portion of the shell were performed with the aid of an ANSYS model. This analysis was used to obtain the critical thermal gradient under
) ~ '7[, the LOCA condition. The gradient provided the temperature dis-tribution in the BOSOR4 analysis. The results of the LOCA transient pressure analysis was provided by Duke Power Company.
The Wilson-Ghosh computer program was used for this analysis, and the mathematical model used is presented herein for the sake of completeness. 4.1 BOSOR4 Model The BOSOR4 model of the containment shell is depicted in a meridional plane in Figure 4.1. BOSOR4 utilizes the finite difference energy method to analyze the shell. The basic building block in its shell model is the segment. There are 22 segments in this model. Segment I represents the 1 inch thick portion of the cylinder while segments 2 through 6 describe the remaining 0.75 inch thick cylinder. Segments 8 and 9 represent the 0.688 inch thick spherical dome. The ring stiffeners are modeled as segments 10 through 22. p
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All variation in the circumferential direction is modeled by Fourier series expansions in that direction. Hence the model is restricted in that any circumferential cutting plane must yield the same system as that depicted in Fig. 4.1; i.e., axisymmetric. This requirement is satisfied by " smear-ing" the small meridional stringers over the shell wall. There-fore the shell is orthotropic. The orthotropic properties are computed in the BOSOR4 program. The segments are analyzed with the aid of a finite differ-ence mesh in the meridional direction; the number of points in the mesh for a given segment are indicated in Figure 4.1. The model for the ring stiffener is also shown in this figure. As can be seen, the ring stiffener flange is modeled as a discrete ring. The ring stiffener model was chosen so that the ring stiffener deformations could be included in the BOSOR4 analyses. (~N The shell depicted in Figure 4.1 is fixed at the base. x- Regularity conditions at the apex of the dome are automatically ss imposed by the BOSOR4 program. There are no other boundary conditions except for the obvious requirements that the ring stiffeners must be joined to the containment shell. 4.2 NASTRAN Model The NASTRAN model is shown in Figures 4.2 and 4.3. Figure 4.2 depicts the nodes while Figure 4.3 shows the finite elements employed in the model. Two types of elements were used. The ring stiffeners in the hoop direction and the stringers in the meridional direction were modeled as three dimensional beam ele-l ments. Quadrilateral shell elements were used to model the l containment shell. The increased plate thickness and the pene-l tration sleeves (represented by beam elements) around the equip-l ment and personnel hatches were included in the model. The critical stress state in this region of the cylinder consisted of a somewhat constant meridional membrane compres-
/"'N \ l sive force and membrane shear forces. The hoop membrane ' w./
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forces were tensile. The system depicted in Figure 4.2 is simply supported on all four sides. It is, however, free to translate in the meridional direction along the top face and the two sides. This condition is necessary to distribute the meriodional stress applied at the top boundary throughout the shell. In addition to this prestress, the shell was subjected to an in-ternal pressure which was chosen to mitigate the high circum-ferential compressive stresses due to the participation of the ring stiffeners and stringers in carrying the prestress. Such compressive stresses are not in the critical stress state, but in attempting to apply prestress in the model, they do arise and must be cancelled out in order to approximate the actual stress state. Even applying internal pressure it wac not possible to eliminate these compressive stresses completely
,s in the circumferential direction, a factor which makes the
(,,)' buckling load conservative. There is some shear in load combination 10. This shear was not included in the model because of the difficulty in adequately distributing it through the system. The support conditions required to distribute a uniform shear over the panel would not permit the internal pressure to act effectively in cancelling out the fictitious circumferential compressive stresses described above. Since the shear stress did not af-feet the buckling capacity found in the BOSOR4 analysis, it was decided not to use it in the NASTRAN analysis. The re-sults are still conservative because the model contains com-pressive circumferential stresses whereas the actual load combination contains tensile circumferential stresses. Another conservatism used in the model is the fact that the shell thick-ness was taken as 0.7 inches rather than 0.75 inches, which results in E bending stiffness of 80% of the nominal value. g ENCONTROLLED 19
1 1 l l
,ev
( ) N J' l
%m/
l 4.3 ANSYS Model The containment shell is subjected to a large thermal gradient due to the rise in temperature during LOCA. Therefore, a transient heat flow analysis of a portion of the containment shell surrounding a ring stiffener was carried out using the ANSYS computer program. The model employed is shown in Figure 4.4. An axisymmetric heat flow element, element type 55 of ANSYS, is used in the model. The ambient temperature in the annulus outside the shell was taken at 85 . The temperature rise at the inner face of CO the shell follows the time history depicted in Figure 4.5. A transient analysis up to the time, t= 651 seconds was performed. The thermal properties used in the analysis are presented in Figure 4.5. Steady state analyses were also carried out to ensure that the thermal model behaved in a reasonable manner.
-- The correlation between the transient analysis at a large time and the steady state analysis is quite close, thus pro-( w) viding a check on the model.
4.4 Wil son-Ghosh Model The finite element model employed in the LOCA transient pressure analysis is presented in Figure 4.6. The Wilson-Ghosh computer program is similar to BOSOR4 in that it is restricted to axisymmetric structures and takes into account variation in the circumferential direction with Fourier series in that direction. However, the Wilson-Ghosh program uses a finite element technique rather than a finite difference tech-nique. Elements 1 through 5 (see Figure 4.6) represent the 1 inch thick portion of the shell while elements 38 through 56 model the spherical dome. The remaining elements describe . the 0.75 inch thick containment shell and the ring stiffeners. o o ENCONTROLLED 20
" em e-ee-e--.w-, -
o h so.s L s 7 v m FIGURE 4.4 m s6.t - m m r - n:, M J N M 46.5 - 2 .
.-J
~J 41 8 -
m i P 37.2 - r3
- 2 s :
h+ - 2:.. - g W 07.4 -
- G _.
g R a
- .s y +
m m i .. ,- 5 g m m e-i .1 r g
,i 8
e .) *- l r m 3.5 - i@ ENCONTROLLED
+
m C
-1.3
( ))
' ' ' ' , , , * * . l
-6.:
687 631 636 701 7CE 710 its 7: 7:5 77; 73, EATA=82 00hfAINMfNT V($$(L TRAN3lgNi ingq.qq ggggg; gqggy$gg , wCOMETRY AN5fs i i
ENCONTROLLED p')
' FIGURE 4.5 %/
g#i tdE F.LAA CotF Fl4 LEWT w 400 5To/de / ff */'F tut 9see %s ct,cFFtcicai = 1.16 sto /de-/ rf/* F teapena m oF mew - so exah r./eT /.,
'>fc(artt. H Ai cf ettct. = S4.9 5To /FT'/
- F E
i u. la+ irs coat AiwmM 4+-e u (tie nG (19 E A b\t E O F Co.w Fitautt G .7. 1 - l b sF F 6 A 9. ) Ts % 1*F r W
= \**
0 3 a j s.. r j cvT ,s F E Cc4T Ai d M t dT Y C 49 t L- ( AIC\ I l 5 / l s, ss e
-- t
. ... 2., ,.. ,.. w.c tun O
... 3.. ... ... .
Awbied Teuperatun s 4-w 5+eam a w d A 6- D w/imj LocA i l
.)
ENCONTROLLED V .
,@,g FIGURE 4.6 52 ~*
3, CATAWBA CONTAINMENT 5 as'8 VESSEL 4"g
. WILSON-GHOSH MODEL 47 6 . .
4:S 4EO 44'@ 43S 42 E-COORD. ELEV. spes. 6 5* t q n. (in)
" p 690_ 40 1405 669+1 J' . 3s\ @
6 37 1285 659+1 o 3g 3, V 33 34 116 9 649t5 3 3i 1049 639 + 5 29* G 1 27 28 929 629+5 Axis of Symmetry , 26 24 % 25 809 619 + 5 [ # 2 bb 22 689 609+5 R=690 2o se* *@@ '9 569 599 + 5 17 e is 497 593+5 12 13 383 583 +11 6 257 573+5 jg 10 L 3+ 0
, ,KD I
O 6 7 l 13 7 563+5 'Q 5j } I, $ 4 34 5 54+ l0
= 0 552&O r
r ;
\
v CHAPTER 5: LOADS ACTING ON CONTAINMENT VESSEL As stated earlier, the containment shell was analyzed for its stress states under various loadings. The BOSOR4 model was used for all such analyses except the LOCA pressure transient which was analyzed with the aid of the Wilson-Ghosh model. The results of these analyses are presented herein. 5.1 Dead Load The shell's behavior under dead load was investigated first. The meridional stress distribution and the circumferential stresses are presented in Figures 5.1 and 5.2, respectively. As can be seen, the membrane stress resultants are quite low, never exceeding 900 lb/in. 5.2 Seismic Loads The horizontal seismic inertia forces were computed from
) the seismic response spectra provided by Duke Power Company.
fw/ N'ss The seismic response spectra at various elevations along the shell axis were computed by Duke Power Company. The stress states which arose from this BOSOR4 analysis are depicted in Figures 5.3, 5.4 and 5.5. Again, it should be noted that the horizontal seismic stress levels are very low. This is, of course, to be expected because the shell is a rigid structure with relatively light weight. The vertical seismic stresses are also very small since they are a factor, 0.20, of the dead losd stresses. This fac-tor was obtained from a vertical response spectra correspond-ing to the shell's vertical fundamental natural frequency. 5.3 Pressure Loads The containment shell is subjected to several different pres-sure states. Plots of the stress states due to a design external pressure of 1.5 psi are presented in Figures 5.6 and 5.7. l l During the LOCA temperature state, a minimum internal pressure p \ UNCONTROLLED
2'M, (. ,,
) .
CATAWBA CONTAINMENT L ii N1 PLOT DEAD LOAD l
% 'N N.
SEG 9 FIGURE 5.1 38 PTS
\
I \ :
. r ~
0 '. [ 69
\. E t
EL M 9'.t* l
!. 34
- 5.312 5 PT5 ;t n y.a.
Et scr.t* I ' Es itH' gg 99 .g.
~
gE ft &19k f* h] uj #c .m
)
r + s. <, . . . , . ., . M
< s i t hi9'. *
- O M W
p E l Es121* & f t ( "9*. ? " l
- =
m-N fu??9'.5" l
,. !&?i
m; z.nr ,, I me r _ c -s M-SE 1 s) ..->- - . .. , ..,.. . i a m: =
-2 'g f r = 4'. .o-lN r.
. y. . .
p.c~t e. ,,
*.o
. + 'O
1 l zd CATAWBA CONTAINMENT n" ' ! i N2 PLOT v 2 g DEAD LOAD FIGURE 5.2 l SEG 9 30FT5
?
E I
.0 &
g.h' ~ 5 i _ _ ,, et uoi I M'C l'p15 0 l/ z.,2.n* ssu* m u r. . s mw. ..
.n --
8 1 ' E s t #4J' .,r is 49' 6* M en b , ft &!9'. f *
^C )
Q . ss
- 2, iL (.29".r*
vs [ C e. ,a.,...
/_ _,
M h l e gs72/* t o L 8LEW.?" ta b snu" ~ .. , t '.
- W e t
- g i +;'t ~ i f _ f t% %*
I hb f !S?'. " x,:.* g 1 r_ E?G T* 0 . , R_ $.. ( 1 g . osy N -' . IL
- e 3 '. T *
* - (
I y ef .
,7,, ,f $ CiI O
~. _ _h. r _ s si. .c-I ,
n - . ..,y ,, o . a
z.u:c_ CATAWBA CONTAINMENT l (vO Ni PLOT l HORIZONTAL SEtSM10, THETA 90 0EG N FIGURE 5.3 l SEG 9 3s PT5 N . l C* g , e t M9'- l I t sEs a red **- f.312* i 5 PTS ~LLeT*9" h 6 8 4'. t ' g , s ,p - ' it @9'* S *
\ 40
**- ft 639'-f" N} #c
!s N S"
_ m a sz, . t= WN oc r t e9'. a . C M EC f> 7 I'
<M b
.m .
7
, s,e , - .,-
O . g f g= , . . r. - -
)
1.!W ,,
- r. c ~? ?
N ! sO h 4
~
\[d'
~ ,,,a 1
. _ . r. -
i 1 l r-et I c
-3
_ t s e..e-
....;3%/I ,=
- . .r. < ,
o - -M
1.a . CATAWBA CONTAINMENT
\n 's ) I N2 PLOT New/ HOR 12CNTAL SEISMIC' THETA *90 DEG FIGURE 5.4 1
SEG S JsPTS
\
l 4 e
;e y '
tt w, . + ' 1 , t_ g SE3 6 1 3 , ,3 , - sm* , s ns " :t o r-s-f e t e s, - i-i . ,,,r .
, < s, . s -
- 4. a g; st or. r- .43
,w
,3 m--
EM' y, '
, g., g.
9E ,<.,,..- C M
-c -
l gr7'I' M k at4'4'.E'
, ,ae . .,,..-
O t
-- h 3
, L !!I* * '"
z w- ,, 4 [ , rt e =f. s* 1 e5
!o \ ,-
s + Q-) d'!=>~D f c_ s a .e-I
.~- f k
- a 5t
;~ ,/ e._ <s.e-l -,, et / -
.3- ,,
r +
- a 2
2 ci:._ - o CATAWBA CONTAINMENT Qv , NIZ PLOT HORIZONTAL SEISMIC, THETA =O FIGURE 5.5 l SEG 9 3 PT5 N /
/7 I
p/ g y' 1 -d' Et M 9'.f* q
/ -
SEGB I/ y , ,m ' 13.'2
- 5 PTS it 5:A'. 9
- _
l ,c a .,- P- *
+=
1 ' Z a id*F " , IL 4+9 '* 6
- 9/ :E
,t m . r-E c y l '
mr . . . . , .. , . :-
-).
WU e n-s t .,, . e - C I is121* ,, M f t E F- ? " k
$O i =; ....s. .
o
...e _
m ,,s - C) i mm
$, _ r_ssY.v' g
vnr ,, l y, c _ e - C. =* 8E
.s e t*r # '
,, e_ u 3 '. e
- i 3 C 21 $b ! ; _ s 5. .. I l . 4 3 ...'o -
2.c _ CATAWEA CONTAINMENT
, ,\
N /
'u 1 v
i NI PLOT l s EXTERNAL PRESSURE I.5 PSI g l
'g FIGURE 5.6 SEG S Ji Pf 5 I
'0 5 ?t 6t.9*. t
- l #
SEG 8 y . 3.k 1
- 5.322' 5 PTS r t ut'. e-E t 699". t '
b m-1 ' E n 110 " , it r,4e'. 5
- O ce ft & 39'. f
- r-
]
g V l , ns- f t (.29'. ?' i' m t t bi9'. a. O C M, l - Es72/* d, EL6'.9.t*
'S l
, .t . ,9. . .. ,
..,,,m-7 a_
e r ser. - w r.nr ,, I m, r e-d e- , 8E 1 J. -
,.~,..
0
<, m , . s . ,-
4 t i ~i
; MI~
), =-f .. ss . .c.
i r l p.faf e e e ? '. .? ' ,,
. -3
l
- z. a CATAWBA CONTAINMENT l ('3 V
v I N2 PLOT EXTERNAL PRESSURE I.5 PSI
, FIGURE 5.7 l l t-SEO 9 P i 31 PTS A l
=
\ l l
[ g[ i et asy g src.ia r..?..- I!J2* < s Pts a o r.,- f ..a s .. ,- t~ m b c-Z s 8 40 ' Et s e'.s
- M.
Ow iE ~ m c,.
. rg y M,
our ' i t i.29*. f *
.g. _
O s
-c _. _ -. -
I r
,a:, -
M u 4 ____ , ate:4.t* 1 :=- I
~' :: _-- ime.c 7
se= Q Z'I2T *
+
l I 3; @ " ____. r = "u-d'
'-) e ' ' "' '
}
. . r. -
~$ ;
-} Mt -
1
,~ _ , a. u. .c- l 3 e. ... 3-l L _. . . .
______J
/ t \ \
v
%/
of 7.5 psi is also developed. The stress states due to this pressure are linearly related to those states shown in Figures 5.6 and 5.7. Hence, there is no need to show them. 5.4 LOCA Pressure State As stated earlier, the LOCA pressure transient analysis using the Wilson-Ghosh computer program was provided by Duke Power to HEA in the form of output tLpes. A small program was developed which read through all the tapes and selected the critirsl stress states. The program chose the critical states for the following types of elements: the 1 inch thick element around the base of the containment shell, a 1 inch thick ele-ment between the first two stiffeners, a 0.75 inch element for the rest of the cylinder, an element in the dome, and the ring stiffeners. That is, the program selected the critical 5 stress states for any element in these five categories at each
,- time step. The following critical stress states were investi-( %) gated:
- 1) Maximum meridional compression,
- 2) Maximum circumferential compression,
- 3) Maximum shear stress,
- 4) Maximum combined meridional compression and circumferential compression,
- 5) Maximum combined circumferential compression and shear stress,
- 6) Maximum combined meridional compression and shear stress.
l Maximum values at each time step were written out as well l l as the exact location of the. maxima. It became evident that the maximum compressive stresses occurred at time step 7, so all output for time steps 5 through 11 was also printed. Al-though this output was not explicitly used in the buckling analysis, its study was deemed necessary to understand the l nature of the loading on the shell. l l n ("\ UNCONTROLLED l 32
/"~
t a iv/ V Figures 5.8, 5.9, and 5.10 depict the membrane stress states at a fixed angle at the seventh time step, 0.14 seconds. As can be seen, the stress states do vary in the meridional direction although the variation is not rapid. A similar vari-ation occurs in the circumferential direction. In effect, the stress states vary as waves in each direction. Therefore, the assumption made in the stability analysis, that the stress states plotted in these figures are uniform in the circumfer-entiai direction, is conservative. 5.5 LOCA Thermal State The LOCA pressure transient decays rapidly. Thereafter the pressure builds up to an internal pressure of 7.5 psi. How-ever, at the same time there is a thermal transient in the shell. This transient was computed with the aid of the ANSYS model ge discussed in section 4.3. The critical transient state occurs ""4 gy ac time = 250 seconds (see Figure 5.11). This temperature M mmq k ,) s gradient was then employed in the BOSOR4 model. The circumfer- zum ential stress state found in this analysis is plotted in .,) Figure 5.12; the meridional membrane stresses are negligible. The large ring stiffeners restrain the expansion of the shell to such an extent that large compressive stresses occur in the M mem( shell. r Note, however, that the ring stiffeners are under high umm( L tensile stresses. Hence, any increase in compression in the p - shell is accompanied by an increase in tension in the stif-feners. ) U E
.C rx
)
\Q, 33
2 c Cii' =
\ ~, . m.
rs CATAWBA CONTAINMENT (v) I N1 PLOT V ANGLE 23 TIMESTEP 7 LOCA WILSON-GOSH ANALYSIS l . FIGURE 5.8 SEO S Jn 9T5
\
\
\
l
\
d \ t' \
. i ~ '
, m 9a.
] .
7, ,p , S U2' 5 PTS f; f.M' 9* ft 659'.t' 0-- C I . . , ,o - .
,t -, . s .
p E 5 << e, r - - , I we ,,
,a.,.,. .
'O o
- W e
SC s e s e. - I mc w@ a nr-
' i at& W.t*
i se R
.. 7
,t..
z +M'n m e m' + ~ i __
$f_ r . m '. . .~
r<nr ,, g , r e-c s-i or m, vv
/ e
.t ,s.
I Gd ; mt 9 24 cu . et s s * -.e-l ,, ;. i /= c er' cL y
- 1. c.u .
CATAWPA CONTAINMENT
,7.~,) 3 N2 PLOT I5 ANGLE 23 TIMESTEP 7 LOCA WILSON-GOSH ANALYSIS g
FIGURE 5.9 Sf0 9 3 Pts
\
'\
l"
.o
- y. s -
, _n se u.s w i $EG 8 I Zei?-.* f !.'2
- 5 Pf5 ; t c 3 *. a.-
E t 6 8 9'. t
- Y l
.l -
.m1
- r. ,,o ....s. .
gE ~ FL [m 39. $ * . o e W sms- o u .w.s-I r. -( w g n.,,... I
* '~'~ '
=
, n. .. . N em W
2
-> :: u w.c l 1
1 Z * *v'e ' , c _ e9 ='. s-l l l m- 1 8 m- s sn. . .. l l
/*32' 9 l 1 .u c_ s-n s-85 m "r f \ 't L e <+ ; . ,,,3...
4 t .* - l - 1
'Ow w -
; ,, ,u.c a,
'~f of{ e Y <2 '. ;
-^
i e- .
zL CATAWBA CONTAINMENT / ,s \% i N12 PLOT i i 3 y ANGLE 23 TlMESTEP 7 . 1 LocA WILSON-GOSH ANALYSIS i FIGURE 5.10
'SEO S 3s PT5 I
,, /
su a9h* 1 SEO 6
,,g,. 1322' S PT5 g g - y, e, -
f ! L 659'* '
- w i ,
- a. .,n- , - . . .. . ,
Q Ob ,u,- i A I or M
, . . .. s -
r'" u w' C (* f _ bi9'* E
- We l
c w; Q
>\ 7 i
$[ taw r C
,, on + -
g Me d5 i !bI * *~ l'I2.3" <> I r_ iM- t*
)N
*i_
$F Nc. gg
.- O l
~m0 I
*2 f I 35 % , ._ s se.r
_, !e ==?
,o 9 '_
2* W fs \ ' CATAWBA CONTAINMENT 1 (/ I N' LO A THEFXA_
%/ INFUT T3 M80F,4 FIGURE 5.11 I
sf0 9 J# PTS 1 b tt M 9;t" SEG 8
,,,p,- S.312* 5 PTS It M Y*9' f
f t 6 8 9'* t
- 2' vi = ,
t ' n -, . - c4, m L Q ct6w.r- ,7 Cw ~ M i E' MS * ' o g m' s* O r m* et en t- ,<.,,.s-W l g 72/* . a t 6C4' E
- e i
E K
. t .,, . s - i
_ m,,<.,- J. \ i FL ?9 3'*tl~ I'I2 <>,me ! F I
%.q f4.9 i s l
7, * ) W 6
- p. ,%ge a M', '
p i e,
- I u ssa e.
v .. ..~,,
.1 ,.v..-
I o~ 4 - 7 g g Q ([ - rt ,,C'
,,y } %. 5 _ r.': - -
2* M MAY 17,252 CATAWM CONTAINMENT I LOCA THERMAL v HOOP STRESS N2 FIGURE 5.12 l SE0 9 38P73 I p h
=
l _4, Et M 9'.e* sto e i 1. e 4. - rEz- , sn3 , u,3., , . l , c w. e P= " et
== M j
g e rI69-is u,. .s- p A rt e,.r-
$,E .-
LD> v l rvs- ' u s:s'* c-Q' 2E m ,- a s ,.,- e& [ I Es72/* , ft639-i* I a ~,y
": , i u w.s- [
s i ]
-- ~
; y m , ,. . .
l Me
&s I
~
M: f. 8 9 5 . . J'723' ,, I g; c_ t-c - N - l CS g et *.?'8" bf
~1 Mt- '*
- 4 r ._ e r,4. .C' i ..o "
.....3 .
e yg +
4 t LJ
\=/ CIIAPTER 6: BUCKLING ANALYSIS The stress states discussed in section 6 must be combined according to Table 3.8.2-1 of the Catawba FSAR. A study of the required load combinations led to the conclusion that for the cylindrical portion of the containment shell only load combinations 3, 6 and 10 could be important in a buckling analy-sis. The hemispherical portion of the dome will be considered in section 6.2.
6.1 Buckling of Cylindrical Shell 6.1.1 Load Combination 10 Load combination 10 includes the stress states due to dead load, seismic loading, and LOCA (timestep 7 angle 23). The crit-ical meridional compressive stresses were combined as well as the shear stresses. Since the circumferential stresses are in ten-sion, they are neglected in this load combination. The knock-(~'} igh down factors for this case are small, 0.515 for the 0.75 inch thick section and 0.63 for the 1 inch thick section; thus the loads applied to the BOSOR4 model were increased significantly. The membrane stress states arising from this load combination are as shown in Figures 6.1, 6.2 and 6.3. This stress state was achieved by applying meridional forces at the top of the shell and at the juncture between the 0.75 inch and 1.00 inch sections, shear forces at the top of the shell, and an internal pressure throughout the shell. The internal pressure was re-quired because a meridional compression in the shell causes circumferential compression as well. Since this fictitious l compression does not exist for the stress state, an internal pressure was applied to cancel this effect. Figure 6.2 indi-cates that this procedure was successful. The BOSOR4 computer program can carry out a linear eigen-value analysis for a structure under appl'ied external loads. [~D This option was used in the buckling analyses discussed herein.
I The program first computes the stress states and deflections.
LNCONTROLLED
l
- 1. x CATAWBA CONTAINMENT O l NI PLOT LOAD COMBNKn0N NO 10
'd m FIGURE 6.1 1
SEG S 3r vis I g&.o'
._ <, ?L M9'.t*
F ' '? ' '
- Ih12* p73 ftg4t'.9*
- p. %
. . f L 6*9'. i' 0_
m l Ze I/O"
+ . h 449'.!* -
fv M 9 en , w FL &?9'. F * ,'
%J
) m,
~
'm
- 1. m - ,,
Q M. mm r
? tt ste". a
- e "t
l Es ?!/ * ' ii
; et s w.c-l 3",
..a. 4
~ tt 9.s-
- ~ . ,,,,.. U l
Mm N
*: __ct ter.,,-
?*?2.t" <>
l I , y r- co-
"O
%J
)
g e l43 ' O f t
- h y *. c a 1
e-
. E-
=
[ M eI, =
< < e s...e-
- - . - - . . _ ... x. .. .
z cu' - CATAWBA CONTAINMENT p(/ I N2 PLOT V LOAD COMBINATION No.10 FIGURE 6.2 i SKs 9 38 P75 l c s ' n v.9;s* j SEGS r e ry s ' 5. N2 ' -i S PT5 l. rt s,s t'- 9" l asw.- O
+=
- l. . s i.,,,,-
y a e. , . ,- rj l J p) w -
=u c
. c, ...
p I
., ~. ,- .
n .,. ,. . p M we # 2' { s==l
#C \
.t 6e'. ?- '
( .
) f t E N'. E ' o I
l ' m ..,x. y Z l t m
. . .,v m u t,r s- W
( l ' m. 0 m_ e m'.n-r nr ,, e,, j m . ,..,. (<% r*W y me 5 . ._ g a *. < - l _ Gr y a. 2
~
?,) i; c. < < 4' e-
,.A
_ . .r. e,-
1 1 l l
- 1. x CATAWM CONTAINMENT l O
v i N12 PLOT LOAC COMBitlATioM NO.10 FIGURE 6.3 1 SEG 9 3eris I
,p
- it 669*.q' l _
sto e 7 041, 5312* a S PT5 e t r.4,3*. 9
- f L 	*. t
- 0*
l. Z 110 * " ,p It M9".9
- s .~
Oc c -
.,t . , ,. . .
I 1 ws-
- su w .s.
-=
s-w it.,.- me r M L r.tzi-ft& &*** k 3
- I
- e= N n i
l
- y it t*9'.!* O
[
@ <> cures'.=-
I mm
== rt < sr...-
I'32Y <> I w ct - 6 .- 05 l *e se l ' ~7J Mt~ e _ e s i.e-1*0" e e ef. y , _ , -A
( i t 's v These stresses are used in the formation of the geometric l stiffness matrix which is then used in the eigenvalue analysis. l The user must input the circumferential wave numbers for the mode shapes in which buckling is expected. BOSOR4 computes the lowest buckling load and its corresponding mode shape at each wave number; the lowest buckling load for all wave num-bers is the critical buckling load for the shell. Load com-bination 10 was investigated for the wave numbers ranging from 18 to 32. This range was determined by the in-house HEA computer program, SHELL, which predicted a meridional buckling force of 43.14 kips /in at nu 26. BOSOR4 yielded a meridional buckling force of 44.73 kips /in at n= 26. It should be pointed out that the in-house program did not take into account shear ano predicted a stringer buckling. Shear was considered when using BOSOR4. Since it describes a stringer buckling mode, the analysis does indicate that any influence of shear on this buckling case is minor. The factor of safety against buckling for the shell analyz-ed is simply the BOSOR4 eigenvalue, 3.05, since the knockdown factors were already applied to the loads. Note, however, that the thickness employed in the analysis was the minimal shell thickness, 0.700 inches, instead of the nominal shell thick-ness. The buckling modes for n= 18 and 25 are depicted in Figures 6.4 and 6.5. There is little difference between the curves shown. In fact, the buckling force does not change much in this wave number range; it is 47.76 kips /in at n= 18 and 47.55 kips /in at n= 32. The position of the critical buckling amplitude coincides with the location of the equipment hatch and the personnel air lock. Therefore, it was decided to investigate the effect of these large penetrations on the buckling values for the shell. This analysis was performed using the NASTRAN model discussed n k
~ UNCONTROLLED 43
' "~ '
CATAWBA CONTAINMENT (- ^' LOAD cogStNAil0N NO 10
\ g
' gucKL)NG MODE V N*lS FIGURE 6.4
' SfG S 3 PTS
/
%.o j -<,
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1 2*C1,. CATAWBA CONTAINMENT l t LOAD COMBlHAT)ON No.10 ( '- l CRITICAL BUCKLING MODE l
%/ N=26 FIGURE 6.5 I
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\
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NJ. r.fe , e._ u r.e-1 l Gr , 31 e4 i e u = u'. e-l ,..
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L-) V in section 4.2. An attempt was made to achieve the same stress states as those depicted in Figures 6.1 through 6.3. An exact duplication was not possible because any loads applied to the boundaries of the NASTRAN model would interact with the ring stiffeners and stringers. Since meridional compression is the critical stress causing buckling an accurate representation of this value was sought for in the NASTRAN model. The circum-ferential compression caused by the meridional compression which was not present in the critical stress state was removed by the application of an internal pressure. It was not pos-sible to reproduce the shears in the NASTRAN model, but as stated earlier, their influence is minor. The stress contours resulting from the NASTRAN analysis are plotted with respect to the local axes of the individual elements rather than the global axis and are pictured in Fig-rx ures 6.6, 6.7 and 6.8. The lowest six eigenvalues correspond-i
\ ,) ing to this stress state were computed by the NASTRAN program.
'~'
Although 1.97 was the lowest eigenvalue, there were several eigenvalues clustered near this value. The six eigenvalues computed were in the range 1.970 to 2.050. The mode shapes are shown on Figures 6.9 through 6.14. It is evident that buckling occurs in a highly localized zone around the penetra-tions. The slignt movements of thg nodes located some distance away from the openings in the shell can be attributed to the remaining fictitious circumferential compressive stresses men-tioned above. The knockdown factor, 0.515, had bean applied t'o the meri-dional loads inputed into the NASTRAN model. This as discussed in section 3.2, is extremely conservative. It is probably more correct to consider this analysis as ene wherein a knockdown a factor due to penetrations is taken as unity. If the view-point is adopted the factor of safety against buckling is 1.97/0.518 = 3.80. Retention of the original knockdown factor
,a i
ENCONTROLLED 46
( FIGURE 6.6 v
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p l FIGURE 6.7 to.nu s 44 l 8
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l ("%. us
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- i :.i#. T.'.? 7:,1 Q ENCONTROLLED 49
_m 4 V FIGURE 6.9
% u s e s s.t*T m N
N_ _/ / N_ _ - - N - - - N / QN N r-
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! '\ \,,,/ V FIGURE 6.10 I
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x N- - - x _- -
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x / x _ __ -- - / N / xx
- /
ccw __ i s q N ' \\ x - -
- f
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x N ~~s_c , 1 x\N ~ N p/ N 1 N x __ - 1 i waer-g~.s UNCONTROLLED 51
eO%W h U FIGURE 6.11 N_ - x- - - -
~
N -- - - - ' / N N
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N _ _ _ - - -
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x
~
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UNCONTROLLED 52
. __ n
l
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N.] FIGURE 6.12
._m. __
x s x __- - N _- - x ~ ' N _- -- / N / x Q ~ __ - // Q '% \\
,lII N '
pyx xx'
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N x 49[ x
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o UNCONTROLLED v . 53
() FIGURE 6.13
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N 'w _ - _ y
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\J 54
m, .,
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V FIGURE 6.14 u..w.n.a .a N N __ N -- _- - / N N
' /
N - __ _-
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1 ("b \ (;l
\"' leaves a factor of safety = 1.97. Note, however, that the shell model used herein uses a minimum shell thickness of 0.700 inches for the whole shell. Therefore the safety factor for the nominal thickness would easily exceed 2.0.
6.1.2 Load Combination 6 and 3 Load combination 6 includes the stress states due to dead load, the LOCA temperature transient, seismic loading, and the LOCA internal pressure. The behevior of the system is domin-ated by the stresses due to temperature and internal pressure with the hoop compression resulting only from the temperature gradient. This being the case, it can be questioned whether this combination presents a legitimate concern for buckling. The hoop compressive stresses due to temperature arise from the restraint of the hoop stiffeners; hence the stresses tend to relieve as radial deformations increase. The internal pres-g) sure results in radial deformation and meridional membrane
\-) tension. In addition, it is not possible for the shell's com-ss pressive stress to increase due to thermal gradient without increasing the tensile resistance of the circumferential ring stiffeners. Because of tension in the ring stiffeners and the membrane tension instability can never occur in this load com-bination. The worrt tnat could happen would be a local wrinkle in the shell. Nevertheless, since the code case requires that temperature stresses be considered as primary stresses, a l buckling analysis was performed.
A BOSOR4 analysis was carried out for the shell under i dead load, an internal pressure of '.5 psi, and'the temperature l gradient computed with the ANSYS model. It was decided that l the knockdown factor would be applied to the buckling stress l obtained from the analysis. Figures 6.15 and 6.16 picture the stress states computed by BOSOR4 which were used in the eigen-value analysis. It was expected that buckling would occur at (D V ENCONTROLLED
m 1.e , x CATAWBA CONTAINMENT p) 13~ Ni i !_OT LOAD COM5tNAT10N NO. 3 FIGURE 6.15 I ; seos t 38 pts ) l l I
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1 MAY I"I,1982 CATAWM CONTAINMENT
/,s LOADCOMBINATION NO 6: LOCA, I
() I INTERNAL PRESSURE, DEADLOAD v HOOP STRESS N2 l SEG 9 FIGURE 6.16 3sPTS
\
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the circumferential wave number n = 60 so the lowest buckling loads in the range n = 52 to n = 62 were computed. Buckling did occur at the expected wave number ; the buckling factor was 2.72. Application of the knockdown factor of 0.80 for circumferential compression results in a factor of safety of 2.18 for the shell with the minimum thicknesses. This value increases for the nominal shell thickness. The mode shape corresponding to the wave number n = 60 is depicted in Figure 6.17. There is no need to plot the other modes; the only change is in the value of the circumferential wave number, n. The maximum value of the buckling amplitude occurs in the 0.75 inch thick portion of the shell wherein tensile, as well as compressive stresses, exist (see Figure 6.16;. Since n = 60 corresponds to a buckling wave with nodes at each stringer even thouch the stringers were " smeared" over the Lhell, this buckling analysis determines the critical 7-() v position for local buckling as well although it does not give the local buckling stress. Load combination 3 requires little discussion. The thermal stresses are due to an internal shell temperature of 120 F. This causes a small thermal gradient across the shell and ring stiffeners. The thermal stresses were found by scaling the re-sults of the thermal analysis utilized in load combination 6. In addition, the circumferential buckling stress obtained in the BOSOR4 analysis for load combination 6 was used in the com-putation of the stringer buckling factor of safety. As could be _ expected, the factors of safety are extremely high for this load combination. The containment is even stronger than these fac-tors indicate, because as stated earlier, compression in the shell due to thermal stresses is accompanied by tension in the ring stiffeners. Buckling could not lead to reduced load-carrying capacity.
,'w g 6.2 Buckling of Scherical Dome i ,
_3 The spherical dome portion of the containment shell is ENCONTROLLED
l 1 I I' MAY l'i,is22 CATAWEA CONTAINMENT V
\ LOAD COMBINATlON NO fo l
CRITICAL BUCKLING MODE N40 ! i FIGURE 6.17 SEG S Ji PT5 I p h
- E L 6p'e9* l' i
\ SEGS
) 7, ,p i - IN2' i 5 PT5 f t t.t.3*+ 9*
f E L 6'9.* i . t g PM 9 m - m T ! I s 118)'
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ata.3.c' 3,1 st _ _ ru es . .c-
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%' stressed by its own weight in combination with either the ex-ternal pressure of 1.5 psig (combination 7) or the LOCA tran-sient pressure (combination 10) loadings. All other loads are insignificant as far as buckling is concerned. The combination of external pressure and dead load is critical for the dome, because, although the combined membrane stress is not large, 0.932 ksi, the knockdown factor is very small, 0.124. This factor is applied to the classical buckling stress found for a complete sphere under uniform pressure. For the Catawba dome, this classical buckling stress is 16.71 ksi. Despite the great difference in these values, the factor of safety after the knockdown factor is. applied is 2.23 based upon the nominal thick-ness of 0.688 inches.
The membrane state under the LOCA pressure transient is pictured in Figures 5.8 and 5.9. Whenever there is a large 7-s compressive stress in the meridional direction, there is a () correspondingly large tension stress in the circumferential direction. A similar situation occurs when there is compres-sion in the circumferential direction. There is never a significant stress level at which both membrane forces are in compression. Since this situation is not covered in the code case, an in-house program was developed by HEA, Inc. to compute the bifurcation forces for spherical panels. This program carries out the same bifurcation analysis discussed in refer-ence (19). It is valid for the hemisphere under investigation because the classical buckling modes for spheres are highly localized and buckling can be described in terms of small shal-low panels cut out of the complete sphere. The critical buckl-ing stress for the case of equal stress values but with different signs is 18.24 ksi, a surprisingly small increase over the value of 16.71 ksi which governs when both directions are in equal compression. fx V ENCONTROLLED
l l f~') (_/ There is no knockdown factor presented in the code case for the sphere under equal tension and compressive membrane forces. The literature on shell buckling is no help either. A knockdown factor of 0.60 was chosen. It is based on the local shear buckling of a cylindrical shell, probably the closest approximation to the stress state currently under con-sideration. When this knockdown factor is used, the factor of safety against buckling is 4.01 for the load combination of LOCA transient pressure and dead load. l ) sc i l l Q ENCONTROLLED
I p
\, j}
%/ REFERENCES
- 1. American Society of Mechanical Engineers, ASME Boiler and Pres-sure Vessel Code, ANSI /ASME BPV-III-1-NE, Section III, Code Case N-284.
- 2. Seide, P., Weingarten, V., and Masri, S., " Buckling Criterion and Application of Criteria to Design of Steel Containment Shell",
NUREG/CR-0793, May, 1979.
- 3. Baker, E. H., Kovalevsky, L., Rish, F. L., " Structural Analysis of Shells", McGraw-Hill, .Tnc., 1972.
- 4. Duke Power Company, File No. CNC-ll44.09-01-0004, Catawba Nuclear Station.
- 5. Duke Power Company, " Containment Vessel Local Structural Re-sponse to' Hydrogen Detonation", McGuire Nuclear Station, Feb.
15, 1981.
- 6. Anderson, C. A., and Bennet, J. G. " Containment Buckling Pro-(7) gram" submitted to Ninth Water Reactor Safety Research Informa-tion Meeting, Oct., 1981, Washington, D.C., Los Alamos Scientific Laboratory.
- 7. Babcock, C. D., " Experiments in Shell Buckling", Thin Shell Structures, Fung, Y. C. and Sechler, E. E. (editors), Prentice Hall, Inc., 1974.
- 8. Galletta, L. J., and Morris, N. F., " Inelastic Buckling of Spherical Shells", Journal of the Engineering Mechanics Divi-sion, ASCE, Aug., 1974. pp 795-810.
( 9. Freskakis, G. N., and Morris, N. F., " Asymmetric Buckling of Imperfect Spherical Shells.", Journal of the Engineering Mech-anics Division, ASCE, Oct., 1972, pp 1115-1131.
- 10. Hutchinson, J. E., and Koiter, W. T., "Postbuckling Theory",
Applied Mechanics Reviews, Vol 23, 1971, pp 1353-1362.
- 11. Ball, R. E., " Dynamic Buckling of Structures", Shock and Vibra-
_ tion Comnuter Procrams- Reviews and Summaries, Pilkey, W. and e )
.,/
UNCONTROLLED
l 1
'b L/ \"# Pilkey, B., (editors), The Shock and Vibration Information Center, 1975.
- 12. Budiansky, B., and Roth, R. S., "Axisymmetric Dynamic Buckling of Clamped Shallow Spherical Shells," NASA TN D-1510, 1962, pp 597-606.-
- 13. Danielson, D. A., " Theory of Shell Stability", Thin Shell Struc-tures, Fung, Y. C., and Sechler, E. E. (editors), Prentice Hall, Inc., 1974.
- 14. Seide,.P., "A Reexamination of Koiter's Theory of Initial Post-buckling Behavior and Imperfection Sensitivity of Structures",
Thin Shell Structures, Fung, Y. C. and Sechler, E. E. (Editors), Prentice Hall, Inc., 1974.
- 15. Bushnell, D., "BOSOR4. Program for' Stress, Buckling and Vibra-i tion of Complex Shells of Revolution", Structural Mechanics Software Series, Volume 1, Perrone, N., and Pilkey, W.,
University of Virginia Press, 1977.
\/ 16. Bushnell, D., " Thin Shells", Structural Mechanics Computer %s Procrams, Pilkey, W., Saczalski, K., and Schaffer, H. (editors),
University of Virginia Press, 1974. 11 7 . Starnes, J. H., "The Effect of Cutouts on the Buckling of Thin Shells", Jhin Shell Structures, Fung, Y. C., and Sechler, E. E. (editors) , Prentice Hall, Inc., 1974.
- 18. Almroth, B. O., Brogan, F. A., and Marlowe, M. B., " Stability of Cylinders with Circular Cutouts", AIAA Journal, vol. 11, pp 1582-1584, November, 1973.
- 19. Hutchinson, J. W., " Imperfection Sensitivity of Externally .
Pressurized Spherical Shells," J. Applied Mechanics, vol. 34, pp 49-55. O ENCONTROLLED
l ("~\ l b APPENDIX I l
%/
Glossary bifurcation - theoretical state at onset of buckling for which the shell may be in the original position or in a de-flected position. buckling factor - the ratio by which loads must be increased to cause buckling. This includes no consideration of knockdown factors, buckling mode - shape of deflected structure corresponding to a buckling eigenvalue. dynamic buckling - buckling under loading which includes iner-tial forces. general b.uckling - buckling of shell including stringers and ring stiffeners. knockdown factors - factors by which the calculated buckling loads are reduced to empirical buckling loads. {~(}) T j LOCA - Loss of Coolant Accident. local buckling - buckling of curved panels formed by stringers and ring stiffeners safety factor - the factor by which the loads must be increased to cause buckling. This includes the effect of knockdown factors. stringer buckling - buckling of shell including stringers between ring stiffeners TMD loads - time mass distribution loads resulting during very early stages of LOCA. Obtained from analysis using Wilson-Ghosh computer program. Q,^ UNCONTROLLED . l
p- % ) Q,>
%/
Several computer programs were developed at HEA to in-vestigate the bucklin'g of simple supported stiffened cylindrical shells and simply supported stiffened doubly curved panels. Since the code case equations for cylindrical containment are based on the same theory, the cylindrical shell program can be used to reproduce the code case computations (article 1712.2.2). Therefore, this program was only used as an aid in the work described herein. However, the program for a doubly curved panel had to be employed in the investigation of the dome under the LOCA transient pressure load. Therefore a listing of this program is presented in this Appendix. It is well known that buckling of a spherical dome occurs in a localized dimple in the shell (19). Therefore, the buckling load can be computed with the analysis of a small shallow spherical cap which is removed from the shell. The only restriction is that the diameter of this cap must be
}
(', several times larger than the buckling wave length. A spheri-cal cap containing a 15 degree opening angle was employed in the analysis of the Catawba containment dome. SHELL 3 was checked by the analysis of a dome under uniform pressure; the buckling stress found, 16.77 ksi, compares favorably to the exact value, 16.71 ksi. It can be concluded that both the program and the model are satisfactory for this dome. Q UNCONTROLLED}}