ML19308A327

Review of OPS Rept 7270-RP-16A51,Buckling Criteria & Application of Criteria to Preliminary Design of Steel Containment Shell for Floating Nuclear Power Plant, Revision B,780501

ML19308A327
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Site:	Atlantic Nuclear Power Plant
Issue date:	03/31/1979
From:	INTERNATIONAL STRUCTURAL ENGINEERS, INC.
To:
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ML19308A325	List: ML19308A326 ML19308A327 ML19308A328
References
CON-NRC-03-77-131, CON-NRC-3-77-131 NUDOCS 7905030042
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REVIEW 0F 0FFSHORE POWER SYSTEMS REPORT NO. 7270-RP-16A51 BUCKLillG CRITERIA AllD APPLICATION OF CRITERIA TO PRELIMIflARY DESIGN OF THE STEEL (.0NTAlilfiEflT SHELL FOR THE FLOATlilG iluCLEAR PLANT DRAFT REVISION B MAY 1, 1978 INTERNATIONAL STRUCTURAL E!;GINEERS Glendale, California 91206 Date Submitted - March 19/9 Prepared for Structural Fy1r?n.iriny T r inch Division of Systems Safety U.S. Nucl ear P. ac t or re- nission Under Contract NRC-03-17-131

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TABLE OF CONTENTS

1. Abstract of Offshore Power Systems Report . . 1

2. ISE Evaluation f Offshore Power Systems Report . 2

a. Design Procedure . . . . . 2

b. Stress Analysis Procedure . . . 2

c. Buckling Analysis Procedure . . 3

d. Knockdown Factors . . . . 3

e. Preliminary Conclusions . . 5

3. Initial Review by ISE and OlS Response to Request for Additional Information . . . 6

4. ISE Recommended Method of Buckling Analysis 8

5. Evaluation of OPS Response to ISE Questions 11

6. Conclusions . . . . 12 References Appendixes A. ISE Critique of OPS Report and Request for Additional Information B. OPS Response to ISE Questions C. Additional Informatisn from OPS

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1. AlmTRACT

• Offshore Power lvi;tgs Report _(Ref_.,_(1])

This report presents the buckling criteria for the design of the pressurized water reactor ice condenser steel conta inment shell for the floating nuclear plant. The criteria utilize the classical buckling (linear bifurcation) surface technique for a perfect shelI with simply supported edge conditions. These classical buckling capacities are knocked down to the critical buckling capacities of the shell under consideration by applying capacity reduction factors which reflect the effects of initial imperfections, dynamic loadings and base displacements due to plat form deformation. The allowable buckling limits are established by applying overall factors of safety against the critical buckling capacities. In determining the capacity reduction factors due to initial imperfections, methodn of imperfection sensitivity analysis based on Koiter's Theory are emplc yed. The report provides basic information which defines the theory, piocedure, computer codes and verification programs used in the criteria. Sample calculations, arbitrarily selected f rom various phases of preliminary design, are presented in the report for the purpose of demonstrating the application of these buckling criteria in the design porcess. Also included are sample calcula-tions comparing these criteria against other well established buckling criteria to substantiate the adequacy of these buckling criteria.

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• Numbers in brackets designate items in the Reference 1ist.

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2. ISE Evaluation of_ Offshore Power Systems Paport_(Ref._ill)

a. Design Procedure _

The following design method was proposed in Ref. [1] :

1. Initial shell thicknesses and stiffening are assumed. The basis for these initial assumptions is presumably the use of stress-intensity criteria in conjunction with certain assumed design loads, simplified theories of bending and buckling of shells, and the designers' ex per ien c e.

2. The assumed shell is then analyzed under the design static and dynamic Icading to obtain more accurate stress intensity values.

The shell is strengthened, if necessary, to neet stress intensity requirements.

3. The shell is next analyzed for buckling capability. The axial ,

circumferential, stress and shear combinations at various points on the structure are compared with buckling surf aces caelulated for a uniformly loaded uniform simply supported shell with both longitudinal stif feners and circumf erential rirgs, a simply supported cylinder with uniform longitudinal stif feners only (t he structure between stiffening rings), and for a simply supported curved plate (the structure between rings and stiffeners). A similar procedure is used f or doubly curved portions of the shell. Again the shell is strengthened, if necessary.

4. Steps 2 and 3 are repeated with the new shell thickness and stif f en-ing until both stress int eunity and buckling criteria are fulfilled.

b. Stress Analysis Procedure The analyses in steps 2 and 3 are simplified. The stress analysis pro-

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posed for step 2 makes use of "one-dimensional" shell of revelution analysis

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codes oy omitting the ef f ect of openings and penet rat ions. Thus Fourier components of the loading and step dist ribut len can be analy: ed separately.

The justification for this approximation is the replacement of the openings.

The possibility of stress concentrations and inadequate stiffening is not investigated.

c. Buckling Analysis Procedure The buckling analysis is even further simplified since only uniform structures under uniform loading are investigated. While the actual cylinder consists of three bays of differing stresses and stiffener sizes, the possbility o r general instability of the entire shell is not considered.

The basis for this neglect appears to be the design of rings to withstand buckling. Although uniform stress distributions appear to be most severe, by comparing the stress-state at a point to the buckling surface, the pos-sibility of interaction of stresses at different parts of the shell is neglected.

d. Knockdown Factors Since theoretical buckling stress results for shells are often in very poor agreement with experiments, u knockdown factor is used with the theore-tical results.

In [1] the reduction f actors were chosen to be based upon an analytic theory of postbuckling behavior of shells. Reduct ion factors based on Koiter's asymptotic theory of shell post-buckling behavior depend on a number of parameters.

The reduction factor is the value of A g/A in the equation

/ A -

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1 - [ /2 C

=

f 68 [ C where T is the maximum amplitude of initial imperfections in the shape of

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the initial buckled shape. The parameter b, which is negative for buckling

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less than the classical value is a function of a sbell gremet ry parameter.

For the worst geometries the value of b for unstiffened shells is -0.77 for axial compression, -0.29 for lateral load, and -0.23 for t orsion leading to curves of reduction factors versus imperfection amplitude ratio given by Figures 5.6-1;2,3 of [1 ] . If these " worst" curves are used, the reduction factor thus depends only on the chosen imperf ect ion amplitude. For an imper-fection amplitude ratio of 1.0 (amplitude equal to shell thickness) the reduction f actors for axial compression, circumferential compression, and shear are 0.24, 0.36 and 0.40 respectively. The value for axial compression is less than that given in [3] for cylinders with radius-thickness ratios less than 900. The values for circumferential compression and shear are conservative for all values of R/h. If the imperfection amplitude ratio is reduced to 0.5 the values become 0.34, 0.50, and 0.53. The value for axial compression is now conservative compared to [3] for values of R/h less than 450. Values for circumferential compression and shear are still conservative for all values of R/h. For smaller amplitude ratios or lesser values of -b, the reduction factors increase and will eventually become larger than those of [3] for all values of R/h.

The danger of using Koiter's asymptotic theory is that the imperfection amplitude ratio is an arbitrary quantity. Thus ops uses the value of 1.0 in one place of [1] and 0.5 in another. It is not inconceivable that even lower values might be used, resulting in unconservative buckling values.

To use Koiter's theory effectively requires test data f or the determination of conservative values of imperfection a,plitudes ratio as a function of geometry. This essentially is equivalent to using test data to determine lower bound values of reduction factor.

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e. Preliminary Gnclusions In view of the uncertainties of the accuracy in the assumptions of the method outlined in the report, the reviewers are unable to reach any definite conclusions as to its degrees of conservativeness or unconservativeness. The method outlined is a plausible simplified method for pr_e_liminary design which, however, should be verified by more accurate analyses. The stress analysis should treat the shell as a two-dimensional surf ace structure and should include the effects of cutouts, penetrations and their reinf o rc emen t. A verification buckling analysis which uses the accurate stress analysis model and which utilizes the actual stress distribution together with appropriate amplification f actors to account for discrepancies between theory and experiment should be made as well.

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3. Initial Review and OPS Response to Request f o. id_i t i onal Information After reviewing Ref. [1], ISE reviewers could ac: reach a conclusion as to whether the OPS buckling analysis was conservative or not. Consequently, a number of questions based upon the f oregoing observat ions were directed to OPS through NRC in a request for additional infonnat ion dated November 6,1978.

(Docket No. STN 50-437, Containment Shell Buckling Criteria and Applications.)

The ISE critique of the OPS report and the request f or add itional information can be found in Appendix A. These questions were discussed at a meeting at OPS in Jacksonville, Florida, attended by an ISE consultant and an NRC representative on November 16 and 17, 1978 and the answers were documented in a 1ctter (FNP-MNE-879) f rom OPS to NRC dated Dec. 21, 1978 (Appendix B).

While the answers gave the basis for the assumptions of the method, they did not succeed in allaying the reviewer's concern for their accuracy.

Thus, even after this meeting ISE reviewers still felt that they could not reach a conclusion, regarding whether or not OPS buckling criteria are con-servative or not, without an independent evaluation of the OPS buckling approach. It is worth noting that af ter the Jacksonville neeting, ISE consultants found that there was a previous commitment between the applicant OPS and NRC for OPS to perform an independent evaluation of their containment shell buckling criteria.

It was agreed at the meeting of Nov. 16 and 17, 1978 that an independent verification of the OPS method was required. Subsequent discussions have succeeded in establishing the outline of the independent verification which was given to NRC in a letter (FNP-SE-1313) dated reb. 8, 1919 (contained in Appendix C). The verification consists of "an accurate t wo ,l ii m n s i onal (three-dimensional thin shell) linear clastic step analysis of the shell including the

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ef f ects of st if fening , pc..et ra tions , and dynanic leading.. The axial, cir-

cumferential and shear stresses at each nodal point are increased by dividing each by a reduction f actor for uniform axial, clicumf erential, and shear stress... The shell model is analyzed for linear bifurcation buckling under the increased stress distribution. " This method is in agreen<mt wi th the reviewers '

recommendations in their report, " Buckling Criteria and Application of Criteria to Design of Steel Containment Shell," Ref. [2], under contract NRC-03077-131 submitted to NRC March 1979. The recommended method of stability analysis in Ref. [2] is detailed in Section 4.below.

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4. Recommended !!ethod of Buckling Analysis

a. An accurate two-dimensional linear stress analysis of the shell including the effects of stiffening, cutouts, penetrations, and dynamic loading is made. The analysis should be shown to be accurate by comparing the stress state for finite element or finite dif ference models having increasingly larger numbers of subdivisions.

b. For a particular instant of time, the compressive axial and circum-ferential stresses and the positive or negative shear stresses at each nodal point are increased by dividing each by a suitable knockdown factor for uniform axial, circumferential, and shear stress. Tensile axial and circumferential stresses should not be increased since, in general, they serve to increase the buckling load. Thus, the knockdown factor for these stresses is unity. A knockdown factor greater than unity may be used with tensile stresses for an even more conservativt result.

c. The shell model used in the most accurate stress analysis is analyzed for linear bifurcation buckling under the increased stress distribution. In this analysis the modified stress distribution is multiplied by a constant fact er ,

say A, which is then determined as the lowest eigenvalue of the buckling problem.

A value of A greater than unity then indicates that the structure is safe. A value of A equal to or less than unity indicates that the structure is unsafe.

d. A sufficient number of " time snapshots" of the stress state must be consi. red to ensure the inclusion of the worst possible condition.

In the discussion of the preceding method, nothing concrete has been stated about what knockdomi factors should be used. Experimental data that can be used to establish reduction factors for axial, circunferential, and shear stress states for cylinders are available in publications associated with the aero-

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space industry. In [3], for example, the following, values are recommended for

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the reduction of calet lated stresses of unreinforced 1sotropic cylinders:

Axial Compression: 1 - 0.901 1 - exp - R/t External Pressure: 0.75 Torsion: 0.67 The external pressure reduction factor was actually recommended for hydrostatic ;'ressure, which includes an axial compressive stress equal to half the circumferential stress. Sicne the effect of the axial stress is negligible except for short cylinders, the value of 0.75 nay be used for compressive c ir-cumferential stress alone, values of knockdown factors for buckling of fabri-cated cylinders under axial compression and external pressure are given in

[4] and [5].

Although considerable data ecist for stiffened cylinders and have been compared with theoretical results [6,7], no specific recommendations for reduction factors have been made. It is known that the reduction factor is larger for stiffened shells than for unstiffened shells, but a lower-bound curve as a function of significant parameters has not been established.

Design rules for ring and stif fener sizes to prevent general instability are given, however, in [5]. A conservative recommendation for stif fened shells is the use of reduction factors for the unstiffened shell that has a pertinent uniform buckling load equal to that of the stif fered shell. Since reduction factors for circumferential and shear stress arn independent of thickness, all that needs to be established is the equivalent shell for uniform axial stress.

In that calculation the effects of cutouts would be omitted.

In the buckling analysis of stiffened shells, the nunber of longitudinal

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stiffeners or circumferential rings may be large, in which case they may be

" smeared" and the shell treated as a continuous structure. Local buckling

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-10, should be considered as an alternative possibility if the buckle half-wavelergth in the appropriate direction is close to the ring or sti f f ener spacing. For local buckling between closely spaced longitudinal stiffeners, the reduction factor may be taken as 1.0. Studies summarized in [7] suggest that it is important, if at all feasible, for rings to be treated as discrete stif fening elements.

The factor of safety specified in the ASME Pressure Vessel Code [8] is 3.

If the reduction factors given above are reduced by this value and compared with values suggested by Part (b) of the ASME Code provisions for buckling

[8] and [7], i.e. , a reduction factor of 1/10 for axial compression and 1/3 for external pressure (Fig. 4-31 in Ref. [2]), the two values for axial compression are about equal for shells with a radius-to-thickness ratio of 500 or so, where n the ASME Code value for external hydrostatic pressure is actually larger than 1/3 of the NASA recommended reduction factor. A safety f actor of 2 would make the reduced NASA circumferential stress about equal to the recommended ASME value.

It is felt that a safety factor of 2 is sufficient to achieve a conservative design for all states of stress if applied to reduction factors obtained as the minimum of experimentally obtained data. It is satisfactory, however, to abide by the experience embodied in the ASME Pressure Vessel Code [9] and to une reduction factors of 1/10 and 1/3 for axial and circumferential stress, respec-tively, without an additional safety f actor. Since the experinental reduction factor for shear stress is about equal to that of circumferential stress, the same factor of 1/3 might be used for shear. For deep spherical shells under external pressure, the recommended reduction f ac tor given by the ASME Pressure Vessel Code [9] is 0.1, whereas the reconaended NASA value [10] is 0.14. Here

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again, the ASME value is sufficient, while a safety factor of 2 should be used with reduction f actors experimentally deternined as ninimum values obtained from experimentally obtained data.

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5. Evaluation of OPS Response to ISE_ Questions The load amplification f actors (the inverse of the knockdown factors) called for in FNP41NE-889 (Appendix C) are those outlined by OPS in FNP-MNE-879 (Appendix B) . For stiffened or unstiffened cylindrical shells the knockdown factors of Ref. [3] are to be used for compressive circumferential and shear stresses.

For axial compression the value of the knockdown f actor depends on the value of the stiffener-cylinder area ratio. A linear reintion is used between the value of [3] for unstiffened shells and a .ralue of 0.5 for cylinders having an area ratio of 0.1. The value of 0.5 is a lower bound value established frem test data. For values of the area ratio greater than 0.1, the knockdown factar is constant and equal to 0.5. For doubly curved shell surfaces values of 0.25 for longitudinal and circumferential compressive stress and 0.5 for shear are to be used unless the case is covered in [10]. Tensile longitudinal, and circumferential stresses that are not mentioned in [3] and [10] may be 1cf t unchanged in the analysis. The values for cylinderical shells are satisfactory provided it is understood that these do not contain a factor of safety as indicated. The multiple of the basic stress distribution obtained from the buckling analysis then represents the factor of safety against buckling and pre-sumably should be at least 2.0 for the worst case. The values for doubly curved shells suggested by OPS need justification since they contradict some data in [10i The OPS procedure new states that "a sufficient number of " time snapshots" of the stress state will be considered to ensure the inclunion of the worst condition." The procedure also st at es , however, that "several critical loading cases are selected for independent verification analysis." Whether these two sta tements are contradictory or not remains to be seen. It should be understood

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that the sufficiency of the number of cases analyzed ufil have to be justified or demonstrated by calculations.

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6. Conclusions The conclusion of the reviewers is that the prelIninary design procedures followed by OPS do not reflect the latest state of the art on the subject.

The analysis does follow standard static design procedures and can tentatively.

be accepted until a more accurate design analysis is performed. The more accurate design procedure should follow the general stability analysis recommen-dations given in [2] and in particular should include the following:

1. An accurate 2-D analysis should be per formed for both the dynamic stress and quasi-static buckling analyses. Modeling should contain enough detail to accurately describe penetrations, stiffening, imperfections, local buckling, etc.

2. The knockdown factors given in NASA SP-8007 (Ref. [3]), NASA SP-8019 (Ref. [11]) and NASA SP-8032 (Ref. [10]) should be used as described in Ref. [2].

3. It is recommended that OPS not use a safety factor below 2.0 for the worst case.

4. The method described in Ref. [2] should be used for combining. load effects and analyzing stiffened shells.

5. OPS should demonstrate or justify that the " time snapshots" chosen contain the worst buckling loading condition.

6. The analysis should contain enough information on the dynamic stress state so that buckling spot checks can ca'sily be done by a reviewer.

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REFERENCE,S,

1. Offshore Power Systems (OPS) Report No. 7270-RP-16A51, lluck1_ing Criteria and Application of Criteria to Preliminary Desinn of the Steel Containment Shell for the Floating Nuclear Plant _, Draft Revision B, May 1, 1978.

2. I:.ternational Structural rngineers (ISE) Report, Buqklinn Criteria and Application af Criteria to Design of Steel Containment Shell, prepared under NRC contrac t NRC-03-7 7-131, March 19 79.

3. NASA Space Vehicle Design Criteria (Structures): Buckling of Thin-Valled Circular Cylinders, NASA SP-8007, Rev. August 1968.

4. Miller, C.D., " Buckling Stress f or Axially Cor. pressed Cylinders ," Proc.

ASCE Str. Eng. Conf., Madison, Wisc., August 22-25, 1976.

5. Miller, C.D., " Fabricated Cylindrical Shells under Combined Axial Comprensive Load and External Pressure," rev., Chicago Bridge and Iron Co., Plainfield, Ill. , January 1979.

6. Singer, J. " Buckling of Integrally Stif f ened Cylindrical Shells--A Review of Experiment and Theory," in CoM ributions to the Theory _ of Aircraf t Structures. Rot te rd am : Delft University Press, 1972, pp. 325-358.

7. Singer, J. and Rosen, A. " Design Criteria for Buckling and Vibration of Imperfect Stiffened Shells," ICAS Paper No. 74-06, Proc., The Ninth Congress of the International Council of the Aeronautical Fciences, liaif a , Israel, Aug. 25-30, 1974.

8. Okubo, S.; Wilson, P.E., and Whittier, J.S., " Influence of Concentrated Lateral Loads on the Elastic Stabilty of Cylinders in Bending," Experimental Mechanics, 10:9, 1970, pp. 384-389.

9. American Society of Mechanical Engineers, ASME Boiler and Pressure Vessel Code, ANSI /ASME BPV-III-1-A,Section III, Rules for Construction of Nuclear Power Plant Components, Division 1--Appendixes, 1977 Edition, 1 July 1977, Appendix 7, pp. 224-225.

10. NASA Space Vehicle Design Criteria (Structures): Buckling of Doubly Curved Shells, NASA Sp-8032, August 1969,

11. NASA Space Vehicle Design Criteria (Structures): Buckling of Thin-Walled Truncated Cones, NASA SP-8019, September 1968.

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Appendix A ISE Critique of OPS Report and Request Additional Information

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CRITIQUE OF BUCKLING CRITERIA A!,'3 APPLICA TIO . OF CRITERIA TO DESIGN OF STFEL CONTA T!.clGT SiiELL A study has been made of the Offshore Power S stems (OPS) Report i

No. 7270-RP-16A51, Buckling Criteria and Application of Cvheria to Prclininary Design of the Steel Containment Shcli for the Floating Nuc! car Plan t (Draf t), November 1978. The report, which clearly represents the culmination of a great deal of work and study of the available literature, proposes a method of stress and buckling analysis that is simple and well within the capabilities of presently available computer codes. Iloweve r ,

the accuracy of the method proposed is so questionable as to render it unacceptable for the design of nuclear containment vessels. The questions leading to this judgment are as follows:

a. A primary assumption of the recommended method is that cutout

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and penetration reinforcement is sufficient to alleviate stress concentra tion and to permit the use of one-dimensional stress analysis codes. The proposed amount of edge reiuforcement is that prescribed by the ASME Pressure Vessel Code {Il. For cylinders under external pressure, the cutout volume is to be replaced by an equal volume of edge reinforcement. Some avail-able studies I cast doubt on the adequacy of this rule of thumb. Ilow certain, th e n , is OPS as to the cufficiency of the proposed amount of edge stiffening? What studies are available to substantiate the claim?

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b. The reviewers are concerned by the fact that even though the one-dimensional shell model used for stress analysis was simplified, the same model was reduced even more drastically for the buckling analysis. Although the actual cyl.inder consisted of three bays o: differing stresses and stiffener sizes, the possibility of general instability of the entire shell was not considered. Each bay was assumed to act indepen-dently of the others. What is the justifica tion for this simplification? It does not seem unreasonable to expect the same model to be used for both the buckling analysis and the stress analysis.

c. Another disturbing aspect of the buckling analysis is the assumption that there is no interaction between stresses at different parts of the shell. The stress state at a point is to be compared to the critical uniform combined stress state without regard to the possible ef f ects o f the s t resses at other points. The results of [5] suggest that this assumption is not completely tenable. There, the stress state is axial bending stress, which is maximum at a location for which the shear stress is zero combined with variable shear stress that is maximum at a location for which the axial stress is zero.

The suggested criterion would be that either the maximum shear stress is equal to the critical torsional stress or that the maximum bending stress is equal to the crit ical stress in pure

' bending. Test results indicate, however, that there is an

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interaction between the two stress states which lowers the buckling load (Fig. 1). Is there any investigating circum-stance that justifies the assumption?

d. Capacity reduction fac tors have been defined on the basis of Koiter's asymptotic imperfection sensitivity studies and assumed deformation amplitudes. In the present study, the deformation amplitudes are taken as the maximum out-of-toundness values permissible under the ASME Pressure Vessel Code, the shell thickness. With such a large " imperfection," the reduction factors are conservative. The choice of amplitude is rather arbitrary, however, and may be too severe. Lesser amplitudes may yield unconservative results, since it is not at all certain that the ASME tolerances control all of the imperfections that reduce buckling loads. Wuy isn' t aerospace industry experience in the form of empirical buckling criteria used, for example, NASA SP-8007 and SP-8032?

e. Dynamic reduction factors are in question, since the literature indicates that for axial load, the dynamic buckling load is at least 70.7% of - the s tatic buckling load of the imperf ect struc-ture. Why, then, is the capacity reduction factor rather than the static reduction factor, taken as equal to unity, when in fact the dynamic stress is greater than 1.4? (1/0.707) of the static stress?

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The methous of stress and buckling analysis proposed by OPS thus appear to be simplified and unacceptable approaches to the problem. Even if the question of cutout reinforcement is answered, there still remains the question of nonuniform stress-state interac tion, which is not so easily answered. The reviewers would recommend the use of two-dimensional models f or both s tress and buckling analysis and tha t effort be expended for their efficient and accurate solution.

REFERENC ES

1. American Society of Mechanical Engineers, ASMS Scilcr and Frass:a'c Vessel Code, ANSI /ASME BPV-III-1-NE,Section III, " Rules for Construction of Nuclear Power Plant Components," Division 1--

" Class MC Components, Section NE-3332, Reinforcement Requirements for Openings in Shells and Formed lleads," pp. 67-58, 1977 Ed.,

1 July 1977.

2. Beskin, L., " Strengthening of Circular Holes in Plates under Edge Loads ," J. Appl. Mech., 11: 3, September 1944, pp. 140-148.

3. Levy, S., McPherson, A.E.; and Smith, F.C., "I!einforcement of a Small Circular Hole in a Plane Sheet under Tension," J. Appl. Msch.,

15:2, June 1948, pp. 160-169.

4. Timoshenko, S. , Strength of Materials, Vol. 2, 3rd ed., D. Van Nostrand, New York, 1956, pp. 305-306.

5. Peterson, J.P. and Updegraff, R.G., " Test of Ring-Stiffened Circular Cylinders Subjected to a Transverse Shear Load," NACA TN 4403, September 1958.

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Appendix B OPS Response to ISE Quest. ions

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