stress analysis and evaluation of a rectangular pressure vessel

8/13/2019 Stress Analysis and Evaluation of a Rectangular Pressure Vessel

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WHC-SA-1619-FP

Stress Analysis andEvaluation of aRectangular PressureVessel

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WHC SA1619DE93 004990

Stress Analysis ndEvaluationofRectangular PressureVesselM.A.RezvaniH.H.ZiadaWestinghouse Hanford CompanyM.S.ShurrabWestinghouse Savannah River CompanyDate PublishedOctober 1992ToBePresented atNational Design EngineeringConferenceandShowChicag o, IllinoisMarch 7 - 1 1 1993

Prepared for th e U.S. DepartmentofEnergyOfficeofEnvironmental Restoration andWaste Management

W e s t i n g h o u s e P . O . B O X 1 9 7 0Hanford Company Richland, Washington 99352Hanford Operations and Engineenng Contractortor theU.S Departmentof Energy under Contract DE-AC06-87RL10930C o p y r i g h t L I c s n s o Byacceptance ofthis article, the publisher and/or recipient acknow ledges the U S Government s nghttoretainanonexclusive, royalty-free license inand to anycopyright covering this paper.

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Stress Analysis and Evaluation of aRectangular Pressure Vessel

Mohamad A. RezvaniHassan H. ZiadaWestinghouse Hanford ConnpanyRichland, WashingtonMazen S. ShurrabWestinghouse Savannah River CompanyAilcen, South Carolina

ABSTRACTThis study addresses the structural analysis and evaluation ofan abnormal rectangular pressure vessel. The vessel was tohouse equipment for drilling and coUccting samples fromradioactivewastestored in high-capacity waste storage tanks onthe Hanford Site. The vessel had to be fabricated with aremovable cover plate.The dimensions and working pressure ofthevessel classifiedit as a pressure vessel; therefore it had to be qualified accordingto the American Society of Mechanical Engineers (ASME)

Boiler and Pressure Vessel Code, Section VIII, referred tohereafter as the Code (ASME 1989).Section VIII of the Code provides guidelines, rules, andexamples for analyzing and evaluating rectangular pressurevessels. However, the subject vessel had the cover plate boltedto the vessel along the long face of the vessel, a configurationnot addressed by the Code. A])plying the Code formulas foranalysis would lead to very conservative stress results andexcessive fabrication costs.Finite-element methodologywasusedtoanalyze and calculatethe stresses resulting from the internal pressure. The stresseswere then used to evaluate and qualify the vessel. Becausefatigue was shown not to be a con cern, the subject vessel can beexempted from fatigue analysis. Thu s, it can be built according

to the ASME Code, Section Vffl, Division I (ASME 1989a)instead of Section Vm , Division 2 (ASME 1989b). The resultwas a considerable cost savings.Results ofthestress analysis were checked against the C ode.To satisfy Code requirements, the design was modified byadding a stayed plate to stiffen the long s ide ofthevessel. Theformulas of the Code for rectangular vessels, although notdirectly applicable, were also considered and are addressed inthis study.

INTRODUCTIONA rectangular-shaped pressure vessel was analyzed andevaluated to the ASME Code requirements. This papersummarizes the approach used in the analysis, the exampleguidelines in the C ode, the evaluation criteria in the C ode, andthe difference between the general shapes of the rectangularvessels assumed in the Code and the shape of the subjectvessel.The vessel has inside dimensions of 39.25 by 12.0 in. (99.7by 30.5 cm) and is 15.5 in. (39.4 cm) deep. The vessel is not

an integral unit. To allow maintenance and service for theequipment housed inside the vessel, the cover plate (43.0 by15.75 in. (109.2 by 40.0 cm)) has to be removable. A stay-plate stiffener 12.0 by 15.0 in. (30.5 by38 1cm) was weldedto the inside of the vessel at a distance of 16.0 in. (40.6 cm)from the inside edge ofthevessel (22.5 in. (57.2 cm) from theother edge). Figure1is a sketch of the vessel with the coverplate removed.The subject vessel will operate at 37.0 Ibf/in (255 KPa)internal pressu re. The design press ure, as outlined by theCode, is 1.5 times the operating pressu re. Henc e, for theanalysis, an internal pressure of 55.0 Ibf/in' (379.2 KPa) wasapplied to the vessel to calculate the displacements, reactions,and stresses.The vessel will be used as part of the machinery to collectsamples from radioactive waste stored in the waste storagetanks. The vessel is expected to be pressurized 500 times peryear. Thelifeexjjectanc y of the vesselis 10 years. Therefore,it had to b e considered for a total of5 000pressurized cycles.

1 Mohamad A. Rezvani


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Working pressure = 37.0 Ibf/in^ = 255 KPaDesign pressure = 55.0 Ibf/in' = 3 79 KPaWall thickness = 0.75 in. = 1 . 9 cmAll dimensions in inches (1 in. = 2.54 cm)

FIGURE 1. SCHEMATIC CONFIGURATION OF THERECTANGULAR PRESSURE VESSEL.

GEOMETRY AND MATERIALAs mentioned in the Introduction, the inside dimmsions of the

vessel are 39.25 by 12.0 in. (99.7 by 30.5 cm), and it is15.5 in. (39 .4 cm ) deep. The side walls and the stay plate are0.75 -in. (1.9 cm) thick. The stay plate is added as a stiffenerto reduce the stresses at the long side of the vessel wall. Thecover plate is 1.0 in. (2.54 cm) and has outside dimensions of43. 0 by 1 5.75 in. (109.2 by 40.0 cm ). Twenty-eight boltesecure it to the flange of the vessel at the outside edge s. Thebolts are 7/16-14UN C-2A and are made of ASTM A1 93, GradeB8 steel. A 1/16-in. (0.16 cm) neoprene gasket was used toprevent the vesselfit>meakin g. The operating temperature ofthe vessel is below 200 'F (93.3 *C). The material ofth sidewalls, the stay plate, and the cover plate are ASTM-A240316 stainless steel.

The material properties o f the materials used are listed below .ASTM-A240. 316 Stainless Steel

Fy = yield strength = 30 ,00 0 Ibf/in^ (206 ,850 KPa)Fu = ultimate tensile strength

= 75,000 Ibfin* (517, 125 KPa)

S = maximum allowable stress (ASME 1989a)= 18,8 00 Ib in' (129 ,626 KPa)

S . = allowable stress intcaisity (ASME 1989b)= 20,000 Tbflrn^ (137,900 KPa)S. = alternating stress (used for fatigue evaluation)

ASTM - A193. Grade B8Fy = 100,000 Ib^in' (689,500 KPa)Fu = 125,000 IbCin '(861,87 5 KPa)S = 25,00 0 Ibf/in* (1 72,3 75 KPa)

A P P R O A C HThe analysis used two different approaches. First, finite-

element methodology was usedtocalculated the displacements,reactions, and the stresses. The stresses were evaluated bycomparing them to the allowables of the Code withconsideration given to the reduction factors for the welds.Using the guidelines in Appendix 13 of the ASME Code,Section VIII, Division 1 (ASME 1989a) that address vesselswith noncircular cross-sections showed that the C ode approachis very conservative.

Because the vessel will undergo 5 000operational cycles inits 10-year lifetime, fatigue considerations also need to beinvestigated. Cyclic fatigue requires compliance with theASME Code Section Vm , Division 2 (ASME 1989b).However, in this case, the two conditions (A and B, below)were statisfied and showed that the vessel could be exemptedfrom fatigue analysis. Therefore, the subject ves sel can beanalyzed and constructed according to Section VIII, Division1 rules (ASME 1989a).Fatigue Analysis

The ASME Code Section VIII, Division 2, provides rules todetermine whether fatigue evaluation is required or not. Th eserules include two conditions, of w hich one m ust be satisfied toexempt the structure from fatigue analysis. These twoconditions were checked.

Cond ition A. Fatigue analysis is not mandatory for m aterialshaving a specified minimum tensile strength not exceeding80,000 Ibf/in' (551,600 KPa) when the total expected numberof pressure cycles does not exceed 1,000 cycles.

The 3 16 SS m aterial has a minimum tensile strength less than80,0 00 Ibf/in' (551 ,600 KPa), but the number of pressurecycles (5,000 cycles) exceeds the specified 1,000 cycles.Therefore, Condition A is not satisfied.

Cond ition B. When the foUowing conditions are met, fatigueanalysis is not mandatory.(a) The expected design number of full-range pressure cyc les,

including startup and shutdown, does not exceed the



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number of cycles in the applicable fatigue curve of theCode corresponding to an S, value of three times S, valuefound in the tables of design stress intensity values.S. = 3 S, = 60,000 Ibf/in^ (413,700 KPa)This stress value translates to a maximum of 13,000allowable cycle s (se e Figure 2 rq>roduced fromASME 1989b), which is greater than the 5,000 cyclesexpected.

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HGU RE 2. DESIGN FATIGUE CURVE FOR SERIES 3XXHIGH ALLOY STEEL.(b) Additionally, the maximum allowable pressure calculated by

the formula below should envelope the 55.0 Ibfin* (379.2KPa) internal design pressu re, Pj.

whereSa = alternate stress for 5,0 00 cycl es, Ibf/in'

= 75,000 (517,125 KPa)Sm = maximum allowable design stress, Ibf/in^

= 20,000 (137,900 KPa)P,n. = 68.75 Ibf/in' (474.0 KPa)

Therefore, the ves sel could be exempted from fatigue analysis.Finite-Element Analysis

As an alternate approach to the Code de sign formulas, finite-element methodology (Cook 1981) was used to calculate thestresses in the vessel. The COSMOS/M' software package wasused to model the body of the assembly with four-nodedquadrilateral shell elements having membrane and bendingcapabilities. The locations of the bolts on the bottom plate

flange, representing the bolts mounting the vessel to thefoundation, were characterized as nodal points and fixedagainst movement in the vertical direction. One additionalnode, a comer node on the bottom, was constrained againsttranslation in both planes of th e bottom plate and in the verticaldirection.

The bolt locations on the top fiange, where it mounts to thecover plate, were modeled with spring elements using thestiffness of the bolts. The junction where the outer boundaryof the top flange meets the assembly cover plate wascharacterized by gap elements with 0.005 -in. (0.01 27-c m)openings. The gap elements were introduced to account for theprying action of the flange. Figure 3 depicts the fm ite-elementmodel with locations of interest.

9 taiam tm ri l prinry Mbr tM ttrtss - Huiiia w ibriM ^tus budiiig strtti - NixtMi )Ka1 prfianr Mitin M phs pr ln tj bendln] rtttlj

FIGURE 3. THE PRESSURE VESSEL HNITE-ELEM ENTMODEL WITH LOCATIONS OF INTEREST.

The stress results indicate a maximum general primarymembrane stress of1 245.0 Ibf/in' (8,584 KPa) in the middleof the long side of th e vessel. The maximum membrane-plus-bending stress, a value of 7,929 Ibf/in' (54,670 KPa), occursin the long side of the ves sel close to the top flange. Themaximum local primary membrane stress plus the primarybending stress, a value of 9,048 Ibf/in' (62,386 KPa), occursat the location of the stay plate. The cover plate, 1-in.(2.5 4 cm) thick, has a maximum membrane stress o f14,7 00 Ib in' (101,3 57 KPa) . All these stresses are within theallowables set by the ASME Code, Section VIII, Division 1(ASME 1989a).



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A S M E CODE ANALYSISThe minimum requirements for design and analysis of

rectangular cross-section vessels are covered in Append ix 13 ofthe ASM E Code (ASME 1989a). In particular. Figure 13-2(a),Sketch 7 (rq>roduced as Figure 4 in this paper), addresses therectangular vessel with a stay plate. How ever, the stay plate isshown at the middle of the vessel; in the subject vessel, thedistance from the inside edge of the side of the vessel to the stayplate is 22 .5 in. (57.2 cm ), with a total overall length of39.25 in. (99.7 cm). For a conservative analysis the length istaken as twice the distance from the edge to the stayplate, i.e ., h = 22.5 in. (57.2 cm) , whe re h is the inside lengthof the long side of the rectangular vessel. Th e length of thevessel, L, in this case the depth of the vessel is equal to15.5 in. (39.4 cm). Th e Code equations are developed forvessels with an aspect ratio, L^H or L,/h, greater than 4.0.Thus,the equations in the Code (ASME 1989a) are not directlyapplicable to the subject pressure vessel, and some dimensionalchanges have to be assumed to perform the analysis. In thiscase the aspect ratio is less than 4.0 and leads to veryconservative stress results for the combined stresses. How ever,for the purpose of comparison to the finite-element analysisresults, the calculations are carried through. Th e equations usedhere are from the ASME Code Appendix 13, Subsection 13-9.

Ph^c12 I j [ 1 + j r (3 - o*)1 ^ 2K

The above notations are defined below.Si = gen eral primary mem brane stress, Ibf/in' (KPa)52 = genera l mem brane plus bending stress Ibf/in^ (KPa)53 = local primary mnn bra ne plus the primary bending

stress, Ibfin^ (KPa)S = mem brane stress, Ibf/in^ (KPa)P = internal pre ssu re, Ibf/in* (KPa)h = inside length of long side of rectangular vessel,

in. (cm)t, = thickness of short-side plates of vesse l, in. (cm)K = vessel parame ter (Ij/Ii)^C = distance from neutral axis of cross section to extreme

fiber, in. (cm)I, = mom ent of inertia of strip of thick ness , t in^ (cm*)I2 = mom ent of inertia of strip of thick ness , tj, in* (cm*)

ct = rectangular vessel parameter, H/hH = inside length of short side of rectangular vesse l, in, cmh = inside length of long side of rectangular vessel, in., cm .

The resulting stresses for equations (1) through (3) are listedbelow:

S, = 750 Ibfin ' (5,171 KPa)Sj = 29,760 Ib in* (205,195 KPa)S, = 16,050 IbPin* (110,665 KPa).

E x c ^ for the S, value, the other stresses are conservativewhen compared to the finite-element stress results.1i

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1HG UR E 4 . RECTANGU LAR VESSEL WITH A STAYPLATE.C O N C L U S I O N S

Two approaches were taken to analyze a rectangular pressurevesse l with a design internal pressure of 55.0 Ibf/in' (379 KPa ).First the vessel was modeled and analyzed with finite-elementmethodology to establish a benchmark for calculating theminimum wall thickness required by the ASM E Code . Next,the ASME Code-recommended algorithm was applied tocalculate the stresses. Th e equations of the Code we re notdirectiy applicable. The design dimensions were modified, andthen the vessel was analyzed . A comparison of the resultsshow that, for low aspect ratios, the stresses calculated by theCode are very conservative.



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REFERENCESASME, 1989a,American Society of M echanical Engineers

Boiler and Pressure Vessel Code Section VIII, Division 1,ASM E Publications, New York, N ew Yoric.ASME, 1989b,American Society of MechanicalEngineers Boiler and Pressure Vessel Code Section V m ,Division 2, ASME Publications, New York, New York.Cook, R. D., 1981, Concepts mtd Applicationscf Finite Element Analysis Second Edition, John Wtlcy andSons, Inc., New York, New York.COSMOS/M, 1990, COSMOS/M Finite ElementSystem Version 1.61, Structural Research and AnalysisCorporation, Santa Monica, California.

stress analysis and evaluation of a rectangular pressure vessel

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