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International Journal of Pressure Vessels and Piping 87 (2010) 239e244

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International Journal of Pressure Vessels and Piping

journal homepage: www.elsevier .com/locate/ i jpvp

Stress distributions in a horizontal pressure vessel and the saddle supports

Shafique M.A. Khan*

Department of Mechanical Engineering, King Fahd University of Petroleum and Minerals, Dhahran 31261, Saudi Arabia

a r t i c l e i n f o

Article history:Received 18 July 2008Received in revised form5 March 2010Accepted 8 March 2010

Keywords:Pressure vesselSaddle supportsStressFinite element method

* Tel.: þ966 3 860 7225; fax: þ966 3 860 2949.E-mail address: skhan@kfupm.edu.sa

0308-0161/$ e see front matter � 2010 Elsevier Ltd.doi:10.1016/j.ijpvp.2010.03.005

a b s t r a c t

This paper presents analysis results of stress distributions in a horizontal pressure vessel and the saddlesupports. The results are obtained from a 3D finite element analysis. A quarter of the pressure vessel ismodeled with realistic details of saddle supports. In addition to presenting the stress distribution in thepressure vessel, the results provide details of stress distribution in different parts of the saddle sepa-rately, i.e. wear, web, flange and base plates. The effect of changing the load and various geometricparameters is investigated and recommendations are made for the optimal values of ratio of the distanceof support from the end of the vessel to the length of the vessel and ratio of the length of the vessel to theradius of the vessel for minimum stresses both in the pressure vessel and the saddle structure. Physicalreasons for favoring of a particular value of ratio of the distance of support from the end of the vessel tothe length of the vessel are also outlined.

� 2010 Elsevier Ltd. All rights reserved.

1. Introduction

Horizontal pressure vessels are usually supported with twosaddle supports, which cause additional stresses in the pressurevessel in addition to the stresses generated by the internal pressurein the vessel. The saddle structure itself is obviously stressed too.Therefore the design of a saddle and determination of the stressesinduced is an important step during the design of a horizontalpressure vessel. The ASME [1] pressure vessel code does notprovide specific design procedure for the saddle design or theinduced stresses. The current practice is to use the semi-empiricalmethod developed by Zick [2,3], which is based on the beam theoryand various assumptions to simplify the problem. Due to theseassumptions, Zick’s method may not yield accurate results.However, Zick’s analysis is better judged on the performance it hasdemonstrated since it was first published, and therefore, it is alsothe basis of the saddle design guidelines given in pressure vesseldesign handbooks; see for example Megyesy [4]. The work of Toothand collaborators [5e7] is also invaluable literature on the saddledesign and it has been incorporated in the British Standard BS 5500[8]. It is important to note that the work of Tooth and collaboratorsis based on a more rigorous analysis as compared to Zick’s methodand employs analytical solutions using Fourier expansion terms.Nevertheless, a more accurate analysis is always desirable. With theadvancement in the computational technology and numericalmethods, it is now possible to obtain more detailed stress

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distributions in the saddle and the vessel and thus improve thesaddle design guidelines. One of such first studies is carried out byWidera et al. [9], which performed a complete 3D finite elementanalysis of a quarter of a pressure vessel using symmetric boundaryconditions. The pressure vessel was assumed to be full of fluid asthis is the most critical condition of loading while considering theself weight of the pressure vessel. The saddle supports areconsidered to be flexible and welded to the pressure vessel. Theyanalyzed various saddle locations and recommended to use 0.25 asthe ratio of the distance of the saddle from the tangent line of vesselto the total length of vessel for minimum stresses in the pressurevessel. Ong [10] carried out numerical studies to study the effect ofa fixed or loose fitting wear plate on the stresses induced in thepressure vessel and concluded that the peak stress in the vessel atthe saddle horn is reduced by 15e40% with wear plate, which hasthe same thickness as the vessel and extends at least 5� above thesaddle horn. It was also found that a fixed (welded) wear plateperforms better in reducing stresses in the pressure vessel thana loose fitting wear plate. Ong and Lu [11] performed a parametricstudy to determine the optimal support radius of a loose fittingsaddle and recommended the use of a clearance fit saddle supportto reduce the localized stresses in the pressure vessel at the saddlehorn. Chan et al. [12] presented results from an experimental studyaimed at understanding the pressure vessel collapse mechanismonto the saddles. They concluded that the collapse mechanism isdependent on the two parameters studied, i.e. radius-thicknessratio of the pressure vessel and the type of support (loose fitting orwelded). El-Abbasi et al. [13] performed a 3D finite element anal-ysis of a flexible and loose fitting saddle-supported pressure vessels

120o

B

W

G

K

H

D

C

H1

mm52

mm52

5o

120

B

W

G

K

H

D

C

H

mm52

mm52

5

R

A

L/2R/2

NA

PSDI

M

daeHlesse

V

neewteblesse

VelddaS

&dae

H

ehttalesse

Vnro

HelddaS

lesseV

noitcesdiM

b

a

Fig. 1. a: Pressure Vessel Configuration, b: Saddle support structure.

Nomenclature

R The radius of the pressure vesselL The length from tangent to tangent line of the

pressure vesselA The distance from the tangent line to the saddle

centerB The distance from the base plate to the centerline of

the vesselW The width of the base plate of the saddleC The width of the base plate and lower end of the

flange plate of the saddleD Thewidth of the upper end of the flange plate of the

saddleG The thickness of the base plate of the saddleH The thickness of the flange plate of the saddleH1 The thickness of the web plate of the saddleK The thickness of the wear plate of the saddlesMises,max Maximum value of von Mises stressE Elastic modulus of steeln Poisson’s ratio of steelr Density of steel

Fig. 2. Meshed finite element model with saddle model inset.

S.M.A. Khan / International Journal of Pressure Vessels and Piping 87 (2010) 239e244240

using a newly developed finite element that accounts for thecontact stresses between the vessel and the saddle supports. Theyconcluded that a saddle radius 1e2% larger than that of the vesselleads to a 50% reduction in the stresses and an overhang of 5e10�

leads to 25e40% reduction. In addition, the optimal horizontallocation of saddles is recommended as 0.1e0.15 for the ratio of thedistance from the pressure vessel tangent line to the saddle to thetotal length of the vessel. This is different than the one recom-mended byWidera et al. [9], however the results ofWidera et al. [9]are for welded saddles. Magnucki et al. [14] performed a parametricanalysis of horizontal pressure vessel with flexible and weldedsaddle supports using finite element method. They recommendeda value of 1/30 for the ratio of distance from the vessel tangent lineto the saddle to the total length of the vessel, which is in completecontradiction with Widera et al. [9]. They also recommend a valueof 12e16 for the length to radius ratio of the pressure vessel forminimum stresses.

It is noted that the open literature is focused more on the stressesinduced in the pressure vessel and less on the stresses developed inthe saddle supports. El-Abbasi et al. [13] looked into the contactstresses only in thewear plate but rest of their saddle support modellacks realistic design. Magnucki et al. [14] have analyzed themaximum stress in the saddle structure as a whole without anyregard as towhere thismaximumstress is occurring. In addition, theyrecommended the use of same thickness plates for all parts of thesaddle, which is contrary to the current practice as available in thepressure vessel design handbooks [4]. The author has previouslypresented a preliminary analysis of the stress distributions in thesaddle supports [15]. This study aims to take a sample case from thesaddle designs given in Megyesy [4] and build a solid model withrealistic geometryof the saddle togetherwith thepressure vessel, andemploy finite elementmethod to analyze the effect of various factorson the stress distributions both in the saddle and the pressure vessel.

2. Problem setup

2.1. Pressure vessel and saddle structure

A pressure vessel with radius R, tangent to tangent line length ofL and with ellipsoidal heads is considered. The depth of head is

equal to R/2. The saddle is located at a distance A from the tangentline and is consideredwelded to the vessel. The details of the saddledesign are taken from Megyesy [4] for a nominal pressure vesseldiameter of 660 mm. The geometric parameters of the pressurevessel and saddle supports are given in Fig. 1. B is the height fromthe base of the saddle (i.e. the rigid surface) to the center of thepressure vessel, W is the width of the saddle, C is the width of thebase plate and the flange plate at the lower end, and D is the width

80

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110

120

130

140

15 20 25 30 35 40 45 50 55

No. of Finite Elements (x1000)

xam,sesi

M)a

PM(

Vessel

Saddle Structure

σ

Fig. 3. Mesh sensitivity analysis.

S.M.A. Khan / International Journal of Pressure Vessels and Piping 87 (2010) 239e244 241

of the flange plate at the upper end. G, H, H1 and K are the thick-nesses of the base plate, flange plate, web plate and wear platerespectively. A contact angle of 120� is consideredwith 5� overhangfor the wear plate. Numerical values of parameters that are

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400

0.20 0.40 0.60 0.80

Normal

xam,sesi

M)a

PM(

A/L = 0.15L/R = 10

Vessel between

Head & Saddle

σ

a

b

Fig. 4. a: Effect of increasing the load on saddles; A/L ¼ 0.15, L/R ¼ 10, b: S

constant for the study are: R¼ 330mm, B¼ 482 mm,W¼ 572 mm,C ¼ 100 mm, D ¼ 150 mm, G ¼ 6 mm, H ¼ 6 mm, H1 ¼ 6 mm,K ¼ 6 mm. The values of the rest of the parameters will change andwill be mentioned with the results.

2.2. Finite element model

Commercial finite element software ANSYS version 11 is usedfor finite element analysis. The solid model as detailed in theprevious section is built completely in the ANSYS environment.Taking advantage of the symmetry of the problem, only a quarter ofthe pressure vessel and saddle is modeled. The material propertiesused for steel are E ¼ 207 GPa, n ¼ 0.3, and densityr¼ 7.85�10�3 kg/m3. The pressure vessel is considered full of fluidand the self weight of the pressure vessel is also considered in theanalysis. The solid model is meshed using 8-noded brick elements.At least three layers of finite elements are used through thickness ofthe pressure vessel and two layers through thickness of the saddlestructure. The meshed model is shown in Fig. 2. Symmetricboundary conditions are applied at all the outer faces of the model.In addition, lower face of the base plate of the saddle is fixed in all

1.00 1.20 1.40 1.60

ized Load

Vessel Head

Vessel at the

Saddle Horn

Vessel Midsection

Wear Plate

Web Plate

Flange Plate

Base Plate

tress distribution (in MPa) in saddle parts, for normalized load of 0.9.

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450

0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40

A/L

xam,sesi

M)a

PM(

L/R = 10

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Vessel between

Head & Saddle

Vessel at the

Saddle Horn

Vessel Midsection

Wear Plate

Web Plate

Flange Plate

Base Plate

0

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0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40

A/L

xam,sesi

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PM(

L/R = 14

Vessel Head

Vessel between

Head & Saddle

Vessel at the

Saddle Horn

Vessel

Midsection

Wear PlateWeb Plate

Flange Plate

Base Plate

a

b

σσ

Fig. 5. Effect of the ratio A/L; a: L/R ¼ 10, b: L/R ¼ 14.

S.M.A. Khan / International Journal of Pressure Vessels and Piping 87 (2010) 239e244242

degrees of freedom to prevent rigid body motion. The vessel isloaded with 1 MPa internal pressure.

2.3. Mesh sensitivity analysis

A mesh sensitivity analysis is performed, both in the pressurevessel and saddle structure, to ensure optimummesh size for properconvergence and accurate numerical results. The value ofmaximumvonMises stress (sMises,max) occurring in the structure is used as theconvergence criterion. Results are shown in Fig. 3; starting with18,000finite elements, themesh isfirst refined in thepressurevesselonly, up to 26,500 finite elements and it is found out that themesh isalready sensitive enough in thepressurevessel. This is due to the factthat because of certain geometric restrictions for mapped meshing,an initial fine mesh was inevitable to use. Once the convergence isestablished in the vessel, then the mesh is refined step by step indifferent parts of the saddle structure until themaximumvonMisesstress reaches a plateau, at which point the mesh in both the vesseland saddle structures is converged. The chosen meshed model isshown in Fig. 2, which will be used for further studies.

3. Results and discussion

Results from parametric studies for the effect of variousparameters will be presented in this section. Themaximumvalue ofvon Mises stress (sMises,max) will be observed, analyzed and pre-sented in eight sections of the model. The first four sections are thesaddle components, i.e. web, wear, flange and base plates. Further,the pressure vessel is divided into four sections: the vessel head,the section supported by the saddle, the section between theprevious two sections and the rest of pressure vessel towards themid span (please see Fig. 1a). 3D stress contours of the critical parts

of the pressure vessel and saddle will be presented and discussedwhere appropriate.

3.1. Maximum load on the saddle

The maximum load a saddle can support is an important designparameter. Different components of the saddle may yield underdifferent maximum loads. Therefore, in this section the effect ofincreasing the load on a saddle is investigated. Avalue of 0.15 for A/Land 10 for L/R is used for this section. Results are plotted in Fig. 4a.To make the results more understandable, normalized load isplotted on the abscissa. The normalizing parameter used is themaximum load on a saddle as per Megyesy [4] so that a value ofunity on the abscissa in Fig. 4a (and Figs. 7 and 8) implies themaximum weight as recommended by Megyesy [4]. This isreasonable as the saddle design and dimensions are also taken fromthe same source, and it will better access the standard design.Assuming that the yield strength of the carbon steel used in vessel/saddle construction is close to 220 MPa, let’s analyze the results.The highest stresses are occurring in three sections, which are theflange plate, the base plate and the pressure vessel at the saddlehorn. The vessel shows yield at the saddle horn at about 10%additional load than the maximum load as recommended byMegyesy [4]. The base and flange plates approach the yield strengthat 30% additional load and at 73% of the maximum load respec-tively. All of the other sections are well under yield value for up to33% additional load. To check the design at this point, for normal-ized load of 0.9, three parameters were changed to see the effect.The results are listed in Table 1. It is noted that the maximum stressin the vessel at the saddle horn is only affected by the wear plateoverhang and a reduction of 20% is observed by increasing theoverhang from 5� to 10�, which is consistent with previous studies[10,13]. Increasing the flange plate thickness, H, causes themaximum stress to reduce only in the flange and actually increasesthe maximum stress in the base plate. Changing the thickness ofthe base plate, G, does not affect the stresses in other parts andreduces stress only in the base plate. The maximum stress values inthe other five sections remain essentially unchanged for the fourcases. Please note that all dimensions are changed back to theoriginal values (Case 1 in Table 1) for further studies. The curves inFig. 4a show a slight non-linear behavior, which may be attributedto the fact that each part making up the saddle is being analyzedseparately. Although the overall saddle will be in linear elasticrange, however individual components may experience high localloads giving the non-linear behavior.

Fig. 4b represents the stress contours corresponding to normal-ized load of 0.9 in Fig. 4a. The stress distribution is not uniform andthe flange plate is the highly stressed part of the saddle structure.

3.2. Effect of the A/L ratio

Next the effect of the ratio A/L is investigated, which is variedfrom 0.05 to 0.35 with 0.05 increments. The first set of results isshown in Fig. 5a for L/R ¼ 10. The stresses in all the saddle partsshow a dip at A/L ¼ 0.25. The most critical section in the vessel, i.e.at the saddle horn and the vessel midsection also shown a dip atA/L ¼ 0.25, whereas the other two vessel sections considered(vessel head and the section between the head and saddle) are notaffected by the A/L ratio. The same conclusion can be drawn byanalyzing the second set of results for a different L/R ¼ 14 ratio inFig. 5b. Therefore, the overall recommendation is to use a value ofA/L close to 0.25 for minimum stresses in the pressure vessel andthe saddle. This conclusion is inline with the recommendation ofWidera et al. [9] but contradicts the recommendation of Magnuckiet al. [14]; this may be explained based on the geometry of the

Fig. 6. Stress distributions in the vessel at the saddle horn and the flange plate corresponding to Fig. 5a.

S.M.A. Khan / International Journal of Pressure Vessels and Piping 87 (2010) 239e244 243

saddle used by them [9,14] and the present study. As mentionedpreviously, these two studies are in contradiction with each otherover the suitable value of A/L ratio, although both have consideredflexible saddles welded to the pressure vessel.

Fig. 6 presents stress contours for two sections, one each for thepressure vessel and the saddle for varying A/L ratio correspondingto Fig. 5a. These two sections are chosen as they depict the higheststresses and therefore symbolize the pressure vessel and the saddle

structure respectively. It is observed that as the ratio A/L increases(i.e. the saddle moves towards the vessel mid span), the stressdistribution becomes uniform when the ratio A/L approaches 0.25.For A/L < 0.25, both the vessel and the saddle have higher stressvalues on the vessel midsection side and for A/L > 0.25, the higherstress values shift towards the vessel head side. For A/L values closeto 0.25, both the pressure vessel and the saddle have uniform stressdistributions and therefore minimum stresses. It is worth

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0.60 0.80 1.00 1.20 1.40 1.60 1.80 2.00

Normalized Load

xam,sesi

M)a

PM(

A/L = 0.25L/R = 10

Vessel Head

Vessel between

Head & Saddle

Vessel at the

Saddle Horn

Vessel

Midsection

Wear Plate

Web Plate

Flange Plate

Base Plate

σ

Fig. 7. Effect of increasing the load on saddles, A/L ¼ 0.25.

Table 1Effect of varying the thickness of the flange and base plates and the wear plateoverhang.

H(mm)

G(mm)

Wear plateoverhang

Vessel at thesaddle horn (MPa)

Base plate(MPa)

Flangeplate (MPa)

Case 1 6 6 5� 185 160 255Case 2 7 6 5� 187 166 236Case 3 7 8 5� 187 152 237Case 4 7 8 10� 147 152 233

S.M.A. Khan / International Journal of Pressure Vessels and Piping 87 (2010) 239e244244

mentioning that for A/L ¼ 0.25, each saddle is in the center of itsside of the half length of the pressure vessel. This means that eachsaddle is carrying roughly half of the total weight and this might bethe physical reason as to why a value of 0.25 for A/L gives minimumstresses irrespective of the L/R ratio.

Fig. 7 presents a look back at the effect of the load increase onthe saddles with the new value of A/L ¼ 0.25, which is found to bethe optimal for minimum stresses. For this A/L value, the flangeplate reaches yield stress after taking an additional 32% load andthe vessel at the saddle horn after taking an additional 42% load.Considering the results of Fig. 4a (the vessel at the saddle hornyielded at 10% additional load and the flange plate yielded at 73% ofthe maximum load), it is concluded that the maximum load onsaddles as given in Megyesy [4] depends on the ratio A/L. Forexample, for the flange plate, it is overestimated for A/L ¼ 0.15 andunderestimated for A/L ¼ 0.25. Keeping in mind the results pre-sented in Table 1, the saddle parts can be selectively redesigned tooptimize the design, e.g., by increasing the thickness of the flangeplate and the overhang of the wear plate to 10�.

3.3. Effect of the L/R ratio

Fig. 8 represents the results for the effect of the slenderness ratioL/R. For A/L¼ 0.25, L/R is varied between 10 and 20 with incrementsof 2. The maximum stress in the flange plate shows a differentbehavior than the other sections with a steady rise in themaximumstressvaluewith increasing L/R ratio. Forall the other sevensections,the value of the maximum stress is nearly constant between 10 and16 for L/R. It is therefore recommended to use L/R< 16 forminimumstresses in the vessel and the saddle. This recommendation is inlinewith the recommendation of Magnucki et al. [14].

0

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8 10 12 14 16 18 20 22 24

L/R

xam,sesi

M)a

PM(

A/L = 0.25

Vessel Head

Vessel between

Head & SaddleVessel at the

Saddle Horn

Wear Plate

Web Plate

Flange Plate

Base Plate

Vessel Midsection

Fig. 8. Effect of the ratio L/R; A/L ¼ 0.25.

4. Conclusions

1. The highly stressed area, beside the pressure vessel at thesaddle horn, is the flange plate of the saddle.

2. The maximum load on a saddle as given byMegyesy [4] may beconservative or liberal, depending upon the value of the ratioA/L used. Furthermore, the design of the saddle structure maybe optimized by redesigning selectively.

3. A value of 0.25 for the ratio A/L is favored for minimum stressesin the pressure vessel and the saddle. This is the same as rec-ommended by Widera et al. [9] but differs from the recom-mendation of Magnucki et al. [14].

4. The physical reason for favoring an A/L close to 0.25 may lie inthe fact that at this ratio, each saddle is located roughly at thecenter of the half of the pressure vessel thus supporting thepressure vessel (or alternatively loading the saddle) uniformly.

5. The slenderness ratio (L/R) of less than 16 is found to generateminimum stresses in the pressure vessel and the saddle. This isthe same as recommended by Magnucki et al. [14].

Acknowledgements

The author acknowledges the support of King Fahd University ofPetroleum and Minerals (KFUPM), Dhahran, Saudi Arabia incarrying out this research work.

References

[1] ASME. Boiler and pressure vessel code, section VIII, pressure vessels division.New York: ASME; 1989.

[2] Zick LP. Stresses in large horizontal cylindrical pressure vessels on two saddlesupports. Weld J Res Suppl 1951;30:435e45.

[3] Zick LP. In: Stresses in large horizontal cylindrical pressure vessels on twosaddle supports. Pressure vessel and piping: design and analysis e a decade ofprogress, vol. 2. New York: ASME; 1985. p. 959e70.

[4] Megyesy EF. Pressure vessel handbook. Tulsa, Oklahoman, USA: PressureVessel Publishing, Inc.; 2001.

[5] Duthie G, White GC, Tooth AS. An analysis for cylindrical vessels under localloading e application to saddle supported vessel problems. J Strain Anal1982;17(3):157e67.

[6] Tooth AS, Duthie G,White GC, Carmichael J. Stresses in horizontal storage vesselse a comparison of theory and experiment. J Strain Anal 1982;17(3):169e76.

[7] Tooth AS, Jones N. Plastic collapse loads of cylindrical pressure vessels sup-ported by rigid saddles. J Strain Anal 1982;17(3):187e98.

[8] British Standards Institution. Unfired Fusion Welded Pressure Vessels, BS5500. BSI; 1997.

[9] Widera GEO, Sang ZF, Natarajan R. On the design of horizontal pressurevessels. ASME J Pres Ves Tech 1988;110:393e401.

[10] Ong LS. Effectiveness of wear plate at the saddle support. ASME J Pres VesTech 1992;114:12e8.

[11] Ong LS, Lu G. Optimal support radius of loose-fitting saddle support. Int J PresVes Pip 1993;54(3):465e79.

[12] Chan GCM, Tooth AS, Spence J. An experimental study of the collapse ofhorizontal saddle-supported storage vessels. Proc IME Part E J Process MechEng 1998;212(3):183e95.

[13] El-Abbasi N, Meguid SA, Czekanski A. Three-dimensional finite elementanalysis of saddle supported pressure vessels. Int J Mech Sci2001;43:1229e42.

[14] Magucki K, Stasiewicz P, Szyc W. Flexible saddle support of a horizontalcylindrical pressure vessel. Int J Pres Ves Pip 2003;80:205e10.

[15] Khan SMA. Initial investigation into optimizing design of a pressure vesselsaddle. Proc ASME-PVP2008; PVP2008e61271.