Flexible saddle support of a horizontal cylindrical pressure vessel

K. Magnuckia,b,*, P. Stasiewicza, W. Szyca

aInstitute of Applied Mechanics, Poznan University of Technology, ul. Piotrowo 3, Poznan 60-965, PolandbInstitute of Rail Vehicles ‘TABOR’, ul. Warszawska 181, Poznan 61-055, Poland

Received 29 January 2002; revised 16 December 2002; accepted 16 January 2003

Abstract

The subject of this paper is the supporting saddle of a horizontal cylindrical pressure vessel filled with liquid. A parametric model of the

saddle support has been developed; the effect of the geometrical parameters on the stress values arising in the structure has been examined by

means of the Finite Element Method. The shape and location of the supporting saddle have been determined with a view to minimizing the

concentration of stresses. Results of numerical analysis allow determination of the effective proportions of the geometrical parameters of the

vessel.

q 2003 Elsevier Science Ltd. All rights reserved.

Keywords: Numerical analysis; Finite element method; Parametric shaping; Circular cylindrical vessel

1. Introduction

Stationary horizontal cylindrical vessels supported on

two supporting saddles (Fig. 1) are usually loaded with

uniform internal pressure and hydrostatic pressure. Such a

vessel is subject to a non-uniform stress distribution. The

stiffness of the supporting saddles and the distance between

them have a considerable effect on the maximum stresses

occurring in the structure. The problem has been the subject

of many research works. El-Abbasi, Meguid and Czekanski

[1] performed a 3D analysis of a pressure vessel freely

supported on two deformable supports by means of FEM.

They developed a seven-parameter thick shell finite element

taking into account friction between the support and the

vessel, as well as the changes of stresses and strains across

the shell thickness. They investigated the effect of geometric

parameters of the vessel and support on the state of stress

and calculated optimal proportions between these quan-

tities. They showed that in the case of a supporting saddle

with a radius 1–2 percent greater than that of the vessel the

stresses occurring in the structure are reduced by 50%.

Boutros [2] discussed the results of parametric analysis of

deformable saddle supports of circular cylindrical vessels of

large diameter. He indicated the influence of proportions

between vessel dimensions and support location on the

stresses occurring in the structure. He took into account the

guidelines provided by British Standards, Australian

Standards, and ASME. He also compared stiff and

deformable supports, with regard to stress concentration at

the saddle horn. Magnucki et al. [3] developed a parametric

FEM-model of the vessel and its support. The support and

vessel of the structure considered were joined by welding.

The stiffness of the support was smaller than that

recommended by European standards. They investigated

the effect of the geometric parameters of the vessel and

support on the stresses in characteristic regions of the

structure. Magnucki and Szyc [4] proposed a method of

determining the thickness of a cylindrical vessel resting

upon two supports. They effected a numerical FEM analysis

of a family of vessels and developed corrections for

determining the thickness of the walls of pressure vessels.

The British Standard BS5500 [5] provides guidelines for

designing pressure vessels and their supports. The proposed

methods are based on the theory of beams and the results of

experimental research published by Zick in 1951. The

standard recommends welded connection between the

vessel and support; however, the saddle supports have

excessive stiffness resulting in increased stresses. Ong and

Lu [6] determined the optimal radius of the support with a

preliminary clearance between the vessel and saddle. In

0308-0161/03/$ - see front matter q 2003 Elsevier Science Ltd. All rights reserved.

doi:10.1016/S0308-0161(03)00023-1

International Journal of Pressure Vessels and Piping 80 (2003) 205–210

www.elsevier.com/locate/ijpvp

* Corresponding author. Address: Institute of Applied Mechanics,

Poznan University of Technology, ul. Piotrowo 3, Poznan 60-965,

Poland. Fax: þ48-61-665-2307.

E-mail address: krzysztof.magnucki@put.poznan.pl (K. Magnucki).

the area of the vessel–saddle contact they assumed a

constant distribution of the contact pressure along the

vessel, but varying circumferentially. They performed a

parametric analysis aimed at reducing the stress concen-

tration at the saddle horn. Tooth et al. [7] analytically and

experimentally determined the stresses in real supports of

multi-layered Glass Reinforced Plastic (GRP) vessels. They

divided the region of the vessel-support contact into small

areas, assuming uniform radial and tangent pressure

distributions in each. Variable distributions of contact

pressure were assumed in the direction of support width.

In the experimental part, they presented strain gauge results

for three vessels with equal overall dimensions but different

laminate layers. They investigated two types of saddle with

radii exceeding the external radius of the vessel and

proposed a useful method for calculating the maximum

strain, particularly in the absence of computer software.

Banks et al. [8], presented an approximate solution of the

strain state of a horizontal cylindrical vessel, making use of

the earlier paper [7].

2. Structure of the horizontal vessel

The structure considered in this paper is a typical thin-

walled horizontal cylindrical vessel, supported on two

deformable supports, welded to the vessel and located

symmetrically near its ends at a distance s from the middle

Fig. 1. Geometric model of a horizontal pressure vessel.

Fig. 2. Structure of the saddle support.

K. Magnucki et al. / International Journal of Pressure Vessels and Piping 80 (2003) 205–210206

symmetry plane. The length 2L of the cylindrical part of the

vessel and its radius r are variable parameters, while the

capacity of the vessel is constant and equal to V0 ¼ 300 m3

(Fig. 1). The vessel is closed with two ellipsoidal heads of

convexity b0 equal to a half of the radius ðb0 ¼ r=2Þ:

Moreover, it is assumed that the vessel is made of steel of

density rs ¼ 7:85 £ 103 kg m23; filled with a liquid of

density rl ¼ 103 £ kg m23; and additionally loaded with

uniform internal pressure p0 ¼ 2:5 MPa: It is assumed that the

structure is described by 10 parameters: vessel radius r; length

L; spacing between supports s; height of vessel axis H above

support base, characteristic dimensions of the support b; c; and

e; thicknesses h1 of the heads, h2 of cylindrical shell, and h3 of

the supports. A simple design of the support is adopted with

the shape shown in Fig. 2. It is a welded support made of steel

plate, formed to avoid excessive deformation of the vessel,

with an angle of contact with the vessel by its load carrying

structure of ws ¼ 1208 and by its support cover plate of wc ¼

1408: The cover plate width cn depends on vessel length and is

cn ¼ 2L=45: Initial values of particular geometrical par-

ameters of the vessel are taken as r ¼ 1:8 m, L ¼ 14:1 m,

s ¼ 12L=15; H ¼ 1:15r; b ¼ r=2; c ¼ 300 mm, e ¼ 210 mm,

h1 ¼ 16 mm, h2 ¼ 14 mm, h3 ¼ 8 mm.

3. Numerical analysis

A parametric model of 1=4 of the vessel structure with the

supports has been developed. The model was used to carry

out static finite element analysis by means of the

COSMOS/M system. It included 2374 shell elements and

enabled easy changing of the ten geometric parameters of

the structure. Results of each have been produced in the

form of contour maps of equivalent Huber–Mises stresses.

Their values have been analyzed in eight characteristic

regions shown in Fig. 1 with the symbols A1; A2; B; C1; C2;

C3; D; and E: Regions A1; A2 and B surround the saddle

support of the vessel, more precisely they touch edges of the

support cover plate. Those are the places where local stress

concentration occurs, as an effect of the support and the

vessel skin interaction. The maximum equivalent stress

values in these regions are selected. Regions C1; C2; C3 are

located in the middle cross-section of the vessel at upper,

medial and lower generatrix, and the stress values calculated

in these points are taken into account. Region D is located in

the ellipsoidal head near the joint with the cylindrical shell

where maximum equivalent stresses occur. Region E

includes the whole saddle support and from this area the

maximum stresses are selected.

Maximum values of the equivalent stresses in each area

are presented in Fig. 3–6. There are not greater stress values

elsewhere. In Fig. 3 the examples of the results obtained for

calculations with different values of the parameter b (width

of support bed) in the range 0:39r # b # 0:83r are

presented. The value of b has little effect in the areas D

(the head) and C (the middle of the vessel). Effects are also

relatively small in the areas A1 (next to the support) and B

(above the support). However, in the area E (the support) a

Fig. 3. Influence of width of the saddle support bed b on stress level.

K. Magnucki et al. / International Journal of Pressure Vessels and Piping 80 (2003) 205–210 207

distinct minimum in stress is observed as the value of b

increases beyond r=2:

The height of the end of the support arm, e; also

influences the stiffness of the support. Changes in equivalent

stress in particular parts of the structure with e in the range

0:094r # e # 0:28r are shown in Fig. 4. The most

significant effects are observed in the areas A1 and E: In

particular, near the support ðA1Þ; a clear increase of stress

with increase of the dimension e is observed. This means

that an elastic support of relatively low stiffness is the most

advantageous solution for a vessel to give low stresses in the

area of the support. However, stress in the support ðEÞ will

increase if the value of e is too small. Hence, a reasonable

recommendation in this case would be to use supports

Fig. 4. Influence of the saddle support tip height e on stress level.

Fig. 5. Influence of the saddle support base s on stress level.

K. Magnucki et al. / International Journal of Pressure Vessels and Piping 80 (2003) 205–210208

having a tip dimension e ¼ ð0:1–0:12Þr: Fig. 5 shows how

the equivalent stress values change with increase of the ratio

s=L; i.e. with moving the location of the saddle supports. The

figure suggests that the most favourable location of the

supports would be near the ends of the vessel. For increasing

s=L; the stresses decrease in almost all areas, including the

middle part of the vessel, C1: In the area C3 maximal

equivalent stresses have the similar values as in the area C1:

However, the stresses in the head (D area) increase slightly

at larger s=L: Therefore, a reasonable compromise would

consist of the use of a slightly thicker head (the model

assumes the head thickness h1 ¼ 16 mm and the cylindrical

shell thickness h2 ¼ 14 mm) and positioning the supports

near the ends of the vessel, at about s=L ¼ 14=15:

Considering the vessel as a beam subject to uniform load

and supported at two points, as sometimes found in the

literature, is inappropriate.

The set of curves in Fig. 6 shows the changes in stress

level in the same areas of vessels having different

proportions but the same capacity ðV0 ¼ 300 m3Þ: The

stresses are indicated for outer and inner surfaces of the

cylindrical shell. The run of the curves show that reasonable

proportions are for L=r in the range 6–8, corresponding to

L ¼ ð11:8–14:3Þ m or r ¼ ð2:0–1:8Þ m. in this case.

In practice, vessels with radius exceeding 2 m are

often avoided because of problems with possible road

transport. With increasing L=r; higher stresses occur in the

area B closest to the support and in the middle section of the

vessel ðC3Þ:

Analyses were also made to assess the effects of

support height H; the dimension c; and the width cn of the

cover plate. The results indicate that preliminary values

for these parameters, specified in the end of Section 2, are

reasonable.

4. Conclusions

The results enable selection of the most favourable

values of basic structural parameters of a thin-walled

cylindrical pressure vessel. The vessel is treated as an

integral system, including the deformable supports with

stiffness adjusted to minimize the stress concentration in the

vessel shell. The support should be of appropriate shape,

simple design, and suitable thickness relative to the

thickness of the vessel shell (the results suggest

h3=h2 ¼ 0:6 2 0:7). The use of supports of high stiffness

(e.g. concrete, in the form of a bed) is certainly unfavourable

taking into account the strength of the vessel. The supports

should be located near the vessel ends, thus taking full

advantage of the increased stiffness of the head, due both to

its shape and increased thickness relative to the vessel shell.

Calculations have shown that the thickness of the ellipsoidal

head should equal 1.15–1.25 of the thickness of the

cylindrical shell. A ratio of support to vessel lengths equal

to s=L ¼ 14=15 is most favourable, although a beam model

of the vessel would suggest location of the supports nearer

the middle, to reduce the bending moment at the middle

Fig. 6. Influence of the vessel slenderness ratio L=r on stress level.

K. Magnucki et al. / International Journal of Pressure Vessels and Piping 80 (2003) 205–210 209

cross-section. The geometrical slenderness of the vessel,

defined as the length to radius ratio, should be in the range

2L=r ¼ 12–16:

Similar proportions would apply to vessels of smaller

capacity. Similar calculations have been carried out for

vessels of capacities 200, 100 m3, and smaller. Conclusions

are very similar and the main proportions should be

maintained even for capacities down to 15 m3. However,

other rules for the shapes of vessels and their supports may

be required for smaller internal pressure, when the

contribution of hydrostatic pressure is more important

relative to the pressure inside the vessel.

References

[1] El-Abbasi N, Meguid SA, Czekanski A. Three-dimensional finite

element analysis of saddle supported pressure vessels. Int J Mech Sci

2001;43:1229–42.

[2] Boutros YA. Flexible saddle support for large diameter cylindrical

vessels. Proc Ninth Int Conf Pressure Vessel Technol, Sydney 2000;1:

91–8.

[3] Magnucki K, Szyc W, Stasiewicz P. Selection of design parameters of a

cylindrical pressure vessel together with its support. 36th Symposium

‘Modelling in Mechanics’, Silesian Technical University, Gliwice

1997;4:211–6. in Polish.

[4] Magnucki K, Szyc W. Shell thickness of a horizontal cylindrical vessel

filled with liquid. 37th Symposium “Modelling in Mechanics’, Silesian

Technical University, Gliwice 1998;7:207–12. In Polish.

[5] British Standard BS5500, Specification for unfired fusion welded

pressure vessels. 1. Supports and mountings for horizontal vessels. Brit

Std Inst 1997;G3.3:64–77.

[6] Ong LS, Lu G. Optimal support radius of loose-fitting saddle support.

Int J Pressure Vessel Piping 1993;54:465–79.

[7] Tooth AS, Banks WM, Seah CP, Tolson BA. The twin-saddle support

of horizontal multi-layered GRP vessels—theoretical analysis, exper-

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Process Mech Engng 1994;208:59–74.

[8] Banks WM, Nash DH, Flaherty AE, Fok WC, Tooth AS. The

derivation of a best fit equation’ for maximum strains in a GRP vessel

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