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BUCKLING OF DOUBLE BELLOWS EXPANSION JOINTS UNDER INTERNAL PRESSURE
By D. E. Newland*
Corrugated bellows expansion joints may buckle under internal pressure in the same way as an elastic strut may buckle under an axial load. This paper is concerned with the analysis of this phenomenon for the ‘universal expansion joint’ which incorporates two bellows joined by a length of rigid pipe. Theprincipal conclusion is that, by providing a correctly designed supporting structure, the critical buckling pressure can be increased to up to four times its value for the same system with no supports.

INTRODUCTION

incorporating two bellows expansion joints is shown in Fig. 1. Such an arrangement is often used in practice because the assembly can accommodate expansion of the connecting pipeand also lateral and axial movement of the anchorages. The anchorages might be two process vessels which have to be dircaly connected, or perhaps a process vessel and a fixed pipe support. At a high enough internal pressure an instability may occur in which the connecting pipe moves off its centre-line and the two bellows deform. This buckling phenomenon involves motion of the connecting pipe andbellows only, since it is assumed (as is usually the case) that the anchorages are infinitely rigid compared with the flexibility of the bellows and the bellows supporting structure. T o reduce the susceptibility to buckling, lateral supports may be provided as shown in Fig. 1. These resist movement of the ends of the connecting pipe away from its centre-line while not resisting expansion of theconnecting pipe or small lateral or axial movements of the anchorages caused by temperature changes. The problem is to predict the maximum internal pressure that the system can withstand without this buckling instability occurring. Haringx ( ~ ) t considered the buckling of a single has bellows expansion joint. A conclusion of his work is that the pressure buckling of a bellows is closelyanalogous to the buckling of an axially loaded strut. For a strut it is well known that buckling first occurs when the axial load (P,) is given by X2EI 42EI P, = - or
A TYPICAL PIPE LAYOUT
~

depending on whether the ends of the strut are pinjointed or clamped. These same formulae have been shown to be applicable ta the buckling of a bellows under internal pressure where, if D, is the mean bellowsdiameter and p , is the internal gauge pressure when buckling occurs,

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The M S . of this puper mas f i r s t recezved at the Institution on 14th January 1964 and in i t s revised f o r m , as accepted by the Council for publicutzon, on 16th April 3964. * Lecturer, Department of Mechanical Engineering, Imperial College, f London. Associate Member o the Institution. t References are Rivenin Appendix II.
J 0 U R N A L M E C HA h‘I C A L E N G I N E E R I X G S C I E N C E

The EI in the latter case is the equivalent bendkg stiffness of the bellows. Some notes on the accuracy of this result and on the calculation of EI for a corrugated bellows are given in Appendix I. T h e present paper is concerned with an extension of Haringx’s theory to the more complicated case of the‘universal expansion joint’ shown in Fig. 1. On account of the above results, the problem can be reduced to the analysis of the buckling of an axially loaded discontinuous strut supported by lateral springs in two locations as shown in Fig. 4a. Two uniform elastic members representing the two bellows are joined by a rigid section representing the connecting pipe. The two ends of the composite strut areassumed to be rigidly clamped to represent the two fixed anchorages at each end of the assembly. However, since the loading now comes, not from internal pressure, but from an equivalent external axial force, it is assumed in this model that one of these clamped ends can move axially to allow the external load to be applied. Two lateral springs, one at each end of the rigid section, represent...