A common application of bolted joints is for detachable connections which contain pressurised fluid. These may be rendered leakproof either by O-rings or by gaskets. An O-ring is an endless ring of circular cross- section, which is relatively compliant and usually elastomeric. It is lightly nipped when assembled, subsequent application of fluid pressure extrudes the ring to plug all potential leakage paths. Such joints are called self- energising as they do not rely on preload for their effectiveness.

This example demonstrates the static analysis of a self-energising joint.

O-rings are suitable where the environment is non-aggresssive, temperatures are sensibly ambient, and relatively high manufacturing / assembly costs can be tolerated - otherwise gaskets are used. Pipes are frequently connected by welding similar flanges to each and bolting the flanges together with a gasket and multiple bolts as shown below. Gaskets are common also in heat exchanger tube plates and the cylinder heads of i/c engines, however we shall explain gaskets in the context of flanged pipe joints. Dimensions of flanges suitable for various combinations of pipe size, fluid pressure and temperature are standardised ( AS 2129 ).

Gasket materials range from cork to copper - each material best suiting a particular combination of fluid corrosiveness, pressure, temperature, leakage implications, cost, and so on. Most gaskets are non-metallic, highly compliant compared to other joint components, and non-linear. Their low stiffness means that other joint components may usually be neglected when figuring joint overall stiffness :   1/k_j = 1/k_gasket + Σ 1/k_{other large} - that is the joint overall stiffness is essentially the same as the gasket stiffness, which has far-reaching implications in fatigue since it may not be possible to ensure that   k_b << k_j as desired for low bolt load amplitude.

Soft gaskets usually extend over the whole flange ( full face ), whereas gaskets made of stiffer materials are narrow and extend out only to the bolt holes. It is assumed that multiple bolts are loaded equally, and that the   gasket stress - ie. the average contact pressure between gasket and flange - is uniform over the gasket area   A_g. Clearly the gasket stress must be higher than fluid pressure if leakage is to be avoided, and, for a given gasket stress, a raised face flange with a narrow gasket will require less preload and hence less flange strength than a full face gasket. So the tendency is for high pressure gaskets to be narrow.

In service, the pipe acts as a closed cylinder with axial load   P in the wall due to fluid pressure acting over the internal area. This loading - a preload due to initial tightening, together with an external service load - is typical of joints in general.

Codes traditionally classify gasket materials by two property values - the 'y' factor and the 'm' factor, eg. Table 3. These are necessary minimum values for the avoidance of leaks :

Theses limits are sketched on the joint characteristic, in which the external axial load   P equals the fluid pressure   p times the internal transverse area   A_i. The initial gasket stress induced by the tightening load   F_i must be less than the gasket crushing stress   p_crush and greater than the 'y' appropriate to the gasket material. Initial loading is the most severe since the joint load decreases thereafter as the external load is applied - but the external load should not be so large that the gasket stress becomes less than 'm' times the fluid pressure. Failure of a joint - as opposed to leakage - will be most likely at initial tightening, so joint design ( selection of bolting, flange thickness etc.) is based upon that state.

There has been a deal of debate on the suggested values of 'm' and 'y' which appear in the Pressure Vessel Codes. While the values have been found satisfactory bases for safe joint design, they are but poor indicators of leakproof operation. The Pressure Vessel Research Committee ( PVRC ) of the Welding Research Council has instituted comprehensive new tests to clarify the behaviour of gaskets, with results shown on the left below. Initial tightening proceeds along a-b; as the external load is applied the gasket unloads along b-c. Further cycling of the external load leads to the gasket loading/ unloading along the same b-c-b trajectory. If the bolts are further tightened then the gasket ( un )loads along the d-e-d locus.
Gaskets cannot be absolutely leak free when containing gas; locii of constant leakage rates are shown superimposed upon the characteristic. Behaviour may be described most conveniently by graphs similar to the one on the right, in which a leakage parameter replaces deflection. A material can be characterised by three constant properties - the slope and intercept of the initial loading regression line ( log-log ), together with the point through which all subsequent linear ( un )loading trajectories pass. These results have yet to be incorporated into Codes.

It is clear from the PVRC findings that non-metallic gaskets do not behave elastically. Table 4 gives the range of stiffnesses that may be experienced - stiffness being expressed as gasket stress ( force/A_g ) per unit deflection, ie. modulus/ thickness. Calculation of load sharing from ( 3a) is thus fraught with uncertainty if the gasket stiffness is not known accurately, however load sharing may be characterised by :

( 3b)         F_b =   F_i + C P  ;         F_j =   F_i - ( 1 - C ) P

in which the   joint factor C is a typical measure of the fraction of the total external load   P seen by the bolts. Although comparison with ( 3a) indicates that   C = k_e /k_j = k_b /( k_b + k_j ) ≤ 1,   the joint factor should be regarded more as an overall approximate figure of merit, which incorporates all vagaries of behaviour and which is experimentally determined in its own right, rather than as a ratio of elastic stiffnesses.

Experience suggests the values of Table 5.

'Flange rotation' refers to the initially disc-shaped flange assuming a flat conical form under fluid pressure loading, and can be significant when a narrow gasket is used. The cause of rotation may be appreciated from the sketches below which show rotation grossly exaggerated. At ( a) is shown part of the flange with the bolt load   F_b equilibrating the external load   P and the joint load   F_j, as above. Accordingly   F_b is split into its superimposed components ( b), which are shown separately at ( c) and ( d).

It is clear that both the   P- and   F_j -couples tend to rotate the flange as sketched. This rotation is exacerbated by the fluid pressure   p tending to expand the pipe connected to the flange, however the flange is relatively rigid radially and so prevents pipe wall local expansion as suggested by ( e).
Free bodies of the separate pipe and flange appear at ( f) and ( g). The interface remains essentially rigid whilst rotation occurs - that is the deformed pipe and deformed flange remain perpendicular to one another. This requires the action/ reaction sketched - the radial force   F_i and the bending moment   M_i at the interface. Clearly   M_i contributes to the rotation of the flange ( g).
It is common practice to allow for rotation empirically by considering an effective gasket width somewhat less than the actual width, as suggested by ( h) - further details appear in AS1210.

Operation at high temperatures leads to further difficulties with creep, ratcheting and so on.