Primary stress

A primary stress is required to keep an external load in equilibrium. Internal pressure tries to expand the pipe, weight tries to bend it – the wall has to carry both and cannot escape the task by yielding. If the material yields, the load remains at its full value.

This distinguishes it from secondary stress, which arises from restrained deformation and decreases as soon as the material yields locally. A primary stress is not self-limiting: if it exceeds the load-carrying capacity of the cross-section, gross plastic deformation follows and ultimately failure – in a single load application, not only after many cycles.

In pipe stress analysis these are all loads that act independently of the deformation of the line.

The codes check primary stresses in two steps. Internal pressure alone determines the wall thickness. Then the longitudinal stresses from sustained loads – pressure and weight – are combined and compared with the allowable stress at operating temperature. ASME B31.3 writes this as SL ≤ Sh; EN 13480-3 performs the same check with its design stress.

For occasional loads such as wind or earthquake the codes permit a higher limit because they act only briefly – in ASME B31.3, 1.33 times the allowable stress. The principle remains: the limit is derived from the strength of the material at temperature, not from a fatigue consideration.

Primary stresses from weight fall with every additional support: shorter spans mean smaller bending moments. Against internal pressure only wall thickness or a stronger material helps.

More flexibility in the routing – the remedy of choice against thermal stresses – does not help here. On the contrary, a long, soft expansion loop without support increases the weight stresses. This conflict is why a piping system cannot be optimised by a single rule. Supports that carry weight must not block thermal expansion.

Primary stresses are regarded as the easy part of pipe stress analysis. The errors lie in the load assumptions.