Secondary stress

A secondary stress arises when a component wants to deform and is prevented from doing so. A hot pipe wants to grow longer; anchors, equipment nozzles and its own geometry allow this only in part. There is no external load to be held in equilibrium – only a deformation that has to be accommodated.

This explains its most important property. If the material yields slightly at the most highly stressed point, the deformation is accommodated and the stress rises no further. Secondary stress limits itself.

Thermal expansion is the most frequent source but not the only one.

A single heat-up does not cause a properly designed line to fail. Repetition does the damage: every start-up and shutdown is a load cycle, and over the service life fatigue cracks form at bends, branches and welds. The codes therefore limit the stress range and reduce the allowable value with the number of cycles.

Self-limitation has a boundary. Where a large, stiff system meets a short, weak section, the entire deformation concentrates there. The section is strained far beyond what the elastic calculation shows. Such unbalanced systems demand particular attention.

Against restraint, flexibility helps: longer legs perpendicular to the direction of expansion, expansion loops, expansion joints and anchors in the right place.

Greater wall thickness does not help. It makes the pipe stiffer; the same imposed deformation then produces larger forces at anchors and nozzles while the bending stress in the pipe stays practically the same. Additional rigid supports can also increase secondary stresses if they block a movement that was previously free.

Besides primary and secondary stresses the codes recognise peak stresses: the highest local value at a notch, a weld toe or an abrupt change of section. They do not noticeably deform the component and matter only for fatigue. In pipe stress analysis they are not calculated individually but covered by the stress intensification factors of the components.