Pipe stress calculation

Piping codes do not compare a single equivalent stress with a single limit. They carry out separate checks for different kinds of load, because these lead to failure in different ways: pressure and weight through plastic collapse in a single overload, thermal expansion through fatigue over many cycles.

A pipe stress calculation is therefore a series of checks, each with its own load combination and its own allowable value. A line is justified only when all of them are satisfied.

Sustained loads: the longitudinal stresses from internal pressure and weight are compared with the allowable stress at operating temperature – in ASME B31.3 the check reads SL ≤ Sh.

Occasional loads: wind, earthquake or the forces of a discharging safety valve are added to the sustained loads. Because they act only briefly, the limit is raised; ASME B31.3 permits 1.33 times Sh.

Thermal expansion: what is assessed is the stress range between the temperature states. The limit in ASME B31.3 is SA = f · (1.25 · Sc + 0.25 · Sh), where Sc and Sh are the allowable stresses in the cold and hot condition. The factor f accounts for the number of cycles and is 1.0 up to 7000 cycles.

EN 13480-3 has the same structure – sustained loads, sustained plus occasional loads, stress range, and a separate check in the creep range – but uses its own symbols and factors.

The beam model delivers the bending and torsional moments at every node for every load case. The bending stress is the resultant moment divided by the section modulus of the pipe. At bends, tees and branches the moment is multiplied by the stress intensification factor of the component.

The longitudinal stress from internal pressure is added. The ratio of calculated to allowable stress is the utilisation; it is reported for every node and every check.

Stresses from restrained thermal expansion are self-limiting. During the first heat-up the material may yield locally at highly stressed points; afterwards the line cycles elastically between its cold and its hot condition. What causes damage is not the stress level in either condition but the difference between them and the number of repetitions.

Two things follow. The range is taken between the coldest and the hottest condition the line is intended to reach – not merely between installation and normal operation. And cold spring at installation does not change the stress range; it only shifts the condition in which the forces occur.

Errors in a pipe stress calculation rarely arise in the equation and almost always in the load assumptions.