 # Pipe stress III

In this article I will discuss allowable thermal stress range equations given in piping code B 31.3. As per piping code B31.3, there are two equations for allowable stress range and we will explore different condition when one equation can be applied versus other equation. Please see the figure below. We will start from the chart below and I will use analogy with a cup of water. For example, when the cup of water is brimful we will say that capacity of the cup is exhausted. Note that chart above is taken from my blog Pipe stress II. Let’s chart allowable stress on the cup. Please see the figure below. Now, let’s suppose that we have the piping system where stress from sustain load is small in a value and stress from thermal expansion is a close but less than allowable thermal expansion given in Eq.1. This case is illustrated in the figure below. We can say that our piping system is satisfactory since stresses are less than allowables and our cup still has some capacity unused. Now, suppose that in the same system temperature has been increased, and stress from thermal expansion is greater than allowable stress range given by Eq.1. This case is illustrated in the figure below. Thermal stress is larger than allowable stress range given in Eq.1 and therefore our piping system is not satisfactory. But, by looking the figure above we can see that capacity of our cup is not exhausted and our piping system has some capacity leftover. We can conclude that Eq.1 cannot be applied to all situations and in situation like this Eq.2 comes into play. In other words, unused capacity from sustain load can be used for thermal expansion.  Please see the figure below. Eq.2 should be used when stress that comes from sustain load is much lower than allowable hot stress Sh. But if stress from sustain load is close but lower to allowable hot stress Sh, than Eq.1 should be used, since using Eq.2 has little or no benefit. In conclusion, if stress from sustain load is less than 80% of allowable hot stress Sh, than Eq.2 should be used otherwise use Eq.1. Note that piping code B 31.3 does not specify conditions when equations for thermal stress range shall be used . That it is left for personal judgment. Stress at elevated temperature or creep stress is out of scope in this blog, but it is worth to mention that creep stress should be checked as per Appendix K (B31.3 code).