The piping code stress equations are a direct outgrowth of the theoretical and investigative work discussed above, with specific limitations established by Markl in his 1955 paper. The stress equations were quite similar throughout the piping codes (i.e., between B31.1 and B31.3) until the winter of 1974, when the power codes, having observed that Markl was incorrect in neglecting intensification of the torsional moment in a manner analogous to the bending component, combined the bending and torsional stress terms, thus intensifying torsion.
It should be noted that the piping codes exactly calculate the stress intensity (twice the maximum shear stress) only for the expansion stress, since this load case contains no hoop or radial components, and thus becomes an easy calculation. Including hoop and radial stresses (present in sustained loadings only) in the stress intensity calculation makes the calculation much more difficult. When considering the hoop and radial stresses, it is no longer clear which of the principal stresses is the largest and which is the smallest. Additionally, the subtraction of S1-S3 does not produce a simple expression for the stress intensity. As it turns out, the inclusion of the pressure term can be simplified by adding only the longitudinal component of the pressure stress directly to the stress intensity produced by moment loadings only. This provides an equally easy-to-use equation and sacrifices little as far as accuracy is concerned.
The explicit stress requirements for the piping codes addressed by CAESAR II follow below. Note that most codes allow Pdi2 / (do2 - di2) to be used in place of Pdo / 4t.