Hi Robin,
What you are seeing in Woods and Baguley is the TRESCA failure theory that is used in the B31 series of Codes. That is to say the Code used the TRESCA method of combining principal stresses. On page 67 Glynn is showing the equation for calculated displacement stress range (this is a combined stress):
Se = ((Sb**2) + (4 X St**2))**1/2
Where Sb is the square root of the sum of the squares of the two bending stresses, Si (in-plane) and So (out-of-plane)and this is given by:
Sb = (((Mi / Z)**2) + ((Mo / Z)**2))**1/2
and the torsional stress, St, is given by:
St = (Mt / 2Z)
Mi is the inplane bending moment
Mo is the out-of-plane bending moment
St is the torsional moment
Z is the section modulus of the pipe section being analyzed
In the book, Glynn is including the stress intensification factors that we multiply the moments by to include the effect of the various component geometries which tend to intesnsify the stresses.
But how are these moments calculated? By classic beam theory as used in structural analysis for decades. Many of the programs use an adaptation of Castigliano's second theorm. The beam (pipe) is allowed to deflect under loading with no restraint and the forces and moments required to "pull the beam back together" (e.g., reattach disjoint branch connections) are calculated. Of course this is very different from FEA or even shell theory. This basic limitation (the limitation of beam theory) is somtimes not really understood by the piping engineer. The might be much greater local membrane stresses that will be present but are not calculated by beam theory. You can look at the Kellogg book or the 1955 book by Spielvogle for more on "hand methods" for calculating these moments.
But I digress. If you want to read another (other than Woods and Baguley) discussion of the B31 Code stress calculations I would recommend the books by David Burgreen: The most useful one is "Design Methods for Power Plant Structures", but to answer your specific questions perhaps Burgreen's book "Principles of Piping Analysis" would interest you m(although it doesn't have much for the practical piping engineer - more for the mathmetician). Of course these excellent books are out of print now, last being published by Arcturus Publishers.
I hope this helps a little.
Regards, John.
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