robinho

Thank you very much for your reply😛. I look for analytic solutions. I'm aware that analysis is only valid for a range of width to length or depth to length ratios. But analytic solutions for torsion isn't aspect ratio sensitive. Yes, I refer to torsion. When you twist a bar and if the bar is not of round cross section, there is longitudinal (z) displacement and this is where the warping function psi(x,y) comes from. When the cross section is round, psi=0. I don't have the book Formulas for Stress, Strain, and Structural Matrices. Don't know if I can find it online.

thank you so much! I checked the books you suggested. For example, I couldn't find warping function formulae of common cross sections of a beam. Imagine having a straight bar of known cross section, then twist it from both ends, and compute the longitudinal displacement, then we need a warping function satisfying a poisson equation. The solution depends only on the cross section, not anything else. Is there a table listing such warping functions?

Where can one find warping and bending function formulae of common cross sections of a beam in St Venant problems in elasticity?