Abstract
A simple successive-approximations procedure for the solution of the problems of Saint-Venant torsion and bending of beams of arbitrary cross section is presented. The shear stresses in a cross section of the beam are first calculated from the formulas valid for thin-walled sections, on the basis of an assumed set of lines of shearing stress. From these a first approximation to the stress function of either the torsion or the bending problem is found. The second approximation to the stress function is then obtained from the governing equation of the problem, expressed in finite-difference form; this in turn allows the determination of an improved set of lines of shearing stress, and hence of the shearing stress itself. The procedure can be repeated until the results of two successive steps are sufficiently close. Applications are presented for a beam cross section for which the exact solutions are known, and it is shown that no further difficulties arise in applications to more complicated shapes.
Determination of Shear Center of Arbitrary Cross-Section
