A finite element solution for Saint-Venant bending

Abstract

symmetric, and those of the last row to the value of n for which Ref. 5 leads to a minimum (namely n = 3/2, 0.50, 0.90 and 3/ for the four sections, respectively). As expected, Eq. (6) gives too conservative values, and so does Eq. (10b) in the case of section B. For sections A, C, and D, the ratios of the values for the minimum A7cr given in the last two rows are 0.70, 0.92, and 0.69, respectively; these may be considered sufficiently close to unity to be useful either for quick preliminary estimates or for rough checks on more accurate calculations. It may be indeed concluded that this will always be the case for all sections, except those in which the bulk of the material is concentrated, as in section B, away from the tip regions r > p.