Torsion Analysis of Heavy Box Beams in Structures

Heavier box sections with thicker walls without the need of longitudinal stiffeners are widely used to resist combined torsion and bending loads in machines such as earth-moving and mining equipment. To solve for the torsion stresses and the angle of twist for such boomless boxes, a part of the area of the wall cross section is assumed to be concentrated at the corners and to be equivalent stiffeners. The transformed box is then solved by the customary procedures. A new method of solving for the stresses and angles of twist in a heavy walled box is given. It is based upon the fact that the longitudinal and shearing streses associated with restraining a cross section from warping when pure torque is applied, consist of two separate but related self-equilibrating systems that are distributed throughout the walls. Both systems are completely determined, and these two systems are superposed on the St-Venant (Bredt-Batho) System that is based upon complete freedom of every cross section to warp.