Action of Deep Beams Under Combined Vertical, Lateral, and Torsional Loads

This paper is devoted to a discussion of the behavior of beams when the primary vertical load acts at the same time as the secondary lateral and torsional loads. Beam loading of this type occurs in the case of shop traveling cranes, measurements indicating that the lateral and torsional loads are much smaller than the primary vertical load. The author considers the problem of the “deep beam” in which the moment of inertia of the cross section about the horizontal axis is much greater than about the vertical axis. The solution is achieved by determining the equation of twist in the beam and the moment or load where small increases of their values cause large increases in the values of angle of twist.