Moving Loads on Restrained Beams and Frames

Engineers have long been familiar with the criterion for placing a load on a simple beam, for maximum moment under one of its concentrations, which requires that the center of the span bisect the distance from the center of gravity of the load to the concentration in question. There is also that other criterion for placing the load for maximum moment at a given point, which requires that the average load in each segment of the span shall be the same as that throughout the span. When the ends of a beam are restrained these criteria cannot be applied; and the problem is further complicated when the object is to find the loading position for maximum moment at the restrained ends. In the past the problem of placing moving loads on fixed spans has usually been solved, rather laboriously, by the use of influence lines.