A hydrodynamic analogy for shearing stress distribution in bending

Abstract

It is shown here that the shearing stress distribution in the combined shear and bending is represented with practical accuracy by the distribution of velocity in the flow of a perfect fluid over the area of the cross section. This flow is produced by a linear distribution of sources above the neutral axis and of sinks below the neutral axis, the intensity of these sources and sinks being proportional to the distance to the neutral axis. For hollow beams the additional condition must be added that the circulation of the velocities is zero around each hole of the cross section. The analogy which is rigorous for a material of zero Poisson ratio holds within a small correction for the general case. © 1938 The American Institute of Physics.