Single‐Span Deep Beams

Abstract

The multiple Fourier technique is used to compare the stress fields in single span deep beams due to uniform loading at the top edge and at the bottom edge. The method involves the superposition of three stress functions. The first stress function is used to satisfy the boundary conditions on the upper and lower edges of the beam. The second and third stress functions are used to satisfy the boundary conditions on the vertical edges of the beam. This approach allows to satisfy all the required boundary conditions. Contour maps of the stress field reveal the existence of regions of pure tension and pure compression. These regions indicate proneness to spalling, bursting or crushing.