Deep and Multilayered Beams

A nonlinear theory for multilayered shells is particularized for deep beams. The results are linearized and applied to small deflection analyses of such beams. In the solution, a finite difference scheme is used which takes advantage of the fact that higher derivatives of variables do not all appear simultaneously in any one equation, thereby admitting introduction of two interlacing nets and improving the efficiency of the scheme. As a test case, a continuous beam with span depth ratio L/ =1, supported by columns 0.1 L wide and subjected to a uniformly distributed load along the lower edge is solved and results compared with those obtained from an exact solution. Results from the present theory and solution method are in good agreement with those obtained from an exact solution. As a second example, the stress distribution in deep beam was obtained. The results from this second example indicate that convergence of the solution is quite good with relatively small number of layers.