Determine the middepth deflection at the free end and the maximum principal stresses and their location for the beam subjected to the shear load variation shown in Figure P7-20. Do this using 64 rectangular elements all of size 12 in. × 1/2 in.; then all of size 6 in. ×1 in.; then all of size 3 in. × 2 in.. Then use 60 rectangular elements all of size 2.4 in. × 2 2/3 in.; then all of size 4.8 in. × 1 1/3 in. Compare the free-end deflections and the maximum principal stresses in each case to the exact solution. Let E = 30 × 106 psi, v = 0.3, and t = 1 in. Comment on the accuracy of both displacements and stresses.

Figure P7-20

40,000-lb total shear load parabolically distributed 8 in. 48 in.