The beam has a rectangular cross section and is subjected to a load P that is just large enough to develop a fully plastic moment M_p= PL at the fixed support. If the material is elastic perfectly plastic, then at a distance x < L the moment M = Px creates a region of plastic yielding with an associated elastic core having a height 2y­¢. This situation has been described by Eq. 6€“30 and the moment M is distributed over the cross section as shown in Fig. 6€“48e. Prove that the maximum shear stress in the beam is given by Ï„_max= 3/2 (P/A­¢), where A¢­ = 2y¢ ­b, the cross-sectional area of the elastic core.

Plastic region 4- Elastic region -L-