Consider a beam with a rectangular cross$-$section of $35mm90mm(b2c)$ under pure bending. The material of the beam exhibits an elastic$-$perfectly plastic behavior with a yield strength of $450$ MPa and a modulus of elasticity of $250$ GPa $.$ Compute and draw the distribution of residual stresses, if one applies and then removes a bending moment large enough to induce plasticity in the outer upper and lower zones of the beam of a thickness of $15$ mm out of $90$ mm $,$ i$.$e$.y_{\text{y}\text{i}\text{e}\text{l}\text{d}}=30mm.$