Beer & Johnston — Pure Bending: Problem 4.78

4.78 Beam of Prob. 4.74. [Determine (a) the plastic moment \(M_p\), (b) the shape factor of the cross section.] 4.74 A beam of the cross section shown is made of a steel that is assumed to be elastoplastic with \(E = 200 \text{ GPa}\) and \(\sigma_Y = 240 \text{ MPa}\). For bending about the \(z\) axis, determine the bending moment at which (a) yield first occurs, (b) the plastic zones at the top and bottom of the bar are \(30 \text{ mm}\) thick.