고체역학 (Beer) — Pure Bending: Problem 4.77

4.77 through 4.80 For the beam indicated, determine (a) the plastic moment \(M_p\), (b) the shape factor of the cross section. 4.77 Beam of Prob. 4.73. 4.73 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. (From Fig. P4.73: Rectangular cross section with width \(b = 60\text{ mm}\) and height \(h = 90\text{ mm}\)).