고체역학 (Beer) — Pure Bending: Problem 4.80

4.77 through 4.80 For the beam indicated, determine (a) the plastic moment \(M_p\), (b) the shape factor of the cross section. 4.80 Beam of Prob. 4.76. 4.76 A beam of the cross section shown is made of a steel that is assumed to be elastoplastic with \(E = 29 \times 10^6 \text{ psi}\) and \(\sigma_Y = 42 \text{ ksi}\). 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 1 in. thick. (From Fig. P4.76, the cross section is an I-shape with: flange width = 3 in., flange thickness = 1 in., web height = 2 in., and web thickness = 1 in.)