고체역학 (Beer) — Pure Bending: Problem 4.79

4.77 through 4.80 For the beam indicated, determine (a) the plastic moment \( M_p \), (b) the shape factor of the cross section. 4.79 Beam of Prob. 4.75. (From Prob. 4.75): 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 \( \sigma_Y = 42 \text{ ksi} \). The cross section (Fig. P4.75) is an I-shape with the following dimensions: Total width of flanges: \( b = 0.5 \text{ in.} + 2 \text{ in.} + 0.5 \text{ in.} = 3 \text{ in.} \) Thickness of flanges: \( t_f = 1 \text{ in.} \) Thickness (width) of web: \( t_w = 2 \text{ in.} \) Height of web portion between flanges: \( h_w = 2 \text{ in.} \) Total height: \( h = 1 \text{ in.} + 2 \text{ in.} + 1 \text{ in.} = 4 \text{ in.} \)