고체역학 (Gere) — Stresses in Beams (Basic Topics): Problem 5.5-25

5.5-25 A beam with a T-section is supported and loaded as shown in the figure. The cross section has width $b = 65\text{ mm}$, height $h = 75\text{ mm}$, and thickness $t = 13\text{ mm}$. (a) Determine the maximum tensile and compressive stresses in the beam. (b) If the allowable stresses in tension and compression are $124\text{ MPa}$ and $82\text{ MPa}$, respectively, what is the required depth $h$ of the beam? Assume that thickness $t$ remains at $13\text{ mm}$ and that flange width $b = 65\text{ mm}$. (c) Find the new values of loads $P$ and $q$ so that the allowable tension ($124\text{ MPa}$) and compression ($82\text{ MPa}$) stresses are reached simultaneously for the beam. Use the beam cross section in part (a) (see figure) and assume that $L_1, L_2,$ and $L_3$ are unchanged.