고체역학 (Beer) — Pure Bending: Problem 4.46

4.46 For the composite beam in Prob. 4.42, determine the radius of curvature caused by the couple of moment $450\text{ kip}\cdot\text{in.}$ Reference Prob. 4.42: The $6 \times 12\text{-in.}$ timber beam has been strengthened by bolting to it the steel reinforcement shown. The modulus of elasticity for wood is $1.8 \times 10^6\text{ psi}$ and for steel is $29 \times 10^6\text{ psi}$. Knowing that the beam is bent about a horizontal axis by a couple of moment $M = 450\text{ kip}\cdot\text{in.}$, determine the maximum stress in (a) the wood, (b) the steel. (The figure for 4.42 shows a $6\text{ in.}$ wide, $12\text{ in.}$ high timber beam with a C8 x 11.5 steel channel attached to the bottom face).