고체역학 (Beer) — Principal Stresses Under a Given Loading: Problem 8.45

8.45 Three forces are applied to the bar shown. Determine the normal and shearing stresses at (a) point a, (b) point b, (c) point c. Given values from Figure P8.45: Bar dimensions: width $w = 4.8\text{ in.}$, thickness $t = 1.8\text{ in.}$, height $h = 10.5\text{ in.}$ Applied forces at the top: Axial force $P = 50\text{ kips}$ (downward) acting at the center of the top back edge. Transverse force $V_z = 2\text{ kips}$ (acting towards the back, $-z$ direction) at the center of the top back edge. Transverse force $V_x = 6\text{ kips}$ (acting to the left, $-x$ direction) at the top back right corner. Points $a, b, c$ are on the front face ($z = 0.9\text{ in.}$) at the base ($y = 0$): Point $b$ is at the center of the width ($x = 0$). Point $a$ is $1.2\text{ in.}$ to the left of $b$ ($x = -1.2\text{ in.}$). Point $c$ is $1.2\text{ in.}$ to the right of $b$ ($x = +1.2\text{ in.}$).