Gere & Goodno — Axially Loaded Members: Problem 2.3-12

2.3-12 A bar $ABC$ of length $L$ consists of two parts of equal lengths but different diameters. Segment $AB$ has diameter $d_1 = 100$ mm, and segment $BC$ has diameter $d_2 = 60$ mm. Both segments have a length $L/2 = 0.6$ m. A longitudinal hole of diameter $d$ is drilled through segment $AB$ for one-half of its length (distance $L/4 = 0.3$ m). The bar is made of plastic having a modulus of elasticity $E = 4.0$ GPa. Compressive loads $P = 110$ kN act at the ends of the bar. (a) If the shortening of the bar is limited to 8.0 mm, what is the maximum allowable diameter $d_{max}$ of the hole? (See figure part a.) (b) Now, if $d_{max}$ is instead set at $d_2/2$, at what distance $b$ from end $C$ should load $P$ be applied to limit the bar shortening to 8.0 mm? (See figure part b.) (c) Finally, if loads $P$ are applied at the ends and $d = d_2/2$, what is the permissible length $x$ of the hole if shortening is to be limited to 8.0 mm? (See figure part c.)