고체역학 (Gere) — Axially Loaded Members: Problem 2.3-31

2.3-31 A bar \(ABC\) revolves in a horizontal plane about a vertical axis at the midpoint \(C\) (see figure). The bar, which has a length \(2L\) and cross-sectional area \(A\), revolves at constant angular speed \(\omega\). Each half of the bar (\(AC\) and \(BC\)) has a weight \(W_1\) and supports a weight \(W_2\) at its end. Derive the following formula for the elongation of one-half of the bar (that is, the elongation of either \(AC\) or \(BC\)): \[ \delta = \frac{L^2 \omega^2}{3gEA}(W_1 + 3W_2) \] in which \(E\) is the modulus of elasticity of the material of the bar and \(g\) is the acceleration of gravity.