고체역학 (Gere) — Axially Loaded Members: Problem 2.6-5

2.6-5 A brass wire of diameter \( d = 1.6 \text{ mm} \) is stretched between rigid supports with an initial tension \( T \) of 200 N (see figure). Assume that the coefficient of thermal expansion is \( 21.2 \times 10^{-6}/^\circ\text{C} \) and the modulus of elasticity is 110 GPa. (a) If the temperature is lowered by \( 30^\circ\text{C} \), what is the maximum shear stress \( \tau_{\text{max}} \) in the wire? (b) If the allowable shear stress is 70 MPa, what is the maximum permissible temperature drop? (c) At what temperature change \( \Delta T \) does the wire go slack?