고체역학 (Gere) — Stresses in Beams (Basic Topics): Problem 5.4-5

5.4-5 A thin strip of steel with a length of \( L = 0.5 \text{ m} \) and thickness of \( t = 7 \text{ mm} \) is bent by couples \( M_0 \) (see figure). The deflection at the midpoint of the strip (measured from a line joining its end points) is found to be \( 7.5 \text{ mm} \). (a) Determine the longitudinal normal strain \( \epsilon \) at the top surface of the strip. (b) If allowable strain \( \epsilon_a = 0.0008 \), what is the maximum acceptable thickness of the strip? (c) If allowable strain \( \epsilon_a = 0.0008 \), \( t = 7 \text{ mm} \), and \( L = 0.8 \text{ m} \), what is deflection \( \delta \)? (d) If allowable strain \( \epsilon_a = 0.0008 \), \( t = 7 \text{ mm} \), and the deflection cannot exceed \( 25 \text{ mm} \), what is the maximum permissible length of the strip?