고체역학 (Beer) — Stress and Strain—Axial Loading: Problem 2.78

2.78 Two blocks of rubber with a modulus of rigidity \( G = 10 \text{ MPa} \) are bonded to rigid supports and to a plate \( AB \). Knowing that \( b = 200 \text{ mm} \) and \( c = 125 \text{ mm} \), determine the largest allowable load \( P \) and the smallest allowable thickness \( a \) of the blocks if the shearing stress in the rubber is not to exceed \( 1.5 \text{ MPa} \) and the deflection of the plate is to be at least \( 6 \text{ mm} \).