고체역학 (Beer) — Stress and Strain—Axial Loading: Problem 2.77

2.77 Two blocks of rubber with a modulus of rigidity \( G = 12\text{ MPa} \) are bonded to rigid supports and to a plate \( AB \). Knowing that \( c = 100\text{ mm} \) and \( P = 45\text{ kN} \), determine the smallest allowable dimensions \( a \) and \( b \) of the blocks if the shearing stress in the rubber is not to exceed \( 1.4\text{ MPa} \) and the deflection of the plate is to be at least \( 5\text{ mm} \).