110年 - 110 國立臺灣大學_碩士班招生考試_土木工程學研究所大地工程組(一般、在職生):材料力學(A)#125226

Problem 1 (25%)
A cylindrical pressure vessel with flat ends is subjected to a torque T and tensile forces P. The tank has a radius r = 125 mm and the wall thickness t = 6.5 mm. The loads are T = 850 N·m, P = 400 kN, and the internal pressure p = 7.25 MPa.
Determine the maximum shear stress τ_max in the wall of the cylinder.

Problem 2 (25%)
Draw the shear-force and bending-moment diagrams for the beams shown in the figure below.

Problem 3 (25%)
Using moment-area method, obtain formula for the maximum deflection δmax at the midpoint for a simple beam AB with a uniform load of intensity q.

Problem 4 (25%)
A stepped shaft ACB is held against rotation at ends A and B and subjected to a torque T₀ acting at section C. The two segments of the shaft have diameters d_A and d_B, respectively, and polar moments of inertia I_pA and I_pB, respectively. The shaft has length L and segment AC has length a. For what ratio a/L will the maximum shear stresses be the same in both segments of the shaft?