105年 - 105 國立嘉義大學_碩士班(甲組)招生考試試題_土木與水資源工程學系：材料力學#145952

1. 1. An aluminum bar AD (Fig. 1) has a crosssectional area of A = 250 mm² and is loaded by forces P₁ = 7560 N, P₂ = 5340 N, and P₃ = 5780 N. The lengths of the segments of the bar are a = 1525 mm, b = 610 mm, and c = 916 mm shown in Fig.1. Assuming that the modulus of elasticity E = 72 GPa, calculate the change in length of the bar. Does the bar elongate or shorten? (20%)

2. A pressurized cylindrical tank with flat ends is loaded by torques T and tensile forces P as shown in Fig. 2. The tank has inner radius of r = 125 mm and wall thickness t = 6.5 mm. The internal pressure p = 7.25 MPa and the torque T = 850 N-m. What is the maximum permissible value of the forces P if the allowable tensile stress in the wall of the cylinder is 80 MPa? (20%)
Fig. 2

3. Fig. 3 shows a pentagon. Determine the moment of inertia of the shaded area about the y axis. (20%)

4. The state of stress at a point in a member is shown in Fig. 4. Determine the stress components acting on the inclined plane AB. (20%)
Fig. 4

5. A beam is subjected to two concentrated loads as shown in Fig. 5. Determine the distance a as a function of the beam’s length L for locating the roller support so that the moment in the beam at B is zero. (20%)