103年 - 103 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#145966

1. The beam below has an axial release just to the left of C. Find the axial force (N), shear (V), and moment (M) diagrams along the beam. Label all critical N, V, and M values and also the distance to points where N, V, and/or M is zero.(20%)

2. A tubular beam ACB with a length of L = 1.5 m is pin supported at its ends, A and B. A powered winch at E lifts load W below C using a cable which passes over a frictionless pulley at midlength (point D). The distance from the center of the pulley to the longitudinal axis of the tube is d = 140 mm. The cross section of the tube is square with an outer dimension of b = 15 cm, area of A = 125 cm², and moment of inertia of I = 3385 cm⁴. Determine the maximum tensile and compressive stresses in the beam due to a load W = 13.5 kN.(20%)

3. Determine the normal (σ) and shear (τ) stresses on the element shown below by using Mohr’s circle. Show these stresses on sketches of properly oriented elements.(20%)

4. The members of the truss in Fig. 1 have equal cross-section areas A=400 mm². The suspended mass is m=3400 kg. What are the normal stresses in the members?(20%) Fig. 1

5. Draw the shear force and bending moment diagrams for the beam in Fig. 2. (20%)