101年 - 101 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：工程力學#146243

(a) Determine the stresses on the element inclined at an angle θ=45°. (8%)

(b) Determine the principal stresses. (6%)

(c) Determine the maximum shear stresses. (6%)

2. A simple beam consists of a wood member that is reinforced by 0.25 in. thick steel plates on top and bottom, as shown in Fig-2. \( E_s=30 \times 10^6 \) psi and \( E_w=1.5 \times 10^6 \) psi, respectively. Calculate the maximum bending stresses \( \sigma_s \) in the steel plates and \( \sigma_w \) in the wood member due to the uniform load. (20%)

3. Draw the shear force and bending moment diagrams of Fig-3. (20%)

4. Draw the Mohr’s circle and find the normal stress and shear stress on the plane for α=35° in the Fig-4. (20%).

5. The beam AB shown in the Fig-5 supports a uniform load of intensity 3000 N/m acting over half the length of the beam. The beam rests on a soil layer that produces a uniformly distributed pressure load over the entire length. Draw the shear-force and bending-moment diagrams for this beam. (20 %).