课程名称︰材料力学 课程性质︰必修 课程教师︰郑荣和 开课学院：工学系 开课系所︰机械工程学系 考试日期（年月日）︰2012/06/15 考试时限（分钟）：2hr 是否需发放奖励金：是, 感谢 （如未明确表示，则不予发放） 试题 : 材料力学补考 《需画图说明或 Free Body Diagram 而未画者，扣该题 1/5 分数》 (20% will be deducted from the designated score of that problem if you fail to draw a free-body diagram.) 1. A bolt and sleeve (套筒) assembly (both are made of steel) is shown below in (A) with the nut being turned up just tight by hand. Suppose that the bolt has 16 threads (螺牙) per inch. Using wrenches (扳手), the nut is given an extra quarter turn (90度) so that the bolt is put in tension and the sleeve in conpression. (a) Draw a simple diagram toshow forces on the sleeve and the bolt, respectively (15%) (b) What is the tensile force in the bolt? The Young's modulus of steel is 6 E= 30x10 psi. (15%) (c) How large must be the force F in (B) be to reduce the force of sleeve to zero? (10%) (A)　 　　 100 in 　　　 ├──────────────┤ 　 　　　 ┌┼──────────────┼┐ 　　　┌┤╞══════════════╡├┐ 　　　│││ Bolt (Steel A= 10平方寸) │││ 　　　└┤╞══════════════╡├┘ 　　　 └┼──────────────┼┘← Sleeve (Steel A =15平方寸) (B) 　 　　 100 in 　 　　├──────────────┤ 　　　 　　　 ┌┼──────────────┼┐ 　　　┌┤╞══════════════╡├┐ 　Ｆ←│││ Bolt (Steel A= 10平方寸) │││→ Ｆ 　　　└┤╞══════════════╡├┘ 　　　 └┼──────────────┼┘← Sleeve (Steel A= 15平方寸) 2. A beam of stiffness EI and length L shown below is built in at both ends. (a) Use the superposition method to determine the reaction forces and moments at both fixed ends. (30%) (b) Draw the shear force and bending moment diagram. (10%) (c) Determine the deflection at the applied load. Draw the deflection curve. (20%) ═╡　　　　　　　Ｐ　　　　　　　╞═ ═╡　　　　　　　│　　　　　　　╞═ ═╡　　　　　　　↓　　　　　　　╞═ ═╪═══════════════╪═ ═╡ ╞═ ═╪═══════════════╪═ ═╡　　　　　　　　　　　　　　　╞═ ═╡←──────Ｌ──────→╞═ Some useful formulae: F L Axially loaded member: δ=----- E A ←╮ 2 2 ╪══════╗│Ｍ M x M L M x M L ╪══════╝│ ψ=----- ψmax=----- υ=------- υmax=------- ─╯ E I E I 2 E I 2 E I 　　　 Ｆ 2 2 3 ↑ P ｘ P Ｌｘ ｘ ╪══════╗ ψ=-----(Lx - ─ ) υ=-----(── - ─ ) ╪══════╝ E I ２ E I ２　　６ ←──Ｌ──→ 2 3 　　　　　　　　　　　　　 P L P L 　　　　　　　　　　　 ψmax=------- υmax=------- 　　　　　　　　　　　　　　 2 E I 3 E I --

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