[試題] 100下 鄭榮和 材料力學 補考
課程名稱︰材料力學
課程性質︰必修
課程教師︰鄭榮和
開課學院：工學系
開課系所︰機械工程學系
考試日期（年月日）︰2012/06/15
考試時限（分鐘）：2hr
是否需發放獎勵金：是, 感謝
（如未明確表示，則不予發放）
試題 :
材料力學補考
《需畫圖說明或 Free Body Diagram 而未畫者，扣該題 1/5 分數》
(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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