[試題] 97下 施文彬 材料力學 期中考
課程名稱︰材料力學
課程性質︰系定必修
課程教師︰施文彬
開課學院：工學院
開課系所︰機械系
考試日期（年月日）︰980414
考試時限（分鐘）：(表訂)110+(臨時加時)20
是否需發放獎勵金：是
試題：
1. (30%) At room temperature (21 degree Celsius) a 0.6 mm gap exists between the
ends of thr rod shown. Assume linearly elastic and perfectly plastic. Neglect
gravity.
(a) At what temperature does the gap become zero?
(b) At what temperature does one of the rods start to yield? Which rod will
yield at this temperature?
(c) At a later time when the temperature has reached 160 degree Celsius,
determine the normal stress in each rod.
(d) Following (c), determine the change in length of the steel rod.
(e) The rods are colled down to room temperature after step (c). Determine the
length of each rod after cooling down.
Figure 1
▄▄▄▄▄▄ __
████ ↑ Aluminum
████ 2
████ 300mm A=1806mm , E=72GPa
████
████ ↓ α=23.9E-6/Celsius, σY=20MPa
████ __
0.6mm__
██ ↑ Stainless steel
██ 2
██ 250mm A=774mm , E=190GPa
██ ↓
██ __ α=17.3E-6/Celsius, σY=280MPa
▄▄▄▄▄▄
2. (30%) Torsion
(a) In Figure 2.1, a torque T is applied to a solid tapered shaft AB. Given
the shear modulus G, derive the angle of twist at A by integration.
(b) Following (a), the shaft AB is connected to another shaft AC as shown in
Figure 2.2. The torque is applied at the midpoint of the shaft AC. Assume
the same material for both shafts. Derive the angle of twist at A.
(c) Following (b), find the maximum shearing stress in the shaft AB. Please
specify the location along the shaft and on the cross section where this
maximum shearing stress occurs.
Figure 2.1 Figure 2.2
__ ▄▄▄▄▄▄
↑ │ │
│ │
│ Ｔ │
2L │──→│
↑ │ │
│T │ │
│ ↓ │ │
A________________ __ A___⊥______⊥___
\ 2c───→/ ↑ \ 2c───→/
\ / Ｌ \ /
\ / ↓ \ /
B\ ｃ─→/ __ B\ ｃ─→/
▄▄▄▄▄▄▄▄ ▄▄▄▄▄▄
3. (10%) Given the Young's modulus E and Poisson's ratio υ of an isotropic,
linearly elastic material. Derive the mulk modulus of the material and show
that υ=0.5 for incompressible materials.
4. (30%) A complsite cantilever beam is subjected to loading as shown below.
The cross section of this prismatic beam is also given. The beam material is
isotropic and linearly elastic. The young's moduli of the beam materials are
given in the cross section of the beam.
(a) Draw free body diagram of the beam.
(b) Find all reactions of the beam.
(c) Draw shear diagrams and find V(x).
(d) Draw bending moment diagram and find M(x).
(e) Find the maximum magnitude of normal stress along the beam. Please
specify the location along the beam and on the cross section where this
maximum magnitude occurs.
←╮
←1.6m→←1.6m→←1.6m→▌┌─┐─
████████████▌│ │↑
◥██◤ ╯ ▌│ │
↑ πx Ｔ │ │3a E=190GPa
w=-6sin(---) 48kN*m │ │
1.6 │ │↓
├─┤─
│ │ａ E=72GPa
└─┘─
│ａ│
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※ 編輯: dn890221 來自: 140.112.202.116 (04/14 17:49)
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