課程名稱︰材料力學
課程性質︰必修
課程教師︰施文彬
開課學院：工學院
開課系所︰機械工程學系
考試日期（年月日）︰104/3/31
考試時限（分鐘）：110分鐘
試題 :
Prelim 1, Mechanics of Materials, Spring 2015
10:20 am-12:10 noon, Mar. 31
Please prmide details of your calculation. Good luck!
1. (20%) A rigid bar is supported by a pin at A and two linearly elastic wires
at B and C, as shown in the figure. The area of the wire at B is 80 mm^2 and
for the one at C is 100 mm^2. Determine the reactions at A, B, and C caused
by the applied force P= 6 kN.
http://imgur.com/pgwsoEq
2. (20%) A rod is fixed at A and loaded with an axial force P, as shown in the
figure. The material is elastic-perfectly plastic, with E = 200 GPa and a
yield stress of 20 MPa. Prior to loading, a gap of 3 mm exists between the
end of the rod and fixed support C. The cross section from A to B is 200 mm^2
and that from B to C is 100 mm^2.
(a) What is the maximum load P than can exert on the rod?
(b) Following (a), the axial force increases from zero to its maximum load
for the rod, and is then released, What will be the residual displacement
of point B upon release of the applied force?
http://imgur.com/W3wOZUF
3. (20%) A 1.5-m-long hollow steel shaft of 38-mm outer diameter d_1 is to be
made of a steel forwhich τ_all = 65 MPa and G = 77.2 GPa. Knowing that the
angle of twist must not exceed 4 degree when the shaft is subjected to a
torque of 600 N-m, determine the largest inner diameter d_2 that can be
specified in the design.
http://imgur.com/3a2as8e
E
4. (20%) For Isotropic and linearly elastic material, derive that G = -------
2(1+ν)
where G is the shear modulus; E the Young's modulus; ν the Poisson's ratio.
5. (20%) Two vertical forces are applied to a beam as shown in the left figure.
The beam has the cross section which is formed by securely bonding brass and
aluminum stock, as shown in the right figure. The Young's modulus of the
aluminum is 70 GPa, and that of the brass is 105 GPa. Assume that the beam
does not yield.
(a) Determine the maximum tensile stress in the brass in the portion BC of
the beam.
(b) Determine the minimum tensile stress in the aluminum in the portion BC of
the beam.
(c) In the portion BC of the beam, determine the total bending moment acting
on the aluminum portion of the given cross section.
http://imgur.com/7ukZROJ
http://imgur.com/gHPudUz
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※ 編輯: NTUkobe (140.112.73.139), 05/21/2015 23:06:15