材料力學：96 學年度作業一
義守大學機械與自動化工程學系 材料力學 作業一
注意：不必抄題目，將計算過程和答案寫在 A4 紙上。
注意：不要寫在本題目紙上，否則沒有分數。
1.
交作業日期：4/21/2008
10 kN
The frame is subjected to the load of
10 kN. Determine the required
diameter of the pin at A and B if the
allowable shear stress for the material

allow = 60 MPa. Pin A is subjected to
double shear, whereas pin B is
subjected to single shear.
0.64 m
C
m
1.6 m
A
m
B
m
D
m
1.5 m
2.
1.5 m
The control arm is subjected to the loading
shown in the figure. Determine (1) the
required cross-sectional area of member AB
and (2) the required diameter of the steel pin
at C if the allowable normal stress for AB is
allow = 100 MPa and the allowable shear
stress for the pin is 
allow =60 MPa. Note in
the figure that the pin is subjected to double
shear.
20cm
7.5cm
5cm
5 kN
6 kN
3.
A steel bar is shown in Fig. P10. The original length is L and the original width is w at
temperature T = T1. The bar is acted or constrained, or the temperature is raised to T2 by three
cases. For each case, determine the average normal stress and the average normal strain
developed in the bar. w = 1.2 cm, L = 70 cm, L = 0.4 cm, P = 22 kN, = 10-5/oK cm, T1 =
25oC, T2 = 55 oC, E = 200 GPa.
Original Length
w
w
T=T1
L
Case 1
Case 2
Case 3
Fixed End
Fixed End
Fixed End
T=T1
T=T1
L-L
T=T2
L
Free End
P
W.T.Cheng
Fixed End
1
Fixed End
上午 01:42 2008/4/8
材料力學：96 學年度作業一
4.
The piece of plastic is originally
rectangular. Determine (1) the average
normal strain occurs along the
diagonals AC and DB and (2) the shear
D
2 mm
C
strains 
xy and 
x'y’developed at point
A.
400 mm
B
3 mm
5.
The piece of plastic is originally
rectangular. Determine the average normal
strain occurs along the diagonals AC and
DB.
400 mm
400 mm
3 mm
6.5 mm
2 mm
5 mm
2 mm
400 mm
6.
The rigid beam rests in the horizontal
position on two 2014-T6 aluminum
cylinders having the unloaded lengths
shown. If each cylinder has a diameter of
40 mm, determine the placement x of the
applied 100 kN load so that the beam
remain horizontal. What is the diameter of
cylinder A after load is applied? Eal = 70
GPa, al = 0.35.
2 mm
600 mm
3.5 mm
100 kN
450 mm
400 mm
2m
7.
The stress-strain diagram for a polyester resin is given in the figure. If the rigid beam is
supported by a link AB and post CD made of this material, determine the largest load P that
can be applied to the beam before either AB or CD fractures and the stresses of members AB
and CD for the largest load P. The diameter of the link is 20 mm and the diameter of the post is
25 mm.
B

1.2 m
P
A


C
1.0 m
0.5 m
0.4 m
D
W.T.Cheng

2
上午 01:42 2008/4/8
材料力學：96 學年度作業一
8.
The three A-36 steel bars shown in the
figure are pin connected to a rigid member.
If the applied load P on the member is 30
kN, determine the force developed in each
bar. Bars AB and EF each have a
cross-sectional area of 40 mm2, and the bar
CD has a cross-sectional area of 30 mm2.
B
1.2 m
D

F

0.9 m
0.9 m
A

C

E
0.6 m
P
9.

Three bars each made of different materials are connected together and placed between two
walls when the temperature is T1=10oC. Determine the force exerted on the (rigid) supports
and the average normal stress of each bar when the temperature becomes T2=30oC. The
material properties and cross-sectional area of each bar are given in the figure.
Abr=800 mm2
2
Ast=400 mm
600 mm
Acu=1200 mm2
400 mm
0.6 m
200 mm
10. A rod is made from two segments: AB is A-36 steel (Gst = 75 GPa) and has a diameter of 30
mm and BD is C83400 red brass (Gbr = 37 GPa) and has a diameter of 60 mm. It is fixed at its
ends and subjected to a torque of T = 700N•m.
(1) Determine the torsional reactions at the walls A and D.
(2) Determine the absolute maximum shear stress in the shaft.
700 N.m
1.2
0.6 m
0.8 m
W.T.Cheng
3
上午 01:42 2008/4/8