160 120
.
(MPa)
30
80 40
zC
400 60
0 -40
t
M
M
b Dimensions in mm Fig. I-2
-80
Fig. I-3 , the amplitude of
3.
(6 points) A stress cycle is shown in Fig. I-3, the mean stress m = stress a = , the character of cycle r = .
P
P
(a) Fig. I-1 2.
(b)
(6 points) A T-beam made of cast iron is in pure bending. Knowing the ratio of tensile allowable stress to compressive allowable stress is [t]/[c]=1/4, the reasonable width b of the flange is
4.
(6 points) Four different cases of supports for a column are shown in Fig. I-4, case highest critical load.
has the
A卷 第 2 页 共 5 页
y B
Mz
A
h/2
z
h/2
My
b
x C
Pl 3 for the case shown in Fig. IV(c). 3EI
(5) If the free end C is connected to a vertical bar (elastic modulus E2, cross section area A, length h) before vertical load P is applied, as shown in Fig. IV(b), determine the stress in the bar.
A卷
中国石油大学（北京）2011—2012 学年第二学期
《工程力学（双语） 》期末考试试卷
考试方式（闭卷考试）
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No.
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（试卷不得拆开，所有答案均写在题后相应位置）
A卷 第 1 页 共 5 页
I 1.
(Total 30 points) Fill up the blanks with correct answer. (6 points) Stress-strain curves for three materials are shown in Fig. I-1, along with a loading device which can make specimens made of each material and with same dimensions to have equal end displacements. Material increasing, Material (1, 2, 3) has the highest ultimate stress. With the tensile load P (1, 2, 3) in the device will fracture first.
=0.25. Assume that ri ro r .
Fig. III
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IV (40 points) A horizontal bracket ABC is fixed at support A and free at C, as shown in Fig. IV(a). The bracket is constructed from a circular cross-sectional bar with constant diameter d. A vertical load P acts at the free end C. E1 is known. (1) Determine the places of the critical points. (2) Draw stress elements to show the stress state of the critical points. (3) Determine the equivalent stresses of 3th strength condition at critical points. (4) Find the vertical displacement v at C. Note: the deflection at the free end of a cantilever beam is given by vB
E2
h
v
C A a (a) B
E1
C P A a (b) Fig. IV B
E1
a
a
P
EI
P
B
l
(c)
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II
(15 points) For a beam shown in Fig. II, draw its shear force and bending moment diagrams.
30kN/m 20kN 30kN/m
A 1m
C 1m
D 1m
E 1m
B
Fig. II
A卷 第 3 页 共 5 页
III (15 points) Consider a closed cylindrical steel pressure vessel, as shown in Fig. III. The radius of the cylinder is 1000mm and its wall thickness is 10mm. (a) Determine the hoop and the longitudinal stresses in the cylindrical wall caused by an internal pressure of 0.80MPa. (b) Calculate the change in diameter of the cylinder caused by pressurization. Let E =200GPa, and
DHale Waihona Puke AB Fig. I-4
C
D Fig. I-5
5.
(6 points) The internal forces on a cross section of a doubly symmetric beam made of ductile material are shown in Fig. I-5, are critical points.