Exam10-11-0107A

中国石油大学（北京）2010—-2011学年第1学期《Engineering Mechanics》期末考试试卷/A Class: Name：Registration No.： Score：
I.(25points) Give the answer for the following questions.
1.(2 points) Mechanics of Materials deals with the abilities of solid bodies which
including 、Rigidity、.
2.(3 points) In general, the condition of equilibrium has independent
equations for a non-coplanar force system and independent equations for a coplanar force system. The condition of equilibrium has independent equations for a non-coplanar parallel force system.
3.(2 points) The endurance limit of specimen which has stress concentration is
than the polished specimen that has no stress concentration. The endurance limit of polished small specimen is than the large polished specimen.
4.(3 point) During reduction of a coplanar force system, the vector sum of the forces is
taken as its and the vector sum of moments of forces about new action point of forces is known as its . The value of is related to the new action point.
5.(3 points) For two slender columns with same length, same support condition and
made of same material but different cross sections as shown in Fig.1.5, please compare their critical stresses.
6. (3 points) The stress state of a point in a body is shown as
Fig.1.6, the equivalent stress 。

7. (3 point) The square thin plate with loads is shown as Fig. 1.7.
If the maximum static friction coefficient between the plate and
ground is 0.5, the maximum value of force P is which
keeps the plate in rest. A ． W 2；B ．32W ；C ．42W ；D ．22W
8. (3 Points) The columns with their impact loads are shown as Fig. 1.8. The columns
are made of same steel. The upper black part of column C is made of rubber.
has the maximum dynamic stress.
=3r σFig.1.7
P Fig.1.6
Fig.1.5 Fig.1.8 50MPa
30MPa
9.(3 Points) A cantilever beam with loads is shown in Fig.1.9. Its deflection expression
in
is right.
Ⅱ. (10 points) For the structure shown in Fig.2., AB=BC=1 m, EK=KD, P =1732 kN, Q =1000 kN. Determine the reactions at A and E, and the force in bar DC, neglecting the weights of the bars.
Ⅲ.(15 points) As shown in Fig.3, the stresses
on planes AB and AC of a regular triangle stress element of a point are all only shear . Let the thickness of the element is t. (1) Determine the normal stress and shear stress on plane BC. (2)
Draw the Mohr’s circle for the point. (3) Find
the principal stresses for the point.
Fig.1.9
Fig.2
Fig.3
C
Ⅳ. (10 points) For the beam shown as following, draw its bending moment and shear force diagrams. Indicated the . and max max V M
Ⅴ(15 points) The thin-walled cylindrical pressure vessel with internal pressure p is shown in Fig.5. The two strain gauges are pasted on the surface at A in x and y directions respectively. From the test we know that strains εx = 200⨯10-6 and εy = 100⨯10-6. Let the mean vessel diameter d=200mm, thickness t=5mm, elastic modulus E=200GPa, Poisson's ratio ν = 0.3 and allowable stress σallow = 70 MPa. (1) Draw the stress element of the point A. (2）Find the normal stresses x σ and
y σ, and the
internal pressure p. (3) Exam the strength with 4th strength theory.
VI. (15 points) Find the deflection and the rotation angle at the free end B of the cantilever with loads as shown in Fig. 6. (Energy Method recommended)
Fig.5
A ●
Ⅶ. (10 points) A concentrated force F and a uniformly distributed load of constant intensity q are acted on a prismatic bar which is fixed on two ends. The cross section area A, the length a and elastic modulus E of the bar are known. Find the reactions at
ends and plot axial force diagram.
Fig.6 B C
Fig.7
A EI
中国石油大学（北京）2010—-2011学年第1学期 《 Engineering Mechanics 》期末考试试卷A(留学生)
Class: Name ： Registration No .： Score ：
2011 I. (40 Points) Give the correct answer for the following questions
1. (5 Points) A stress cycle is shown in Fig. 1.1, the character of cycle r = , the mean stress
m σ = , the amplitude of stress a σ = .
2. (5 Points) The following figure 1.2 is a typical low-carbon steel σ-ε diagram in tension. Points a, b, c, d, e, f and g represent different aspects of mechanical behavior for the material. Please connect the label with its meaning.
a ultimate stress
b yield stress
c elastic limit
e proportional limit p
g percent elongation
Fig.1.2
3. (5 point) During reduction of a coplanar force system, the vector sum of the forces is taken as its and the vector sum of moments of forces about new action point of forces is known as its . The value of is related to the new action point.
4. (5 point) Mechanics of Materials deals with the abilities of solid bodies which including 、Rigidity 、 .
5. (10 Points) Weight of the body is W, and pushing force is P. W=100N,
P=500N. The static and kinetic sliding friction coefficients between the
weight and the wall are μS =0.3, and μk =0.25 respectively. Then the
friction between the weight and the wall is____.
A. 150N;
B. 125N;
C. 100N;
D. 500N.
6. (10 points) For two slender columns with same length, same support condition and made of same material but different cross sections as shown in Fig.1.6, please compare their critical stresses.
Ⅱ (20 points) For the beam shown as following, draw its bending moment and shear
Fig.1.6 Fig.1.5
force diagrams. Indicated the . and max max V M
Ⅲ (20 points) A circular shaft (d=85 mm ) with tensile load P =280 kN and torque T =10 kN-m is shown in the figure 3 . Let [ ] = 160 MPa. (a) Draw the stress element at A and label the stress values on it ；（b ）Exam the shaft with 4th strength theory.
A T
Ⅳ (20 points) Find the deflection and the rotation angle at the free end B of the cantilever with loads as shown in Fig. 4. (Energy Method recommended)
Fig. 4 C
Fig.2 Fig.3。