C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）
班级： 姓名： 学号：
No.
Ⅰ
Ⅱ
Ⅲ
Ⅳ
V
Total
Score
（试卷不得拆开，所有答案均写在题后相应位置）
I 1.
(Total 30 points) Answer the following questions briefly. (5 points) An overhanging beam with its bending moment diagram is shown in Fig. I-1. Its allowable tensile and compressive stresses are [T]=39.3MPa and [C]=58.8MPa respectively. The most reasonable section is .
q
A D C B
ql 2
E C l C C
l
l
l
Fig. II
III (14 points) Bar OA rotates about point O at the uniform speed =4rad/s and drives a slider moving freely in circular slot of guiding bar BC(R=100mm). When length of OA is 100mm and =30, determine the velocity and accelerate of BC using the theorems for composition velocities and accelerations.
Fig. III
IV (10 points) A homogeneous circular plate with mass m and radius r is rolling without slipping on a circular guider with radius R after a small interference( sin
A
B
C
பைடு நூலகம்
F C
A D E
B
Fig. I-5 6. II
Fig. I-6
(5 points) For the truss shown in Fig. I-6, propose a measure to improve the stability of columns. (26 points) For a structure shown in Fig. II that consists of two beams AB and BC which are connected by a smooth pin B: (1) Determine the reactions of supports A, C as well as pin B. (2) Draw the shear force and the bending moment diagrams of beam BC. (3) Write the boundary conditions of the beams at supports A, C, and the continuity conditions at pin B and sections D, E.
s ). Find the differential Rr
equation of motion for the mass center C using the theorem of the kinetic energy.
Fig. IV
V
(20 points) A circular shaft with diameter d shown in Fig. V is subjected to a combination of twisting and tension. (1) Explain the function of the tail rotor(尾旋翼) of helicopter. (2) Determine the places of the critical points. (3) Draw stress elements to show the stress state of the critical points. (4) Determine the equivalent stresses of 3rd strength condition at critical points.
y
z
(a)
(b)
(c)
(d)
Fig. I-1 2. (5 points) For the linkage shown in Fig. I-2, determine the instant center for velocities of bar BC.
A
y x
Fig. I-2 3.
Fig. I-3
(4 points) When a train pass through a steel bridge, the strains tested by instrument are x = 0.0004, y = -0.00012 at point A. The normal stresses in directions x and y at point A are y = = . (E=200GPa, =0.3, z=0) , x
4.
(6 points) Three main factors that will influence the endurance limit of a real member are _______________, _______________ and ________________.
5.
(5 points) For the statically indeterminate beam shown in Fig. I-5, write out its released form and corresponding compatibility equation.
P T
T
P
Fig. V