《 Engineering Mechanics》期末考试试卷/A
Class: Name， Registration No.， Score，
No. I II III IV V Total
Date: Jan. 12, 2007
I. For the each question following, please choose a right answer. (5 Points/question).
1. Two forces act on a cubic frame with side length a as shown in Fig. 1. If this force system is reduced to an equivalent force-couple system acting at point O, the
magnitude of the resultant couple is:
3；2Pac. ( 6
2. The weight A and B are 100kN and 25kN respectively. Neglecting the friction at pulley,
then the friction between weight A and earth is a. 20kN
c. 15kN ，=0.2 S
3. For two slender compressing bars with same support conditions and made of same
material but different cross sectional areas as show in Fig 3, P= P. Cr2Cr1
a. 4 b. 8 c. 12 d. 16
Fig.3 (1) Fig. 3 (2)
4. For a real member undergoing repeated stress, its character of cycle r= . When r
= , its endurance limit is the smallest.
((maxmin a. b. c. +1 d. –1 e. 0 f. – ； g. 0.5 ((maxmin
5. If a circular bar in torsion fails along its cross section, it is made of _______ material.
If a circular bar in torsion fails along its section inclined at an angle 45，, it is made of
c. Cannot be judged.
II. (15 points) Neglecting the weights of the members, determine the magnitude of the
pin reaction at D when the frame is loaded by the 200-N.m couple.
III. (15 points) For a beam shown in the Fig. III, draw bending moment and shear force
m B A 1m 1m 2
IV. (20 points) Please solve one of IV (a) and IV (b). (a) The deflections and the rotation angles at x-section of three beams with flexural rigidity EI in Fig. IV a are given as following.
y qx323 y(x)？；(l；2lx;x)24EIB A x 3ql，？；，？；AB24EI
2qx22y(x)？；(x；4lx;6l) q 24EI
2PxP y(x)？；(3l；x) 6EI
Mx 22y y(x)？；(l；x)6EIl
x Ml？； ，A6EI
Fig. IV a
As shown in Fig. IV b, a beam ABC (EI) rests on simple supports at A and B and is 11
supported by a cable (EA) at point C. The beam has total length 2L and supports a 22
uniform load of intensity q. Prior to the application of the load, there is no force in the
cable nor is there any slack in the cable. When the load is applied, the beam deflects downward at point C and a tensile force T develops in the cable. Find the magnitude
of this force.
aq C b B
Fig. IV b Fig. VI c
(b) As in Fig. IV c, a continuous frame ABC has a rigid corner connection at B.
Members AB and BC each has flexural rigidity EI. The load is shown in the figure.
Find all reactions of the frame (Only flexure is considered). V. (25 points) A circular shaft (d=200 mm) with bending moment M and torque M is yx
shown in the figure. Points A and B are on the surface of the shaft. From the test we
know that the axial normal strain at A and the normal strain along 45， direction with
-4-4 axis at B are ？= 6：10 and ？= 4：10respectively. Let E=200GPa, ！ = 0.25 and 0 45
( = 160 MPa. (a) Draw the stress element at A and B(，b！Find the magnitudes of allow
th M and M; (c) Exam the shaft with 4strength theory. z yx
M A Myy
B M x
45， B x