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     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:

    32Paa. (

    3Pab. (

    32Pac. ( 6



    Fig. 1

    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

    b. 16kN

    c. 15kN =0.2 S

    d. 12kN

     Fig. 2

     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

    2a a

     2a 2a

    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

    _______ material.

    a. Ductile

    b. Brittle

    c. Cannot be judged.

    Fig. II

    Fig. 5

    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


    P=20kN q=30kN/m

    m B A 1m 1m 2

     Fig. III

    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)(l2lx;x)24EIB A x 3qlAB24EI

    2qx22y(x)(x4lx;6l) q 24EI

    3ql B6EI

    2PxP y(x)(3lx) 6EI

    2Pl B2EI

    Mx 22y y(x)(lx)6EIl

    x Ml A6EI

    Ml B3EI

     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 = 610 and = 410respectively. Let E=200GPa, = 0.25 and 0 45

    ( = 160 MPa. (a) Draw the stress element at A and B(,bFind 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

     M x

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