哈工大材料力学期末考卷.doc

试 题： 班号： 姓名：
(NOTE: This final exam, 100 marks in total, is worth 50 percent of your final score.)
1. Single Choice Questions: (8 questions, 3 marks each, 24 marks in total)
1-1. About virtual work and virtual displacement, the right one is ( ).
A. The work done by force along its virtual displacement is
B. Virtual displacement must satisfy the displacement constraints.
C. The variation of system energy due to the virtual displacement is less than that by the real one.
D. Virtual work can only be caused by external forces.

1-2. In the following statements, which one is NOT a feature of fatigue? ( )
A. Upon the rupture of materials, the nominal stress equals to the corresponding statical strength.
B. Structural elements will only fail after a certain number of stress cycles.
C. The fracture surface can be divided into a shiny area and a rough area.
D. It is a brittle fracture.

1-3. A circular and a square cross sections have the same area (see Fig. 1-3). Then on their capability to resist bending about their own principal axis , it is true that ( )
A. . B. .
C. . D. the difference between and is more than 50%.

Fig. 1-3 Fig. 1-4

1-4. The degree of statical indeterminacy of the structure shown in Fig. 1-4 is ( ).
A. 1 B. 2 C. 3 D. 4

1-5. As shown in Fig. 1-5, a concentrated force is applied at the middle point of the simply supported beam. The beam width is assumed to be a constant and its height needs to be determined. The beam will take approximately a shape like ( ) to make it in equal strength.

Fig. 1-5

1-6. For a circular cross-section with diameter and a square with side length , their radius of gyration with respect to their own principal axis are ( ), respectively.
A. and B. and
C. and D. and

1-7. Which of the following statements is true about the third and fourth strength theories? ( )
A. If the 3rd strength theory is satisfied, then is the 4th one.
B. If the 4th strength theory is satisfied, then is the 3rd one.
C. Sometimes (A) is valid, sometimes (B) is valid.
D. There is no definite connection between the two strength theories.

1-8. On the bending of beams, which of the following statements is NOT true? ( )
A. The various differential equations of elastic curve are valid piecewisely.
B. On each separated segment, the functions of distributed load, transverse shear force and bending moment become more and more smooth.
C. If the bending-moment equation is applied, the matching of transverse shear can then be used to determine the unknown integration constants.
D. The deflection function and its first derivative are always continuous.
2. As shown in Fig. 2, a weightless beam AC is pin-supported at A and spring-supported at point B. The spring has a stiffness of . The flexural rigidity of beam AC is . Before the clockwise concentrated moment is applied, points A, B and C lie on the same horizontal line. Determine: (1) the magnitude of , such that the free end C in the loaded structure comes back to the original level; and (2) the equation of the elastic curve of beam AC in terms of (measured from pin A).
（16 marks）

Fig. 2

3. A rectangular sign, weighted , is supported by a bar having a diameter of (see Fig. 3). The sign and the bar are rigidly tied to each other with two short rods. A wind pressure against the sign (along the direction) has a magnitude of . All other dimensions can be read from the figure. At point A, which is located on the front outer surface at the base of the bar, there have two strain gauges marked as 1 and 2, as shown in the magnified window. Gauge 1 reads , and gauge 2 reads . The elastic constants of the bar are ，，. Note all elements except the bar can be assumed as rigid bodies. (1) Determine the weight of the sign and the wind pressure ; and (2) If the allowable stress of the bar is , perform a full checking of the strength of the bar using the third strength theory. Note the transverse shear stress can be neglected in this step. （16 marks）

Fig. 3

4. Shown in Fig. 4 is a truss with an axial rigidity of for all its rod members. A horizontal force is applied at B. Determine the vertical displacement at D. (14 marks)

Fig. 4

5. The structure shown in Fig. 5 is made of two parts: a beam AC and a connecting rod BC, with a flexural rigidity of and an axial rigidity of , respectively. A concentrated force is applied at the middle point of the beam’s left arm.
(1) Determine the axial force developed in rod BC;
(2) If , draw the bending moment diagram of beam AC；
(3) Go on with step (2), now determine the slope of the beam at point C.
(14 marks)

Fig. 5

6. As shown in Fig. 6, beam AB is pin-supported at both A and C. CD is a connecting rod. Beam AB and rod CD are made of the same material and both have a solid circular cross-section with a diameter of and , respectively. The dimension . A weight falls from above the beam at a height to the free end B. If , check the stability of the rod CD. Take the following material constants for the rod CD: , , , , . (16 marks)

Fig. 6
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