哈工大2007年春季学期 材料力学期中考试试题Mechanics of Materials Midterm Exam Spring 2007(NOTE: This midterm exam, 100 marks in total, is worth 25 percent of your final score.) 1. S INGLE C HOICE Q UESTIONS : (7 questions, 3 marks each, 21 marks in total) 1-1. After cold-work hardening processing,which of the following properties of steel will remain approximately the same?( )A. modulus of elasticityB. proportional limitC. percent elongationD. percent reduction in area1-2. On the mechanical properties of cast iron, the following two statements are made: (1). its shear resisting capability is weaker than that of tension resisting;(2). its compressive strength is higher than its tensile strength. Among them, ( ) A. (1) is true, (2) is false . B. (1) is false, (2) is true . C. (1) is true, (2) is true . D. (1) is false, (2) is false .1-3. In Fig. 1-3, two prismatic bars are shown, one with a circular cross-section, the other one with a square cross-section. If both bars are made of the same material and they have the same cross-sectional area, but with different length, when subjected to the same axial force F , their ( ) are NOT the same.A. axial normal stress sB. axial strain eC. axial elongation l DD. lateral strain e ¢Fig. 1-3 Fig. 1-41-4. In Fig. 1-4, among the three strain gauges bonded to the surface of a circular shaft subjected to torsion, the reading of strain from gauges ( ) will almost be zero. A. 1 and 2 B. 2 and 3 C. 1 and 3 D. 1, 2 and 31-5. For an arbitrary shape shown in Fig. 1-5, when the z axis moves downward away from the centroid C in a parallel fashion, then ( )(Note: z S is the first moment of the area about the z axis)A. z S increases , z I decreases .B. z S decreases , z I increases .C. z S increases , z I increases .D. z S decreases , z I decreases .Fig. 1-5 Fig. 1-61-6. The two bars (a) and (b) shown in Fig. 1-6 are made of the same material and have identical cross-sectional area. After deformation, their longitudinal axes become two concentric arcs. If a s and b s are the maximum normal stress in beam (a) and (b), respectively, then ( )A. a b s s <.B. a b s s =.C. a b s s >.D. it is uncertain about a s and b s ’s relation .1-7. A cantilevered beam is made from two channel sections laid back to back without any bonding in between, as shown in Fig. 1-7. A concentrated force F is applied at its right end. Which of the following plots describes the correct normal stress distribution on the cross-section? ( )Fig. 1-72. Shown in Fig. 2 is a differential element from a structural member. AC is a free surface (traction free). Determine: (1) all the three principal stresses; (2) the distortion strain energy density f u . Take 200GPa E = and 0.3n =. (12 marks)Fig. 23. For a material with two elastic constants E and n , if x e and y e are obtained from experiment, show that for a general plane stress state, the following statements are true,22,1,1().1x yx y xy z x y EE e ne s n e ne s n ne e e n +=-+=-=-+- (12 marks)4. Shown in Fig. 4 are two prismatic bars connected by a rigid triangular plate. Bar 1 (the horizontalone) is made of steel and has a cross-sectional area of 2110cm A =. Bar 2 (the vertical one) is made of copper and has a cross-sectional area of 2220cm A =. All members are pin-supported or pin-connected. Determine the average normal stress acting on the cross sections in bars 1 and 2 when a load of 200kN F = is applied. Take 1200GP a E = and 2100GP a E = for the modulus of elasticity for steel and copper, respectively. (15 marks)Fig. 45. The cross-section of a solid circular shaft is shown in Fig. 5. The shaft has a diameter of 50mm d = and is subjected to a torque of 1kN m T = applied at its two ends. Determine (1) the shear stress and shear strain on the cross-section at a radius of /4A d r =; (2) the maximum shear stress and the angle of twist per unit length.Take the shear modulus of elasticity 80GPa G =. (15 marks)Fig. 56. Draw the shear and moment diagrams for the beam shown in Fig. 6. (12 marks)Fig. 67. For the cantilevered beam shown in Fig. 7, draw the state of stress of elements located at pointsA B C D E. Also, present the formulas for the calculation of all the stress components at each point. ,,,,(13 marks)Fig. 7。
