MECH 101 Midterm Exam March 30, 2010 1. Simple Questions (20pts) (1) The stress-strain curve of a material obtained from the standard tensile test is plotted in Figure 1. In this figure, nominal stress and nominal strain are employed. On the plot, please identify the ultimate stress and the fracture stress. Which stress should be higher and why? Figure 1. (2) Thermal stress always occurs when temperature changes. True or False? (3) There is no normal stress inside a torsional shaft which is subject to torques only. True or False? (4) In the two cases illustrated in Figure 2, the only difference is that in case b, the bar is heated about T degree after P is applied. Find the reaction force in both cases. P (a) P (b) Figure 2. 2. (40pts) A device illustrated in Figure 3 is made of steel and consists of a solid inner shaft CB surrounded by a tube AB which is connected to shaft CB through a rigid ring at B. The other end of the tube AB is attached to a fixed ring A. If the allowable shear stress for the material is allow 84 MPa and the angle of twist at C is limited to allow 3o , determine the maximum torque T that can be applied at the end C. The shear modulus of the material is 80 GPa. Figure 3. 3. (40 pts) Two rods, one of aluminum and the other of copper, are fixed to the rigid walls as shown in Figure 4. The gap between the two rods is 0.2 mm. When the temperature increases about 100oC, find the reactions and the location of the interface between the two rods? The diameter of each rod is 30 mm. The thermal expansion coefficients are copper 17 106 / oC , al 24 106 / oC and the Young’s modulus are Ecopper 126 GPa , Eal 70 GPa . Figure 4.
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