Unformatted text preview: Mechanics of Materials Homework #4 Problem 1: An aluminum stepped tension bar is to carry a load of P = 56 kN. The normal yield strength of aluminum is 160 MPa. The bar in the figure has H = 300 mm, d = 100 mm, and t = 10 mm. For a factor of safety of 1.6, determine the minimum value r of the fillet radius if yielding is to be avoided. Use the expanded chart shown below, also valid for the tension bar stepped on both sides: Problem 2: The temperature is increased by 60°C in both steel (Es = 200 GPa, αs = 12.0 x 10‐6/°C) and aluminum (Ea = 72 GPa, αa = 23.0 x 10‐6/°C). Determine the angle by which the pointer rotates from the vertical position. NOTE: The steel bar remains horizontal as it lengthens. There are pin connections at both ends of the aluminum bar and at the “rigid” 50 mm vertical connector (α = zero) between the steel and aluminum bars. Problem 3: The cross section of the punch and die shown in the figure is a circle of 1 inch diameter. A force P = 6 kips is applied to the punch. If the plate thickness, t, is 1/8 inch, determine the average shear stress in the plate along the path of the punch. Problem 4: Problem 5: A solid circular bar of 200 mm length and 20 mm diameter is subjected to a tension test. Due to an axial force of 77 kN, the bar is seen to elongate by 4.5 mm and the diameter is seen to reduce by 0.172 mm. Determine the Young’s modulus, E, and the shear modulus, G. ...
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- Spring '10
- 10 mm, 50 mm, 20 mm, 8 inch, 6 kips, 4.5 mm