HW02_solutions - Mechanics of Materials Homework#2 –...

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Unformatted text preview: Mechanics of Materials Homework #2 – SOLUTIONS Problem 1: A plastic bar of diameter d = 1.0 in. is compressed in a testing device by a force P = 25 lb applied as shown in the figure. Determine the normal and shear stresses acting on all faces of stress elements oriented at: (a) an angle Θ = 0°, (b) an angle Θ = 22.5°, and (c) an angle Θ = 45°. In each case, show the stresses on a sketch of a properly oriented element. Problem 2: A steel pad supporting heavy machinery and equipment rests on four short, hollow, cast iron piers. Each pier is to be designed for a compressive load of 280 kN. The ultimate strength of the cast iron in compression is 350 MPa. The designer decides to design the piers with a wall thickness t of 10 mm and a factor of safety of 4.0 with respect to the ultimate strength. Compute the minimum required outside diameter dmin of the piers. Problem 3: A pressurized cylinder has a sealed cover plate fastened with steel bolts. The pressure p of the gas in the cylinder is 280 psi, the inside diameter D of the cylinder is 10 in., and the diameter db of the bolts is 0.5 in. If the allowable tensile stress in the bolts is 10,000 psi, find the number of bolts n needed to fasten the cover. Problem 4: The data shown in the accompanying table were obtained from a tensile test of high‐ strength steel. The test specimen had a diameter of 0.505 in. and a gage length of 2.00 in. The total elongation between the gage marks at fracture was 0.12 in., and the minimum diameter was 0.42 in. Plot the nominal stress‐strain curve for the steel and determine the proportional limit, modulus of elasticity (i.e. the slope of the initial part of the stress‐strain curve), yield stress at 0.2% offset, ultimate stress, percent elongation in 2.00 in., and percent reduction in area. Problem 5: A bar of length 1.5 m is made of structural steel having the stress‐strain curve shown below. The yield stress of the steel is 250 MPa and the modulus of elasticity is 200 GPa. The bar is loaded axially until it elongates 7.5 mm, and then the load is removed. How does the final length of the bar compare with its original length? Problem 6: A high‐strength steel wire, 1/8 inch in diameter, stretches 1.41 in. when a 50 ft length of it is stretched by a force of 850 lb. What is the modulus of elasticity E of the steel? ...
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