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A steel [E = 200 GPa; ν = 0.3; α = 10.9 ×10-6/°C] plate has a rectangular hole at its center and four circular holes at the corners. At an initial temperature of Ti = –16°C, the plate is 85 mm wide, 140 mm long, and 13 mm thick. The rectangular hole is 25 mm wide and 75 mm long. The circular holes have a diameter of 25 mm. At a final temperature of Tf = 48°C, determine the length of the rectangular hole.

A load of 88 kN is applied to a triangular shape that protrudes 15.3 mm from a brass plate. The triangular shape has a base of 26.9 mm and a height of 18.2 mm. Determine the average shear stress between the plate and the protrusion.

A load of P = 395 lb is applied to beam ABC. Determine the vertical ground reaction at B. Let a = 36 in., b = 15 in., and c = 11 in.

If the length of a timber [E = 1,100 ksi] column cannot change by more than 0.045 in., determine the maximum load P that can be applied to the column. Let b = 5.00 in., d = 9.50 in., and L = 102 in.

A triangular piece of rubber is stretched causing A to move downward. Determine the magnitude of the shear strain that occurs at A when a = 25.0 mm, b = 50.0 mm, and c = 35.0 mm.

An aluminum rod with a 18.5-in. gage length and a 0.530-in. diameter is loaded in tension. At the proportional limit, a load of 17,000 lb elongates the gage length by 0.123 in. and reduces the diameter by 0.0011 in. Determine the Poisson’s ratio.

A Ro-Tel can weighs 0.78 lb and is 2.56 in. in diameter. A Libby’s can weighs 1.03 lb and is 2.86 in. in diameter. What is the largest bearing stress that occurs between the cans and the table? Assume each can has a smooth base and sits flat on the table.

If rod (1) elongates 0.366 mm and rod (2) elongates 0.382 mm, determine how far downward E moves. Let a = 0.48 m and b = 0.78 m.

A load of P = 420 lb is applied to beam ABC. Determine the vertical ground reaction at B. Let a = 34 in., b = 16 in., and c = 10 in.

Rigid beam ABC supports two rods that initially have no strain. If a temperature increase in rod (1) creates a normal strain of 2,545 μin./in. in it, determine the normal strain in rod (2). The initial lengths are a = 10 in., b = 13 in., c = 38 in., and d = 11 in. Assume there is no slack in the connections.