Question

A cylindrical bronze sleeve (2) is held in compression against a rigid machine wall by a high-strength steel bolt (1), as shown in the figure. The steel [E = 199 GPa; α = 11.7 × 10^-6/°C] bolt has a diameter of 24 mm. The bronze [E = 110 GPa; α = 22.0 × 10^-6/°C] sleeve has an outside diameter of 73 mm, a wall thickness of 9 mm, and a length of L = 550 mm. The end of the sleeve is capped by a rigid washer with a thickness of t = 4 mm. At an initial temperature of T₁ = 14°C, the nut is hand-tightened on the bolt until the bolt, washers, and sleeve are just snug, meaning that all slack has been removed from the assembly, but no stress has yet been induced. If the assembly is heated to T₂ = 88°C, calculate

(a) the normal stress (positive if tensile and negative if compressive) in the bronze sleeve.
(b) the normal strain (positive if stretched and negative if compressed) in the bronze sleeve.

Answer 1