thermal deformation

Problem 273
The composite bar shown in Fig. P-273 is firmly attached to unyielding supports. An axial force P = 50 kips is applied at 60°F. Compute the stress in each material at 120°F. Assume α = 6.5 × 10^-6 in/(in·°F) for steel and 12.8 × 10^-6 in/(in·°F) for aluminum.
 

Problem 272
For the assembly in Fig. 271, find the stress in each rod if the temperature rises 30°C after a load W = 120 kN is applied.
 

Problem 271
A rigid bar of negligible weight is supported as shown in Fig. P-271. If W = 80 kN, compute the temperature change that will cause the stress in the steel rod to be 55 MPa. Assume the coefficients of linear expansion are 11.7 µm/(m·°C) for steel and 18.9 µm/(m·°C) for bronze.
 

Problem 270
A bronze sleeve is slipped over a steel bolt and held in place by a nut that is turned to produce an initial stress of 2000 psi in the bronze. For the steel bolt, A = 0.75 in², E = 29 × 10⁶ psi, and α = 6.5 × 10^-6 in/(in·°F). For the bronze sleeve, A = 1.5 in², E = 12 × 10⁶ psi and α = 10.5 × 10^-6 in/(in·°F). After a temperature rise of 100°F, find the final stress in each material.
 

Problem 269
As shown in Fig. P-269, there is a gap between the aluminum bar and the rigid slab that is supported by two copper bars. At 10°C, Δ = 0.18 mm. Neglecting the mass of the slab, calculate the stress in each rod when the temperature in the assembly is increased to 95°C. For each copper bar, A = 500 mm², E = 120 GPa, and α = 16.8 µm/(m·°C). For the aluminum bar, A = 400 mm², E = 70 GPa, and α = 23.1 µm/(m·°C).
 

Problem 268
The rigid bar ABC in Fig. P-268 is pinned at B and attached to the two vertical rods. Initially, the bar is horizontal and the vertical rods are stress-free. Determine the stress in the aluminum rod if the temperature of the steel rod is decreased by 40°C. Neglect the weight of bar ABC.
 

Problem 267
At a temperature of 80°C, a steel tire 12 mm thick and 90 mm wide that is to be shrunk onto a locomotive driving wheel 2 m in diameter just fits over the wheel, which is at a temperature of 25°C. Determine the contact pressure between the tire and wheel after the assembly cools to 25°C. Neglect the deformation of the wheel caused by the pressure of the tire. Assume α = 11.7 μm/(m·°C) and E = 200 GPa.