# Solution to Problem 270 Thermal Stress

**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 in^{2}, E = 29 × 10^{6} psi, and α = 6.5 × 10^{-6} in/(in·°F). For the bronze sleeve, A = 1.5 in^{2}, E = 12 × 10^{6} psi and α = 10.5 × 10^{-6} in/(in·°F). After a temperature rise of 100°F, find the final stress in each material.

# Solution to Problem 269 Thermal Stress

**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 mm^{2}, E = 120 GPa, and α = 16.8 µm/(m·°C). For the aluminum bar, A = 400 mm^{2}, E = 70 GPa, and α = 23.1 µm/(m·°C).

# Solution to Problem 268 Thermal Stress

**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.

# Solution to Problem 267 Thermal Stress

**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.

# Solution to Problem 266 Thermal Stress

**Problem 266**

Calculate the increase in stress for each segment of the compound bar shown in Fig. P-266 if the temperature increases by 100°F. Assume that the supports are unyielding and that the bar is suitably braced against buckling.

# Solution to Problem 265 Thermal Stress

**Problem 265**

A bronze bar 3 m long with a cross sectional area of 320 mm^{2} is placed between two rigid walls as shown in Fig. P-265. At a temperature of -20°C, the gap Δ = 2.5 mm. Find the temperature at which the compressive stress in the bar will be 35 MPa. Use α = 18.0 × 10^{-6} m/(m·°C) and E = 80 GPa.

# Solution to Problem 264 Thermal Stress

**Problem 264**

A steel rod 3 feet long with a cross-sectional area of 0.25 in.^{2} is stretched between two fixed points. The tensile force is 1200 lb at 40°F. Using E = 29 × 10^{6} psi and α = 6.5 Ã— 10^{-6} in./(in.·°F), calculate (a) the temperature at which the stress in the bar will be 10 ksi; and (b) the temperature at which the stress will be zero.

# Solution to Problem 263 Thermal Stress

**Problem 263**

Steel railroad reels 10 m long are laid with a clearance of 3 mm at a temperature of 15°C. At what temperature will the rails just touch? What stress would be induced in the rails at that temperature if there were no initial clearance? Assume α = 11.7 µm/(m·°C) and E = 200 GPa.

# Solution to Problem 262 Thermal Stress

**Problem 262**

A steel rod is stretched between two rigid walls and carries a tensile load of 5000 N at 20°C. If the allowable stress is not to exceed 130 MPa at -20°C, what is the minimum diameter of the rod? Assume α = 11.7 µm/(m·°C) and E = 200 GPa.

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