# 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 267**

$\delta = \delta_T$

$\dfrac{PL}{AE} = \alpha \, L \, \Delta T$

$P = \alpha \, \Delta T \, AE$

$P = (11.7 \times 10^{-6})(80 - 25)(90 \times 12)(200\,000)$

$P = 138\,996 \, \text{N}$

$F = 2P$

$pDL = 2P$

$p(2000)(90) = 2(138\,996)$

$p = 1.5444 \, \text{ MPa}$ *answer*

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