Problem 265 A bronze bar 3 m long with a cross sectional area of 320 mm2 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 265
$\alpha \, L \, (\Delta T) = \dfrac{\sigma \, L}{E} + 2.5$
$(18 \times 10^{-6})(3000)(\Delta T) = \dfrac{35(3000)}{80\,000} + 2.5$
$\Delta T = 70.6^\circ \text{C}$
$T = 70.6 - 20$
$T = 50.6^\circ \text{C}$ answer
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