Question

A concrete highway is built of slabs 18.0 m long (at 25 °C). How wide should the expansion cracks be (at 25 °C) between the slabs to prevent buckling if the annual extreme temperatures are −32 °C and 52 °C?(the coefficient of linear expansion of concrete is 1.20 × 10 − 5 °C-1) g

Answer 1

To solve the problem it is necessary to apply the concepts related to thermal expansion of solids. Thermodynamically the expansion is given by

$\Delta L = L_0 \alpha \Delta T$

Where,

$L_0 =$ Original Length of the bar

$\Delta T$= Change in temperature

$\alpha$= Coefficient of thermal expansion

On the other hand our values are given as,

$L_0 = 18m$

$\alpha = 12*10^{-6}/\°C$

$T_2 = 52\°C$

$T_1= 25\°C$

Replacing we have,

$\Delta L = L_0 \alpha (T_2-T_1)$

$\Delta L = (18)(12*10^{-6})(52-25)$

$\Delta L = 5.832*10^{-3}m$

The width of the expansion of the cracks between the slabs is 0.5832cm