Question

A concrete highway is built of slabs 12 m long .How wide should be the expansion cracks between the slabs at 15 Celsius to prevent buckling if the range of temperature is -30 to 50 Celsius?

Answer 1

Answer:

$x=4.2\ mm$

Explanation:

Given:

• length of the concrete slab, $l=12\ m$

• temperature of observation, $T_o=15^{\circ}C$

• we've the coefficient of linear expansion for concrete, $\alpha=10^{-5}\ ^{\circ}C^{-1}$

• lower temperature limit, $T_l=-30^{\circ}C$

• upper temperature limit, $T_u=50^{\circ}C$

Change in length due to temperature can be  given as:

$\Delta l=l.\alpha.(T_u-T_l)$

$\Delta l=12\times 10^{-5}\times (50-(-30))$

$\Delta l=0.0096\ m=9.6\ mm$

Now at temperature 15°C:

$\Delta l'=12\times 10^{-5}\times (15-(-30))$

$\Delta l'=0.0054\ m=5.4\ mm$

Hence the expansion crack between the slabs at this temperature must be:

$x=\Delta l-\Delta l'$

$x=9.6-5.4$

$x=4.2\ mm$