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

`x=4.2\ mm`

Step-by-step 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* 10^(-5)* (50-(-30))`

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

Now at temperature 15°C:

`\Delta l'=12* 10^(-5)* (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`