A concrete highway is built of slabs 12 m long (20°C). How wide should the expansion cracks between the slabs be (at 20°C) to prevent buckling if the range of temperature is - 30° to + 50°C? (12 x 10⁻⁶ °C⁻¹ for concrete)

0.001152m

Explanation:

Linear expansivity of a material is the change in length of the material per unit length per degree rise in temperature. Mathematically,

¢ = ∆L/L1∆°C

¢ is the linear expansivity of the material = 12 x 10⁻⁶ °C⁻¹

Where ∆L is the change in length = L2-L1

L2 is the final length = ?

L1 is the initial length = 12m

∆°C is the change in temperature = °C2 - °C1 = 50 - (-30) = 80°C

Substituting this values inside the formula to get the final length L2 after expansion, we have;

12 x 10⁻⁶ °C⁻¹ = L2-12/12*80

12 x 10⁻⁶ °C⁻¹ = L2-12/960

L2-12 = 960*12 x 10⁻⁶ °C⁻¹

L2-12 = 0.001152

L2 = 12+0.001152

L2 = 12.001152m

Expansion will be the change in length L2-L1 = 12.001152-12

= 0.001152m

The expansion cracks between the slabs should be 0.001152m wide to prevent buckling