Concrete Highway Expansion Cracks Calculation for Prevention of Buckling

How wide should the expansion cracks between the slabs be to prevent buckling?

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)

Answer:

0.001152m

To prevent buckling of the concrete highway due to temperature variations, we need to determine the width of the expansion cracks between the slabs. This can be calculated using the linear expansivity of the concrete material and the temperature range.

Linear expansivity of a material is the change in length of the material per unit length per degree rise in temperature. For concrete, the linear expansivity is given as 12 x 10⁻⁶ °C⁻¹.

Given that the initial length of the concrete slab is 12m at 20°C and the temperature range is -30°C to +50°C, we can calculate the width of the expansion cracks as follows:

Using the formula ¢ = ∆L/L1∆°C, where ¢ is the linear expansivity of the material, ∆L is the change in length, L1 is the initial length, and ∆°C is the change in temperature:

Substitute the values into the formula to get the final length L2 after expansion:

12 x 10⁻⁶ °C⁻¹ = L2 - 12 / 12 × 80

L2 = 12 + 0.001152m

Therefore, the expansion cracks between the slabs should be 0.001152m wide to prevent buckling of the concrete highway.