A highway of concrete slabs is to be built in the Libyan desert, where the highest air temperature recorded is 57.8 °C. The temperature is 23.1 °C during construction of the highway. The slabs are measured to be 11.7 m long at this temperature. How wide should the expansion cracks between the slabs be (at 23.1 °C) in order to prevent buckling at the highest temperatures?
To calculate the width of the expansion cracks between the concrete slabs, we need to consider the coefficient of thermal expansion (CTE) of concrete and the change in temperature.
The CTE of concrete typically ranges from 8 to 12 x 10^-6 per °C. Let's assume a conservative value of 10 x 10^-6 per °C for our calculations.
First, let's calculate the temperature change from 23.1 °C to 57.8 °C:
Temperature change = 57.8 °C - 23.1 °C
= 34.7 °C
Next, we need to determine how much the concrete slabs will expand due to the temperature change. We can use the following formula:
Expansion = Length * CTE * Temperature change
Expansion = 11.7 m * 10 x 10^-6 per °C * 34.7 °C
Now we have the amount of expansion in meters. To prevent buckling, the expansion needs to be accommodated by the gaps between the slabs. Let's assume we have 'n' number of expansion cracks, and they are of equal width 'w'. The total width of the expansion cracks should be equal to the expansion of the slabs:
Total width of expansion cracks = n * w
Since we know the length of each slab and the total width of the expansion cracks, we can calculate the width of each crack:
w = (Total width of expansion cracks) / (Number of expansion cracks)
w = Expansion / n
Plugging in the values:
w = (11.7 m * 10 x 10^-6 per °C * 34.7 °C) / n
The value of 'n' may vary depending on the design considerations and requirements. Assuming we have 5 expansion cracks, we can calculate the width of each crack:
w = (11.7 m * 10 x 10^-6 per °C * 34.7 °C) / 5
Please note that this calculation assumes linear expansion and that the slabs are free to expand without constraints. It's also essential to consult with experts and follow appropriate design standards and regulations for constructing highways in extreme climates.