Concrete highway slabs are poured in lengths of 9.00m .
Part A
How wide should the expansion gaps between the slabs be at a temperature of 22∘C to ensure that there will be no contact between adjacent slabs over a temperature range of -25 ∘C to 48∘C?
α=12•10⁻⁶ K⁻¹
T₁=22° T₂=-28°, T₃= 48°
ΔT₁ = T₃-T₂ = 48-(-25) = 73°
ΔT₂ =48-22 = 26°
ΔL₁=L αΔT₁=9•12•10⁻⁶•73=0.0079 m
If the slabs are in contact at 48° =>
they are at 0.0079 mm at -25°
ΔL₂=L αΔT₂ = 9•12•10⁻⁶•26=0.0028 m
ΔL= ΔL₁-ΔL₂=
=0.0079-0.0028=0.0051 m=5.1 mm (at 22°)
To determine the width of the expansion gaps between the concrete highway slabs, we need to consider the coefficient of thermal expansion of concrete and the temperature range.
The coefficient of thermal expansion (α) of concrete is typically around 10 x 10^(-6) °C^(-1), which means that for every 1°C increase in temperature, concrete expands by 10 x 10^(-6) times its original length.
Given that the temperature range is from -25°C to 48°C, we can calculate the total temperature change as follows:
Temperature change = 48°C - (-25°C) = 73°C
Now, we need to calculate how much the 9.00m slab will expand within this temperature range. We can use the formula:
Expansion = Original Length × temperature change × coefficient of thermal expansion
Expansion = 9.00m × 73°C × 10 x 10^(-6) °C^(-1)
Expansion = 0.00657m or 6.57mm (rounded to two decimal places)
To ensure there is no contact between adjacent slabs, we need to leave a gap that is equal to or greater than the calculated expansion. Therefore, the width of the expansion gaps should be 6.57mm or slightly larger to accommodate any additional expansion.
Note: It's important to consider local building codes and guidelines which may specify recommended or required expansion gap sizes for concrete highway slabs in your specific region.