# How to Calculate the Width of Expansion Cracks Between Concrete Slabs

## What are the necessary concepts to apply in calculating the width of expansion cracks?

To solve the problem, it is essential to apply the concepts related to thermal expansion of solids. Thermodynamically, the expansion is given by the formula: ΔL = L₀αΔT. Where, L₀ = Original Length of the bar, ΔT = Change in temperature, and α = Coefficient of thermal expansion.

## What are the given values for the calculation?

The given values are: L₀ = 18m, α = 12 × 10^-6/°C, T₂ = 52°C, and T₁ = 25°C.

## How to calculate the width of expansion cracks?

Use the formula: ∆L = L₀α(T₂ - T₁) to find the change in length. Then convert the change in length to the width of the expansion cracks.

## Calculation and Solution:

Given values: L₀ = 18m, α = 12 × 10^-6/°C, T₁ = 25°C, T₂ = 52°C

Using the formula: ∆L = L₀α(T₂ - T₁)

Substitute the values: ∆L = 18 × 12 × 10^-6 (52 - 25)

∆L = 3.24 × 10^-4 × 18

∆L = 5.832 × 10^-3m

Therefore, the width of the expansion cracks between the slabs to prevent buckling should be 0.5832cm.

## Explanation and Further Details:

When calculating the width of expansion cracks between concrete slabs, it is crucial to consider the thermal expansion properties of the material. In this scenario, the given values provide the necessary information to determine the change in length due to temperature variations.

The coefficient of thermal expansion (α) plays a significant role in calculating the width of expansion cracks. The formula ΔL = L₀α(T₂ - T₁) helps in finding the change in length, which can then be converted to the required width measurement.

By applying the values and formula in the calculation, the width of the expansion cracks is determined to be 0.5832cm. This measurement is essential for ensuring the stability and structural integrity of the concrete highway slabs to prevent buckling.