# How to Calculate Gap Between Concrete Slabs on a Bridge

## Understanding the Change in Length

**Change in Length Formula:**ΔL = αLΔT

Where:

- ΔL is the change in length
- α is the coefficient of linear expansion of concrete
- L is the original length of the slab
- ΔT is the change in temperature from the day the slab was cast

## Calculating the Gap

Given:

- Original length of the slabs (L) = 315 cm
- Coefficient of linear expansion of concrete (α) = 12 × 10⁻⁶/°C
- Temperature difference between the hottest day and 0°F (ΔT) = 115°F - 0°F = 115°F

Using the formula:

ΔL = αLΔT

ΔL = (12 × 10⁻⁶/°C) (315 cm) (115°F)

ΔL ≈ 0.423 cm

To find the gap between the slabs on a 0°F day:

Gap = Elongation - Original Length

Gap = 0.423 cm - 315 cm

Gap ≈ -0.577 cm

The negative value indicates contraction when cooling. Therefore, the gap between the slabs on a 0°F day is approximately 0.577 cm.