How to Calculate Gap Between Concrete Slabs on a Bridge

What is the formula to determine the gap between concrete slabs on a bridge when the temperature changes from the hottest day to 0°F?

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.

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