Calculation of bridge deck slope and side length

Bridge deck slope is calculated using the rise-over-run principle, and side length can be determined from deck width and slope geometry.

Bridge Deck Slope

The slope of a bridge deck is typically expressed as a percentage or ratio, representing the vertical rise per unit of horizontal run. There are two main types:

• Longitudinal slope: along the length of the bridge, used for drainage and vehicle safety.
• Cross slope (transverse slope): across the width of the deck, usually 1–2% for concrete decks to ensure water runoff ( ). The slope can be calculated using the formula:

For example, if a bridge deck rises 0.3 meters over a horizontal distance of 15 meters:

Determining Side Length

The side length of a sloped deck can be calculated using basic trigonometry. If the deck has a width $W$ and a cross slope $\theta$ (in degrees), the sloped side length $L$ is:

For small slopes (1–2%), the difference between horizontal width and sloped side length is minimal, but for precise construction, this calculation ensures accurate formwork and reinforcement placement ( ).

Example

• Deck width: 12 m
• Cross slope: 2% → $\theta \approx \arctan (0.02)\approx {1.15}^{\circ }$

This shows a negligible increase, but it is important for formwork alignment and concrete placement.

Additional Considerations

• Haunch thickness: The deck may have variable thickness along the slope, which affects side length and reinforcement layout ( ).
• Deck overhangs: Side slopes and overhangs must be included in calculations for girder spacing and load distribution ( ).
• Construction tolerances: Formwork and screed rails must account for slope to maintain proper deck elevation ( ). By combining geometric calculations with structural design requirements, engineers can accurately determine both the slope and side length of a bridge deck, ensuring proper drainage, structural integrity, and constructability.