Thermal Expansion of Bridge Calculator

Example Data Table

Formula Used

The calculator applies the linear thermal expansion relation: ΔL = α × L × ΔT.

• ΔL is the change in bridge length (expansion or contraction).
• α is the coefficient of thermal expansion (per °C).
• L is the effective length between restraint points.
• ΔT is the temperature change over the design range.

Per-end movement equals ΔL/2 when both ends share movement, or ΔL when one end is fixed.

How to Use This Calculator

1. Enter bridge length using the same restraint spacing used in design.
2. Select a material preset, or choose custom and set α.
3. Enter the expected temperature change for your region.
4. Choose whether movement is shared by both ends or one end.
5. Optionally add joint capacity and bearing allowance to check limits.
6. Set a safety factor and press Calculate to view results.
7. Download CSV or PDF after a successful calculation.

Practical Guidance

• Use conservative ΔT for extreme events and long-term exposure.
• Temperature gradients can cause additional rotations and stresses.
• Check bearings for travel, uplift, and minimum seat width.
• Detail joints for debris, drainage, and maintainability.

Professional Article

1) Why thermal movement matters

Bridge superstructures expand and contract as temperature changes. If movement is underestimated, expansion joints can tear, bearings can bind, and deck drainage gaps can misalign. For long spans, small strains accumulate into large displacements, affecting serviceability and durability. Movement demands also influence diaphragm cracking and approach slab transitions.

2) Typical temperature ranges used in design

Many regions see seasonal swings of 25–45 °C between cold nights and hot afternoons. Short-term daily gradients can add local distortions, but the primary joint movement is driven by the overall design ΔT. Conservative ΔT selection reduces maintenance risks on critical routes. Bridge codes often define uniform temperature ranges and effective gradient cases.

3) Coefficient of expansion by material

Common coefficients are about 10 µm/m/°C for concrete and 12 µm/m/°C for structural steel. Prestressed concrete is often slightly lower (around 9.5 µm/m/°C). Composite systems frequently fall between 11–12 µm/m/°C depending on section proportions. Using microstrain units helps avoid decimal errors during quick field checks.

4) What the equation predicts

The calculator applies ΔL = α·L·ΔT. For a 60 m steel span with α = 12 µm/m/°C and ΔT = 35 °C, the unfactored movement is 25.2 mm. With two-end sharing, each end moves about 12.6 mm before safety factors. If contraction governs, use negative ΔT; magnitude drives joint gap.

5) Effective length and restraint points

Movement accumulates between restraint points, not necessarily the full bridge length. Fixed piers, integral abutments, and continuity details can shorten or lengthen the effective movement length. Use the distance between the elements that actually restrain translation in the chosen direction. For skewed bridges, movement components should be resolved along joint line.

6) Bearings and expansion joints: matching capacities

Bearings must accommodate the per-end movement plus construction tolerances. Joints must accommodate the total factored movement plus debris and seal compression demands. If a joint is rated 80 mm, but the factored demand is 95 mm, premature distress is likely under extreme events. Always verify bearing manufacturer stroke and shear key clearance under movement.

7) Factoring movement for reliability

Thermal movement is affected by uncertainty in ΔT, gradients through the section, and restraint behavior. A safety factor (often 1.10–1.30 for preliminary checks) provides a conservative design movement. This tool reports both unfactored and factored totals to support quick screening. Higher factors may be justified for long spans or limited maintenance access.

8) Practical detailing notes

Provide clear movement paths, avoid snag points, and ensure joint glands are compatible with expected travel. Confirm minimum seat widths, limit stops, and uplift restraints where required. Document assumed ΔT, α, and restraint model so future inspections understand the original movement basis. Regular cleaning and seal replacement can preserve capacity through service life.

FAQs

1) What length should I enter?

Enter the effective length between restraint points in the direction of movement. For continuous bridges, use the length between fixed elements or the segment that shares a common expansion joint strategy.

2) Can I use Fahrenheit?

Yes. If you select °F, the calculator converts ΔT to an equivalent Celsius change internally. The expansion result is identical because only temperature difference matters, not the absolute reference.

3) Why do I see per-end movement?

If both ends share movement, each end typically moves about half the total. If one end is fixed, the full translation occurs at the free end. The tool reports both to support joint and bearing checks.

4) What safety factor should I use?

For screening, many engineers use 1.10–1.30 depending on uncertainty and importance. Final values should follow your project criteria and governing specifications, considering gradients, restraint, and construction tolerances.

5) How accurate are the material presets?

They represent typical coefficients used for preliminary work. Actual α can vary with mix design, moisture, and steel grade. Use project-specific test data or specification values when available for final design.

6) Does this include creep or shrinkage?

No. The calculator isolates thermal expansion. Long-term movements from creep, shrinkage, and settlement can be significant and should be evaluated separately, then combined in joint and bearing detailing checks.

7) What if my joint capacity is unknown?

Leave the joint capacity field blank. You will still get movement predictions. Later, enter vendor-rated capacity to quickly see whether factored movement fits within the selected joint system.