# Thermal Expansion Calculator - Expansion Joints, Thermal Stress, Bimetallic Strip

> Linear, area and volume expansion, expansion joints, rail stress and buckling, bimetallic thermostat, shrink fits, liquids and the 4 °C water anomaly.

- URL: https://qilingtools.com/en/physics/thermal-expansion
- Category: Physics Tools (https://qilingtools.com/en/physics)
- Tags: [Physics](https://qilingtools.com/en/tags/physics), [Education](https://qilingtools.com/en/tags/education)
- Last updated: 2026-10-29
- Price: Free, no sign-up
- Privacy: Runs locally in the browser; files are never uploaded

Almost everything grows when heated: a 100 m steel bridge moves several centimetres between winter and summer, and a fully restrained rail can build up nearly a hundred tonnes of force. This tool uses real expansion coefficients to compute movement, thermal stress and buckling, animates a bimetallic thermostat, works out how hot a hub must be for a shrink fit, and simulates how water's density maximum at 4 °C makes lakes freeze from the top down.

## How to use

1. In Linear / area / volume pick a material, dimension and temperatures to see the change and an exaggerated drawing
2. In Joints & thermal stress set the span and yearly temperature range to get the gap to leave at installation; below it, watch a heated rod buckle
3. In Bimetallic strip choose the metals and thicknesses, then press Run to see a thermostat control a room
4. In Shrink fit and Liquids enter dimensions for the heating temperature, contact pressure or overflow
5. In Water anomaly set the air temperature and play a lake cooling and freezing through winter

## Features

- Table of α and E for 17 materials, with exact vs linearised area and volume expansion
- Expansion-joint gaps, restrained rail stress and axial force, Euler buckling temperature and post-buckling deflection
- Timoshenko bimetal curvature, tip deflection and sensitivity, plus a thermostat animation with hysteresis and room-temperature chart
- Shrink and freeze-fit temperatures (liquid nitrogen, dry ice), contact pressure, torque capacity and hoop stress
- Thermometer column sensitivity and overflow from a brim-full container (gasoline, ethanol and more)
- Water density curve and a 1-D lake model: overturning, a 4 °C bottom layer and ice growth

## FAQ

### Why do bridges and railways need gaps?

Steel expands about 12×10⁻⁶ per kelvin, so a 100 m girder moves about 8.4 cm over a 70 K range. If both ends are held, the movement turns into stress σ = EαΔT — about 100 MPa for a 40 K rise in steel, regardless of length. Bridges therefore use expansion joints and jointed track leaves rail gaps, while continuous welded rail is laid at a chosen neutral temperature and clamped to carry the stress.

### Why does a bimetallic strip bend?

Two metals with different expansion coefficients are bonded together. When heated the high-expansion layer wants to grow more, so the pair curls into an arc with that layer on the outside. Timoshenko's formula gives the curvature; for equal thicknesses and moduli κ = 3(α₂ − α₁)ΔT / (2h). Invar barely expands, so invar-brass strips are very sensitive and common in thermostats and circuit breakers.

### How hot must a bearing or gear be for a shrink fit?

The temperature rise is ΔT = (interference + assembly clearance) / (α × bore). A 50 mm steel bore with 40 μm interference and 30 μm clearance needs about 117 K, so roughly 137 °C. You can also chill the shaft in liquid nitrogen; combining both lowers the heating temperature and avoids tempering the bearing.

### Why do lakes freeze from the top so fish survive?

Water is densest at 3.98 °C. In autumn the cooling surface water sinks and the lake overturns until it is about 4 °C throughout. Colder water is lighter, stays on top and freezes, and the ice insulates the water below, which stays near 4 °C. Without the anomaly the whole lake would have to reach 0 °C before freezing, and shallow lakes could freeze solid.

### Why does a brim-full fuel tank overflow in the sun?

Liquids expand far more than metals: gasoline about 9.5×10⁻⁴ per kelvin versus about 3.6×10⁻⁵ for the volume of a steel tank. Warming 50 L of gasoline from 10 °C to 35 °C adds about 1.1 L. That is why fuel tanks, water heaters and heating loops need ullage or an expansion vessel.

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