Free · Material properties

Restrained-Bar Thermal Stress — Compression Positive

Estimate thermal stress for a fully restrained linear-elastic bar using entered expansion coefficient, modulus and temperature change.

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How to use this calculator

  1. Enter the known values in the units shown. Results update as you type.
  2. Where results are editable, change one to solve backwards. Lock a value to hold it fixed.
  3. Use the worked example to check the method. Reset restores the starting fields.

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Formula and method

With E = 200 GPa, α = 0.000012 per kelvin and a 50 °C rise, the fully restrained model gives 120 MPa compression. This tool defines compression as positive.

Compression-positive thermal stress = Young’s modulus × expansion coefficient × temperature change

Worked example

Enter these known values and leave the other values blank.

Young’s modulus
200 GPa
Linear expansion coefficient (per kelvin)
.000012 / K
Initial temperature
20 °C
Final temperature
70 °C
Temperature change
50 °C
Thermal stress — compression positive
120 MPa

Assumptions and limitations

  • The bar is fully restrained axially, uniformly heated or cooled, initially unstressed, and remains linear elastic with constant properties.
  • Positive results mean compression and negative results mean tension. This explicitly stated convention reverses the sign used by tension-positive stress notation.
  • The expansion coefficient is entered per kelvin, not in millionths: 12 micrometres per metre per kelvin is 0.000012 per kelvin.
  • Material presets are illustrative constants. Actual alloy, temperature, direction and manufacturing condition can change properties.
  • The model does not evaluate yield, buckling, creep, joints, thermal gradients or failure. Initial and final temperatures exceed absolute zero.

Common questions

Does heating produce tensile stress?

With positive expansion coefficient and full restraint, heating produces compression. This tool displays that as a positive result.

What if the bar expands freely?

This fully restrained model does not apply. A freely expanding, uniformly heated bar does not develop this restraint stress.

References

Pounds-force per square inch use the exact international pound and inch with standard gravity, replacing the rounded captured factor.

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