Calculateur de Réglage PID — Formule

Thermal Expansion and Strain

Materials expand or contract when their temperature changes. The thermal strain is proportional to the temperature change and the coefficient of thermal expansion (CTE).

Formula

epsilon_thermal = alpha × delta_T

delta_L = alpha × delta_T × L

where alpha is the CTE, delta_T is the temperature change, and L is the original length. If the component is constrained from expanding, a thermal stress develops: sigma = E × alpha × delta_T.

Exemple Résolu

A 1000 mm steel bar (alpha = 12 × 10⁻⁶/°C) heated by 100°C.

  1. epsilon = 12 × 10⁻⁶ × 100 = 0.0012 (0.12%)
  2. delta_L = 0.0012 × 1000 = 1.2 mm
  3. If constrained: sigma = 200000 × 0.0012 = 240 MPa