# Linear Thermal Restrained Expansion

Written by Jerry Ratzlaff on . Posted in Thermodynamics

## Linear Thermal Restrained Expansion Formulas

 $$\large{ \Delta p = \lambda\; A_i \; \alpha_l \; \Delta T }$$ $$\large{ \sigma_c = - \frac{p}{A_i} }$$ $$\large{ \sigma_c = - \lambda\; A_i \; \overrightarrow{\alpha_l} \; \Delta T }$$

### Where:

 Units English Metric $$\large{ \Delta p }$$ = pressure differential $$\large{ \frac{ lbf }{ in^2 } }$$ $$\large{ Pa }$$ $$\large{ \sigma_c }$$  (Greek symbol sigma) = compressive stress $$\large{ deg }$$ $$\large{ rad }$$ $$\large{ \overrightarrow{\alpha_l} }$$   (Greek symbol alpha) = linear thermal expansion coefficient $$\large{ \frac{in}{in\;F} }$$ $$\large{ \frac{mm}{mm\;C} }$$ $$\large{ A_i }$$ = initial area of object $$\large{ in^2 }$$ $$\large{ mm^2 }$$ $$\large{ \lambda }$$  (Greek symbol lambda) = modulus of elasticity $$\large{ \frac{ lbf }{ in^2 } }$$ $$\large{ Pa }$$ $$\large{ p }$$ = pressure $$\large{ \frac{ lbf }{ in^2 } }$$ $$\large{ Pa }$$ $$\large{ \Delta T }$$ = temperature differential $$\large{ F }$$ $$\large{ C }$$