Linear Thermal Restrained Expansion

Written by Jerry Ratzlaff on . Posted in Thermodynamics

expansion restrained 1Linear 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 \(\large{ F }\) \(\large{ C }\)

 

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Tags: Thermal Equations Expansion Equations