Elastic Modulus

Written by Jerry Ratzlaff on . Posted in Classical Mechanics

Youngs modulus 3Elastic modulus (Young's modulus), abbreviated as \(\lambda\) (Greek symbol lambda), also called modulus of elasticity, is the ratio of the stress applied to a body or substance to the resulting strain within the elastic limits.

 

Elastic Modulus formulas

\(\large{ \lambda = \frac { \sigma } { \epsilon } }\) 
\(\large{ E = \frac{ \sigma \left( F_i\;-\;F_f \right) l_i }{ \left( \delta_i\;-\;\delta_f \right)\;A_c } }\) 

Where:

 Units English Metric
\(\large{ \lambda }\)  (Greek symbol lambda) = elastic modulus \(\large{\frac{lbf}{in^2}}\) \(\large{Pa}\)
\(\large{ A_c }\) = area cross-section \(\large{in^2}\) \(\large{mm^2}\)
\(\large{ \delta_f }\)  (Greek symbol delta) = final deformation \(\large{in}\) \(\large{mm}\)
\(\large{ \delta_i }\)  (Greek symbol delta) = initial deformation \(\large{in}\) \(\large{mm}\)
\(\large{ F_f }\) = final force \(\large{lbf}\) \(\large{N}\)
\(\large{ F_i }\) = initial force \(\large{lbf}\) \(\large{N}\)
\(\large{ l_i }\) = initial length \(\large{in}\) \(\large{mm}\)
\(\large{ \epsilon }\)  (Greek symbol epsilon) = strain \(\large{\frac{in}{in}}\) \(\large{\frac{mm}{mm}}\)
\(\large{ \sigma }\)  (Greek symbol sigma) = stress \(\large{\frac{lbf}{in^2}}\) \(\large{Pa}\)

 

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Tags: Strain and Stress Equations Modulus Equations Soil Equations