Key Equations

First Equilibrium Condition	${\displaystyle \sum _k{\overrightarrow{F}}_k=\overrightarrow{0}}$
Second Equilibrium Condition	${\displaystyle \sum _k{\overrightarrow{\tau }}_k}=\overrightarrow{0}$
Linear relation between stress and strain	$\text{stress}=\text{(elastic modulus)}\times \text{strain}$
Young’s modulus	$Y=\frac{\text{tensile stress}}{\text{tensile strain}}=\frac{F_{\perp }}{A}\frac{L_0}{\text{Δ}L}$
Bulk modulus	$B=\frac{\text{bulk stress}}{\text{bulk strain}}=\text{−}\text{Δ}p\frac{V_0}{\text{Δ}V}$
Shear modulus	$S=\frac{\text{shear stress}}{\text{shear strain}}=\frac{F_{\parallel }}{A}\frac{L_0}{\text{Δ}x}$