Young's Modulus

Young's modulus can be thought of as the spring constant for solids. Consider an ideal rod (or bar) of length $L$ and cross-sectional area $S$. Suppose we apply a force $F$ to the face of area $S$, causing a displacement $\Delta L$ along the axis of the rod. Then Young's modulus $Y$ is given by

$$Y \isdef \frac{\mbox{Stress}}{\mbox{Strain}} \isdef \frac{F/S}{\Delta L/L}$$

where

$$\begin{eqnarray*} F &=& \mbox{total applied force}\\ S &=& \mbox{area over whic... ...a L/L &=& \mbox{\emph{strain} = displacement per unit length}\\ \end{eqnarray*}$$

For wood, Young's modulus $Y$ is on the order of $10$ N/m$\null^2$. For aluminum, it is around $70$ (a bit higher than glass which is near $65$), and structural steel has $Y\approx 200$ [181].