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

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

where

$$\begin{eqnarray*} F &=& \mbox{total applied force}\\ S &=& \mbox{area over which force is applied}\\ F/S &=& \mbox{\emph{stress} = force per unit area}\\ L &=& \mbox{rest length}\\ \Delta L &=& \mbox{displacement}\\ \Delta L/L &=& \mbox{\emph{strain} = displacement per unit length}\\ \end{eqnarray*}$$

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].