College Physics (4th Edition)

If there were two wires, a force of $F$ would be required for each wire, thus, a total force of $2F$ would be required to produce the same strain $\frac{\Delta L}{L}$ in each wire. If there were $N$ wires, then a total force of $N\times F$ would be required. $Force \propto (Strain \times N)$ $Force \propto (Strain \times Area)$ $Strain \propto \frac{Force}{Area}$ We can see that the total force required is proportional to the total cross-sectional area. Thus, the strain is proportional to the force per unit area.