doubling-force-doubles-stress - Elasticity: Stress, Strain, and Material Response Step by Step

With area fixed, the normal stress follows the force. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

Keep the area fixed before changing force

This contrast holds the area marker steady. Only the force input is larger than the base case.

F=24\ \text{N}\qquad A=3\ \text{m}^{2}

Doubling force doubles stress in the table

The area column is unchanged. The force and stress columns scale together in exact integer steps.

\begin{array}{c|c|c}F&A&\sigma\\12\ \text{N}&3\ \text{m}^{2}&4\ \text{Pa}\\24\ \text{N}&3\ \text{m}^{2}&8\ \text{Pa}\\36\ \text{N}&3\ \text{m}^{2}&12\ \text{Pa}\\\end{array}

Doubling force doubles the stress when area stays fixed

The area is unchanged, so the checked stress doubles with the force.

\sigma=\frac{24\ \text{N}}{3\ \text{m}^{2}}=8\ \text{Pa}