force-over-area-defines-normal-stress - Elasticity: Stress, Strain, and Material Response Step by Step

Normal stress is a force ledger divided by a checked area. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

Normal stress starts with force and area

The force vector and area marker are separate inputs. The stress number is not trusted until both are checked.

F=12\ \text{N}\qquad A=3\ \text{m}^{2}

With area fixed, stress follows force

Hold area fixed and scan three exact forces. Each stress entry is the force divided by the same area.

\begin{array}{c|c|c}F&A&\sigma\\6\ \text{N}&3\ \text{m}^{2}&2\ \text{Pa}\\12\ \text{N}&3\ \text{m}^{2}&4\ \text{Pa}\\18\ \text{N}&3\ \text{m}^{2}&6\ \text{Pa}\\\end{array}

Normal stress is checked as force divided by area

The stress label is trusted only after the force and area vectors match the exact ledger.

\sigma=\frac{F}{A}=\frac{12\ \text{N}}{3\ \text{m}^{2}}=4\ \text{Pa}