Stress Equivalent Pairs Three-Row Scan - Elasticity and Nonlinear Dynamics Step by Step

A stress-equivalent-pairs scan varies force and area together across three rows, checking that pairs giving the same F / A land at the same stress. The arithmetic is exact only for the stated forces, areas, and rows in the ideal uniform-loading model. Real materials add nonlinearity, hysteresis, geometry tolerances, temperature effects, load-cell/length calibration, finite precision, and measurement uncertainty.

Stress is a quotient, so scaled force-area pairs can land on the same value. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

A different force-area pair can give the same stress

Force 6 N over area 2 square meters gives stress 3 Pa.

\sigma=\frac{F}{A}=\frac{6\ \text{N}}{2\ \text{m}^{2}}=3\ \text{Pa}

A different force-area pair can give the same stress

Force 9 N over area 3 square meters gives stress 3 Pa.

\sigma=\frac{F}{A}=\frac{9\ \text{N}}{3\ \text{m}^{2}}=3\ \text{Pa}

A different force-area pair can give the same stress

Force 12 N over area 4 square meters gives stress 3 Pa.

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