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

A strain-equivalent-pairs scan varies extension and length together across three rows, checking that pairs giving the same delta-L / L land at the same strain. The arithmetic is exact only for the stated extensions, lengths, and rows in the ideal uniform-extension model. Real materials add nonlinearity, hysteresis, geometry tolerances, temperature effects, load-cell/length calibration, finite precision, and measurement uncertainty.

Strain is a ratio, so scaled extension-length 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 scaled extension-length pair can give the same strain

Extension 1 m over original length 4 m gives strain 1 over 4.

\epsilon=\frac{\Delta L}{L_0}=\frac{1\ \text{m}}{4\ \text{m}}=\frac{1}{4}

A scaled extension-length pair can give the same strain

Extension 2 m over original length 8 m gives strain 1 over 4.

\epsilon=\frac{\Delta L}{L_0}=\frac{2\ \text{m}}{8\ \text{m}}=\frac{1}{4}

A scaled extension-length pair can give the same strain

Extension 3 m over original length 12 m gives strain 1 over 4.

\epsilon=\frac{\Delta L}{L_0}=\frac{3\ \text{m}}{12\ \text{m}}=\frac{1}{4}