Bar Stiffness Force Three-Row Scan - Elasticity and Nonlinear Dynamics Step by Step

A bar-stiffness-force scan varies area, length, and extension together across three rows, checking that geometry sets bar stiffness k = E A / L before extension sets force F = k * delta-L. The arithmetic is exact only for the stated forces, lengths, extensions, areas, and modulus values in the ideal linear-elastic bar model. Real materials add nonlinearity, hysteresis, geometry tolerances, temperature effects, load-cell/length calibration, finite precision, and measurement uncertainty.

Geometry sets bar stiffness before extension sets 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

Bar stiffness comes before extension force

Area 2 square meters and length 4 m give stiffness 8 newtons per meter; extension 1 m then gives force 8 N.

k=\frac{EA}{L}=8\ \text{N/m},\quad F=k\Delta L=8\ \text{N}

Bar stiffness comes before extension force

Area 4 square meters and length 8 m give stiffness 8 newtons per meter; extension 1 m then gives force 8 N.

k=\frac{EA}{L}=8\ \text{N/m},\quad F=k\Delta L=8\ \text{N}

Bar stiffness comes before extension force

Area 4 square meters and length 8 m give stiffness 8 newtons per meter; extension 2 m then gives force 16 N.

k=\frac{EA}{L}=8\ \text{N/m},\quad F=k\Delta L=16\ \text{N}