Stress and strain

When a bar is pulled, every cross-section shares the load. Stress is that load divided by the area that carries it, so it tells us how hard the material is working regardless of the bar's size. Strain is the change in length divided by the original length: a pure number that tells us how much the material has stretched.

For most structural materials, at working loads, stress is proportional to strain. The constant of proportionality is the modulus of elasticity, E. Steel has an E of roughly 200 GPa; normal concrete is far softer, of the order of 25 to 35 GPa depending on its strength. That difference is why steel bars in a concrete column pick up a much larger stress than the concrete around them at the same strain.

Beyond the elastic range, steel yields: strain grows with little extra stress, which gives ductile warning before failure. Concrete in compression is not linear even at moderate stress and crushes at a strain of a few thousandths. Design codes turn these behaviours into idealised stress-strain curves.

Stress can be normal (pulling or squeezing the cross-section) or shear (sliding one face over another). Both are measured in N/mm² or MPa, which are the same unit.