Ductility

Ductility is the ability to deform well beyond yield without losing much strength. A ductile member bends, cracks and yields visibly but keeps carrying load; a brittle one fails suddenly. It is measured as a ratio, the displacement ductility, maximum displacement divided by yield displacement, or as curvature or rotation ductility at a section.

Earthquake design depends on it. Elastic design for the full earthquake would make buildings very heavy. Instead, codes divide the elastic force by a response reduction factor and rely on the structure to yield and dissipate energy through hysteresis. Two classic rules link the force reduction to ductility. For long-period structures, the equal-displacement rule says the inelastic displacement is about the same as the elastic one, so the reduction factor equals the ductility. For short-period structures, the equal-energy rule gives a smaller reduction, the square root of two times ductility minus one.

Ductility in concrete comes from under-reinforced sections, confinement by closely spaced hoops that let the core strain far beyond the crushing strain of plain concrete, and reinforcement with adequate elongation and a suitable ratio of tensile to yield strength. In steel, compact sections and capacity-designed connections give ductility. Brittle modes, shear failure, bond splitting, buckling of bars and weld fracture, must be suppressed by giving them more strength than the ductile mode.

Ductility demand is not uniform: it concentrates in the hinges that form. That is why detailing rules focus on beam ends, column ends, joints and wall boundaries.