Ductile behaviour and how it is induced

Ductile behaviour means that a structure can deform well beyond its yield limit, absorbing and dissipating energy, while still carrying load. It gives visible warning (large cracks and deflections) before failure instead of collapsing suddenly like a brittle structure. Ductility is measured by the ductility ratio $\mu = \Delta_u/\Delta_y$ (ultimate displacement over yield displacement).

  Load
   |      ___________  ductile
   |    /            \
   |   /              \___
   |  /   brittle: |
   | /     ________|
   |/_____/________________ Deformation

How ductility is induced

1. Under-reinforced sections: limit the tension steel so that the steel yields before the concrete crushes ($x_u \le x_{u,max}$, and $\rho \le 2.5\%$).
2. Compression steel: increases flexural ductility by reducing the neutral axis depth.
3. Confinement: closely spaced closed hoops with $135^\circ$ hooks, especially at column ends, joints and beam ends, keep the concrete core intact.
4. Capacity design: strong column - weak beam, and shear capacity greater than flexural capacity, so that failure is controlled by yielding of the beams.
5. Proper anchorage and lap splices: bars anchored into joints, and laps placed away from hinge zones.
6. Good materials: Fe 415/Fe 500 steel with fairly high elongation, concrete not weaker than M20, and structural regularity in plan and elevation.
7. Avoiding short columns and soft storeys, where deformation concentrates.