Define ductility; ductility in joints

Ductility

Ductility is the capacity of a member or structure to deform inelastically by a large amount (beyond yield) without an appreciable loss of strength, thereby absorbing seismic energy. Ductility ratio: $\mu = \Delta_u/\Delta_y$.

Ductility requirements in joints (IS 13920)

1. Confinement of the joint core: the special confining hoops (closed, $135^\circ$ hooks, $6\phi$ tail) of the column end zone are continued through the joint at a spacing $\le 100$ mm (relaxed to 150 mm, with half the confining steel, where beams frame into all four faces of the joint).
2. Anchorage of beam bars: in an exterior joint, the bars are anchored in the column for the development length $L_d$ measured from the inside face of the column, plus a $90^\circ$ bend with a $10\phi$ standing leg turned into the joint core (top bars down, bottom bars up).
3. Continuity of column bars: no lap splice in the joint; column laps only in the central half of the column height.
4. Strong column - weak beam: at each joint the flexural strength of the columns should exceed that of the beams, so that hinges form in the beams, not in the joints or columns.
5. Joint shear check: the core must resist the shear induced when the beam bars yield. IS 13920:2016 limits the joint shear strength to $1.5\sqrt{f_{ck}}A_{ej}$ for joints confined by beams on all four faces, $1.2\sqrt{f_{ck}}A_{ej}$ for three faces or two opposite faces, and $1.0\sqrt{f_{ck}}A_{ej}$ for other joints.
6. Bar diameter and bond: the diameter of beam bars passing through an interior joint is limited relative to the column depth (column dimension $\ge 20$ times the largest beam bar diameter) to prevent bar slip.

   Column ##### s=100       Beam bars anchored
   -------+=====+-------    from inner face + bend
   hoops continue through
   the joint   ##### s=100