Ductility requirement for beam, column, joints

Ductility requirements follow IS 13920, and are meant to force plastic hinges into the beams and to prevent brittle shear or bond failure.

Beam

• $b \ge 200$ mm, $b/D \ge 0.3$, $D \le L/4$.
• $\rho_{min} = 0.24\sqrt{f_{ck}}/f_y$, $\rho_{max} = 2.5\%$; two bars continuous top and bottom; bottom steel at the joint face $\ge$ 50% of top steel.
• Lap splices only in the middle half, with hoops at $\le 150$ mm.
• Closed hoops with $135^\circ$ hooks: $s \le \min(d/4, 8\phi, 100)$ mm within $2d$ of supports; $s \le d/2$ elsewhere.

Column

• Size $\ge 200$ mm (300 mm for long members), $b/D \ge 0.4$.
• Confining hoops over $l_o = \max(D, h/6, 450\text{ mm})$ at each end with spacing 75-100 mm and $\le b_{min}/4$; area from $A_{sh} = 0.18\,s\,h\,(f_{ck}/f_y)(A_g/A_k - 1)$.
• Splices in the middle half only; design shear based on beam hinge moments.

Joint

• Column confining hoops continue through the joint at $\le 100$ mm (150 mm if beams on all four sides).
• Beam bars anchored for $L_d$ from the inside face of the column plus a $90^\circ$ bend of $10\phi$.
• No splices in the joint.

Together, the strong-column weak-beam rule and shear capacity above flexural capacity give the ductile mechanism.