Factors affecting ductility, IS 13920 beam

Factors affecting ductility

1. Tension steel ratio: a higher $\rho$ gives lower ductility; under-reinforced sections are ductile.
2. Compression steel: reduces the neutral axis depth and increases ductility.
3. Grade of steel: a higher yield strength (and smaller elongation) reduces ductility; Fe 415/500 with good elongation is preferred.
4. Grade of concrete: for the same steel ratio, higher-strength concrete reduces the neutral axis depth and so increases section ductility, although very high-strength concrete is itself more brittle (it has a smaller strain capacity after the peak).
5. Confinement: closely spaced stirrups/hoops increase the strain capacity of the concrete.
6. Axial load: high axial compression reduces the ductility of columns.
7. Shear and bond: a shear or bond failure prevents flexural ductility from developing.
8. Detailing of anchorages and laps: poor detailing causes bar slip.

Ductility requirements of beams (IS 13920)

• $b \ge 200$ mm, $b/D \ge 0.3$, $D \le L/4$.
• $\rho_{min} = 0.24\sqrt{f_{ck}}/f_y$, $\rho_{max} = 2.5\%$.
• At least two 12 mm bars continuous at the top and bottom.
• Bottom steel at a joint face $\ge 50\%$ of the top steel; capacity anywhere along the span $\ge 25\%$ of the maximum end capacity.
• Splices in the middle half only, with hoops at $\le 150$ mm over the lap; none in the joint or within $2d$ of it.
• Closed stirrups with $135^\circ$ hooks and a $10\phi$ tail; diameter $\ge 6$ mm (8 mm for spans > 5 m).
• Spacing: $\min(d/4,\ 8\phi,\ 100)$ mm within $2d$ of supports, with the first stirrup at 50 mm; $\le d/2$ elsewhere.
• Shear design based on the hinge (flexural) capacity.