Ductility & Ductile Detailing (IS 13920) Notes

Last reviewed 16 Sept 2026 · 9 min read

Ductility in reinforced concrete

Ductility is the ability to undergo large inelastic deformations without substantial loss of strength.

FormulaDuctility measures

Curvature ductility $μ_{ϕ} = \frac{ϕ _{u}}{ϕ _{y}}$

Displacement ductility $μ_{Δ} = \frac{Δ _{u}}{Δ _{y}}$ $ϕ_{y} = \frac{ε _{y}}{d - x _{y}}$ ; $ϕ_{u} = \frac{ε _{c u}}{x _{u}}$ — ductility increases when the neutral axis depth at failure is small and the ultimate concrete strain is large.

Factors increasing ductility of RC sections

Confinement by closely spaced transverse reinforcement (hoops, spirals) — increases ultimate compressive strain and strength of concrete.
Lower tension steel ratio (under-reinforced sections) and compression reinforcement.
Lower axial compression (high axial load reduces ductility of columns).
Higher concrete strength (reduces neutral axis depth) and steel with good elongation and a margin between yield and ultimate strength.
Preventing premature shear failure, bond/anchorage failure and buckling of bars.

IS 13920: 2016 — scope

IS 13920 (Ductile design and detailing of reinforced concrete structures subjected to seismic forces — code of practice) applies to RC structures designed as special moment resisting frames and special structural walls; it is mandatory for such systems in higher seismic zones as required by IS 1893.

Materials (outline)

Minimum concrete grade M20 (higher grades for taller buildings as specified).
Reinforcement of high-ductility grades with minimum specified elongation; grades with high yield strength beyond limits are restricted.
Actual yield strength should not greatly exceed the specified value (to preserve the capacity design hierarchy).

Beams (flexural members)

Geometry

Width-to-depth ratio $b / D \geq 0.3$ .
Width $b \geq 200$ mm.
Depth $D \leq$ 1/4 of clear span.
Width not to exceed column width plus limited extensions on each side.

Longitudinal reinforcement

At least two bars continuous at top and bottom.
Minimum tension steel ratio $ρ_{min} = 0.24 f_{c k} / f_{y}$ on any face; maximum steel ratio 2.5%.
Positive steel at the joint face ≥ half the negative steel there.
Steel at any section (top or bottom) ≥ one-quarter of the maximum negative steel at either joint face.
Bars anchored into columns with development length and 90° bends (in exterior joints) beyond the inner face of the column.

Lap splices

Lap splices not within joints, not within a distance of 2d from the joint face, and not in regions of potential plastic hinges.
Not more than 50% of bars spliced at one section.
Hoops over the entire lap length at close spacing (the code limits spacing to 150 mm).

Transverse reinforcement

Closed hoops with 135° hooks and extension of 6 times the bar diameter but not less than 65 mm, embedded in the confined core.
Minimum hoop bar diameter 8 mm (larger for longer spans as per code).
Over a length of 2d from each joint face (and on either side of any section where flexural yielding may occur): hoop spacing ≤ d/4, 6 times the smallest longitudinal bar diameter and 100 mm (IS 13920: 2016; the 2002 edition used d/4 and 8 times the bar diameter).
First hoop within 50 mm of the joint face.
Elsewhere, spacing ≤ d/2.

(Limits are summarised; refer to the code clause for exact wording for each case.)

Capacity-based shear design of beams

FormulaDesign shear in beams

V_{u, a} = V_{a}^{D + L} - 1.4 \frac{M _{u, l im}^{A s} + M _{u, l im}^{B h}}{L _{A B}}, V_{u, b} = V_{b}^{D + L} + 1.4 \frac{M _{u, l im}^{A s} + M _{u, l im}^{B h}}{L _{A B}}

(and the corresponding case for sway to the other side)

$M_{u, l im}^{s}$ , $M_{u, l im}^{h}$ = sagging and hogging moment capacities at the beam ends (with actual reinforcement); $L_{A B}$ = clear span; $V^{D + L}$ = shear due to factored gravity loads (1.2(DL + IL)). Design shear is the larger of this capacity-based shear and the shear from analysis. The contribution of concrete is often ignored in plastic hinge regions under high seismic shear (as per code).

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