Introduction to Earthquake Resistant Design and Provisions for Ductile Detailing

Ductility is the ability of a member to undergo large inelastic deformation without significant loss of strength. In a beam it is obtained by making the tension steel yield before the concrete crushes and by preventing early shear failure. IS 13920 gives the following detailing rules.

Geometry

• Width $b \ge 200$ mm and $b/D \ge 0.3$.
• Depth $D \le \tfrac14$ of clear span.

Longitudinal steel

• At least two bars (12 mm or more) continuous at top and at bottom.
• $\rho_{min} = 0.24\sqrt{f_{ck}}/f_y$ and $\rho_{max} = 2.5\%$ on any face.
• Positive steel at a joint face is not less than 50% of the negative steel there.
• Along the span, neither positive nor negative capacity is less than 25% of the maximum capacity at either joint face.
• Lap splices only in the middle half of the span, never within the joint or within $2d$ of a joint face. Not more than 50% of bars are spliced at one section and the splice is enclosed by closely spaced hoops (spacing $\le 150$ mm).

Transverse steel (stirrups)

• Closed hoops with $135^\circ$ hooks and a tail of $10\phi$ (not less than 75 mm) so that they stay effective after the cover spalls.
• Diameter $\ge 6$ mm (8 mm if clear span exceeds 5 m).
• Over a length $2d$ from each joint face the spacing is the least of $d/4$, $8\phi_{min}$ and 100 mm, with the first hoop at 50 mm. Elsewhere the spacing is $\le d/2$.
• Stirrups are designed for the shear that develops when plastic hinges form at both ends (capacity design).

  Column |<-- 2d -->|<------ L/2 ------>|<- 2d ->| Column
  -------+-+-+-+-+-+---------------------+-+-+-+-+-------
         | | | | | |  hoops at d/2       | | | | | |
         | | | | | |                     | | | | | |
  -------+-+-+-+-+-+---------------------+-+-+-+-+-------
   50 mm, then s <= min(d/4, 8phi, 100)      lap splice only
                                              in middle half

Columns must stay stable while the beams yield, so IS 13920 asks for good confinement at the ends, where plastic hinges can form.

General requirements

• Minimum dimension 200 mm (300 mm if the unsupported length exceeds 4 m or beam span exceeds 5 m); $b/D \ge 0.4$.
• Longitudinal steel 0.8% to 6% (IS 456); lap splices only in the central half of the column height, designed as tension splices, with hoop spacing $\le 150$ mm over the lap.

Special confining reinforcement

• Provided over a length $l_o$ at both ends of each column, measured from the joint face, where $l_o \ge$ the largest of: larger lateral dimension, $h/6$ (clear height) and 450 mm.
• Hoop spacing in this zone: $s \le \tfrac14 b_{min}$ but between 75 mm and 100 mm.
• Hoops are closed with $135^\circ$ hooks, tail $\ge 6\phi$ (not less than 65 mm). Minimum diameter 8 mm (10 mm for bars over 32 mm).
• Area of one leg-group (rectangular hoop) per spacing:

$$A_{sh} = 0.18\, s\, h \,\frac{f_{ck}}{f_y}\left(\frac{A_g}{A_k} - 1\right)$$

where $h$ is the longer dimension of the confined core measured c/c of hoops, $A_g$ is the gross area and $A_k$ is the core area. For circular spirals, $A_{sh} = 0.09\, s\, D_k \frac{f_{ck}}{f_y}\left(\frac{A_g}{A_k}-1\right)$.

• Where a column supports a discontinued stiff member (wall), the confining steel runs over the full height of the column below.
• Outside $l_o$ the spacing follows IS 456 (not more than the least lateral dimension, $16\phi$ or 300 mm).

   Joint ---------------
     ^     | # # # # # |  s = 75-100 mm
     | lo  | # # # # # |  (closely spaced hoops)
     v     | # # # # # |
   ------- |#  #  #  # |  
     h-2lo | #    #    |  normal spacing (IS 456)
   ------- | # # # # # |  close spacing again

Ductile detailing makes the structure deform plastically in a controlled way during an earthquake without sudden collapse. IS 13920 governs the detailing of beams, columns and joints.

Beam

• $b \ge 200$ mm, $b/D \ge 0.3$, $D \le L/4$.
• Two bars continuous at top and bottom; $\rho$ between $0.24\sqrt{f_{ck}}/f_y$ and 2.5%.
• Bottom steel at a joint face $\ge 50\%$ of top steel.
• Splices in the middle half only, with hoops at 150 mm or closer.
• Closed stirrups with $135^\circ$ hooks. Within $2d$ of the support, spacing $\le \min(d/4,\ 8\phi,\ 100\text{ mm})$; elsewhere $\le d/2$.

Column

• Minimum size 200 mm, $b/D \ge 0.4$.
• Special confining hoops over $l_o = \max(D,\ h/6,\ 450\text{ mm})$ at each end, at 75-100 mm spacing and $\le b_{min}/4$.
• $135^\circ$ hooks with $6\phi$ tail; splices only in the middle half.
• Strong-column weak-beam: the columns at a joint should be stronger than the beams so that hinges form in the beams.

   BEAM                              COLUMN
  |-2d-|--- d/2 ---|-2d-|        ---------
  |||||| | | | | | ||||||        | ##### |  s=75-100
                                 | ##### |  over lo
                                 |  # #  |  s per IS456
                                 | ##### |  s=75-100
                                 ---------

Members are also designed for the shear produced by plastic hinge capacity, not only by analysis, so that shear failure (brittle) cannot precede flexural yielding (ductile).

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 deflection) before failure instead of sudden brittle collapse. Ductility is measured by the ductility ratio $\mu = \Delta_u/\Delta_y$ (ultimate over yield displacement).

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

How ductility is induced

1. Under-reinforced sections: limit tension steel so that steel yields before concrete crushes ($x_u \le x_{u,max}$, and $\rho \le 2.5\%$).
2. Compression steel: adds ductility in flexure by lowering 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 failure is controlled by yielding of beams.
5. Proper anchorage and lap splices: bars anchored into joints, laps away from hinge zones.
6. Good materials: Fe 415/Fe 500 with fairly high elongation, concrete not weaker than M20, and structural regularity in plan and elevation.
7. Avoid short columns and soft storeys where deformation concentrates.

          Column above (hoops s=75-100)
                  | | | |
           +------#########------+
 top bars  =====>#  joint  #<====  top bars
 anchored  |     #  hoops   #     |  continuous
 Ld from   |     #  s<=100  #     |
 inner face|=====>#         #<====|
 + 90 bend +------#########------+
 (10 phi)         | | | |
          Column below (hoops s=75-100)

  Beam: hoops 50 mm from face, s <= d/4, 8phi, 100

Ductile details shown:

• Column confining hoops (closed, $135^\circ$ hooks, $6\phi$ tail) run continuously through the joint at $\le 100$ mm (up to 150 mm if beams frame in on all four faces).
• Beam longitudinal bars at an exterior joint extend to the far face of the column, are anchored for $L_d$ measured from the inside face, and end in a $90^\circ$ bend with a standing leg of $\ge 10\phi$ turned down.
• Column bars are continuous through the joint; no lap splice within the joint or within $2d$ of its face.
• Beam stirrups start 50 mm from the joint face, spacing $\le \min(d/4,\ 8\phi,\ 100\text{ mm})$ over $2d$.
• Strong-column weak-beam proportioning, so the joint remains elastic.

Ductility

Ductility is the property of a structure or member to undergo large plastic (inelastic) deformation before failure without a significant reduction in load capacity. It is expressed by the ductility ratio $\mu = \Delta_u/\Delta_y$ or curvature ductility $\phi_u/\phi_y$.

Beam-column joint with ductile details

          Column above (hoops s=75-100)
                  | | | |
           +------#########------+
 top bars  =====>#  joint  #<====  top bars
 anchored  |     #  hoops   #     |  continuous
 Ld from   |     #  s<=100  #     |
 inner face|=====>#         #<====|
 + 90 bend +------#########------+
 (10 phi)         | | | |
          Column below (hoops s=75-100)

  Beam: hoops 50 mm from face, s <= d/4, 8phi, 100

Ductile details shown:

• Column confining hoops (closed, $135^\circ$ hooks, $6\phi$ tail) run continuously through the joint at $\le 100$ mm (up to 150 mm if beams frame in on all four faces).
• Beam longitudinal bars at an exterior joint extend to the far face of the column, are anchored for $L_d$ measured from the inside face, and end in a $90^\circ$ bend with a standing leg of $\ge 10\phi$ turned down.
• Column bars are continuous through the joint; no lap splice within the joint or within $2d$ of its face.
• Beam stirrups start 50 mm from the joint face, spacing $\le \min(d/4,\ 8\phi,\ 100\text{ mm})$ over $2d$.
• Strong-column weak-beam proportioning, so the joint remains elastic.

A beam-column joint transfers the moments and shears of beams into columns. During an earthquake it is subjected to very high horizontal and vertical shear and bond demands, and its failure can bring down the whole frame. Ductile detailing is therefore needed because:

• High shear in the joint core: the opposite stresses from beam top and bottom bars produce a large diagonal tension that can crack the core.
• Bond and anchorage stress: bars pass through the joint with yielding on one side and compression on the other, so they may slip. Hence the beam bars must be anchored by their full development length from the inside face of the column, with a $90^\circ$ bend.
• Loss of confinement: the joint concrete spalls under cyclic reversals. Closed hoops with $135^\circ$ hooks keep the core and the bars together.
• Joint should not yield first: a joint failure is brittle and cannot be repaired, so it must be stronger than the adjoining members.
• Cyclic loading: stiffness and strength degrade quickly in unconfined joints.

As per IS 13920, the special confining hoops of the column ends are continued through the joint at 75-100 mm spacing (up to 150 mm when beams frame on all four sides). Lap splices are never made in the joint.

Ductility

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

Ductility requirements in joints (IS 13920)

1. Confinement of the joint core: special confining hoops (closed, $135^\circ$ hooks, $6\phi$ tail) of the column end zone are continued through the joint at spacing $\le 100$ mm (relaxed to 150 mm where beams frame into all four faces of the joint).
2. Anchorage of beam bars: in an exterior joint, bars are anchored in the column for development length $L_d$ measured from the inside face of the column, plus a $90^\circ$ bend with $10\phi$ standing leg. Bars should not be bent up or bent into the joint region in any way that opens the core.
3. Continuity of column bars: no lap splice in the joint or within $2d$ of its face; laps only in the central half of the column.
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 beams, not in joints or columns.
5. Joint shear check: the core must resist the shear induced by beam bars yielding, with shear stress limited as per IS 13920 (about $1.2\sqrt{f_{ck}}$ for joints confined on all faces).
6. Bar diameter and bond: large beam bars passing through interior joints should be limited relative to column depth to prevent slipping.

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

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.

Meaning

Ductility is the ability of a structure or member to undergo large deformation beyond the elastic limit, without a sudden loss of strength, so that it can absorb and dissipate energy. Ductility ratio $\mu = \Delta_u/\Delta_y$.

Significance in RC structures

• Warning before failure: large cracks and deflections occur first, so occupants can escape; brittle failure gives no warning.
• Earthquake resistance: a ductile building can be designed for a force much smaller than the elastic demand, using the response reduction factor $R$ (IS 1893) because yielding dissipates energy. Without ductility, the structure would need to stay elastic at a huge cost.
• Moment redistribution: ductile sections allow redistribution of moments in continuous beams, giving economy.
• Resistance to overload and unforeseen actions such as settlement, blast, impact or temperature.
• Prevents collapse: hinges form in beams first (strong column-weak beam), keeping the vertical load path intact.
• Better use of material: yielding steel and confined concrete use their full strain capacity.

Factors affecting ductility

1. Tension steel ratio: higher $\rho$ gives lower ductility; under-reinforced sections are ductile.
2. Compression steel: reduces neutral axis depth and raises ductility.
3. Grade of steel: high-strength steel with small elongation reduces ductility; Fe 415/500 with good elongation is preferred.
4. Grade of concrete: higher-strength concrete is more brittle (smaller ultimate strain).
5. Confinement: closely spaced stirrups/hoops increase concrete strain capacity.
6. Axial load: high axial load reduces ductility of columns.
7. Shear and bond: shear or bond failure prevents flexural ductility from developing.
8. Detailing of anchorage and lap: poor detailing causes 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 top and bottom.
• Bottom steel at a joint face $\ge 50\%$ of top steel; capacity anywhere $\ge 25\%$ of the maximum end capacity.
• Splices in the middle half only, hoops $\le 150$ mm over the lap; none in the joint or within $2d$.
• Closed stirrups with $135^\circ$ hooks, tail $10\phi$; diameter $\ge 6$ mm (8 mm for span > 5 m).
• Spacing: $\min(d/4,\ 8\phi,\ 100)$ mm within $2d$ of supports, first stirrup at 50 mm; $\le d/2$ elsewhere.
• Shear design for hinge capacity.

Ductile design of beam flexural reinforcement

1. Analyse the frame for gravity and seismic load combinations ($1.5(DL\pm EL)$, $1.2(DL+LL\pm EL)$, $0.9DL \pm 1.5EL$) and get design hogging and sagging moments at the faces of supports.
2. Check geometry: $b \ge 200$ mm, $b/D \ge 0.3$, $D \le L/4$.
3. Design the steel for $M_u$ using IS 456 limit state design, keeping $x_u \le x_{u,max}$.
4. Detail it: $\rho_{min} = 0.24\sqrt{f_{ck}}/f_y \le \rho \le 2.5\%$; two bars continuous at top and bottom; bottom steel at joint face $\ge 50\%$ of top steel; capacity at any section $\ge 25\%$ of maximum end capacity.
5. Shear: design for the shear from hinge capacities,

$$V_{u} = V_{u,a}^{D+L} \pm 1.4\,\frac{M_{u,lim}^{As} + M_{u,lim}^{Bh}}{L_{AB}}$$

where $M_{u,lim}$ are the moments of resistance of the sagging and hogging steel provided at the two ends A and B. Provide closed stirrups with $135^\circ$ hooks, spacing $\le \min(d/4,\ 8\phi,\ 100)$ within $2d$ of the joint.

Ductile design of columns (axial load plus biaxial bending)

1. Size: $b \ge 200$ mm and $b/D \ge 0.4$.
2. Design for $P_u$ and biaxial moments $M_{ux}$, $M_{uy}$ using IS 456 cl. 39.6:

$$\left(\frac{M_{ux}}{M_{ux1}}\right)^{\alpha_n} + \left(\frac{M_{uy}}{M_{uy1}}\right)^{\alpha_n} \le 1$$

with $\alpha_n$ from $P_u/P_{uz}$ (1.0 to 2.0). Steel between 0.8% and 6% (4% at laps). 3. Strong column-weak beam: $\sum M_{c} \ge 1.1\ (\text{to}\ 1.4)\sum M_b$ at each joint. 4. Column shear: $V_u = 1.4\,\dfrac{M_{u,lim}^{bL} + M_{u,lim}^{bR}}{h_{st}}$; provide confining hoops over $l_o = \max(D,\ h/6,\ 450)$ at 75-100 mm, with $A_{sh} = 0.18\,s\,h\,(f_{ck}/f_y)(A_g/A_k-1)$.

 BEAM: |hoops 2d @ <=100|   d/2    |hoops 2d @ <=100|
 COLUMN: hoops lo @ 75-100 | normal | hoops lo @ 75-100

Ductile detailing is the arrangement of reinforcement (IS 13920) that lets RC members deform plastically in an earthquake without brittle failure.

Importance

• Allows design for a reduced seismic force ($R$ factor in IS 1893), so the building is economical.
• Dissipates energy through hinges, preventing sudden collapse and saving lives.
• Gives warning before failure through large deformation.
• Confined concrete has greater strain capacity and strength.
• Prevents brittle shear, bond and joint failures.
• Moves hinges to the beams, keeping the columns, which carry gravity load, intact.

Beam detailing

 |-2d-|------- d/2 --------|-2d-|
 ||||| |  |  |  |  |  |  | |||||   closed hoops
 =====================================  2 bars continuous
 ===  =====================  ===      top / bottom
  s<=min(d/4,8phi,100)       lap in middle half

• Closed stirrups with $135^\circ$ hooks and $10\phi$ tails; first at 50 mm; $s \le \min(d/4,\ 8\phi,\ 100)$ over $2d$; $\le d/2$ elsewhere.
• Bottom bars at the joint face $\ge$ 50% of top bars.

Column detailing

  --------------
  | ##########  |  lo = max(D, h/6, 450)
  | ##########  |  s = 75-100 mm
  |     #  #     |  normal spacing in
  |     #  #     |  mid-height
  | ##########  |  lo again
  --------------

• Hoops with $135^\circ$ hooks, tail $6\phi$; splices only in the middle half.
• Strong column - weak beam at each joint.

Philosophy of design in earthquake-prone regions

It is uneconomical to design buildings to remain elastic in a severe earthquake. The accepted philosophy (IS 1893, NBC 105) is:

• Minor, frequent shaking: the structure should suffer no damage (stays elastic).
• Moderate shaking: structural damage is limited and repairable; some non-structural damage is acceptable.
• Severe, rare shaking (design earthquake): the structure may be heavily damaged but should not collapse, so life is protected.

This is achieved by combining adequate strength, stiffness and, above all, ductility.

Design for strength

The structure is designed for the design lateral force instead of the full elastic force:

$$A_h = \frac{Z}{2}\cdot\frac{I}{R}\cdot\frac{S_a}{g}, \qquad V_B = A_h W$$

where $Z$ is the zone factor, $I$ the importance factor, $R$ the response reduction factor and $S_a/g$ the spectral acceleration. The base shear is distributed over the height ($Q_i = V_B\,W_i h_i^2/\sum W_j h_j^2$) and members are designed with load combinations such as $1.2(DL+LL\pm EL)$, $1.5(DL\pm EL)$ and $0.9DL \pm 1.5EL$.

Design for ductility

Because $R > 1$ allows lower strength, the structure must be able to yield and deform inelastically in a controlled manner. This is ensured by:

• under-reinforced sections and limited steel;
• strong column - weak beam, with hinges forming in beams;
• capacity design for shear (shear capacity greater than flexural);
• confined hoops (closely spaced, $135^\circ$ hooks) at beam and column ends and joints;
• proper anchorage and splice locations (IS 13920);
• regular configuration with no soft storey or short column.

Earthquake loads are considered as equivalent static lateral forces (or by response spectrum analysis for tall or irregular buildings), as per IS 1893 (Part 1) or NBC 105:2020 in Nepal.

Steps

1. Seismic weight $W$ = dead load + a percentage of live load (25% if live load $\le 3$ kN/m$^2$, 50% if more; roof live load is neglected).
2. Time period of a bare RC frame: $T = 0.075\,h^{0.75}$ (s), $h$ in m.
3. Design base shear:

$$V_B = A_h W,\qquad A_h = \frac{Z}{2}\frac{I}{R}\frac{S_a}{g}$$

with $Z$ from the zone map, $I$ importance factor, $R$ response reduction factor (5 for special moment resisting RC frames, 3 for ordinary) and $S_a/g$ from the spectrum for soil type. 4. Distribute over height: $Q_i = V_B \dfrac{W_i h_i^2}{\sum W_j h_j^2}$ and apply at each floor in both directions (plus 30% of the orthogonal force). 5. Load combinations (IS 456 cl. 18.2): $1.5(DL+LL)$, $1.2(DL+LL\pm EL)$, $1.5(DL\pm EL)$, $0.9DL\pm 1.5EL$. 6. Design and detail members for the worst combination and provide ductile detailing as per IS 13920.