Ductile detailing of reinforced concrete structures subjected to seismic forces - Code of practice

IS 13920: Scope & Key Parameters

IS 13920 covers ductile detailing of reinforced concrete structures subject to seismic forces, focusing on:

Key Symbols & Definitions (Clause 1.2 & 3.8.2)

Important Specifications

• Loads: Dead + Live loads factored by 1.2 for shear calculations.
• Material: Concrete and steel properties as per IS 456 and IS 1786.
• Reinforcement: Detailing for ductility, including minimum and maximum reinforcement ratios.
• Member Dimensions: All dimensions in mm, stresses in MPa, loads in N.
• Shear & Moment Resistance: Design shear and moment capacities must satisfy factored forces.

Typical Shear Force Design Formula

[ V_u = 1.2 \times (Dead\ Load + Live\ Load) ]

Neutral Axis Depth (approximate)

[ x_u = \frac{0.36 f_{ck} b d}{f_y \rho} ]

flowchart LR
    Loads[Dead + Live Loads]
    Loads -->|Factor 1.2

IS 13920 Key References: Formulas, Tables & Specifications

1. Shear Forces & Resistances

• Factored shear force at beam ends A & B:
  [ V_u = 1.2 \times (D + L) ]
  where D = dead load, L = live load.

• Shear resistance at joint:
  Must resist factored shear (V_u) with adequate reinforcement.

• Shear force to be resisted by reinforcement:
  [ V_s = V_u - V_c ]
  where (V_c) is concrete shear capacity.

2. Neutral Axis & Reinforcement

• Depth of neutral axis (x):
  Depends on section and reinforcement; used in flexure-shear interaction.

• Inclination of diagonal reinforcement (α):
  Typically between 45° to 60° for coupling beams.

• Effective depth (d):
  Distance from extreme compression fiber to centroid of tensile reinforcement.

3. Material Properties

• Elastic modulus of steel: (E_s = 2 \times 10^5 \text{ MPa})
• Characteristic compressive strength of concrete: (f_{ck}) (e.g., 25, 30 MPa)
• Yield stress of steel: (f_y) (e.g., 415 MPa)

4. Confining Reinforcement

• Special confining reinforcement:
  As per Clauses 7-4-1, 8.1, 8.2; minimum spacing ≤ 300 mm.
• Nominal shear stress:
  [ \tau_v = \frac{V_u}{b \times d} ]
  where b = width of section.

5. Important Figures & Tables

• Fig. 8: Design shear force for columns
• Fig. 9: Column & joint detailing
• Fig. 10: Special confining reinforcement in footings
• Fig. 11: Confining reinforcement under discontinuous walls
• Clause 5: Material specs for lateral force resisting elements

Summary Diagram: Shear Force & Reinforcement Interaction

flowchart TD
   

IS 13920 Definitions: Key Formulas, Tables & Symbols

1. Shear Forces & Resistances

• Shear at beam ends A & B (factored):
  [ V_u = 1.2 \times (Dead\ Load + Live\ Load) ]
• Shear resistance at joint: ( V_c ) (concrete) + ( V_s ) (steel reinforcement)
• Shear force to be resisted by reinforcement:
  [ V_s = V_u - V_c ]

2. Neutral Axis Depth

• Depth from extreme compression fiber: ( x_u )

3. Reinforcement & Material Properties

4. Cross-sectional Areas & Reinforcement

5. Moments & Loads

IS 13920: 9.1 General Requirements — Key Formulas & Specifications

1. Shear Forces at Beam Ends (Clause 1.2)

• Shear at end A or B with partial safety factor, γ = 1.2:

  [ V_u = 1.2 \times (V_{dead} + V_{live}) ]

• Factored shear force at joint:

  [ V_u = \text{Shear resistance required} ]

2. Shear Resistance & Reinforcement

• Shear force to be resisted by reinforcement:

  [ V_s = V_u - V_c ]

  where (V_c) = nominal shear strength of concrete.

• Depth of neutral axis (x) from extreme compression fibre is used to calculate moment and strain compatibility.

3. Important Parameters

4. Material Specifications (Clause 5)

• Lateral force resisting elements must use materials conforming to IS 1786 for steel and IS 456 for concrete.
• Reinforcement detailing per IS 13920 ensures ductility and confinement.

Summary Diagram: Shear Force & Reinforcement Interaction

flowchart LR
    A[Dead + Live Loads] -->|Factor 1.2| B[

IS 13920: Key Material Specifications & Formulas

Material Properties & Symbols (Clause 1.2 & 3.8.2)

Important Formulas

• Factored Shear Force at Beam Ends: [ V_u = 1.2 \times (Dead Load + Live Load) ]

• Shear Resistance at Joint: [ V_c = \tau_c \times b_w \times d ] where (\tau_c) = nominal shear stress

• Neutral Axis Depth (x_u): [ x_u = \frac{0.87 f_y A_s}{0.36 f_{ck} b} ]

• Vertical Reinforcement Ratio: [ \rho = \frac{A_{st}}{b_w \times d} ]

• Maximum & Minimum Tension Reinforcement Ratios: [ \rho_{max} \approx 0.025, \quad \rho_{min} \approx 0.0025 ]

Material Specifications

• Use Fe 415 or Fe 500 grade steel as per IS 1786:1985.
• High strength deformed bars (Fe 500, Fe 550)

IS 13920: Design & Detailing of Beams - Key Points

1. Shear Force Calculations (Clause 1.2)

• Shear at ends A & B:
  ( V_u = 1.2 \times (Dead, Load + Live, Load) )
  (Partial safety factor of 1.2 on loads)

• Factored Shear Force at Joint:
  ( V_{u,joint} = \text{Sum of factored shear forces from connected members} )

• Shear to be resisted by reinforcement:
  ( V_s = V_u - V_c )
  where ( V_c ) = shear resisted by concrete.

2. Neutral Axis Depth (x)

• Depth from extreme compression fiber is calculated based on equilibrium of forces in beam section.

3. Reinforcement Detailing

• Diagonal reinforcement inclination (α): angle of coupling beam stirrups.
• Effective depth (d): distance from extreme compression fiber to centroid of tensile reinforcement.
• Nominal shear stress:
  ( \tau_v = \frac{V_u}{b \times d} )
  where ( b ) = width of beam.

4. Material Properties

• ( f_{ck} ) = characteristic compressive strength of concrete cube.
• ( f_y ) = yield stress of steel.
• ( E_s ) = elastic modulus of steel (~200 GPa).

5. Detailing Requirements (Clause 5 & others)

• Minimum and maximum reinforcement limits for flexural members.
• Longitudinal reinforcement splices and anchorage must be detailed explicitly.
• Transverse reinforcement (stirrups) designed to resist shear and provide ductility.
• Special confining reinforcement for joints and columns as per clauses 7.4.1, 8.1, 8.2.
• Development length of bars must be ensured for anchorage.

Summary Table: Shear Design Parameters

IS 13920: Key Formulas & Specifications for Design and Detailing of Columns

1. Design Shear Force for Columns

• Refer Fig. 8 for calculation methodology of design shear force considering axial load and flexure.
• Shear design must include effects of seismic forces and axial loads.

2. Special Confining Reinforcement (Clause 7.4.1 & Fig. 9, 10, 11)

• Required in regions expected to undergo cyclic inelastic deformations (plastic hinge regions).
• Minimum spacing: ≤ 300 mm.
• Transverse reinforcement (hoops/stirrups) must confine the core concrete to enhance ductility.
• Hoop spacing ≤ min(d/4, 8db)
  where:
  • d = effective depth of column
  • db = diameter of longitudinal bar

3. Transverse Reinforcement (Clause 7.3.3 & 7.2.1)

• Provide closely spaced hoops/stirrups in plastic hinge zones.
• Minimum transverse reinforcement as per IS 456 if outside seismic zones or non-structural projections.

4. Longitudinal Reinforcement (Clause 7.2.2)

• Minimum 2 bars along top and bottom faces for projections > 100 mm beyond confined core.
• Minimum longitudinal steel as per IS 456:1978 if the projection is non-structural.

5. Development Length

• Must satisfy IS 13920 provisions to ensure anchorage of longitudinal bars in plastic hinge regions.

Summary Table for Hoop Spacing

flowchart TD
    A[Column Core] --> B[Confined Core with Hoops]
    B --> C[Plastic Hinge Region]
    C --> D[Special Confining Reinforcement ≤ 300 mm]
    B --> E[Longitudinal Bars ≥ 2]
    E --> F[Development Length as per IS 13920]

References:

IS 13920: Design & Detailing of Coupling Beams (Clauses 9.5.1 - 9.5.3)

Key Formulas & Specifications

• Shear Stress Limit for Diagonal Reinforcement:

  If
  [ \frac{V}{bD} > 0.25 \sqrt{f_{ck}} ] where

  • (V) = earthquake-induced shear force
  • (b) = width of beam
  • (D) = overall depth of beam
  • (f_{ck}) = characteristic compressive strength of concrete (MPa)

  Then, entire shear and flexure shall be resisted by diagonal reinforcement.

• Diagonal Reinforcement Area (Clause 9.5.2):

  [ A_{sv} = \frac{V}{0.87 f_y \cot \alpha} ]

  where

  • (A_{sv}) = area of reinforcement along each diagonal
  • (V) = shear force to be resisted by reinforcement
  • (f_y) = yield stress of steel
  • (\alpha) = inclination angle of diagonal bars

• Anchorage Length (Clause 9.5.3):

  Diagonal/horizontal bars anchorage in walls =
  [ 1.5 \times l_d ] where (l_d) = development length in tension as per IS 456.

Important Parameters

Summary Diagram of Coupling Beam Reinforcement

flowchart LR
    A[Coupling Beam] --> B[Diagonal Reinforcement]
    B --> C[Anchored into Adjacent Walls]
   

IS 13920: Design & Detailing of Shear Walls - Key Points

1. Reinforcement Requirements (Clause 9.1.4)

• Minimum longitudinal & transverse reinforcement ratio:
  [ \rho_{min} = 0.0025 \times A_g ] where (A_g) = gross cross-sectional area of the wall.
• Reinforcement must be uniformly distributed across the wall section.

2. Shear & Flexural Strength

• Shear strength and flexural strength must be estimated considering:
  • Concrete contribution,
  • Reinforcement contribution,
  • Boundary elements' strength.
• Use boundary elements (heavily reinforced vertical edges) to resist flexure.

3. Detailing Provisions

• Boundary elements: Provide closely spaced ties/stirrups to confine concrete.
• Wall web: Uniformly spaced vertical and horizontal reinforcement.
• Coupling beams (Clause 9.5): Special detailing with diagonal reinforcement to resist shear.
• Openings & joints: Reinforcement around openings and construction joints must ensure continuity and stress transfer.
• Development & anchorage: Proper anchorage length and splicing as per IS 456.

Typical Reinforcement Detailing Summary

flowchart LR
    A[Shear Wall] --> B[Boundary Elements]
    A --> C[Wall Web Reinforcement]
    A --> D[Coupling Beams]
    A --> E[Openings & Joints]
    B --> F[Heavy Vertical Bars + Ties]
    C --> G[Uniform Vertical & Horizontal Bars]
    D --> H[Diagonal + Horizontal Bars]
    E --> I[Additional Reinforcement]

References:

• IS 13920: Clause 9.1.4 (Reinforcement ratios), 9.5

IS 13920: Development, Splicing & Anchorage of Reinforcement

1. Development Length (Ld) in Tension

• Minimum lap/splice length ≥ Ld (development length in tension).

• Depends on bar diameter (db), concrete strength, and bar grade.

• Typical formula (per IS 13920/IS 456):

  [ L_d = \frac{\phi \times \sigma_{s}}{4 \times \tau_{bd}} ]

  Where:

  • (\phi) = bar diameter (db)
  • (\sigma_s) = stress in steel (usually 0.87 fy)
  • (\tau_{bd}) = design bond stress

2. Lap Splicing (Clause 6.2.6)

• Hoops provided over entire splice length at ≤ 150 mm spacing.
• Lap length ≥ development length in tension.
• Restrictions:
  • No lap splices inside joints.
  • No lap splices within 2d (effective depth) from joint face.
  • No lap splices within ¼ length of flexural yielding zones.
• Max 50% bars spliced at one section.

3. Anchorage in Joints (Clause 6.2.5)

• External Joint: Anchorage length beyond column face =
  [ L_d + 10 \times d_b - \text{allowance for 90° bend(s)} ]
• Internal Joint: Bars continue through column without anchorage length.

4. Confining Reinforcement

• Special confining reinforcement as per Clauses 7.3.3, 7-4-1, 8.1, 8-2.
• Minimum spacing of hoops: ≤ 300 mm.
• Detailed in Figures 8-12 (joint and column detailing).

Summary Table: Lap Splice & Anchorage

IS 13920: Construction Joints and Openings – Key Points

1. Construction Joints (Clause 9.8)

• Vertical reinforcement ratio across a horizontal joint must satisfy:

  [ \rho_v \geq \frac{t_y}{f_y} ]

  where:

  • ( t_y ) = factored shear stress at the joint
  • ( P_u ) = factored axial force (compression positive)
  • ( A_g ) = gross cross-sectional area
  • ( f_y ) = yield strength of steel

• Shear reinforcement must resist the factored shear force at the joint considering dead/live loads with partial safety factor 1.2.

• Neutral axis depth, diagonal reinforcement inclination (α), and effective depths are critical for design.

2. Openings in Walls (Clause 9.6.2)

• Provide reinforcement along edges of openings equal to the area of interrupted bars.
• Vertical bars must extend the full storey height.
• Horizontal bars require adequate development length beyond opening edges to ensure tension transfer.

Typical Reinforcement Detailing for Openings

Summary Diagram for Opening Reinforcement

flowchart LR
    A[Wall with Opening] --> B[Vertical Bars along edges]
    A --> C[Horizontal Bars along edges]
    B --> D[Extend full storey height]
    C --> E[Provide development length beyond opening]

For detailed shear stress and reinforcement calculations, refer to IS 13920 Clause 9.8 and related figures (Fig. 8, 9, 10).

IS 13920: Special Confining Reinforcement (Clause 7.4.1)

Key Specifications:

• Length of special confining reinforcement (l') from each joint face towards mid-span:

  • Not less than the largest lateral dimension of the member at the section where yielding occurs.
  • Not less than 1/6 of the clear span of the member.
  • Not less than 450 mm.

• This reinforcement is mandatory at:

  • Each joint face.
  • Any section where flexural yielding due to earthquake forces may occur.

Transverse Reinforcement Details (Clause 7.3 & 7.4):

• Provide hoops with crossties for confinement.
• h (spacing or dimension for hoops) = larger of hc (column dimension) and Bc (beam dimension).
• For columns with Bc > 300 mm, use hoops with crossties.
• Overlapping hoops with crossties are recommended for enhanced confinement.

Summary Table for Length l':

Conceptual Diagram of Special Confining Reinforcement:

graph LR
  A[Joint Face] -->|Length l'| B[Special Confining Reinforcement Zone]
  B --> C[Mid-span]
  B -.-> D[Flexural Yielding Zone]
  subgraph Transverse Reinforcement
    E[Hoops] --> F[Crossties]
  end

Note: Always check if shear requirements demand more transverse reinforcement than special confining reinforcement. Use the larger amount.

IS 13920: Discontinuous Walls (Clause 9.7) – Key Points

• Definition: Discontinuous walls are walls that do not extend over the full height of the supporting column.
• Requirement: Columns supporting discontinuous walls require special confining reinforcement as per Clause 7.4.4 to ensure ductility and confinement.

Special Confining Reinforcement (Clause 7.4.4)

• Minimum length of special confining reinforcement: ≥ 300 mm beyond the discontinuity.
• Detailing as per Fig. 11 in IS 13920 shows the arrangement around the column to confine the region near the discontinuity.
• Reinforcement typically includes closely spaced ties or hoops with hooks to provide confinement.

Related Specifications:

Conceptual Diagram (Simplified):

graph TB
    A[Column] --> B[Discontinuous Wall]
    B --> C{Discontinuity Zone}
    C --> D[Special Confining Reinforcement ≥ 300 mm]
    D --> E[Transverse Ties & Hoops]

Summary:

• Provide special confining reinforcement around columns at discontinuity zones.
• Reinforcement must extend at least 300 mm beyond the discontinuity.
• Follow detailing in Fig. 11 and related clauses for transverse and joint reinforcement.
• Ensures ductility and prevents brittle failure near discontinuities.

For detailed bar spacing, anchorage, and development length, refer to Clauses 7.4.4, 7.3.3, 8.1, and Fig. 11 of IS 13920.

IS 13920: Calculation of Shear and Flexural Strength – Key Points

1. Shear Strength (Clause 9.2 & 1.2)

• Factored Shear Force (V_u):
  [ V_u = 1.2 \times (D + L) ] where D = dead load, L = live load.

• Shear Resistance at Joint:
  Shear resistance depends on concrete strength, reinforcement, and geometry.

• Shear Force to be Resisted by Reinforcement:
  [ V_{s} = V_u - V_c ] where ( V_c ) = shear carried by concrete.

• Nominal Shear Stress:
  [ \tau_v = \frac{V_u}{b \times d} ] where b = width, d = effective depth.

• Inclination of Diagonal Reinforcement (α): Used in coupling beams for shear reinforcement design.

2. Flexural Strength (Clause 9.3)

• Flexural strength is governed by the moment capacity of the section considering:

  • Effective depth (d)
  • Yield stress of steel (f_y)
  • Characteristic compressive strength of concrete (f_ck)
  • Depth of neutral axis (x_u)

• Moment of Resistance (M_u):
  [ M_u = 0.87 f_y A_{st} (d - \frac{x_u}{2}) ] where ( A_{st} ) = area of tension reinforcement.

3. Important Parameters

IS 13920: Annexes & Committee Composition Summary

Annex A: Moment of Resistance of Rectangular Shear Wall Section

• Applicable for slender rectangular shear walls with vertical reinforcement.

Key formulas:

1. For ( \frac{x_u}{w} < \frac{x_i}{w} ): [ M_{uv} = f_{ck} t_w \frac{w^2}{2} \left(1 + \frac{I_2}{\lambda}\right) ] where,

• ( p = \frac{A_{st}}{t_w w} ) (vertical reinforcement ratio),
• ( p = \frac{0.87 f_y}{0.0035 E_s} ),
• ( E_s ) = Modulus of elasticity of steel,
• ( P_u ) = Axial compression on wall.

2. For ( \frac{x_i}{w} < \frac{x_u}{w} < 1.0 ), moment is calculated through quadratic relations involving parameters ( a, a_s, x_u ) (refer to IS 13920 Annex A for detailed equations).

• Concrete stress-strain as per IS 456:1978.
• Steel modeled as bilinear.

Annex B: Committee Composition (CED 39 - Earthquake Engineering Sectional Committee)

• Chairman: Dr. A. S. Arya, Roorkee
• Members: Representatives from Indian Roads Congress, BHEL, CSIR, Universities, Meteorological Dept, Railways, Power Corporations, CPRI, CPWD, BIS, and others.
• Includes experts from government, research institutes, and industry.

Summary Table: Moment of Resistance Parameters

This annex provides essential formulas for design of shear walls under combined bending and axial loads, and lists the expert committee responsible for the standard's formulation.

If you need detailed derivations or design examples,