Explanatory Handbook to IRC:112-2011: Code of Practice for Concrete Roads Bridges

IRC SP 105 - Scope: Key Points & Specifications

Scope Overview:

• IRC SP 105-2015 covers design, analysis, and detailing of concrete bridges.
• It includes material properties, design values, limit states, durability, and workmanship.
• Applicable for linear and nonlinear analysis of bridge elements under various loads.

Key Specifications from the Code:

Creep Strain Variation Table (Summary):

Formula for Creep Coefficient:

[ PO = PRH \times B(fcm) \times B(t) ]

Where:

• PRH, B(fcm), B(t) are factors from Annexure A2.

Summary Diagram:

flowchart LR
    A[Material Properties] --> B[Modulus of Elasticity (E) = 34000 MPa]
    B --> C[Creep Coefficient PO = 

Key Formulas & Specifications for Design Bending Moments (IRC SP 105)

1. Ultimate Limit State Moments (Clause 8.2)

• Moment due to Concentrated Load: Refer to Fig. 3 (overhanging beam example)
• Moment due to Self-weight: Refer to Fig. 4
• Moment due to Variable (Live) Load: Refer to Fig. 5 & 6

2. Continuous Beam Moments (Clause 8.3)

• Dead Load Moment at mid-span AB:
  [ M_{AB} = 0.08 \times L^2 \times w_d ]
• Dead Load Moment at support B:
  [ M_B = -0.1 \times L^2 \times w_d ]
• Dead Load Moment at mid-span BC:
  [ M_{BC} = 0.025 \times L^2 \times w_d ]

Where:

• (L = 5.2,m) (example)
• (w_d = 30,kN/m) (Dead load)

3. Load Combinations (Clause 18.75)

• Rare Combination Moment:
  [ M = 1.0 \times M_{live} + 0.75 \times M_{dead} ]
• Quasi-permanent Combination: Only Dead Load acts.

4. Design Bending Moment (Clause 9.3.2.2)

[ M_{Ed} = M_{0Ed} + M_2 ]

• (M_{0Ed}): First-order moment (including imperfections)
• (M_2): Second-order moment (accounting for effective length and boundary conditions)

Equivalent first-order end moment: [ M_{0e} = 0.6 M_{02} + 0.

Punching Shear Design: IRC SP 105 (Clause 8.4, 10.12)

Key Formulas

• Punching Shear Stress:

[ V_{Ed} = \frac{B \times U \times F_{Ed}}{d} ]

Where:

• (B) = correction factor (1 for axial load, else calculated for bending)

• (U) = control perimeter (m)

• (F_{Ed}) = design shear force

• (d) = effective depth of slab (m)

• Control Perimeter (U):

• Allowable Shear Stress:

[ V_{Rd,max} = 0.5 \times V_{fcd} = 0.5 \times 0.6 (1 - f_{ck}/310) f_{ck}^{1/2} = 0.134 (1 - f_{ck}/310) f_{ck}^{1/2} ]

• Punching Shear Check:

[ V_{Ed} \leq V_{Rd,max} ]

If not satisfied, redesign by:

• Increasing slab thickness
• Increasing concrete grade (f_{ck})
• Increasing reinforcement

Summary Table for (V_{Rd,max})

Design Steps Flowchart (Simplified)

flowchart TD
    A[Calculate \(V_{Ed}\)] --> B[Calculate control perimeter \(U\)]
    B --> C[Calculate \(V_{Rd,max}\)]
    C --> D{Is \(V_{Ed} \leq V_{Rd,max}\)?}
    D -- Yes --> E[Design OK, no shear reinforcement needed

IRC SP 105: Crack Control & Reinforcement Detailing Summary

Key Points from IRC SP 105 (Clauses 12.2, 12.3.4, and 10.3.3):

• Crack control is ensured by limiting reinforcement stress or bar size/spacing using Tables 12.2 and 12.3.
• For cracks due to direct actions (loads/moments), either Table 12.2 (bar diameter vs. stress) or Table 12.3 (bar spacing vs. stress) can be used.
• For cracks due to restraint actions (shrinkage/temperature), only Table 12.2 applies.
• Reinforcement stress must remain elastic (no yielding) to control crack widths effectively.
• Minimum reinforcement is required to control cracking, estimated by balancing tensile forces in concrete and steel before cracking.
• Crack width limits commonly used: 0.2 mm and 0.3 mm.

Fundamental Formulas:

1. Cracking load in tension:

[ N_o = A \times f_{cm} ]

• (N_o) = cracking load
• (A) = concrete area in tension
• (f_{cm}) = mean tensile strength of concrete

2. Reinforcement force at cracking:

[ N_s = A_s \times f_s ]

• (A_s) = steel area
• (f_s) = stress in steel (must be < yield stress)

3. Equilibrium for crack control:

[ N_s \geq k \times N_o ]

• (k) = factor accounting for stress variation due to bending, shrinkage, temperature

Simplified Crack Control Tables (Conceptual):

Key Points from IRC SP 105 on Prestressing Systems and Curved Tendons

1. Curved Tendons in Thin Sections (Clause 5.8 & 7.10)

• Curved tendons in slabs or shells induce inward, in-plane, and out-of-plane pressures causing local punching shear.
• Webs with curved tendons experience inward thrust, resisted by the web acting as a curved slab.
• Refer Chapter 19 for internal tensile stress derivation due to curvature.

2. Prestressing Steel and Untensioned Reinforcement (Clause 12.3.6)

• Prestress can be treated as an external force; ignore concrete tension.
• For crack control in pre-tensioned beams, use Tables 12.2 & 12.3 with: [ \text{Steel stress} = \text{Total tendon stress after cracking} - \text{Initial prestress after losses} ]
• Avoid sudden section changes; if unavoidable, check stresses by calculation.

3. Losses Due to Friction and Wobble (Clause 7.9.3.2)

• Loss formula for friction & wobble: [ P_x = P_0 e^{-(\mu \alpha + kx)} ] where:
  • (P_x) = stress at distance (x),
  • (P_0) = initial stress,
  • (\mu) = coefficient of friction,
  • (\alpha) = total angular deviation,
  • (k) = wobble coefficient.
• Values of (\mu) and (k) depend on site conditions and must be verified on site.

Summary Table: Friction & Wobble Coefficients (Typical)

Conceptual Diagram: Curved Tendon Effects

flowchart LR
    A[Curved Tendon] --> B[Inward Pressure on Section]
    B --> C[Punching Shear at Tend

Shear Design in Flexural Members (IRC SP 105)

Key Points from Clause 8.2 & 8.2.1:

• Shear arises from:
  • Flexure
  • Interface shear (concrete cast at different times)
  • Shear between flange & web in flanged beams
  • Punching shear
  • Torsional shear
• Design is at Ultimate Limit State.
• Without shear reinforcement: Use empirical formula for shear capacity.
• With shear reinforcement: Use a truss model to calculate required stirrups.
• For concrete grades > M60, shear strength is limited to M60 class to avoid slender web failure.
• Deck slabs (effective width method, Annexure B-3) exempt from flexural shear check.

Shear Strength of Concrete (No Shear Reinforcement)

[ V_{c} = \alpha \times \sqrt{f_{ck}} \times b \times d ]

• (V_c): Shear capacity of concrete
• (f_{ck}): Characteristic compressive strength (limited to M60)
• (b): Width of web
• (d): Effective depth
• (\alpha): Empirical factor (from code)

Shear Reinforcement (Truss Model)

[ V_s = 0.87 f_y A_{sv} \frac{d}{s} ]

• (V_s): Shear resisted by stirrups
• (f_y): Yield strength of stirrup steel
• (A_{sv}): Area of shear reinforcement in spacing (s)
• (d): Effective depth
• (s): Spacing of stirrups

Summary Flow of Shear Types:

flowchart TD
    A[Shear in Flexural Members] --> B(Flexural Shear)
    A --> C(Interface Shear)
    A --> D(Shear between Flange & Web)
    A --> E(Punching Shear)
    A --> F(Torsional Shear)

Reference: Use Clause 8.2 (Shear design model), Clause 8.2.1 (No shear reinforcement), and Annexure B-3 for deck slabs.

IRC SP 105: Material Specifications & Quality Control - Key Points

1. Material Properties & Design Values

• Steel & Concrete: Follow relevant BIS standards (e.g., IS 1786 for reinforcement, IS 456 for concrete).
• Design Properties: Based on statistical characteristic values (5% fractile for steel tensile strength).
• Concrete Strength Conversion:
  [ f_{ck(cylinder)} = 0.8 \times f_{ck(cube)} ] (Cube strength tested on 150 mm cubes, cylinder strength used for design).

2. Pile Foundation Ductility (Clause 3.2)

• Plastic hinges may form at:
  • Pile top (near pile cap)
  • Locations of max bending moment or soil layer interfaces with different shear deformability.
• Confinement Reinforcement:
  • At pile top: vertical length = 3 × pile diameter if pile cap rotation is restrained.
  • At second peak bending moment: length = 2 × pile diameter on either side.
• Use soil-structure interaction analysis for accurate hinge location.

3. Quality Control

• Materials must meet minimum BIS specs or equivalent international standards.
• For existing bridges, use standards valid at construction time.
• Concrete properties derived from cube tests; steel properties from manufacturer specs.
• For higher accuracy, use statistically reliable test data or advanced property models (Annexure A-2).

Summary Table: Confinement Reinforcement Length for Piles

flowchart TD
    A[Pile Foundation] --> B[Plastic Hinge Locations]
    B --> C[Top of Pile]
    B --> D[Max Bending Moment Location]
    B --> E[Soil Layer Interface]

    C --> F[Confinement Reinforcement: 3 × Dia]
    D --> G[Confinement Reinforcement: 2 × Dia each side]
    E --> G

References:

• IRC:SP:105-2015, Chapter 16 Section 18

IRC SP 105: Analysis Methods and Design Approaches (Summary)

Key Points from Clause 13.4 & Section 7:

• Design Stress in Compression (Example):
  [ V_f = 0.6 \times 1 - I_{ck} \times f = 0.5419 \times 13.4 = 7.261 \text{ MPa} ] Where:
  • (I_{ck}) = characteristic strength factor
  • (f) = stress factor
  • (V_f) = design compressive stress
• If the actual stress (\sigma < V_f), the section is safe in compression.

Analysis Methods (Clause 5.1.2 & Section 7):

• Classical Methods:

  • Simplified mathematical models for hand calculations (e.g., elastic analysis, approximate methods).
  • Useful for preliminary design and verification.

• Modern Methods:

  • Computerized, automated tools using realistic models (finite element analysis, non-linear analysis).
  • Capture complex behavior under various loading conditions.

Design Approach:

Recommendations:

• Use classical methods for simple cases and initial sizing.
• Use modern methods for detailed design and complex structures.
• Always verify that stresses satisfy code limits (e.g., ( \sigma < V_f )).

flowchart LR
    A[Bridge Design] --> B[Classical Analysis]
    A --> C[Modern Computerized Analysis]
    B --> D[Elastic Theory]
    B --> E[Simplified Models]
    C --> F[Finite Element Method]
    C --> G[Non-linear Analysis]
    F --> H[Detailed Stress & Deflection]
    G --> H

For detailed formulas and procedures, refer to Section 19 of IRC SP 105 Explanatory Handbook and standard structural analysis textbooks.

Ductile Detailing for Seismic Resistance (IRC SP 105 - Section 17)

Key provisions to ensure ductility in seismic zones III, IV & V:

1. Plastic Hinge Formation

• Plastic hinges should form in substructures (pier base), not foundations.
• Curtailment of longitudinal reinforcement allowed only in tall piers after confirming plastic hinge won't form beyond curtailment.
• No explicit definition of "tall pier" in IRC; refer to international codes (e.g., AASHTO, Eurocode).

2. Sliding Wedge Mechanism (Clause 16.10)

• Reinforcement parallel to loaded face to depth as per Fig. 16.10.
• Reinforcement area:
  [ A_{fu} \geq \frac{F}{2} ] where:
  • (A_{fu}) = area of reinforcement
  • (F) = applied force
• Reinforcement uniformly distributed over height (y_d) or (h).
• Closed links required for anchorage.

3. Suspension Reinforcement (Clause C14.12)

• Required where load transfers indirectly (e.g., beam on beam).
• Adds to reinforcement for other effects.

4. Anchorage Zones for Post-Tensioning (Clause C14.13)

• Length of anchorage zone = max(depth, width) of section.

Summary Table: Ductile Detailing Checks

flowchart TD
    A[Seismic Zone III, IV, V] --> B[Design for Ductility]
    B --> C[Plastic Hinge at Pier

Key Points from IRC SP 105 on Pile Foundation Design & Reinforcement

Plastic Hinge Locations in Piles (Clause 3.2: C15.3.2)

• Plastic hinges may form at:
  • Pile top (fixed with pile cap)
  • Intermediate level (second peak bending moment, often at soil layer interfaces or scour level)
• Provide confinement reinforcement at these locations to ensure ductility.

Confinement Reinforcement Length

• At pile top: vertical length = 3 × pile diameter if pile cap rotation is restrained.
• At intermediate peak moment: length = 2 × pile diameter on either side of the moment peak (approximate methods).
• For soil-structure interaction methods: confinement at all peak moment points.

Reinforcement Specifications (Material & Quality)

• Use materials conforming to BIS or equivalent standards.
• Reinforcement must be anchored with closed links for confinement.
• Follow seismic detailing for ductility, especially in seismic zones III, IV & V.

Example: Confinement Reinforcement for Circular Piles (from Clause 15.2)

Important Formula for Sliding Wedge Reinforcement (Clause 16.10)

[ A_{fu} \geq \frac{F}{2} ]

• (A_{fu}): Area of reinforcement parallel to loaded face.
• (F): Sliding force.
• Reinforcement must be uniformly distributed over height (h) and anchored with closed links.

graph TD
    A[Pile Foundation] --> B[Plastic Hinge Locations]
    B --> B1[Pile Top (3× Diameter)]
    B --> B2[Intermediate Level (2× Diameter)]
    A --> C

IRC SP 105: Shrinkage, Creep & Long-Term Effects Summary

1. Creep Strain

• Creep Coefficient, ( \phi(t,t_0) ) calculated as per Annexure A2.
• Example values of ( \phi(t,t_0) ) at different days (loading at 14 days):

• Modulus of Elasticity, ( E ) = 34000 MPa
• Elastic strain per 10 MPa stress = ( 2.94 \times 10^{-4} )
• Total creep strain per 10 MPa = ( 5.35 \times 10^{-4} )

Creep strain increments:

2. Shrinkage Strain

• Autogenous Shrinkage Strain (Residual strain):

• Drying Shrinkage Strain (Unrestrained):

| Days | ( \beta_{as}(t,t_s) ) | Drying Shrinkage ( \varepsilon_{cd}(t) \times 10^{6} ) | Residual Drying Shrinkage (×10⁻�

IRC SP 105: Worked Examples & Application Guidance Summary

This handbook supports IRC:112 bridge design with detailed worked examples (e.g., Example 10.3-3) illustrating prestressed concrete calculations.

Key Parameters & Formulas

Example Table Extract (Clause 6.6)

Sign Conventions (IRC SP 105: Clause 2.4.3 & A.2.4.2)

• Positive directions follow the right-hand rule in 3D orthogonal coordinate system.
• Forces and stresses: Tensile stresses and forces are positive; compressive are negative.
• Displacements: Positive in the direction of coordinate axes.
• Consistency is critical for plates, shells, and complex 3D structures (see Fig. A.3 in code).

Load Combinations (IRC SP 105: Clause 3.1, CA1-3)

Load Combination Formula (ULS example)

[ \text{Design Load} = \gamma_G G_k + \gamma_Q Q_k ]

• ( G_k ): Characteristic permanent load
• ( Q_k ): Characteristic variable load
• ( \gamma_G, \gamma_Q ): Partial safety factors from IRC:6 (e.g., 1.35 for dead load, 1.5 for live load)

Variable Actions Combination Rule

• One leading variable action at full factor.
• Other accompanying variable actions reduced by combination factors ( \psi ) (from IRC:6).
• Designer chooses leading variable action iteratively.

Summary of 9 Primary Combinations to Check

flowchart TD
    A[Permanent Loads] --> B[Load Combinations]
    C[Variable Loads] --> B
    B --> D{Combination Type}
    D --> E[Rare]
    D -->

Use of High Strength and Hybrid Materials in IRC SP 105

Key Points from IRC SP 105:

• Hybrid Systems: Combination of two or more materials (e.g., reinforced concrete + structural steel, steel tubes with concrete infill) where each material supplements the other’s capacity.
• Material Compatibility: At ultimate limit state (ULS), bond strain consistency at interfaces is not mandatory, but overall deformation compatibility is essential.
• Pile Foundations & Plastic Hinges:
  • Plastic hinges may form at pile top and intermediate levels (e.g., soil layer interfaces).
  • Provide confinement reinforcement at:
    • Pile top: vertical length = 3 × pile diameter (if pile cap rotation is restricted)
    • Intermediate peak moment locations: 2 × pile diameter on either side (approximate methods)
• Material Specifications:
  • Follow BIS or equivalent international standards for reinforcement, prestressing steel, and concrete.
  • For existing bridges, use material specs valid at construction time.

Typical Confinement Reinforcement Lengths for Pile Plastic Hinges:

Hybrid Material Design Notes:

• Hybrid elements include precast segmental, voided slab, continuous, and pretensioned girder bridges.
• IRC SP 105 encourages use of limit state design as per IRC:112 and related special publications (IRC:SP:64, 65, 66, 71).

Simplified Concept Diagram (Hybrid System):

graph LR
A[Structural Steel] -- Load Sharing --> C[Hybrid Element]
B[Reinforced Concrete] -- Load Sharing --> C
C -- Combined Capacity --> D[Bridge Element]

Summary: Use hybrid materials by combining strengths of components, ensure ductility in piles by confining reinforcement at critical hinge locations, and follow BIS or equivalent standards for material properties.

IRC SP 105 - References and Further Reading: Key Points

• Material Properties & Design Values: See Chapter 4 (Section 6), Page 19 for detailed tables and formulas on material strengths and design parameters.

• Ultimate Limit States:

  • Chapter 8 (Section 10) covers shear, punching shear, and torsion design.
  • Chapter 9 (Section 11) discusses ultimate limit state of induced deformation (Page 109).
  • Chapter 10 (Section 12) covers serviceability limit states (Page 127).

• Important Literature:

  • Christian Menn, Prestressed Concrete Bridges (1986)
  • C.R. Hendy & D.A. Smith, Designer’s Guide to EN 1992-2 (2006)
  • R.S. Narayanan & A.B. Beeby, Designers Guide to EN 1992-1-1 and EN1992-1-2 (2005)
  • PD-6687-2:2008, Recommendations for BS EN 1992-2:2005

• Reliability: Refer to fib Model Code 2010 and reliability literature for probabilistic design parameters (Clause 1.28).

Typical Material Design Values (Example)

Sample Formula for Ultimate Moment Capacity (M_u):

[ M_u = 0.87 f_y A_s \left(d - \frac{a}{2}\right) ]

where:

• (f_y) = yield strength of steel
• (A_s) = area of tension reinforcement
• (d) = effective depth
• (a) = depth of equivalent stress block

flowchart TD
    A[Material Properties] --> B[Design Values]
    B --> C[Ultimate Limit State]
    C --> D[Shear, Torsion]
    C --> E[Induced Deformation]
    C --> F[Serviceability]
    A --> G[References]
    G --> H[Books & Codes]
    G -->