Guidelines for Design of Continuously Reinforced Concrete Pavement with Elastic Joints

IRC 101: Introduction - Key Formulas, Tables & Specifications

1. Temperature Stresses (Eisenmann Equations)

• Steel stress, σ_s:

[ \sigma_s = \frac{100 \alpha \Delta T h E_c E_s}{f_s E_c + 100 h E_s} \times (1 - 2\beta) + \frac{100 h E_s}{f_s E_c + 100 h E_s} ]

• Concrete stress, σ_c:

[ \sigma_c = \beta f_y E_c (1 - 2\beta) + \frac{100 h E_c}{f_s E_c + 100 h E_s} ]

Where:

2. Design Charts

• Fig. 2 & 3: Show steel and concrete stresses per °C of ΔT for steel % (0.1 - 0.6) and β (0.1 - 0.4).
• Permissible steel stress: 1400 kg/cm² (with elastic joints).
• Transverse steel: 25% of longitudinal steel.

3. Slab Thickness Design

• Stepwise procedure:

  1. Calculate plain slab thickness as per IRC:58.
  2. Select steel % ensuring steel stress ≤ 1400 kg/cm² (use Fig. 2).
  3. Calculate concrete stress (Fig. 3) and add to Step 1 stresses.
  4. Check total stress ≤ concrete flexural strength.
  5. Adjust slab thickness using Mallinger’s chart (Fig. 4) for effective thickness increase due to steel.

4. Mix & Materials

• Concrete flexural strength ≥

Design of Continuously Reinforced Concrete Pavement (CRCP) with Elastic Joints per IRC 101 involves:

Key Concepts:

• CRCP has no transverse joints; reinforcement controls cracking.
• Elastic joints allow controlled movement and reduce stress.
• Design balances slab thickness, steel percentage, and joint spacing.

Important Parameters:

• Slab Thickness (h): Typically 200-300 mm.
• Steel Reinforcement: High tensile steel, 0.6% to 0.8% of cross-section.
• Joint Spacing: Usually 4.5 to 6 m for elastic joints.
• Concrete Strength: Minimum 30 MPa at 28 days.

Typical Design Formulae:

• Steel Area (As):
  [ A_s = p \times b \times h ]
  where (p) = steel percentage, (b) = slab width, (h) = slab thickness.

• Joint Load Transfer Efficiency (LTE):
  Design joints to achieve LTE ≥ 75%.

Table: Suggested Steel Percentage vs Slab Thickness

Elastic Joint Specification:

• Use neoprene or rubber seals.
• Provide dowel bars for load transfer.
• Ensure proper sealing to prevent water ingress.

flowchart LR
    A[Concrete Slab] --> B[Reinforcement Steel]
    B --> C[Control Cracking]
    A --> D[Elastic Joint]
    D --> E[Load Transfer via Dowel Bars]
    D --> F[Sealing to Prevent Water]

Summary: Design CRCP with 0.6-0.8% steel, 200-300 mm thickness, elastic joints spaced 4.5-6 m with dowel bars and seals for durability and load transfer.

Key Formulas and Specifications for Steel Percentage and Stresses (IRC 101)

1. Steel Percentage Calculation

• Average steel reinforcement, ( r_a ): [ r_a = 0.004 + 25% \times 0.004 = 0.005 = 0.25% ]

2. Stresses in Steel and Concrete at Elastic Joints (Eisenmann Equations)

[ \sigma_s = \frac{100 \alpha \Delta T h E_c E_s}{f_s} (1 - 2) + \frac{100 h E_c^2}{A T f_s E_s} ]

[ \sigma_c = f_y E_s (1 - 2) + 100 h E_c^2 ]

Where:

• (\alpha) = Coefficient of thermal expansion of concrete (per °C)
• (\Delta T) = Temperature difference between construction and coldest period (°C)
• (A T) = Max temperature differential top-to-bottom of slab (°C)
• (h) = Slab thickness (cm)
• (E_c), (E_s) = Modulus of elasticity of concrete and steel (kg/cm²)
• (f_s) = Steel cross-sectional area per meter width (cm²)
• (2) = Ratio of free unbonded steel length to slab length between elastic joints

3. Design Charts (Refer IRC 101 Figures)

• Fig. 2: Steel stress per °C vs. steel % and unbonded length ratio
• Fig. 3: Concrete stress per °C vs. steel % and unbonded length ratio
• Steel stress limit: 1400 kg/cm²

4. Effective Slab Thickness Increase (Mallinger's Chart - Fig. 4)

• Steel percentage (r_a = 0.25%) → Effective slab thickness increase ≈ 31%
• Adjust slab thickness accordingly: [ h_{effective} = h_{initial} \times (1 - 0.31) ]

5. Design Procedure Outline

• Step I: Assume slab thickness (IRC:58)
• Step II: Select steel % from Fig. 2 to keep (\sigma_s \leq 1400)

Design of Slab Thickness (IRC 101 Key Points):

• Given:

  • Total compressive stress, ( \sigma_c = 39.00 , \text{kg/cm}^2 )
  • Flexural strength of concrete, ( f_{cr} = 40 , \text{kg/cm}^2 )
  • Initial slab thickness, ( h_0 = 25 , \text{cm} )

• Step 1: Check Stress vs Strength
  Since ( \sigma_c < f_{cr} ), initial thickness ( h_0 = 25 , \text{cm} ) is acceptable.

• Step 2: Calculate Average Steel Reinforcement Ratio (( r_a ))
  [ r_a = 0.004 + 0.25 \times 0.004 = 0.005 = 0.25% ]

• Step 3: Adjust Thickness for Reinforcement
  From Fig. 4 (IRC 101), for ( r_a = 0.25% ), effective thickness increase = 31%.
  Adjusted thickness:
  [ h = \frac{25}{1 + 0.31} = 19.08 \approx 19 , \text{cm} ]

• Step 4: Temperature Consideration
  At ( 14.3^\circ C ), thickness corresponds to ( 25 , \text{cm} ) (Clause 14.3).

Summary Table:

flowchart TD
    A[Initial Thickness 25 cm] --> B{Check Stress}
    B -- σc < fcr --> C[Accept Thickness]
    C

Cement Concrete Mix Design - IRC 101 Key Points

• Mix Design Method: Absolute volume method as per IRC:44 ("Tentative Guidelines for Cement Concrete Mix Design").
• Target Strength: Flexural strength at 28 days ≥ 40 kg/cm² (field condition).
• Cement: Conform to IS:269 (Ordinary Portland Cement) or IS:8112 (PPC).
• Aggregates: Fine and coarse aggregates as per IS:383.
• Water: Clean, potable water conforming to IS:456.
• Water-Cement Ratio: Typically between 0.4 to 0.5 depending on workability and strength requirements.
• Mix Proportions: Adjusted to achieve target workability and strength; trial mixes recommended.

Absolute Volume Method Formula:

[ V_c + V_w + V_a + V_{air} = 1 ]

Where:

• (V_c) = Volume of cement
• (V_w) = Volume of water
• (V_a) = Volume of aggregate
• (V_{air}) = Volume of air (usually 2-3%)

Typical Mix Design Steps:

1. Select target strength and workability.
2. Determine water-cement ratio.
3. Calculate absolute volumes of cement, water, aggregates.
4. Convert volumes to weights using specific gravities.
5. Adjust proportions based on trial mixes.

This mix design ensures durable, strong concrete suitable for rigid pavements as per IRC 101 specifications.

Key Formulas & Specifications for Materials (IRC 101)

1. Temperature Stresses in Steel and Concrete (Eisenmann Equations):

[ \sigma_s = \frac{100 \times \alpha \times \Delta T \times h \times E_c \times E_s}{f_s \times E_s (1 - 2\beta) + 100 \times h \times E_c \times \beta^2} ]

[ \sigma_c = \frac{A \times T \times f_s \times E_c \times E_s}{f_y \times E_s (1 - 2\beta) + 100 \times h \times E_c \times \beta^2} ]

• (\alpha) = Coefficient of thermal expansion of concrete (per °C)
• (\Delta T) = Temperature difference (°C)
• (h) = Slab thickness (cm)
• (E_c, E_s) = Modulus of elasticity of concrete and steel (kg/cm²)
• (f_s) = Steel cross-section per 1 m width (cm²)
• (\beta) = Ratio of free unbonded steel length to slab length between joints
• Permissible steel stress: 1400 kg/cm² (with elastic joints)

2. Steel Reinforcement:

• Longitudinal: 16 mm dia @ 26 cm c/c
• Transverse: 10 mm dia @ 41 cm c/c (25% of longitudinal steel)
• Steel coated with bitumen over 1/3 to 1/4 joint spacing near elastic joints to break bond.

3. Slab Thickness Design:

• Initial thickness per IRC:58 (plain cement concrete)
• Adjust thickness using Mallinger's chart (Fig.4) for effective increase due to steel reinforcement.
• Use iterative design steps combining wheel load, temperature stresses, and reinforcement stresses.

4. Material Specifications:

• Cement: IS 269 or IS 8112
• Aggregates: IS 383
• Steel: IS 432 (Part I) Mild Steel
• Water: Clean, potable, IS 456 compliant

5. Construction Notes:

• Elastic joints: Dummy contraction joints with continuous reinforcement and bond-breaking coating.
• Expansion joints only at section

Key Specifications and Formulas for Cement in IRC 101 (CRCP with Elastic Joints):

Cement Concrete Mix Design

• Mix Design: Absolute volume method as per IRC:44.
• Concrete Strength: Flexural strength ≥ 40 kg/cm² at 28 days.
• Cement Standards: IS 269 or IS 8112.
• Water: Clean, potable, conforming to IS 456.

Steel Reinforcement

• Steel bars conform to IS 432 (Part I) - Mild Steel.
• Bar spacing: 25 to 35 cm.
• Steel mats placed at mid-depth of slab.
• Minimum lap length: 30 bar diameters, staggered.

Temperature and Shrinkage Stress Formulas (Eisenmann Equations)

[ \sigma_s = \frac{100 \alpha \Delta T h E_c E_s}{f_s E_c + 100 h E_s} \quad \text{(Steel stress, kg/cm}^2) ]

[ \sigma_c = \frac{a \Delta T f_s E_c E_s}{f_s E_c + 100 h E_s} \quad \text{(Concrete stress, kg/cm}^2) ]

Where:

• (\alpha) = Coefficient of thermal expansion of concrete (per °C)
• (\Delta T) = Temperature difference (°C)
• (h) = Slab thickness (cm)
• (E_c), (E_s) = Modulus of elasticity of concrete and steel (kg/cm²)
• (f_s) = Steel cross-section per meter width (cm²)

Design Procedure Summary

1. Calculate slab thickness per IRC:58.
2. Select steel % to keep steel stress ≤ 1400 kg/cm² (permissible for CRCP with elastic joints).
3. Calculate concrete stress and add to load/temperature stresses.
4. Use Mallinger’s chart (Fig. 4) to find effective slab thickness increase due to steel.
5. Adjust slab thickness accordingly.

Construction Notes

• Use mild steel chairs to support longitudinal reinforcement.
• Elastic joints filled with sealing compound or bitumen-coated plywood strips (50 mm wide, 3 mm thick).
• Steel coated with bitumen near joints to allow elongation.

flowchart TD
    A[Assume

IRC 101 does not explicitly provide detailed clauses on Coarse and Fine Aggregates specifications. However, general guidelines based on standard practices and related IS codes (like IS 383) are applicable:

Key Specifications for Aggregates in Concrete (per IS 383 and IRC practices):

• Coarse Aggregate:

  • Size: Typically 20 mm or 10 mm nominal size.
  • Shape: Cubical, hard, and durable.
  • Fineness Modulus: Usually 6.5 to 7.5.
  • Specific Gravity: 2.6 to 2.9.
  • Water Absorption: ≤ 2%.
  • Crushing Value: ≤ 30%.

• Fine Aggregate:

  • Particle size: Passing 4.75 mm sieve.
  • Fineness Modulus: 2.3 to 3.1.
  • Silt Content: ≤ 4%.
  • Specific Gravity: 2.6 to 2.7.
  • Water Absorption: ≤ 3%.

Important Formulas:

• Fineness Modulus (FM):
  [ FM = \frac{\text{Sum of cumulative % retained on standard sieves}}{100} ]

• Mix Proportioning (Approximate):

  • Cement : Fine Aggregate : Coarse Aggregate = 1 : 1.5 : 3 (by volume for M20 concrete)

Aggregate Grading Table (Typical):

flowchart LR
    Cement --> Mix_Pro

IRC 101: Construction Details & Key Formulas for CRCP with Elastic Joints

1. Elastic Joint Details

• Dummy contraction joints with continuous reinforcement.
• Steel coated with bitumen over 1/3 to 1/4 joint spacing on either side to break bond and allow elongation.
• Joint groove filled with sealing compound or bitumen-coated plywood strip (50 mm wide, 3 mm thick).
• Typical spacing: 4 to 5 m.

2. Steel & Concrete Stress Calculation (Eisenmann Equations)

[ \sigma_s = \frac{100 \alpha \Delta T h E_c E_s}{f_s}(1-2) + \frac{100 h E_c^2}{f_s} ]

[ \sigma_c = \text{(similar expression with parameters as per clause)} ]

Where:

• (\alpha) = Coefficient of thermal expansion (per °C)
• (\Delta T) = Temperature difference (mean to coldest)
• (A_t) = Max temperature differential top-bottom
• (h) = Slab thickness (cm)
• (E_c, E_s) = Modulus of elasticity of concrete and steel (kg/cm²)
• (f_s) = Steel cross-section per meter width (cm²)
• (2) = Ratio of free unbonded steel length to slab length

3. Design Charts

• Fig. 2 & 3: Steel and concrete stresses per °C of (A_t) for steel % (0.1-0.6) and unbonded length ratio (0.1-0.4).
• Max permissible steel stress: 1400 kg/cm² (with elastic joints).

4. Slab Thickness Design

• Calculate plain PCC thickness (IRC:58).
• Add concrete tensile stress from elastic joint continuity.
• Use Mallinger's Chart (Fig. 4) for effective slab thickness increase due to steel.
• Reduce thickness by this increase for final design.

5. Reinforcement Specifications

• Longitudinal bars: 16 mm ø @ 26 cm c/c, coated with bitumen over 150 cm length at joints.
• Transverse bars: **10 mm ø

Key Formulas and Specifications for General Construction Practices (IRC 101)

1. Temperature Stress in Steel and Concrete (Eisenmann Equations)

[ \sigma_s = \frac{100 \alpha \Delta T h E_c E_s}{f_s} (1 - 2\beta) + \frac{100 h E_c^2}{f_s} ]

[ \sigma_c = \alpha \Delta T f_s E_c E_s ]

Where:

• Permissible steel stress: 1400 kg/cm² (with elastic joints)
• Transverse steel: 25% of longitudinal steel

2. Slab Thickness Design Procedure

• Step 1: Calculate plain cement concrete slab thickness per IRC:58.
• Step 2: Select steel percentage (0.1% - 0.6%) ensuring steel stress ≤ 1400 kg/cm² using Fig. 2 (steel stress chart).
• Step 3: Calculate concrete stress from Fig. 3 and add to Step 1 stresses; ensure total stress ≤ concrete flexural strength.
• Step 4: Use Mallinger's chart (Fig. 4) to find effective increase in slab thickness due to steel; reduce thickness accordingly.

3. Construction Specifications

• Steel bars spacing: 25 to 35 cm
• Steel bars: Mild steel conforming to IS:432 (Part I)
• Concrete mix: Designed as per IRC:44; flexural strength ≥ 40 kg/cm² at 28 days
• Aggregates: Conform to IS:383

IRC 101: Construction of Elastic Joints in Continuously Reinforced Concrete Pavement (CRCP)

Key Specifications:

• Elastic Joint Type: Dummy contraction joint with continuous reinforcement.
• Reinforcement Treatment: Paint reinforcement with a bond-breaking medium (e.g., bitumen) over 150 cm on each side of the joint groove.
• Joint Groove: Filled with bitumen-coated strip to allow movement.
• Joint Spacing: Typically 4 to 5 m to localize cracking and reduce steel stress.

Reinforcement Details (Typical Example):

Benefits:

• Reduces steel stress by ~50%
• Reduces quantity of steel required
• Localizes cracking at joints, preventing random cracks

Design Calculation Notes:

• Steel continuity causes restraint; bond-breaking length provides gauge length to limit steel strain.
• Calculate steel percentage and stresses considering bond-breaking length and joint movement.

Diagram of Elastic Joint Setup

flowchart LR
    A[Concrete Slab] -->|Continuous Reinforcement| B[Reinforcement]
    B -->|Coated with Bond Breaker (150 cm)| C[Elastic Joint Groove]
    C -->|Filled with Bitumen Coated Strip| D[Allows Movement]
    style C fill:#f9f,stroke:#333,stroke-width:2px

For detailed design formulas and solved examples, refer to Appendix of IRC 101 related to elastic joints.

Key Formulas and Specifications for Reinforcement in CRCP with Elastic Joints (IRC 101):

1. Steel and Concrete Stresses at Elastic Joints (Eisenmann Equations):

[ \sigma_s = \frac{100 \alpha \Delta T h E_c E_s}{f_s} (1 - 2) + \frac{100 h E_c^2}{f_s} ]

[ \sigma_c = \alpha A T f_s E_c E_s ]

Where:

• (\alpha) = Coefficient of thermal expansion of concrete (per °C)
• (\Delta T) = Temperature difference between construction and coldest period (°C)
• (A T) = Max temperature differential between top and bottom of slab (°C)
• (h) = Slab thickness (cm)
• (E_c), (E_s) = Modulus of elasticity of concrete and steel (kg/cm²)
• (f_s) = Steel cross-section per 1m width (cm²)
• (2) = Ratio of free (unbonded) steel length to slab length between elastic joints

2. Design Charts:

• Fig. 2: Steel stress per °C of (A T) vs. steel percentage (0.1% - 0.6%) and unbonded length ratio (0.1 - 0.4).
• Fig. 3: Concrete stress per °C of (A T) for same parameters.
• Permissible steel stress: 1400 kg/cm² (CRCP with elastic joints).

3. Reinforcement Details:

• Longitudinal bars: 16 mm Ø @ 26 cm c/c, coated with bitumen over 150 cm length on either side of elastic joint to break bond.
• Transverse bars: 10 mm Ø @ 41 cm c/c (25% of longitudinal steel).
• Overlap length: Minimum 30 bar diameters, staggered.
• Steel placed at mid-depth on mild steel chairs.

4. Effective Slab Thickness Increase (Fig. 4 - Mallinger's Chart):

• Steel reinforcement increases effective slab thickness, allowing reduction in slab thickness

Design Procedure for CRCP with Elastic Joints (IRC 101)

Key Formulas (Eisenmann Equations):

Calculate stresses near elastic joints:

[ \sigma_s = \frac{100 \alpha \Delta T h E_c E_s}{f_s} (1 - \beta) + \frac{100 h E_c^2}{f_s} ]

[ \sigma_c = \alpha \Delta T f_s E_c E_s ]

Where:

• (\alpha) = Coefficient of thermal expansion (per °C)
• (\Delta T) = Difference between mean slab temperature at construction and coldest period (°C)
• (h) = Slab thickness (cm)
• (E_c, E_s) = Modulus of elasticity of concrete and steel (kg/cm²)
• (f_s) = Steel cross-section per 1 m width (cm²)
• (\beta) = Ratio of free unbonded length of steel to slab length between elastic joints

Design Steps:

1. Assume slab thickness and calculate wheel load & temperature stresses (IRC:58).
2. Select steel % from Fig. 2 so steel stress ≤ 1400 kg/cm². Calculate concrete stress from Fig. 3.
3. Add concrete stress to Step 1 stresses; check against concrete flexural strength. Iterate if needed.
4. Calculate effective slab thickness increase using Mallinger's chart (Fig. 4) and reduce slab thickness accordingly.

Important Specifications:

• Steel stress limit: 1400 kg/cm² (with elastic joints)
• Steel spacing: 25–35 cm
• Steel overlap: Minimum 30 bar diameters
• Concrete flexural strength: ≥ 40 kg/cm² at 28 days
• Transverse steel: 25% of longitudinal steel

Mallinger's Chart (Fig. 4) Summary:

flowchart TD
    A[Assume slab thickness] -->