Plain and Reinforced Concrete – Code of Practice

IS 456: Scope Overview

IS 456 covers the general structural design and construction of plain and reinforced concrete. It provides guidelines for materials, workmanship, structural design, and durability.

Key Points on Scope:

• Applies to all types of concrete structures.
• Covers design values (Clause 36.3) for materials and loads.
• Includes construction practices: compaction, curing, joints (Clauses 13.3-13.6).
• Addresses special concreting conditions (Clause 14).
• Specifies sampling, testing, and acceptance criteria (Clauses 15-16).
• Details design bases: loads, forces, stability, fire resistance (Clauses 18-21).
• Provides analysis methods and effective span definitions (Clauses 22).

Essential Design Formula (Example: Flexural Strength)

[ M_u \leq 0.87 f_y A_s (d - \frac{A_s f_y}{f_{ck} b}) ]

Where:

• (M_u) = Ultimate moment
• (f_y) = Steel yield strength
• (A_s) = Area of tensile steel
• (d) = Effective depth
• (f_{ck}) = Characteristic compressive strength of concrete
• (b) = Width of the section

Typical Tables to Refer:

• Table 24: Design aids for reinforcement.
• Load combinations (Clause 19.7).
• Fire resistance requirements (Clause 21).

flowchart TD
    A[IS 456 Scope] --> B[Material Properties]
    A --> C[Design Loads & Forces]
    A --> D[Structural Analysis]
    A --> E[Construction Practices]
    A --> F[Durability & Fire Resistance]

For detailed design, refer to IS 456 clauses mentioned above and relevant tables like Table 24 for reinforcement design.

IS 456: Key Formulas, Tables & Specifications for Materials

1. Characteristic Strength of Concrete (Clause 36.1 & Table 2)

2. Modulus of Elasticity, E (N/mm²)

[ E = 5000 \sqrt{f_{ck}} ]
Note: Actual E may vary ±20%.

3. Shrinkage (Clause 6.2.4)

• Total shrinkage strain (approximate) = 0.0003 (in absence of test data)
• Influenced by water content, cement content, member size, and environment.

4. Design Values (Clause 36.3)

• Use characteristic strengths reduced by partial safety factors for design.
• Refer to IS 456 for specific partial safety factors.

flowchart TD
    A[Concrete Grade] --> B[fck (N/mm²)]
    B --> C[Calculate E = 5000√fck]
    C --> D[Use E for design]
    A --> E[Shrinkage strain ~ 0.0003]
    E --> F[Consider in deformation calculations]

This summary aids in selecting concrete grade, calculating modulus, and accounting for shrinkage per IS 456.

Concrete Grades and Properties (IS 456:2000)

1. Grades of Concrete (Table 2)

2. Modulus of Elasticity (E)

• Short term static modulus of elasticity:
  [ E = 5000 \sqrt{f_{ck}} \quad \text{(N/mm}^2) ]
• Actual values may vary ±20%.

3. Key Properties

• Shrinkage strain (approximate): 0.0003 (in absence of test data)
• Creep: Depends on mix, curing, and environment (refer IS 1343 for detailed values).

4. Specification Requirements (Clause 9.1.2)

When specifying concrete grade, include:

• Mix type (design or nominal)
• Grade designation
• Cement type
• Max aggregate size
• Min cement content (design mix)
• Max water-cement ratio
• Workability
• Mix proportions (nominal mix)
• Exposure conditions
• Max concrete temperature at placing
• Placing method
• Degree of supervision

This concise summary aligns with IS 456 clauses 6.1, 6.2, 9.1.2, and 15.1.1 for design and quality control of concrete grades.

Workability of Concrete (IS 456: Clause 7.1)

Workability is the ease with which concrete can be mixed, placed, compacted, and finished without segregation.

Suggested Slump Ranges (IS 1199 method)

Notes:

• Internal vibrators (needle type) are recommended for compaction except for tremie concrete.
• Needle diameter depends on reinforcement density and section thickness.
• For very high workability, flow tests per IS 9103 are preferred over slump.

Quick Reference: Workability Levels and Typical Slump

| Workability    | Slump (mm) | Typical Use Cases                          |
|----------------|------------|-------------------------------------------|
| Very Low       | < 25       | Blinding concrete, pavements              |
| Medium         | 50 - 100   | Reinforced sections, pump concrete        |
| High           | 100 - 150  | Trench fill, piling                        |
| Very High      | Flow test  | Tremie concrete (underwater concreting)  |

Summary Diagram

graph LR
A[Workability] --> B[Very Low (<25 mm)]
A --> C[Medium (50-100 mm)]
A --> D[High (100-150 mm)]
A --> E[Very High (Flow test)]
B --> F[Blinding, Pavements]
C --> G[Reinforced Sections, Pumped Concrete]
D --> H[Trench Fill, Piling]
E --> I[Tremie Concrete]

References:

• IS 456:2000, Clause

IS 456 Durability Requirements Summary

1. Clause 8.2 - General Durability Requirements

• Concrete must be designed to resist environmental attacks (chlorides, carbonation, sulfate, freeze-thaw, abrasion).
• Use minimum cement content and maximum water-cement ratio (w/c) as per exposure conditions.
• Use adequate cover and quality concrete mix to ensure durability.

2. Clause 26.4.2 - Nominal Cover for Durability

3. Clause 8.2.2.2 - Abrasive Surfaces

• For surfaces exposed to abrasion (e.g., machinery, metal tyres), specialist literature should be consulted.
• Use dense, well-compacted concrete with low w/c ratio.
• Consider surface hardening treatments or protective layers.

Key Formulas:

• Water-Cement Ratio Limits (typical):

  • Mild: ≤ 0.60
  • Moderate: ≤ 0.50
  • Severe: ≤ 0.45
  • Very Severe: ≤ 0.40
  • Extreme: ≤ 0.40

• Minimum Cement Content (kg/m³):

  • Mild: 300
  • Moderate: 320
  • Severe: 340
  • Very Severe: 360
  • Extreme: 380

flowchart LR
    A[Exposure Conditions] --> B{Durability Requirements}
    B --> C[Water-Cement Ratio Limits]
    B --> D[Minimum Cement Content]
    B --> E[Nominal Cover]
    B --> F[Abrasion Considerations]

Summary: Ensure proper cover, low w/c ratio, and adequate cement content per exposure severity. For abrasion, use dense concrete and specialist guidance.

IS 456: Concrete Mix Proportioning (Clauses 8.2.4 & 9.1)

Key Points:

• Mix proportions must ensure workability, strength, durability, and surface finish.
• Mix design is done to achieve a target compressive strength at 28 days.
• Durability requirements depend on exposure conditions (Clause 8.2).

Basic Mix Design Steps (IS 10262 recommended):

1. Target Strength:
   [ f_{ck, target} = f_{ck} + 1.65 \times \sigma ] where (f_{ck}) = characteristic compressive strength, (\sigma) = standard deviation.

2. Water-Cement Ratio (w/c):
   From IS 456 Table 5 (Durability requirements):

3. Water Content:
   Based on workability (slump) and aggregate size (IS 10262 Table 2).

4. Cement Content:
   [ \text{Cement} = \frac{\text{Water Content}}{w/c} ]

5. Aggregate Proportion:
   Use grading curves and bulk densities (IS 10262).

Summary Table for Mix Proportioning:

flowchart TD
    A[Start: Define Requirements] --> B[Select Target Strength]
    B --> C[Determine Max w/c Ratio (Durability)]
    C --> D[Choose Water Content (Workability)]
    D --> E[Calculate Cement Content (Water / w/c)]
    E

Reinforcement Placement and Assembly as per IS 456

Key Clauses:

• Clause 12.2:
  Reinforcement must be placed and maintained in position using cover blocks, spacers, supporting bars to ensure correct cover and spacing.

• Clause 26.2.2:
  Proper anchorage of bars is essential for load transfer (hooks, bends, or adequate embedment length).

Minimum Tension Reinforcement (Clause 26.5.1.1)

Clear Distance Between Bars (Table 15, Clause 26.3.3)

Note: Use minimum spacing ≥ bar diameter or 25 mm (whichever is greater).

Nominal Concrete Cover (Table 16, Clause 26.4.2)

Notes:

• For bars ≤12 mm in mild exposure, cover may be reduced by 5 mm.
• Actual cover tolerance: +10 mm / 0 mm.
• For severe exposure and concrete grade ≥ M35, cover may reduce by 5 mm.

Summary Diagram: Reinforcement Assembly

graph LR
A[Reinforcement Bars] --> B[Proper Positioning]
B --> C[Cover Blocks & Spacers]
B --> D[Anchorage (

IS 456: Design Methods Key Points

1. Direct Design Method (Clause 31.4)

• Used for one-way slabs and two-way slabs with simple support conditions.
• Simplifies load calculations by directly applying factored loads without moment redistribution.
• Suitable for slabs with uniformly distributed loads.

2. Design Values (Clause 36.3)

• Design Strengths are obtained by applying partial safety factors to characteristic strengths.
• For concrete: [ f_{cd} = \frac{f_{ck}}{\gamma_c} \quad \text{where } \gamma_c = 1.5 ]
• For steel: [ f_{yd} = \frac{f_{yk}}{\gamma_s} \quad \text{where } \gamma_s = 1.15 ]

3. Key Formulas

Summary Diagram: Load to Moment Conversion

flowchart LR
    Wk[Characteristic Load \(w_k\)]
    Wu[Factored Load \(w_u = 1.5 w_k\)]
    Mu[Design Moment \(M_u = \frac{w_u l^2}{8}\)]
    Vu[Design Shear \(V_u = \frac{w_u l}{2}\)]
    Wk --> Wu --> Mu
    Wu --> Vu

Use these for preliminary design and check with detailed methods in IS 456.

IS 456: Moment and Shear Coefficients for Continuous Beams (Clause 22.5)

Key Points:

• Moment coefficients (α) and shear coefficients (β) are used to calculate bending moments and shear forces in continuous beams and slabs.

• Moments per unit width:
  [ M = \alpha \times w \times l^2 ]
  where:

  • ( M ) = bending moment
  • ( \alpha ) = moment coefficient (from tables)
  • ( w ) = uniform load per unit area
  • ( l ) = span length

• Shear force:
  [ V = \beta \times w \times l ]
  where ( \beta ) = shear coefficient (from IS tables).

Moment Coefficients (Excerpt from Table 26 for Rectangular Panels):

Values depend on the ratio of longer to shorter span (l1/l2).

Usage:

• Choose coefficients based on panel support conditions and span ratio.
• Calculate moments and shears using above formulas.
• Refer Clause 22.6 for critical sections for moment and shear design.

Diagram: Moment Distribution in Continuous Beam

flowchart LR
    Load[Uniform Load, w]
    Span[Span Length, l]
    Load --> Beam[Continuous Beam]
    Beam --> Mneg[Negative Moment at Support: M = α_neg * w * l²]
    Beam --> Mpos[Positive Moment at Mid-span:

Effective Width of Flanges (IS 456: Clause 23.1.2)

The effective flange width (b_e) is used to account for the portion of the flange that effectively resists bending.

Key Formulas for Effective Width (b_e):

• For continuous beams/frames, use (l = 0.7 \times) effective span.
• (b_e) should not exceed the web breadth plus half the clear distance to adjacent beams on either side.

Notes on Slabs (Clause 24.3.2.2):

• Effective width depends on the ratio of transverse to longitudinal flexural rigidity.
• If ratio ≈ 1, use solid slab effective width.
• For smaller ratios, reduce effective width proportionally.

Summary:

• Effective flange width is crucial for bending design of flanged beams.
• Use the above formulas as conservative estimates.
• Always check flange width limits based on beam spacing.

flowchart TD
    A[Determine Beam Type] --> B{Beam Type}
    B -->|T-beam| C[Calculate \(b_e = 2b + 6D\)]
    B -->|L-beam| D[Calculate \(b_e = 2b + 3D\)]
    B -->|Isolated Beam| E[Calculate \(b_e = \min(b + l/4, b_{\text{actual}})\)]
    C --> F[Check max limits]
    D --> F
    E --> F
    F --> G[Use \(b_e\) for bending design]

This concise summary follows IS 456 guidelines for effective flange width.

IS 456: Slab Design Key Points

1. Slab Reinforcement (Clause 31.7)

• Minimum reinforcement for slabs (both directions):
  • Tension reinforcement (As,min):
    [ As_{min} = 0.15% \times b \times d ]
  • For temperature and shrinkage, provide minimum 0.12% of total cross-sectional area.
• Use Fe 415 or Fe 500 grade steel.

2. Shear in Flat Slabs (Clause 31.6)

• Check for one-way shear (beam shear) and two-way shear (punching shear).
• One-way shear capacity (V_c):
  [ V_c = 0.5 \sqrt{f_{ck}} b d ]
• Two-way shear (punching shear):
  [ \tau_c = \frac{V_u}{b_0 d} \leq \tau_{c, max} ] where (b_0) is the perimeter at d/2 from the column face.

3. Design Formulas Summary

Slab Design Flowchart

flowchart TD
    A[Start Slab Design] --> B[Calculate Moments]
    B --> C[Check Flexural Strength]
    C --> D{Is Moment > Capacity?}
    D -- Yes --> E[Increase Reinforcement]
    D -- No --> F[Check Shear]
    F --> G{Shear OK?}
    G -- No --> H[Provide Shear Reinforcement]
    G -- Yes --> I[Check Deflection & Cracking]
    I --> J{OK?}
    J -- No --> K[Increase Thickness or Reinforcement]
    J -- Yes --> L[Design Complete]

This summary helps

IS 456: Key Formulas and Tables for Columns and Compression Members

1. Effective Length of Columns (Annex E)

• Effective length factor k depends on end conditions.
• Effective length, L_eff = k × L_actual
• Typical values of k:
  • Both ends hinged: 1.0
  • One end fixed, other free: 2.0
  • Both ends fixed: 0.5

2. Design of Compression Members (Clause 43.2)

• Axial load capacity:

  [ P_u = 0.4 f_{ck} A_c + 0.67 f_y A_s ]

  • (f_{ck}) = characteristic compressive strength of concrete
  • (f_y) = yield strength of steel
  • (A_c), (A_s) = areas of concrete and steel

• Check for slenderness (Clause 39.7):

  [ \lambda = \frac{L_{eff}}{r} ]

  • (r) = radius of gyration
  • Slenderness limits per IS 456 Table 39

3. Slender Compression Members (Clause 39.7)

• Use reduction factor (\chi) for slender columns:

  [ \chi = \frac{1}{1 + \frac{\lambda}{500}} ]

• Design axial load:

  [ P_{design} = \chi \times P_u ]

4. Reinforcement in Compression Members

• Minimum longitudinal reinforcement: 0.8% of gross concrete area.
• Maximum: 6%.
• Transverse ties spacing per Clause 39.7 to prevent buckling.

5. Moment of Resistance for Rectangular Sections (Annex G-1)

IS 456 - Nominal Cover to Reinforcement (Clause 26.4)

• Nominal Cover: The design depth of concrete cover to all steel reinforcements (including links).
• Minimum Nominal Cover: Shall be not less than the diameter of the bar.

Key Points:

• Nominal cover is the design cover used in structural drawings.
• It ensures protection against corrosion, fire, and bond strength.
• As per Clause 8.2.3.2, nominal cover must comply with Clause 26.4.

Typical Nominal Cover Values (from IS 456 Table 26):

Important:

• Nominal cover ≥ bar diameter (ϕ).
• For example, for 16 mm bars, minimum nominal cover = 16 mm.
• Actual cover may be more to meet durability and fire requirements.

flowchart LR
    A[Nominal Cover] --> B[≥ Bar Diameter]
    A --> C[Durability]
    A --> D[Fire Protection]
    A --> E[Bond Strength]

Summary: Use nominal cover ≥ bar diameter and as per exposure conditions in IS 456 Table 26 for durability.

Precast Concrete Elements as per IS 456

IS 456 does not provide detailed design rules for precast concrete elements; it refers to specialized standards for such elements:

• Precast Joists and Hollow Filler Blocks:
  • Concrete filler blocks: Refer IS 6061 (Part 1)
  • Hollow clay filler blocks: Refer IS 6061 (Part 2)

Key Points for Precast Concrete (General Guidance)

• Materials & Quality: Follow IS 456 Section 2 for concrete quality, compaction, curing, and testing.
• Design Considerations: Use IS 456 Sections 18-22 for loads, design methods, stability, and fire resistance.
• Reinforcement & Detailing: Use IS 456 clauses for reinforcement, including torsion (Clause 6.4).
• Deflection & Cracking: Annex C provides methods for deflection and crack width calculations, applicable to precast elements.

Important Symbols for Precast Elements (from IS 456)

Typical Design Formula (Flexural Strength)

[ M_u \leq 0.87 f_y A_{st} (d - \frac{A_{st}}{bn}) ]

Where:

• (M_u) = Ultimate moment
• (A_{st}) = Area of tension reinforcement
• (b) = Width of section
• (d) = Effective depth
• (n = \frac{f_y}{0.45 f_{ck}}) (Modular ratio approx.)

Recommended Standards for Precast Concrete Design

flowchart TD
    A[IS 456 General

IS 456 Key Points for Slab and Beam Design & Detailing

1. Beams (Clause 23)

• Effective Depth (d): Distance from compression face to centroid of tensile reinforcement.
• Moment of Resistance (Mu):
  [ M_u = 0.36 f_{ck} b x_u (d - 0.42 x_u) ] where (x_u) = depth of neutral axis.
• Control of Deflection (23.2):
  Span-to-effective depth ratio limits to control deflection, same for slabs.
• Slenderness Limits (23.3): To ensure lateral stability.

2. Slabs (Clause 24)

• Span to Effective Depth Ratio: For two-way slabs, use the shorter span.
• Continuous Slabs: Moments and shear coefficients from Clause 22.5.
• Loads on Supporting Beams (24.5): Transfer slab loads to beams.
• Design of Two-way slabs: Use moment coefficients and design moments for both directions.

3. Reinforcement & Detailing (Clause 26)

• Nominal Cover: Minimum cover as per exposure conditions (usually 20-25 mm).
• Spacing of Reinforcement: To control cracking and bond.
• Development Length: As per Clause 26.2.
• Minimum Reinforcement: To control shrinkage and temperature cracks.

4. Deflection (Annex C & Clause 30.4)

• Total Deflection = Short-term + Deflection due to Shrinkage + Deflection due to Creep.
• Tables and formulas for simply supported and restrained slabs.
• Deflection limits per span/effective depth ratios.

Summary Table: Span to Effective Depth Ratios (for Deflection Control)

Mermaid Diagram: Load Transfer in Slab-Beam System

graph TD
    Slab -->|Transfer Load| Beam
    Beam -->