Hot Rolled Parallel Flange Steel Sections for Beams, Columns and Bearing Piles – Dimensions and Section Properties

IS 12778 Scope Summary with Key Tables & Symbols

Scope (Clause 4.1)

• Defines symbols used (Tables 1-3).
• Symbols for sectional properties and mass detailed in 4.1.2.
• Applies to Indian Standard Wide Flange Beams (WPB).

Key Specifications from Table 2 (Wide Flange Beams)

Example (WPB 100 x 100 x 12.24 kg/m):

IS 12778 Key References, Tables & Specifications

1. Referenced Standards (Table 2)

• IS 2062:1999 — Steel for general structural purposes.
• IS 8500:1991 — Structural steel microalloyed (medium & high strength).
• IS 12779:1989 — Rolling & cutting tolerances for hot rolled parallel flange beams.

2. Sectional Properties & Symbols (Clause 4.1)

• Symbols for mass (M), area (a), depth (D), width (B), web thickness (t), flange thickness (T), root radius (R).
• Moment of Inertia: Ix, Iy (cm⁴)
• Radius of Gyration: rx, ry (cm)
• Section Modulus: Zx, Zy (cm³)
• Plastic Section Modulus: Zpx, Zpy (cm³)

3. Wide Flange Beam Properties (Sample from Table 2)

4. Important Formulas

• Moment of Inertia (Ix, Iy): Calculated from cross-sectional geometry.
• Radius of Gyration:
  [ r_x = \sqrt{\frac{I_x}{A}}, \quad r_y = \sqrt{\frac{I_y}{A}} ]
• Section Modulus:
  [ Z_x = \frac{I_x}{y_{max}},

IS 12778: Terminology & Definitions (Clause 4.1 & 4.1.2)

Key Symbols for Dimensions (4.1.1)

• B = Flange width (mm)
• D = Depth of section (mm)
• R = Fillet radius (mm)
• t = Thickness of web (mm)
• T = Thickness of flange (mm)

Sectional Properties & Mass Symbols (4.1.2)

Notes:

• These symbols are essential for design calculations involving parallel flange sections (see Fig.1 in IS 12778).
• Refer to IS 2062, IS 8500, and IS 12779 for related steel specifications and tolerances.

flowchart LR
    A[Section Dimensions] -->|B, D, t, T, R| B[Sectional Properties]
    B -->|a, Iₓ, Iᵧ, Zₓ, Zᵧ| C[Structural Analysis]
    B -->|M, rₓ, rᵧ| D[Mass & Stability]

This concise terminology foundation supports structural design and analysis per

IS 12778 — Symbols for Sectional Properties and Mass (Clause 4.1.2)

Key Definitions from Clause 4.1.1 (Dimensions)

• B = flange width (mm)
• D = depth of section (mm)
• R = fillet radius (mm)
• t = web thickness (mm)
• T = flange thickness (mm)

Typical Formulas

• Moment of inertia (I):
  [ I_x = \int y^2 , dA, \quad I_y = \int x^2 , dA ]

• Radius of gyration (r):
  [ r_x = \sqrt{\frac{I_x}{a}}, \quad r_y = \sqrt{\frac{I_y}{a}} ]

• Section modulus (Z):
  [ Z_x = \frac{I_x}{e_x}, \quad Z_y = \frac{I_y}{e_y} ]

• Plastic section modulus (Zp):
  Sum of areas times distance to plastic neutral axis.

Sample Table Extract (Narrow Flange Beams)

| Designation |

IS 12778: Classification of Sections - Key Points

1. Symbols for Sectional Properties (Clause 4.1.2)

2. Section Classification (Clause 5.2)

Indian Standard sections are abbreviated as:

3. Typical Section Properties (Example from Table 1 & 2)

4. Important Form

IS 12778: Dimensions & Sectional Properties Summary

Key Symbols (Clause 4.1.2)

• a = Sectional area (mm²)
• Iₓ, Iᵧ = Moment of inertia about X-X and Y-Y axes (cm⁴)
• rₓ, rᵧ = Radius of gyration about X-X and Y-Y axes (cm)
• Zₓ, Zᵧ = Section modulus about X-X and Y-Y axes (cm³)
• Zₚₓ, Zₚᵧ = Plastic section modulus about X-X and Y-Y axes (cm³)
• M = Mass per meter length (kg/m)
• D = Depth (mm)
• B = Width (mm)
• t = Web thickness (mm)
• T = Flange thickness (mm)
• R = Root radius (mm)

Typical Sectional Properties Table Format (Excerpt)

Important Notes:

• Dimensions and mass tolerances conform to IS 12779.
• Wide flange beams (WPB) and narrow flange beams (NPB) are tabulated separately.
• Plastic section modulus is critical for plastic design methods.
• Moment of inertia and radius of gyration are essential for buckling and deflection calculations.

IS 12778 - Designation of Sections: Key Formulas, Tables & Symbols

1. Symbols for Sectional Properties (Clause 4.1.2)

2. Section Classification & Abbreviations (Clause 5.2)

3. Typical Section Properties Table (Excerpt from Clause 5)

IS 12778: Tolerances for Hot Rolled Parallel Flange Beams

• Clause 7.2 & 9.3: Dimensional and mass tolerances must conform to IS 12779 (refer to IS 12779 for exact tolerance values).

• Rolling and Cutting Tolerances: Not explicitly detailed in IS 12778; IS 12779 provides:

  • Length tolerance
  • Depth and width tolerance
  • Web and flange thickness tolerance
  • Mass tolerance

Typical Tolerance Ranges (from IS 12779):

Sectional Properties (from IS 12778 Tables 1-3):

• Mass (kg/m), Area (cm²), Depth (mm), Width (mm), Web thickness (mm), Flange thickness (mm)
• Moment of Inertia (Ix, Iy) in cm⁴
• Radius of Gyration (rx, ry) in cm
• Section Modulus (Zx, Zy) and Plastic Section Modulus (Zpx, Zpy) in cm³

Summary:

• Use IS 12779 for all tolerance limits.
• IS 12778 provides sectional properties for design.
• Ensure tolerance compliance for dimensional accuracy and mass during fabrication.

flowchart TD
    A[IS 12778] --> B[Sectional Properties Tables]
    A --> C[Refers to IS 12779 for Tolerances]
    C --> D[Length, Width, Depth Tolerances]
    C --> E[Thickness Tolerances]
    C --> F[Mass Tolerances]

Steel Grades per IS 12778 (Referencing IS 2062 & IS 8500)

• Material Strength:
  • Mild steel: As per IS 2062:1999
  • Medium & High strength steel: As per IS 8500:1991

Key Specifications for Wide Flange Beams (WPB)

Important Notes:

• Steel grades and mechanical properties must comply with **IS

IS 12778: Tables of Dimensions and Properties for Steel Sections

The standard provides detailed tables for Wide Flange Beams (WPB) and Narrow Flange Beams (NPB) including:

Usage Notes:

• Dimensional and mass tolerances conform to IS 12779.
• Symbols and definitions are detailed in Clause 4.1.
• Tables cover various sizes from 100x55 mm (NPB) to 250x250 mm (WPB).

Typical formula for radius of gyration:

[ r = \sqrt{\frac{I}{A}} ] where (I) = moment of inertia, (A) = cross-sectional area.

Example snippet from Table (WPB 200x200):

| Mass (kg/m) | Area (cm

IS 12778: Notes on Production and Application - Key Points

1. Sectional Properties (Clause 4.1.2)

• a = Sectional area (mm²)
• Iₓ, Iᵧ = Moment of inertia about X-X and Y-Y axes (cm⁴)
• M = Mass per meter length (kg/m)
• Zₓ, Zᵧ = Section modulus about X-X and Y-Y axes (cm³)
• Zₚₓ, Zₚᵧ = Plastic section modulus about X-X and Y-Y axes (cm³)
• rₓ, rᵧ = Radius of gyration about X-X and Y-Y axes (cm)
• D, B = Depth and width of section (mm)
• t, T = Web and flange thickness (mm)
• R = Root radius (mm)

2. Dimensional & Mass Tolerances (Clause 9.3)

• Conform to IS 12779 for tolerances on dimensions and mass of steel sections.

3. Typical Section Properties Table (Excerpt)

IS 12778 Annexures & Additional Data - Key Formulas and Tables

1. Sectional Properties Symbols (Clause 4.1.2)

• a = Sectional area (mm²)
• Iₓ, Iᵧ = Moments of inertia about X-X and Y-Y axes (cm⁴)
• rₓ, rᵧ = Radius of gyration about X-X and Y-Y axes (cm)
• Zₓ, Zᵧ = Section modulus about X-X and Y-Y axes (cm³)
• Zₚₓ, Zₚᵧ = Plastic section modulus about X-X and Y-Y axes (cm³)
• M = Mass per meter length (kg/m)
• D = Depth (mm), B = Width (mm), t = Web thickness (mm), T = Flange thickness (mm)
• R = Root radius (mm)

2. Key Formulas

• Radius of gyration:
  [ r = \sqrt{\frac{I}{a}} ]
• Section modulus:
  [ Z = \frac{I}{e} ] where e = distance from neutral axis to extreme fiber.

3. Typical Data from Table 2 (Wide Flange Beams)