Clause 9.2 gives the design bending strength of laterally supported beams — i.e., beams with adequate lateral restraint to the compression flange preventing lateral-torsional buckling. The moment capacity depends on the section classification: plastic moment for Class 1 & 2 sections, elastic moment for Class 3 sections.
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Key Requirements
•Md = βb × Zp × fy / γm0 for Class 1 and Class 2 sections
•Md ≤ 1.2 × Ze × fy / γm0 (to prevent irreversible deformation under working loads)
•βb = 1.0 for Class 1 and Class 2 sections; βb = Ze/Zp for Class 3 sections
•Zp = plastic section modulus; Ze = elastic section modulus
•The beam must be laterally restrained at intervals not exceeding the limiting laterally unsupported length (Clause 8.3)
Reference Tables
Beam Moment Capacity for Common ISMB Sections (E250, Class 2)
Section
Zp (cm³)
Ze (cm³)
Md (kN·m)
ISMB 200
254
224
57.7
ISMB 250
413
362
93.9
ISMB 300
611
533
138.9
ISMB 350
836
726
190
ISMB 400
1095
949
248.9
ISMB 450
1350
1170
306.8
ISMB 500
1697
1462
385.7
ISMB 600
2408
2060
547.3
Md = 1.0 × Zp × 250 / 1.10 (Class 2 assumed). Values rounded. Check Md ≤ 1.2 × Ze × fy / γm0 separately. Actual Zp values from IS Handbook SP:6.
Formulas
Md = βb × Zp × fy / γm0
Design bending moment capacity of a laterally supported beam
Md = Design bending moment capacity (N·mm)βb = 1.0 for Class 1/2; Ze/Zp for Class 3 sectionsZp = Plastic section modulus (mm³)fy = Yield stress (MPa)γm0 = Partial safety factor = 1.10
Md ≤ 1.2 × Ze × fy / γm0
Upper limit on moment capacity to prevent irreversible deformation under service loads
Ze = Elastic section modulus (mm³)
Practical Notes
✓For most floor beams in buildings with concrete slab on top, the compression flange is continuously restrained by the slab — these are laterally supported beams. Use Cl. 9.2 directly.
✓The 1.2 × Ze × fy / γm0 upper limit rarely governs for standard rolled sections because Zp/Ze ≈ 1.12–1.15. It becomes relevant only for custom sections with high shape factor.
✓For quick design: ISMB 300 in E250 gives Md ≈ 139 kN·m. This is adequate for a 6 m simply supported beam with UDL ≈ 30 kN/m (wL²/8 = 135 kN·m).
Common Mistakes
⚠Using Zp for Class 3 sections — Class 3 sections must use Ze (elastic section modulus). Using Zp overestimates capacity by 12–15%.
⚠Not checking shear capacity separately (Cl. 8.4) — high shear at supports can reduce moment capacity (Cl. 9.2.2).
⚠Assuming lateral support when the compression flange is not restrained — e.g., bottom flange of a cantilever is in compression and may not be laterally supported.