Clause 38.1 gives the theory and design procedure for flexural members (beams and slabs) under the limit state of collapse. It uses a rectangular stress block with a parabolic-rectangular stress-strain curve for concrete and bilinear curve for steel. The key design parameter is the neutral axis depth xu which determines whether the section is under-reinforced (desirable) or over-reinforced.
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Key Requirements
•Maximum strain in concrete in bending: 0.0035 at the extreme compression fibre
•Maximum strain in steel at failure: 0.87fy/Es + 0.002
Limiting Moment of Resistance Factor Mu,lim / (fck × b × d²)
Steel Grade
Mu,lim / (fck·b·d²)
Fe250
0.149
Fe415
0.1389
Fe500
0.1338
Fe550
0.1292
Formulas
Mu = 0.36 fck · b · xu (d − 0.42 xu)
Moment of resistance from concrete compression (singly reinforced)
Mu = Ultimate moment of resistance (N·mm)fck = Characteristic compressive strength (MPa)b = Width of section (mm)xu = Actual neutral axis depth (mm)d = Effective depth (mm)
Mu,lim = 0.36 fck · b · xu,max (d − 0.42 xu,max)
Limiting moment of resistance (balanced section)
Mu,lim = Maximum moment capacity as singly reinforced (N·mm)xu,max = Limiting neutral axis depth = xu,max/d × d
Ast = (0.5 fck / fy) [1 − √(1 − 4.6 Mu / (fck·b·d²))] × b × d
Area of tension steel required for a given Mu
Ast = Area of tension reinforcement (mm²)Mu = Factored bending moment (N·mm)
Practical Notes
✓For Fe500 in M25: Mu,lim = 0.1338 × 25 × b × d² = 3.345 b·d² (N·mm). For a 230 × 450 beam (d ≈ 410 mm): Mu,lim = 3.345 × 230 × 410² = 129.3 kN·m.
✓If Mu > Mu,lim, the section needs compression steel (doubly reinforced). Consider increasing depth first — it's more economical than adding compression steel.
✓SP:16 tables give direct Ast for given Mu/(b·d²) — faster than manual calculation. Most design offices use SP:16 or software.
Common Mistakes
⚠Using xu,max/d = 0.48 for Fe500 — the correct value is 0.456. Using 0.48 (Fe415 value) overestimates Mu,lim by ~5%.
⚠Not checking minimum steel: Ast,min = 0.85 × b × d / fy (Clause 26.5.1.1). For Fe500, 150 mm slab: Ast,min = 0.85 × 1000 × 125/500 = 212.5 mm²/m.
⚠Confusing factored moment with working moment — IS 456 load factors are 1.5 DL + 1.5 LL (for combination 1).