Formulas (simply-supported beam, UDL)
All formulas assume a prismatic beam with constant EI, an evenly-distributed load along the full span, and small deflections. For point loads, partial UDLs, or continuous beams, the formulas change — use a structural analysis tool.
Typical input values
| Material | Young's modulus E (N/mm²) |
|---|---|
| Concrete (M20) | 22,360 |
| Concrete (M25) | 25,000 |
| Concrete (M30) | 27,386 |
| Structural steel | 200,000 |
| Aluminium | 69,000 |
| Timber (softwood) | 9,000 – 12,000 |
For RCC, IS 456 specifies E = 5000 × √fck (in N/mm²). For a 230×450 mm rectangular beam, I = bd³/12 = 230 × 450³ ÷ 12 ≈ 1.75 × 10⁹ mm⁴.
FAQ
What is the L / 360 rule?
It's a serviceability limit: deflection should be less than span ÷ 360 to avoid visible sag and damage to finishes. For floors with brittle finishes use L/480; for roofs without ceilings, L/240 is often acceptable.
How do I get the moment of inertia?
Rectangular section: I = b × d³ ÷ 12, where b is width and d is depth (both in mm). Standard rolled steel sections (ISMB, ISLB, etc.) have I tabulated in IS 808 / SP 6. For composite sections, compute the equivalent transformed section.
What about self-weight?
Add the beam's self-weight to your UDL. For a 230×450 mm RCC beam: 0.23 × 0.45 × 25 ≈ 2.6 kN/m of self-weight, on top of any imposed load.