Steel Beam Sizing Calculator (ISMB Catalog)
Find the smallest ISMB I-beam section satisfying span, load, deflection, and grade constraints. Bending and deflection checks per IS 800.
How this works
For a simply-supported beam under a uniformly distributed load, the maximum bending moment and mid-span deflection are:
M_max = w × L² / 8
σ = M_max / Z_x ≤ σ_perm
δ_max = 5 × w × L⁴ / (384 × E × I_x)
δ_allow = L / allowableDeflectionRatio (e.g. L/250)
where E = 2 × 10⁵ MPa for all four IS grades
σ_perm = 0.66 × σ_y per IS 800 working stressWe iterate the ISMB catalog from ISMB 100 upwards and pick the first section that passes both checks. Permissible stresses by grade: Fe250 = 165 MPa, Fe415 = 274 MPa, Fe500 = 330 MPa, Fe550 = 363 MPa.
Worked example
A 6 m span carrying 15 kN/m, deflection limit L/250, grade Fe415:
- M_max =
15 × 6² / 8 = 67.5 kN·m - δ_allowed =
6 × 1000 / 250 = 24 mm - Iterate ISMB sections — typical recommended section: ISMB 250 or ISMB 300.
Tighten the deflection limit to L/360 (for brittle finishes) and the recommended section jumps up by one or two sizes — try it.
Sources
- IS 800 — General Construction in Steel (Code of Practice)
- IS 808 — Hot-rolled steel beam, column, channel and angle sections
- Standard Euler-Bernoulli simply-supported beam formulae
FAQ
Which checks does this calculator perform?
Two service-load checks for a simply-supported beam under a uniformly distributed load: bending stress σ = M / Z_x ≤ σ_perm, and mid-span deflection δ = 5wL⁴ / (384·E·I) ≤ span / allowable-ratio. The calculator iterates ISMB sections from smallest to largest and returns the first section that passes both. It does not check shear, web crippling, lateral-torsional buckling, or connection capacity — those are separate IS 800 design steps that need an engineer.
What allowable deflection ratio should I use?
Common defaults: span/250 for general beams under combined dead and live load, span/325 for live-load only, and span/360 for beams that support brittle finishes like glass partitions or large-format tile. Building regulations and codes vary, so check NBC 105 (Nepal), IS 800 (India), or the local code that applies to your project. The deflection check is often more restrictive than bending for long, lightly-loaded spans.
Why ISMB only? Can it pick channels or hollow sections?
For simple flexural members, ISMB I-beams are the most efficient and most commonly stocked option, so we restrict the iteration to ISMB. Channels (ISMC) and hollow sections (SHS / RHS) are valid alternatives for edge beams, lintels, and architectural exposure but require different lateral-stability checks. If you need those, look up the section's Z_x and I_x in the Steel Section Weight calculator and apply the formulae manually.
How are σ_perm values derived for each grade?
Per IS 800 working-stress design, the permissible bending stress is approximately 0.66 × σ_y. For Fe250 σ_y is 250 MPa giving σ_perm ≈ 165 MPa, for Fe415 σ_perm ≈ 274 MPa, for Fe500 σ_perm ≈ 330 MPa, and for Fe550 σ_perm ≈ 363 MPa. These are working-stress allowables. If your project uses limit-state design, recompute with the design strength σ_y / γ_m0 (γ_m0 = 1.10).
What does "No standard ISMB section satisfies these constraints" mean?
Either the span is too long, the load is too high, the deflection limit is too tight, or some combination. Options: pick a larger steel section family (ISMB above 600, plate girders, castellated beams), reduce the span by adding intermediate columns, accept a more relaxed deflection limit, or specify a higher-grade steel. This message is a flag to involve a structural engineer — do not bridge it by upgrading to a fictitious section.
Is the calculator a substitute for a structural engineer?
No. It is a preliminary sizing aid for typical residential and small commercial spans (3 to 9 m) under simple gravity loads. It does not consider seismic detailing, fire rating, connection design, fatigue, dynamic effects, or composite action with floor decking. For any habitable structure, the final beam size must be set by a licensed structural engineer who has reviewed the full load combinations and detailing requirements.