Steel Beam Span and Load Calculator
Calculate the maximum allowable uniform distributed load (UDL) or maximum safe span for a simply supported steel beam using elastic bending theory and standard steel section properties.
Find Z from steel section tables (e.g. UB 305×127×48 → Z ≈ 711 cm³)
S275 = 275 MPa, S355 = 355 MPa, S460 = 460 MPa
Results will appear here.
Formulas Used
1. Allowable Bending Stress:
fallow = fy / SF
2. Allowable Moment Capacity (Elastic):
Mallow = fallow × Z
where Z is the elastic section modulus (cm³ → converted to mm³ × 1000)
3. Maximum UDL for Simply Supported Beam:
Mmax = w × L² / 8 → wtotal = 8 × Mallow / L²
4. Net Allowable Applied Load:
wapplied = wtotal − wself-weight
Wtotal = wapplied × L
5. Maximum Safe Span (given self-weight as governing load):
Lmax = √(8 × Mallow / wsw)
Assumptions & References
- Simply supported beam with uniformly distributed load (UDL) — most conservative common case.
- Elastic bending theory applies (no plastic redistribution assumed).
- Steel modulus of elasticity E = 210,000 MPa (BS EN 1993-1-1, §3.2.6).
- Default yield strength fy = 275 MPa corresponds to Grade S275 steel (BS EN 10025).
- Safety factor of 1.67 corresponds to allowable stress design (ASD); use 1.0 with factored loads for Eurocode LRFD approach.
- Lateral torsional buckling (LTB) is not accounted for — adequate lateral restraint is assumed. For unrestrained beams, check per BS EN 1993-1-1 §6.3.2.
- Shear capacity is not checked here; verify VEd ≤ Vpl,Rd separately.
- Deflection limits (typically span/360 for live load) require moment of inertia (I) and are not computed here without full section data.
- Self-weight values for common UB sections: e.g. UB 203×133×25 ≈ 0.25 kN/m, UB 457×191×98 ≈ 0.96 kN/m.
- References: BS EN 1993-1-1:2005 (Eurocode 3), AISC Steel Construction Manual (16th Ed.), SCI P363 Steel Building Design.