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Calcs.com
EN 1993-1-1:2005 (Eurocode 3)EN 1993-1-5:2006

Steel Beam

Beam reactions link to your column and footing calculations automatically - change a load once and everything downstream updates. Design steel beams to Eurocode 3 (EN 1993-1-1) with checks for section bending capacity, lateral torsional buckling, shear resistance, shear web buckling (EN 1993-1-5), and three EN 1990 deflection limits.

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What it calculates

Beam reactions link to column and footing calculations automatically. Design steel beams to Eurocode 3 (EN 1993-1-1) with unlimited spans and loads - checks cover section capacity in bending, lateral torsional buckling, shear resistance, shear web buckling, and three EN 1990 deflection limits.

Code standards

  • EN 1993-1-1:2005 (Eurocode 3)
  • EN 1993-1-5:2006

How it calculates

Structural model and load combinations

The calculator models the steel beam as a one-dimensional element and computes bending moment, shear, and deflection diagrams under each EN 1990:2002 load combination. Loads are entered by type - permanent (G), variable (Q), wind (W), snow (S) - and the calculator generates governing ULS and three SLS combinations:

  • Characteristic (irreversible): G + Q_k + psi_0 × other variable loads
  • Frequent (reversible): G + psi_1 × Q_1 + psi_2 × other
  • Quasi-permanent (long-term): G + psi_2 × Q

Cross-section classification (EN 1993-1-1:2005 Cl 5.5.2)

Before computing capacities, the calculator classifies the cross-section (Class 1 through 4) by checking the flange and web slenderness limits against epsilon = sqrt(235/fy). This governs whether the plastic, elastic, or effective section modulus is used for bending resistance.

Section bending capacity (EN 1993-1-1:2005 Cl 6.2.5)

Bending resistance M_c,Rd uses the plastic section modulus W_pl for Class 1 and 2 sections, the elastic section modulus W_el for Class 3, or the effective modulus W_eff for Class 4:

bending utilization = M_Ed / M_c,Rd ≤ 1.0

Shear resistance (EN 1993-1-1:2005 Cl 6.2.6)

The plastic shear resistance V_pl,Rd is computed from the shear area A_v (the web area for I-sections) and the yield strength fy. For webs with hw/tw ≥ 72 epsilon/eta, shear buckling governs and the check moves to EN 1993-1-5.

shear utilization = V_Ed / V_Rd ≤ 1.0

Shear buckling (EN 1993-1-5:2006 Cl 5.5)

For slender webs, shear buckling resistance V_b,Rd is computed using the contribution method - adding flange and web contributions. The web buckling coefficient k_tau depends on the panel aspect ratio a/hw between transverse stiffeners. The combined bending-and-shear interaction is then checked per EN 1993-1-1:2005 Cl 7.1 Eq 7.1.

Lateral torsional buckling (EN 1993-1-1:2005 Cl 6.3.2.1)

LTB resistance M_b,Rd is computed from the critical elastic moment M_cr and the reduction factor chi_LT. The relative slenderness lambda_LT is derived from M_cr, which accounts for the unbraced length, moment gradient, and section properties (I_w, I_T, I_z, EI). The reduction factor chi_LT reduces the cross-section moment resistance based on the imperfection factor for the LTB buckling curve applicable to the section.

LTB utilization = M_Ed / M_b,Rd ≤ 1.0

Deflection checks (EN 1990:2002 Cl 6.5.3)

Three independent deflection limit states are verified per span, using the characteristic, frequent, and quasi-permanent serviceability combinations respectively. Each is checked against a user-defined span/n ratio and an optional absolute limit in mm.

Load linking

Support reactions are exported as linked outputs. Connected column and footing calculations placed downstream in the same project receive updated reactions automatically whenever the beam inputs change.

Related calculators

Steel Column (Eurocode 3)→Timber Column (Eurocode 5)→Timber Beam (Eurocode 5)→

What engineers say

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Frequently asked questions

What design standard does this calculator use?
The calculator designs steel beams to EN 1993-1-1:2005 (Eurocode 3), with shear buckling checks per EN 1993-1-5:2006. Load combinations follow EN 1990:2002. Three serviceability deflection combinations are checked - characteristic (irreversible), frequent (reversible), and quasi-permanent (long-term). Partial factors can be adjusted for the relevant National Annex.
What are the key inputs?
Key inputs include the steel section (selected from the built-in database of European hot-rolled and hollow sections), steel grade, beam span and support layout, loads by type (permanent G, variable Q, wind W, snow S), lateral restraint spacing for LTB, transverse stiffener spacing for shear buckling, and deflection limit ratios per span.
What checks and outputs does it produce?
The calculator checks cross-section class (EN 1993-1-1:2005 Cl 5.5.2), section bending capacity (Cl 6.2.5), design shear resistance (Cl 6.2.6), shear buckling of the web (EN 1993-1-5:2006 Cl 5.5), combined bending and shear for shear buckling (Cl 7.1), lateral torsional buckling (Cl 6.3.2.1), and three EN 1990:2002 deflection limit states.
How is lateral torsional buckling checked?
Lateral torsional buckling resistance is computed per EN 1993-1-1:2005 Cl 6.3.2.1 using the general or simplified method. The critical elastic moment M_cr is computed from the unbraced length between lateral restraints. The reduction factor chi_LT is applied to the full plastic or elastic section moment resistance depending on section class. The calculator shows the governing lambda_LT and chi_LT.
How is shear buckling handled?
For webs where the slenderness hw/tw exceeds 72 epsilon/eta, shear buckling is checked per EN 1993-1-5:2006 Cl 5.5. The contribution method separates flange and web contributions to shear resistance. Where transverse stiffeners are present, they are accounted for in the web buckling coefficient k_tau. Combined bending and shear buckling interaction is then checked per EN 1993-1-1:2005 Cl 7.1.
Does this calculator support load linking with column and footing calculations?
Yes - beam reactions link directly to connected column and footing calculations in the same project. When you change a span, load, or section, all downstream calculations update automatically - no manual re-entry of reactions required.

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