Steel Beam

How it calculates

Structural model

The calculator models the steel beam as a one-dimensional Euler-Bernoulli beam element using a finite element method (FEM) engine. You define supports (pins, rollers, or fixed ends) at any position along the span, and the solver computes reactions, bending moment, shear force, and deflection diagrams under each load combination.

Load combinations (NBCC 2015 / CSA S16:19)

Loads are entered by type: dead (D), live (L), roof live (Lr), snow (S), wind up and down (Wu, Wd), and seismic (Eh, Ev). The calculator automatically generates and evaluates all governing CSA/NBCC ultimate limit state (ULS) combinations, for example:

• 1.25D + 1.5L
• 1.25D + 1.5S + 1.0L
• 0.9D + 1.5W (uplift check)

Serviceability load combinations are also generated for deflection checks.

Section classification

Before computing capacities, the calculator determines the section class (Class 1 through 4) by checking flange and web element slenderness ratios against CSA S16:19 limits. This governs which section modulus is used:

• Class 1 and 2: plastic section modulus Z (full plasticity permitted)
• Class 3: elastic section modulus S
• Class 4: effective section modulus S_e, computed by reducing the compression flange width

Moment resistance (Clause 13.5 and 13.6)

Cross-section moment resistance (M_sxn): based on the section class and applicable modulus.

Lateral torsional buckling (LTB): The calculator checks whether the unbraced length L_L between lateral restraints at the compression flange exceeds the limit for full plasticity. If LTB governs, the factored member moment resistance M_r is computed using the omega-2 moment modification factor - either automatically calculated from the bending moment diagram or entered manually. The governing positive and negative moment resistance tables are shown with code references.

Utilization: moment utilization = M_f / M_r ≤ 1.0

Shear resistance (Clause 13.4)

Shear capacity accounts for web buckling. The web plate buckling coefficient k_v and the shear buckling strength coefficient C_v2 are computed from the web slenderness h/w. The factored shear resistance V_r is then:

shear utilization = V_f / V_r ≤ 1.0

For circular hollow sections, the critical shear stress F_cr follows the applicable CSA provision.

Deflection checks

Three independent deflection limits are checked:

1. Span/n ratio (e.g. L/360 for live load) - user-defined per span
2. Long-term deflection - separate L/n limit applied to total long-term deflection
3. Absolute deflection - optional hard limit in mm

Deflections are computed by integrating the curvature diagram from the FEM solution. The governing deflection per span is compared to each active limit.

Section properties

Section properties (I_x, I_y, Z, S, J, C_w, A_g, A_w) are read directly from the built-in steel section database. For angle sections, the orientation and principal axis angle alpha are accounted for.

Load linking

Reaction forces at each support are exported as linked outputs. When this beam is part of a larger project, column and footing calculations placed below it automatically receive the updated reactions whenever the beam inputs change.