Steel Beam

How it calculates

Structural model

The calculator models the steel beam using a finite element method (FEM) engine. Supports are positioned at user-defined locations and can be pins or rollers. The solver produces moment, shear, deflection, and reaction diagrams for every load case and combination.

Load combinations (NZS 1170)

Loads are entered by type: permanent (G), imposed (Q), wind (W), and earthquake (E). The character of the imposed load (office, residential, storage, etc.) affects the combination factors psi. The calculator generates and evaluates all governing NZS strength and serviceability load cases, selecting the worst case for each check.

Section compactness (Clause 5.1 and 5.2)

Sections are classified by comparing flange and web element slenderness ratios to the yield and plastic limits from NZS 3404. Compactness classification (compact, non-compact, or slender) in bending about each axis determines the effective section modulus Z_e used in capacity calculations.

Design moment capacity (Clause 5.1 to 5.3)

Section moment capacity (phiM_s): computed from Z_e and yield stress, factored by phi.

Member moment capacity (phiM_bx): accounts for lateral torsional buckling using:

• alpha_m: moment modification factor derived from the bending moment diagram at quarter-points (M2, M3, M4)
• alpha_s: slenderness reduction factor, a function of the reference elastic buckling moment M_oa and the section moment capacity
• Restraint classification per span (fully, partially, or laterally restrained)

Utilization: moment utilization = M*x / phiM_sx ≤ 1.0

Shear capacity (Clause 5.11)

The nominal shear yield capacity V_w and shear buckling capacity V_b are computed from web area A_w and the shear buckling coefficient alpha_v. The lesser governs. An additional check on the ratio of maximum to average shear stress (f_vm / f_va) is performed for non-uniform shear distributions.

Shear-moment interaction is checked where both V* and M* are significant at a cross-section.

Bearing capacity (Clause 5.13)

At each support, the bearing yield capacity and bearing buckling capacity are computed. The member slenderness reduction factor alpha_c accounts for web buckling under concentrated bearing. An additional bending-bearing interaction check is performed where required.

Deflection checks (Clause 2.3)

Three deflection types are checked against user-defined span/n limits:

1. Short-term serviceability deflection - under short-term service loads
2. Long-term serviceability deflection - including creep and shrinkage effects
3. Imposed load deflection - live and imposed loads only

The governing deflection per span is extracted from the FEM solution and compared to the applicable limit. An optional absolute deflection limit (mm) can also be set.

Section properties

Properties (I_11, I_22, Z_11, S_11, S_22, J, I_w, A_g, A_w, alpha) are read from the built-in NZ/AU steel section database, including UB, UC, PFC, EA, UA, RHS, SHS, and CHS sections. The angle of the major principal axis and the centroid location are used to resolve loads for asymmetric sections.

Load linking

Support reactions are exported as linked outputs. Column and footing calculations placed downstream automatically receive the updated reactions when beam inputs change.