Steel Member (Design Only)

How it calculates

The Steel Member (Design Only) calculator to CSA S16:19 accepts factored design forces and runs all limit states resistance checks for the selected Canadian steel section under combined loading.

Section classification

Section class is determined from the plate element slenderness ratios for the flanges and web (CSA S16 Table 1). Class 1 (plastic), Class 2 (compact), Class 3 (non-compact), and Class 4 (slender) sections are identified. Class 1 sections can develop the full plastic moment. Class 2 sections reach but cannot maintain plastic moment under rotation. Class 3 sections are limited to first yield. Class 4 sections are not supported in this version and will return a failing result if selected.

Flexural resistance and lateral-torsional buckling

Clause 13.6 governs flexural resistance. The plastic moment capacity Mp = Z × Fy is the upper limit for Class 1 and 2 sections. Lateral-torsional buckling reduces the moment resistance when the unbraced length exceeds the yield moment boundary. The factored moment resistance Mr is:

• Class 1 and 2, short segments: Mr = φ × Mp (no LTB)
• Inelastic LTB range: Mr = 1.15 × φ × Mp × (1 - 0.28 × Mp/Mu) ≤ φ × Mp
• Elastic LTB: Mr = φ × Mu

Where Mu is the elastic critical moment computed from the unbraced length, section torsional properties (J and Cw), and the moment gradient factor ω2. The ω2 factor accounts for non-uniform bending moment along the unbraced segment, increasing the effective moment resistance where the moment diagram is non-uniform.

For loads applied above the shear centre (top flange loading), the load height adjustment from Cl. 13.6.1 reduces the elastic critical moment. This is activated by a user input.

Compressive resistance and column buckling

Clause 13.3 covers compressive resistance. The factored compressive resistance Cr depends on the slenderness ratio KL/r for each axis, yielding stress Fy, and the column curve parameter n (n = 1.34 for hot-rolled sections, n = 2.24 for welded sections). The governing slenderness ratio is used to compute the normalized slenderness λ:

λ = (KL/r) × sqrt(Fy / (π² × E))

Cr = φ × Ag × Fy × (1 + λ^(2n))^(-1/n)

For sections with one axis of symmetry (tees, channels), torsional-flexural buckling replaces simple flexural buckling and a modified effective slenderness ratio is used.

Combined actions interaction

Clause 13.8 interaction equations are the primary output. For members under combined axial compression and bending:

interaction ratio = Cf/Cr + (0.85 × U1x × Mfx/Mrx) + (β × U1y × Mfy/Mry) ≤ 1.0

Where Cf is the factored compressive force, Mfx and Mfy are factored moments, Mrx and Mry are the factored moment resistances (including LTB), U1x and U1y are moment amplification factors for P-delta effects within the member, and β equals 0.6 for I-shaped and T-shaped sections or 0.85 for box sections. Both the cross-section (Clause 13.8.2) and member stability (Clause 13.8.3) interaction equations are checked and the governing interaction ratio is reported.

Shear resistance

Clause 13.4 governs shear. The factored shear resistance Vr = φ × Aw × 0.66 × Fy for compact webs. For slender webs, shear buckling reduces Vr via the shear buckling parameter.

Tension resistance

Clause 13.2 covers tension. The calculator checks gross cross-section yielding (Tr = φ × Ag × Fy) and, where applicable, net section fracture (Tr = φu × Ane × Fu). Both limit states are evaluated and the lower controls.