CSA S16-19

This page covers design checks to CSA S16-19, Design of Steel Structures, for W-shapes, welded I-sections, channels, angles, tees and hollow sections. Hollow sections can be Class C (cold-formed) or Class H (hot-formed, or cold-formed and stress-relieved).

Open CSA S16-19 Calculator

Standard Reference

Supported Section Types

• I-Shapes (W-shapes, WWF - rolled and welded wide flanges)
• Channels
• Tees (WT and WWT, beam tees and column tees, with the stem in tension or compression)
• Rectangular Hollow Sections (HSS rectangular and square - Class H and Class C)
• Circular Hollow Sections (HSS round - Class H and Class C)
• Angles (equal and unequal leg)

Checks Performed

The design-check table shows the check and clause used for each member result. Summary by clause group:

• Section classification (Cl 11.2 / Tables 1-2): Classification is action-specific and drives the section or effective-property branch.
• Tension (Cl 13.2): Gross yielding and net-section fracture are checked using optional member An and effective-net factor; blank An defaults to Ag because bolt-hole geometry is not inferred. Blank U uses the lowest Cl 12.3.3.2 value for open sections and 1.0 for hollow sections.
• Compression (Cl 13.3.1 / Cl 13.3.4): Member compression, supported flexural-torsional buckling, and Class 4 effective-area checks use the selected fabrication branch. Every Cr, including the Clause 13.8 section and member terms, uses the Table 1 effective area with Clause 11.3 widths; this is an engineering interpretation of S16-19, not an official CSA ruling.
• Flexure and LTB (Cl 13.5 / Cl 13.6.1 / Cl 14.3): Section paths follow the active section family. The 13.5(a) service-load yield condition for unequal-I and tee plastic resistance is evaluated on SLS-classified combinations only; if a member has no SLS combination, a note reports it as not checked. Service actions are never inferred from ultimate actions. With continuous restraint, major-axis Class 1/2 tees use full Z when the flange is compressed; when the stem tip is compressed (hogging), the 13.6.1 member check applies. Finite Class 1/2/3 tees use verified geometric beta and 13.6.1(e) member resistance, with My replacing Mp whenever the stem tip is compressed. Tee combined plastic eligibility remains limited. Class 4 tee, cantilever and destabilizing-load member methods and unsupported unequal-I LTB are not checked, and the dependent member checks are not reported. Non-square RHS receive the Clause 13.6.1 member LTB check with zero warping constant; SHS and CHS are exempt. Unrestrained cantilevers require rational analysis under Clause 13.6.1(d) and are omitted with a limitation notice; do not bypass this by setting the Cantilever control to Span. The Clause 14.3.1 maximum web slenderness h/w <= 83000/Fy is checked, with an optional separate-analysis waiver. A reported PASS covers only performed checks.
• Shear and torsion (Cl 13.4 / Cl 14.6 / Cl 14.10): Local shear paths are reported where applicable. CHS shear under 13.4.1.3 applies to Class 1/2 tubes only; Class 3/4 CHS shear is not checked. RHS shear uses the 13.4.1.1 web method with Aw = 2(D-4t)t, conservative relative to 13.4.1.3. Clause 14.6 shear-moment interaction applies to single-web beams (I-shapes and channels). Closed-section torsion is checked with an SRSS shear-torsion interaction, sqrt((Vf/Vr)^2 + (Tf/Tr)^2) <= 1.0, adopted as engineering judgement under Clause 14.10.1, not an S16 equation. Open-section warping torsion and the Clause 14.10.4 service-load normal-stress limit are not checked and need separate analysis.
• Combined actions (Cl 13.8 / Cl 13.9): Compression-bending and tension-bending checks use concurrent actions along the member, including the applicable section, member, LTB and moment-only checks. Declare each frame direction as Braced, Unbraced or Unspecified under Clause 13.8.1. Braced directions apply U1 where required, including local member effects in P-Delta FEA; section interactions retain the larger of the analysis and amplified member moments. Unbraced directions use supplied moments with U1 = 1, and unspecified directions conservatively cover both conditions. Supplied actions must include applicable Clause 8.4 stability effects. The standalone calculator does not run frame analysis. Invalid amplification prevents completion of the affected interaction.

Calculator Inputs

The standalone CSA S16-19 calculator accepts the following inputs. All values are in metric units.

Fabrication Type

Fabrication sets the Clause 13.3.1 compression curve exponent n and, for welded I-sections, the web shear area (A_w = h t_w instead of D t_w). It does not affect section classification. The options offered depend on the shape:

Section Geometry

Select a shape group, then enter dimensions or pick from the built-in section library (CISC shapes).

Material Properties

Member Lengths & Bracing

In the FEA Design tab the Cantilever control has three settings: Auto (default) follows the model and shows what it detected, for example "Auto (detected: cantilever, held at Node A)"; Span and Cantilever override the detection. For a cantilever the ω₂ override is not used (ω₂/ω₃ = 1.0). Clause 13.6.1(d) requires a rational analysis for unrestrained cantilevers, so for an unrestrained cantilever with major-axis bending the member LTB resistance and the LTB-dependent member results are not reported and the result is INCOMPLETE; section resistances remain available. Design such members by a separate rational analysis: there is no input for a rationally derived resistance, and ω₂ is not a substitute for one. Do not set the control to Span to bypass this: with a blank ω₂ the automatic factor from a cantilever moment diagram can exceed 2 and is unconservative.

Continuous Restraint means the top flange is continuously restrained, for example by a concrete slab or welded metal deck. Sagging (negative M_fx) compresses the restrained top flange and uses the section resistance. Hogging (positive M_fx) compresses the bottom flange, which is not braced: no credit is taken for the top-flange restraint, and the member is checked under Cl. 13.6.1 over L_u with the ω₂, load-height and cantilever rules and reported as a separate check. For tees, stem-tip compression is the hogging case. The Cl. 13.8, 13.9.3 and 14.6 checks use the resistance that matches the moment sign along the member. Enter KLT = 0 (L_u = 0 in the calculator) if the bottom flange is also braced. For single angles the checkbox applies to the whole member and switches the bending resistance from principal-axis Cl. 13.6.1(g) to geometric-axis Cl. 13.5(d).

Design Actions

Capacity Reduction Factor

The design check uses φ = 0.90 for member and section resistances and φ_u = 0.75 for the net-section (fracture) tension resistance (Clause 13.1(a)). Result details and hand calculations report the factor used by each check.

Class 4 Effective Section Properties

Class 4 sections use reduced effective properties per Clause 13.3.4 (compression) and 13.5(c) (flexure). Result details report the effective area, effective section modulus, or effective yield value used by the governing check.

Every compression resistance C_r, including the section and member terms in Clause 13.8, uses the Table 1 effective area with Clause 11.3 widths. Elastic buckling stress uses gross section properties. Table 2 stress-state classification applies to flexure. This is a documented engineering interpretation of S16:19, not an official CSA ruling. Other software may apply a different load-dependent classification approach, so comparisons can intentionally diverge. Result details and hand calculations show the Table 1 area derivation.

• I-shapes & channels: Effective area and effective section modulus are computed from the gross section while reducing only the relevant slender compression elements.
• Thin-web I-shape bending: When the web ratio exceeds the Clause 14.3.4 threshold and the flanges meet Class 3 limits, major-axis section and member moment resistances include its thin-web factor. Axial compression increases that reduction as specified by the clause; the factor appears in result details and hand calculations.
• Tees: Compression uses the full nominal stem with the Table 1 340/√F_y stem limit and flange outstands with 200/√F_y. Flexural terms retain the active stem stress state. Compression buckling measures both the centroid and thin-wall flange-centre shear centre from the stem tip; their coordinates and offset appear in the hand calculation.
• Angles: Class 4 single-angle checks use the Clause 11.3.1(b) effective-area basis with the Table 1 leg limit 250/√F_y for every C_r, and the Clause 13.5(d) effective-yield branch for flexure where applicable.
• RHS/SHS: Effective flat widths follow the Clause 11.3.2(b) convention. Axial compression preserves gross corner area and reduces all slender walls to Table 1; bending terms use the active stress state where applicable.
• Minor-axis I-shape bending: Clause 13.5(c)(iii) effective section modulus: the part of each compressed flange outstand beyond 200t/√F_y is removed, the neutral axis shifts toward the tension side, and S_e = I_e/c with c measured to the gross compressed flange tip.

Section Classification (Clause 11.2)

Per Clause 11.2, Table 1 applies to members subject to axial compression, while Table 2 applies to elements in flexure or combined flexure and compression. The web interaction limits are used only where Table 2 requires them. RHS/SHS checks use the Cl. 11.3.2(b) flat-width convention and the active stress state for Class 4 bending and the flexural terms of 13.8.4, including the lateral-torsional buckling case 13.8.4(c), whose M_rx is the lesser of the Clause 13.6.1 resistance and the Clause 13.5 resistance. The compression term always retains Table 1.

Limitations & Notes

• Design stiffness: Resistance and stability checks use E = 200,000 MPa and G = 77,000 MPa as CSA S16 assumes. Material stiffness entered for structural analysis does not change these design values.
• Unequal-flange I-sections: Clause 13.6.1(e) monosymmetric member LTB is not calculated, so member bending resistance and the dependent Clause 13.8/13.9 member checks are not reported unless the compression flange is continuously restrained (top-flange restraint under sagging, or both flanges braced). Section checks are still reported.
• Tee bending: Class 1/2/3 member resistance follows Clause 13.6.1(e) using monosymmetry properties and a centroid derived from the flange and stem geometry. Class 4 tee bending uses a conservative effective-yield section resistance under Cl. 13.5(c), reported for the stress state of the governing check rather than as a single member-wide class; Class 4 tee member LTB is not calculated and requires separate verification.
• Frame classification and amplification: Declare each bending direction as Unspecified, Braced or Unbraced under Clause 13.8.1. Braced directions apply U₁ where required, including local member effects in P-Delta FEA; section interactions retain the larger of the analysis and amplified member moments. Unbraced directions use supplied moments with U₁ = 1. Unspecified directions conservatively cover both conditions, including mixed frames. Applicable Clause 8.4 stability effects must be included in supplied actions; selecting a frame condition does not perform that analysis. Where C_f reaches the elastic buckling load C_e the member is reported as FAIL, or INCOMPLETE if C_e cannot be established, and the compression-bending interaction is not reported.
• Custom-section axes: Check that the major and minor axes, moments of inertia, and elastic and plastic section moduli match the section preview. Incorrect axis assignments affect bending, buckling and LTB resistance.
• Net section: Tension resistance under Cl 13.2 uses entered A_n and U; defaults for blank A_n and U are given under Material Properties. Clause 13.9 tension interaction uses the governing Cl 13.2 resistance. For Cl 13.9.2 with a reduced effective net area, a failing result is conclusive but a passing result is reported as OUT_OF_SCOPE until the net-section plastic modulus is verified separately. Bolt holes, staggered paths, and connection shear-lag geometry are not inferred.
• Angles, connection eccentricity: The effect of connection eccentricity (Clause 13.3.2) is not added. Include it in the design actions or check it separately. The general Clause 13.3.1 compression resistance applies with the entered effective lengths.
• Unequal-leg angle LTB: Uses the Clause 13.6.1(g)(ii) angle branch, with the sign convention based on long-leg compression.
• Moment amplification under transverse load: Linear moment diagrams take ω₁ from the end-moment ratio; members with transverse load between supports conservatively use ω₁ = 1.0.
• Welded I-section compression: Class H describes hollow sections, not welded wide flanges. Qualified doubly symmetric three-plate members use n = 2.24 for flexural buckling; other welded and unequal-flange I-sections use n = 1.34. The applicable torsional-buckling exception uses n = 1.34. Check the selected fabrication against the actual section.
• Concentrated forces and reactions: The CSA S16 member check does not perform local bearing, web local yielding, web crippling, web buckling, bearing-stiffener, or column force-transfer checks, and it does not derive these checks from FEA reactions, point loads, or connection forces. Check support bearing and concentrated load introduction regions separately from the member-strength result.
• Torsion (14.10): Not an input in the standalone calculator. In the FEA tool, torsion is checked for closed hollow sections (RHS/CHS) only, using the interaction (V_f/V_r)² + (T_f/T_r)² ≤ 1.0. This is an engineering interpretation of the general strength requirement of Clause 14.10.1, not an equation given in S16. Warping resistance for applied open-section torsion is not calculated (no Clause 14.10.2 moment-torque interaction) and requires separate analysis.
• Torsion service stress (14.10.4): Not checked. Service actions are not inferred from ultimate actions; verify this separately, particularly for open sections under torsion.
• Shear (13.4): CHS shear under Clause 13.4.1.3 applies only to Class 1 and 2 tubes; Class 3 and 4 CHS shear resistance is not reported. RHS shear uses the Clause 13.4.1.1 web method with A_w = 2(D − 4t)t (two webs, clear flat width per Clause 11.3.2(b)), which is conservative relative to the Clause 13.4.1.3 hollow-section expression.
• Shear-moment interaction (14.6): Applied to single-web beams (I-shapes and channels) where the web shear stress from Clause 13.4.1.1 exceeds 0.60 F_y.
• Maximum web slenderness (14.3.1): For I-shapes and channels, a web exceeding h/w = 83 000/F_y (F_y of the compression flange) fails unless the separate-analysis waiver is set, confirming that the compression flange will not buckle into the web at factored load levels.
• Serviceability and special design states: Analysis displacements may be reported separately, but the CSA S16 design check does not perform serviceability limit comparisons, vibration checks, fatigue, fire, corrosion/durability, connection detailing, or execution checks.

Verification

The public verification pages contain 44 published comparisons from S-FRAME examples and Kulak and Grondin, with an average numerical difference of 0.18%. Classification outcomes do not contribute to the numerical mean.