CSA S16-19

The CSA S16-19 engine implements CSA S16-19 - Design of Steel Structures, the Canadian standard for the design of steel structures. It supports Class H (hot-formed/stress-relieved) and Class C (cold-formed) fabrication types for hollow sections.

Open CSA S16-19 Calculator

Standard Reference

Supported Section Types

• I-Shapes (W-shapes, WWF - rolled and welded wide flanges)
• Channels
• Tees (WT - beam tees and column tees with stem compression detection)
• 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

Section Classification (Clause 11)

Sections are classified as Class 1 through Class 4 per S16 Table 2. Classification is action-specific: different limits apply for compression versus flexure.

Tension (Clause 13.2)

• T_r: Gross section yielding (φ × A_g × F_y)
• T_r: Net section fracture (φ_u × A_ne × F_u, where φ_u = 0.75)

Compression (Clause 13.3)

• Section: C_r = φ × A × F_y (A_eff for Class 4)
• Member: C_r = φ × A × F_cr using the S16 column curve with n-exponent
• n-exponent: n = 2.24 for Class H (hot-formed/stress-relieved) hollow sections and WWF (welded wide flanges); n = 1.34 for all other sections
• Flexural-torsional buckling: Full FTB calculation for monosymmetric sections (tees, channels) and singly/doubly asymmetric sections (angles)

Flexure (Clause 13.5 & 13.6)

• Section: M_r = φ × Z × F_y (Class 1/2) or φ × S × F_y (Class 3) or φ × S_e × F_y (Class 4)
• LTB (13.6): Member moment resistance with ω₂ (equivalent uniform moment factor) auto-computed from the moment distribution
• Tee major-axis: Dedicated calculation including stem compression detection, LTB, and yielding. Beam Tee (BT) and Column Tee (CT) library labels are computed identically — both use major-axis bending about the asymmetric stem axis. Use the member sideways flag to model a horizontal-stem orientation.
• Angle bending — default (no continuous LTR): Principal-axis bending per Cl. 13.6(g). The engine rotates all six L-shape corners (heel, both leg tips outer/inner, inner corner) through the library’s α angle to find the principal extreme-fiber distances, giving S_u = I_u/max|v| and S_v = I_v/max|u|. Yielding uses S_u·F_y (or ·F_ye for Class 4 per 13.5(d)(ii)); LTB uses the principal-axis formulas Cl. 13.6.1(g)(i/ii) with factor 0.36 per S16-19. For unequal-leg angles the β_w bracket M_u = (4.9·E·I_z·ω₂/L²)·[√(β_w² + 0.052·(L·t/r_z)²) + β_w] is computed in full from L geometry, with the sign rule −β_w when the long leg is in compression anywhere along the unbraced length. Equal-leg angles use M_u = 0.46·E·b²·t²·ω₂/L: β_w is zero by symmetry, and the standard provides this separate equal-leg formula at cl. 13.6(g)(ii)(1).
• Angle bending — with continuous LTR: When the Continuously Restrained flag is set on the member, Cl. 13.6(g) does not govern (its scope is “without continuous lateral-torsional restraint”) and Cl. 13.5(d) applies instead. M_r = φ × S_min × F_y (or ·F_ye for Class 4), where S_min is the smaller elastic section modulus about the axis of bending — computed on the geometric axes by L-shape integration + parallel-axis theorem. This is typically 20–30% more conservative than the principal-axis form for unequal angles.
• Biaxial bending, moment-only: When M_fx and M_fy both act without axial, two separate checks are emitted — Cl. 13.5(e) Biaxial Bending (Section) using section M_r, and (when LTB governs on the major axis) Cl. 13.6.1(f) Biaxial Bending with LTB using LTB-reduced major M_r. Both use linear interaction M_fx/M_rx + M_fy/M_ry ≤ 1.0.

Shear (Clause 13.4)

• I-shapes and channels: k_v = 5.34 with web buckling check
• RHS: Two webs with clear height h = D − 4t per S16 11.3.2(b)
• CHS: Shear over half the cross-sectional area
• Tees and angles: k_v = 1.2
• Minor-axis shear through flanges (I/channels) or perpendicular walls (RHS)

Combined Actions (Clause 13.8 & 13.9)

• Class 1/2 I-shapes (13.8.2): Three limit states with β = 0.6 + 0.4λ_y≤ 0.85:
  • (a) Cross-section strength
  • (b) Overall member strength (strong-axis buckling)
  • (c) Lateral-torsional buckling + weak-axis buckling
• Class 1/2 Square HSS (13.8.3(b)): C_f/C_r + 0.85·U_1x·M_fx/M_rx + 0.50·U_1y·M_fy/M_ry ≤ 1.0
• Class 1/2 Circular HSS (13.8.3(c)): C_f/C_r + 0.85·√((U_1x·M_fx)² + (U_1y·M_fy)²)/M_r ≤ 1.0
• All other sections (13.8.4): C_f/C_r + U_1x·M_fx/M_rx + U_1y·M_fy/M_ry ≤ 1.0 (includes Class 3/4 HSS)
• Member-strength interactions use section M_r, not LTB-reduced. LTB is captured by a separate Biaxial LTB sub-check: M_fx/M_r,LTB + M_fy/M_ry ≤ 1.0. This split mirrors the Clause 13.8.2(b) / (c) distinction and avoids double-counting LTB in the overall member strength formula.
• Station-coincident demand pairing. Biaxial interactions evaluate M_fx and M_fy at the station that maximises the governing linear combination of bending terms, rather than independently combining peak |M_fx| and peak |M_fy| from different stations. Matches how modern FEA tools evaluate interactions and prevents artificial inflation when the two moment peaks occur at different x.
• Tension + bending (13.9.1): T_f/T_r + M_fx/M_rx + M_fy/M_ry ≤ 1.0. M_rx is the section M_r per Cl. 13.5 (not LTB-reduced) — LTB is handled by the separate Cl. 13.9.3 check. For angles and tees the engine reads M_r,yield directly from the governing bending check’s intermediates so long unbraced members do not double-count LTB inside the tension-bending formula.
• Class 1/2 I-shapes in tension (13.9.2): T_f/T_r + 0.85·M_fx/M_rx + 0.60·M_fy/M_ry ≤ 1.0, plus M_fx/M_rx + M_fy/M_ry ≤ 1.0
• Tension + LTB (13.9.3): M_fx/M_r,LTB + M_fy/M_ry − T_f·Z/(M_r,LTB·A) ≤ 1.0
• Plate girder shear-moment (14.6): For slender-web I-shapes: V_r,reduced = V_r × max(0, min(1, 2.20 − 1.60·M_f/M_r))

Calculator Inputs

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

Fabrication Type

Select the fabrication method - this affects the compression n-exponent and section classification:

• Rolled - standard rolled sections (W, C, WT, angles). n = 1.34
• Class H - hot-formed or stress-relieved HSS. n = 2.24
• Class C - cold-formed HSS. n = 1.34

Section Geometry

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

Material Properties

Member Lengths & Bracing

A Continuously Restrained checkbox sets L_u= 0, bypassing the LTB check. For single angles it also switches the bending-resistance path from principal-axis Cl. 13.6(g) to geometric-axis Cl. 13.5(d) — since Cl. 13.6(g) only applies to angles withoutcontinuous lateral-torsional restraint.

Design Actions

Capacity Reduction Factor

A capacity reduction factor of φ = 0.9 is used for yielding checks (tension yielding, compression, bending, and shear). Net section fracture uses φ_u = 0.75 per CSA S16-19.

Fabrication Types

Class 4 Effective Section Properties

Class 4 sections use reduced effective properties per Clause 13.3.4 (compression) and 13.5(c) (flexure). The engine applies the following section-specific calculations:

• I-shapes & channels: Both the effective area (for axial compression, Cl. 13.3.4) and the effective section modulus S_e (for major-axis bending, Cl. 13.5(c)(iii)) are computed by gross-subtraction: start from the gross section properties and remove only the slender compression-flange-tip strips. This preserves fillet area (~227 mm² for HP 360x108) that a rebuild-from-rectangles approach would lose. The neutral axis shifts toward the tension flange via parallel-axis; S_e = I_eff / c_comp,new. Under combined axial + bending, only the compression-side half-flanges are reduced (tension flange fully effective).
• Tees:When the stem is fully in compression at the governing station (axial stress > bending stress at stem root), the Case 1 outstand limit (200/√F_y) is used for effective area. Otherwise the Case 2 limit (340/√F_y) applies. For Class 4 Tee bending per Cl. 13.5(c)(iii), M_r = φ × S_x × F_yewhere F_ye = F_y × (340/√F_y / (d/t_w))² for stems.
• Angles: Effective area computed per Cl. 11.3.1(b) using the full nominal leg dimension (b_el = D or B, not (D−t_w)). Classification uses 250/√F_y (Table 1 compression) or 340/√F_y (Table 2 flexure).
• RHS/SHS: Effective widths use 670/√F_y per Cl. 11.3.2(b).
• Minor-axis I-shape bending: Effective S_euses a half-flange outstand reduction based on 200/√F_y (Case 1 limit) rather than the major-axis Se formula.

Section Classification (Clause 11.2)

Per Clause 11.2, Table 1 applies only to members subject to pure axial compression. When the member has non-negligible bending (combined loading), Table 2 appliesto the compression classification as well. This is particularly important for RHS/HSS members where Table 2 Case 5 limits (1100/1700/1900/√F_y with C_f/C_yinteraction) typically produce more favourable classifications under combined loading.

Limitations & Notes

• Unequal-leg angle β_w: Computed from L geometry per Cl. 13.6(g)(ii)(2) (midpoint-rule integration of (1/I_w)∫z(w²+z²)dA − 2z_o with shear centre at the intersection of leg centerlines). Sign per the standard: −β_w when the long leg is in compression anywhere along the unbraced length, +β_w otherwise.
• ω₁ for transverse loads: Returns 1.0 for all transverse load cases (UDL and concentrated loads). Uses 0.6 + 0.4κ for linear moment diagrams (end moments only).
• WWF detection: Welded wide flanges are auto-detected from the section description and assigned n = 2.24.
• Torsion (14.10): Not an input in the standalone calculator. In the FEA tool, torsion is checked for closed hollow sections (RHS/CHS) only. Warping torsion for open sections (I-beams, channels, angles, tees) is not performed.
• Tee LTB centroid: The effective radius of gyration r_t for tee LTB is computed using a centroid derived from rectangular geometry (flange + stem), not the library’s centroid which includes fillet radii. The difference is typically < 2%.
• Tee F_ye (Cl. 13.5(c)(iii)): Applied when the stem is fully in compression at the governing station. The engine uses the governing station’s stress state rather than station-by-station classification.
• Angle F_ye (Cl. 13.5(d)(ii)): Applied for Class 4 single angles using F_ye = F_y × (340/√F_y / (max(D,B)/t))². The reduction is derived from classical plate-buckling theory anchored to the Class 3 slenderness limit.
• RHS shear area: A_w = 2(D−4t)t per the clear flat-width convention (matches Canadian textbook verification for HSS152x102x9.5). CSA S16-19 Cl. 13.4.1.1 does not prescribe the formula.

Verification

The engine is benchmarked against 50 independent test casesfrom S-FRAME CSA S16-14 Examples, STAAD.Pro CSA S16-19 Verification, and Kulak & Grondin Limit States Design in Structural Steel (8th Ed), with an average difference of 0.16%.