W840x299 G40.21 350W â Canadian W-Shape Section Properties
Approximate equivalent of W33X201 per AISC A6. Approx. equivalent of W33X201. Verify against CISC Handbook.
Dimensions (Metric)
| Property | Value | Unit |
|---|---|---|
| Depth (d) | 856.0 | mm |
| Flange Width (bf) | 398.8 | mm |
| Flange Thickness (tf) | 29.2 | mm |
| Web Thickness (tw) | 18.2 | mm |
| Cross-Sectional Area (A) | 381.3 | cmÃÂÃÂÃÂò |
| Mass | 299.1 | kg/m |
Elastic Section Properties (Metric)
| Property | Strong Axis (X-X) | Weak Axis (Y-Y) | Unit |
|---|---|---|---|
| Moment of Inertia (I) | 482,827 | 31,176 | cmÃÂâÃÂÃÂÃÂô |
| Elastic Section Modulus (S) | 11,241 | 1,560 | cmÃÂÃÂÃÂó |
| Plastic Section Modulus (Z) | 12,667 | 2,409 | cmÃÂÃÂÃÂó |
| Radius of Gyration (r) | 35.56 | 9.04 | cm |
Torsional Properties
| Property | Value | Unit |
|---|---|---|
| Torsional Constant (J) | 866 | cmÃÂâÃÂÃÂÃÂô |
| Warping Constant (Cw) | 53,163,000 | cmÃÂâÃÂÃÂÃÂö |
| Distance Between Flange Centroids (ho) | 82.80 | cm |
| Effective Radius (rts) | 10.69 | cm |
Imperial Reference
| Property | Value | Unit |
|---|---|---|
| Depth (d) | 33.70 | in |
| Flange Width (bf) | 15.70 | in |
| Area (A) | 59.10 | inÃÂÃÂÃÂò |
| Weight | 201 | lb/ft |
Section Profile Summary
With Ix = 482,827 cmâÃÂô, this wide flange is commonly specified for long-span floor beams and transfer girders where stiffness controls the design.
At 856 mm deep and 299.1 kg/m, this is a heavy section for primary framing — transfer beams, long-span roof girders, and major bridge stringers.
Key Design Checks (CSA S16)
| Check | Formula | This Section |
|---|---|---|
| Plastic moment | Mp = Zx ÃÂàFy | 4,433 kNÃÂ÷m |
| Deflection | ÃÂà= 5wLâÃÂô/(384EIx) | Use Ix = 482,827 cmâÃÂô |
| Torsion | St. Venant = GJ/L | J = 866 cmâÃÂô |
| Column buckling | KL/r âÃÂàFcr | r_x = 35.56 cm |
Design Notes
- Compactness: Most W-shapes in ASTM A992 satisfy the compact limits in CSA S16 Table B4.1b for flexure (ÃÂû âÃÂä ÃÂûp). This allows full plastic moment Mp development before local buckling occurs.
- Flange local buckling (FLB): The flange slenderness ratio bf/2tf is compared against ÃÂûpf = 0.38âÃÂÃÂ(E/Fy) âÃÂà9.0 for compact sections.
- Web local buckling (WLB): h/tw is checked against ÃÂûpw = 3.76âÃÂÃÂ(E/Fy) âÃÂà72 for flexure, and a more restrictive limit for uniform compression.
- Lateral-torsional buckling (LTB): Lp âÃÂà380.3 cm (plastic limit). For unbraced lengths âÃÂä Lp, the full plastic moment is available. Between Lp and Lr, linear interpolation per CSA S16 Eq. F2-2 applies.
Verification (CSA S16): All designs using this section must be verified by a licensed Professional Engineer. Before finalizing member selection, check beam-column interaction (P-M), lateral-torsional buckling, serviceability deflections, and all connection limit states. See Engineering Disclaimer.
Worked Example: School classroom beam — w840x299
Scenario: School building — tighter deflection limit for suspended ceiling integrity. Simply supported wide flange, 16.3 m span, 2.4 m tributary width. Service loads: 3.5 kPa dead + 3.0 kPa live (15.6 kN/m total).
Given:
- Span L = 16264 mm (16.3 m)
- Total service load w = 15.6 kN/m
- Live load portion w_L = 7.2 kN/m
- Section w840x299: Ix = 4828.3 ÃÂà10âÃÂö mmâÃÂô, Sx = 11,241,000 mmÃÂó, Zx = 12,667,000 mmÃÂó
- Steel: fy = 350 MPa, E = 200,000 MPa
- Design moment resistance: ÃÂÃÂMn = 0.9 ÃÂàZx ÃÂàfy = 3,990 kNÃÂ÷m
Step 1 — Live load deflection:
ÃÂÃÂ_LL = 5 w_L LâÃÂô / (384 E Ix)
ÃÂÃÂ_LL = 5 ÃÂà7.2 ÃÂà(16264)âÃÂô / (384 ÃÂà200000 ÃÂà4,828,270,000)
ÃÂÃÂ_LL = 6.8 mm
Step 2 — Deflection limit (L/360):
ÃÂÃÂ_limit = L / 360 = 16264 / 360 = 45.2 mm
Step 3 — Dead + live deflection:
ÃÂÃÂ_total = 14.7 mm
Step 4 — Design check:
âÃÂàLive load deflection is within the L/360 limit.
Verify the design moment M*_Ed (from factored loads 1.35G + 1.5Q per CSA S16) does not exceed ÃÂÃÂMn = 3,990 kNÃÂ÷m. Also confirm shear resistance and bearing details at the supports.
Related Resources
- Steel Beam Capacity Calculator
- Column Capacity Calculator
- Beam Deflection Calculator
- Section Properties Calculator
- Steel Grades Reference
- Section Comparison Tool
Design Resources
- Section Properties Lookup — Compare with similar sections
- Steel Beam Sizes Reference — Standard beam dimensions
Educational reference only. Verify all section properties against the current CSA S16 Manual and mill certificates before design. Results are PRELIMINARY — NOT FOR CONSTRUCTION.