W200x52 G40.21 350W â Canadian W-Shape Section Properties
Approximate equivalent of W8X35 per AISC A6. Approx. equivalent of W8X35. Verify against CISC Handbook.
Dimensions (Metric)
| Property | Value | Unit |
|---|---|---|
| Depth (d) | 206.2 | mm |
| Flange Width (bf) | 203.7 | mm |
| Flange Thickness (tf) | 12.6 | mm |
| Web Thickness (tw) | 7.9 | mm |
| Cross-Sectional Area (A) | 66.5 | cmÃÂÃÂÃÂò |
| Mass | 52.1 | kg/m |
Elastic Section Properties (Metric)
| Property | Strong Axis (X-X) | Weak Axis (Y-Y) | Unit |
|---|---|---|---|
| Moment of Inertia (I) | 5,286 | 1,773 | cmÃÂâÃÂÃÂÃÂô |
| Elastic Section Modulus (S) | 511 | 174 | cmÃÂÃÂÃÂó |
| Plastic Section Modulus (Z) | 569 | 264 | cmÃÂÃÂÃÂó |
| Radius of Gyration (r) | 8.92 | 5.16 | cm |
Torsional Properties
| Property | Value | Unit |
|---|---|---|
| Torsional Constant (J) | 32 | cmÃÂâÃÂÃÂÃÂô |
| Warping Constant (Cw) | 166,202 | cmÃÂâÃÂÃÂÃÂö |
| Distance Between Flange Centroids (ho) | 19.38 | cm |
| Effective Radius (rts) | 5.79 | cm |
Imperial Reference
| Property | Value | Unit |
|---|---|---|
| Depth (d) | 8.12 | in |
| Flange Width (bf) | 8.02 | in |
| Area (A) | 10.30 | inÃÂÃÂÃÂò |
| Weight | 35 | lb/ft |
Section Profile Summary
Hot-rolled W-shape with Sx = 511 cmÃÂó. The section is suitable for primary framing in multi-storey buildings, crane girders, and bridge stringers.
At 206.2 mm deep, this is a mid-range section for secondary beams, roof purlins, and bracing in standard framing.
Key Design Checks (CSA S16)
| Check | Formula | This Section |
|---|---|---|
| Plastic moment | Mp = Zx ÃÂàFy | 199 kNÃÂ÷m |
| Deflection | ÃÂà= 5wLâÃÂô/(384EIx) | Use Ix = 5,286 cmâÃÂô |
| Torsion | St. Venant = GJ/L | J = 32 cmâÃÂô |
| Column buckling | KL/r âÃÂàFcr | r_x = 8.92 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 âÃÂà217.1 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: Roof beam (flat roof) — w200x52
Scenario: Flat roof with services — allowance for mechanical units and drainage. Simply supported wide flange, 5.2 m span, 3.6 m tributary width. Service loads: 2.0 kPa dead + 1.5 kPa live (12.6 kN/m total).
Given:
- Span L = 5155 mm (5.2 m)
- Total service load w = 12.6 kN/m
- Live load portion w_L = 5.4 kN/m
- Section w200x52: Ix = 52.9 ÃÂà10âÃÂö mmâÃÂô, Sx = 511,000 mmÃÂó, Zx = 569,000 mmÃÂó
- Steel: fy = 350 MPa, E = 200,000 MPa
- Design moment resistance: ÃÂÃÂMn = 0.9 ÃÂàZx ÃÂàfy = 179 kNÃÂ÷m
Step 1 — Live load deflection:
ÃÂÃÂ_LL = 5 w_L LâÃÂô / (384 E Ix)
ÃÂÃÂ_LL = 5 ÃÂà5.4 ÃÂà(5155)âÃÂô / (384 ÃÂà200000 ÃÂà52,860,000)
ÃÂÃÂ_LL = 4.7 mm
Step 2 — Deflection limit (L/250):
ÃÂÃÂ_limit = L / 250 = 5155 / 250 = 20.6 mm
Step 3 — Dead + live deflection:
ÃÂÃÂ_total = 11.0 mm
Step 4 — Design check:
âÃÂàLive load deflection is within the L/250 limit.
Verify the design moment M*_Ed (from factored loads 1.35G + 1.5Q per CSA S16) does not exceed ÃÂÃÂMn = 179 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.