W4X13 Steel Beam — Section Properties
Dimensions
| Property | Value | Unit |
|---|---|---|
| Depth (d) | 4.16 | in (105.7 mm) |
| Flange Width (bf) | 4.06 | in (103.1 mm) |
| Flange Thickness (tf) | 0.34 | in |
| Web Thickness (tw) | 0.28 | in |
| Area (A) | 3.83 | in² (24.7 cmÃÂò) |
| Weight | 13 | lb/ft (19 kg/m) |
Elastic Section Properties
| Property | Strong Axis (X-X) | Weak Axis (Y-Y) | Unit |
|---|---|---|---|
| Moment of Inertia (I) | 11.30 | 3.86 | in⁴ |
| Elastic Section Modulus (S) | 5.46 | 1.90 | in³ |
| Plastic Section Modulus (Z) | 6.28 | 2.92 | in³ |
| Radius of Gyration (r) | 1.72 | 1 | in |
Torsional Properties
| Property | Value | Unit |
|---|---|---|
| Torsional Constant (J) | 0.15 | in⁴ |
| Warping Constant (Cw) | 14 | in⁶ |
| Distance Between Flange Centroids (ho) | 3.82 | in |
| Effective Radius (rts) | 1.16 | in |
Section Profile Summary
Hot-rolled W-shape with Sx = 5.46 in³. The section is well-suited for joists, purlins, girts, and bracing elements where depth constraints apply.
At 4.16" deep — one of the smallest standard sections available. Used for light-duty lintels, bracing, handrail posts, and miscellaneous structural iron.
Key Design Checks (AISC 360)
| Check | Formula | This Section |
|---|---|---|
| Plastic moment | Mp = Zx × Fy | 314 kip-in |
| Deflection | Δ = 5wLâÃÂô/(384EIx) | Use Ix = 11.3 in⁴ |
| Torsion | St. Venant = GJ/L | J = 0.15 in⁴ |
| Column buckling | KL/r âÃÂàFcr | r_x = 1.72 in |
Design Notes
- Compactness: Most W-shapes in ASTM A992 satisfy the compact limits in AISC 360 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) âÃÂà9.15 for compact sections.
- Web local buckling (WLB): h/tw is checked against ÃÂûpw = 3.76âÃÂÃÂ(E/Fy) âÃÂà90.5 for flexure, and a more restrictive limit for uniform compression.
- Lateral-torsional buckling (LTB): Lp âÃÂà42.4 in (plastic limit). For unbraced lengths âÃÂä Lp, the full plastic moment is available. Between Lp and Lr, linear interpolation per AISC 360 Eq. F2-2 applies.
Verification (AISC 360): 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: Residential floor beam — w4x13
Scenario: Residential floor joist supporting bedrooms and living areas. Simply supported wide flange, 10 ft span, 10 ft tributary width. Service loads: 40 psf dead + 40 psf live (800 plf total).
Given:
- Span L = 10 ft (120 in)
- Total service load w = 800 plf
- Live load portion w_L = 400 plf
- Section w4x13: Ix = 11.3 in⁴, Sx = 5.46 in³, Zx = 6.28 in³
- Steel: ASTM A992, Fy = 50 ksi, E = 29,000 ksi
- Design moment strength: φMn = 0.9 × Zx × Fy = 24 kip-ft
Step 1 — Live load deflection check:
Δ_LL = 5 w_L LâÃÂô / (384 E Ix)
Δ_LL = 5 × (400/12) × (120)âÃÂô / (384 × 29,000,000 × 11.3)
Δ_LL = 0.27 in
Step 2 — Allowable deflection (IBC Table 1604.3, L/360):
Δ_allow = L / 360 = 120 / 360 = 0.33 in
Step 3 — Dead + live deflection:
Δ_total = 0.55 in
Step 4 — Design check:
âÃÂàLive load deflection is within the L/360 limit.
The required flexural strength at ultimate is approximately w_u LÃÂò/8. With factored loads 1.2D + 1.6L, verify φMn = 24 kip-ft is adequate per AISC 360 Chapter F. Also check shear capacity (φVn = 0.6 Fy Aw × 0.9) and bearing at 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 AISC 360 Manual and mill certificates before design. Results are PRELIMINARY — NOT FOR CONSTRUCTION.