C9X13.4 Steel C-shape — Section Properties
Dimensions
| Property | Value | Unit |
|---|---|---|
| Depth (d) | 9 | 228.6 mm |
| Flange Width (bf) | 2.43 | 6.17 cm |
| Flange Thickness (tf) | 0.413 | 10.5 mm |
| Web Thickness (tw) | 0.233 | 5.9 mm |
| Area (A) | 3.94 in² | 25.4 cmÃÂò |
| Weight | 13.4 lb/ft | 19.9 kg/m |
Elastic Section Properties
| Property | Strong Axis (X-X) | Weak Axis (Y-Y) | Unit |
|---|---|---|---|
| Moment of Inertia (I) | 47.8 | 1.75 | in⁴ |
| Elastic Section Modulus (S) | 10.6 | 0.954 | in³ |
| Plastic Section Modulus (Z) | 12.6 | 1.94 | in³ |
| Radius of Gyration (r) | 3.48 | 0.666 | in |
Torsional Properties
| Property | Value | Unit |
|---|---|---|
| Torsional Constant (J) | 0.168 | in⁴ |
| Warping Constant (Cw) | 28.2 | in⁶ |
| Distance Between Flange Centroids (ho) | 8.59 | in |
| Effective Radius (rts) | 0.814 | in |
Section Profile Summary
Unlike doubly-symmetric sections, channel bending about the weak axis produces twist. Where weak-axis flexure is unavoidable, provide torsional restraint at close intervals or switch to a hollow section.
At 9" deep, this is a compact section commonly specified for joists, mezzanine framing, equipment support beams, and architectural features where depth control matters.
Key Design Checks (AISC 360)
| Check | Formula | This Section |
|---|---|---|
| Plastic moment | Mp = Zx × Fy | 630 kip-in |
| Deflection | Δ = 5wLâÃÂô/(384EIx) | Use Ix = 47.8 in⁴ |
| Torsion | St. Venant = GJ/L | J = 0.168 in⁴ |
| Column buckling | KL/r âÃÂàFcr | r_x = 3.48 in |
Design Notes
- Section asymmetry: The shear center lies outside the web. Loads not applied through the shear center produce torsion. Provide intermediate torsional restraints or stiffeners when the load eccentricity is significant.
- Lateral-torsional buckling: Check Cb (moment modification factor) per AISC 360 Chapter F — channels are more sensitive to load height effects than doubly-symmetric sections.
- Web crippling at supports: For channels used as beams, bearing stiffeners may be needed at concentrated load points per AISC 360 Section J10.
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: Light commercial floor beam — c9x13_4
Scenario: Retail space floor — higher live load for public occupancy. Simply supported channel, 14 ft span, 8 ft tributary width. Service loads: 55 psf dead + 60 psf live (920 plf total).
Given:
- Span L = 14 ft (168 in)
- Total service load w = 920 plf
- Live load portion w_L = 480 plf
- Section c9x13_4: Ix = 47.8 in⁴, Sx = 10.6 in³, Zx = 12.6 in³
- Steel: ASTM A992, Fy = 50 ksi, E = 29,000 ksi
- Design moment strength: φMn = 0.9 × Zx × Fy = 47 kip-ft
Step 1 — Live load deflection check:
Δ_LL = 5 w_L LâÃÂô / (384 E Ix)
Δ_LL = 5 × (480/12) × (168)âÃÂô / (384 × 29,000,000 × 47.8)
Δ_LL = 0.30 in
Step 2 — Allowable deflection (IBC Table 1604.3, L/240):
Δ_allow = L / 240 = 168 / 240 = 0.70 in
Step 3 — Dead + live deflection:
Δ_total = 0.57 in
Step 4 — Design check:
âÃÂàLive load deflection is within the L/240 limit.
The required flexural strength at ultimate is approximately w_u LÃÂò/8. With factored loads 1.2D + 1.6L, verify φMn = 47 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.