C15X50 Steel C-shape — Section Properties
Dimensions
| Property | Value | Unit |
|---|---|---|
| Depth (d) | 15 | 381.0 mm |
| Flange Width (bf) | 3.72 | 9.45 cm |
| Flange Thickness (tf) | 0.65 | 16.5 mm |
| Web Thickness (tw) | 0.716 | 18.2 mm |
| Area (A) | 14.7 in² | 94.8 cmÃÂò |
| Weight | 50 lb/ft | 74.4 kg/m |
Elastic Section Properties
| Property | Strong Axis (X-X) | Weak Axis (Y-Y) | Unit |
|---|---|---|---|
| Moment of Inertia (I) | 404 | 11 | in⁴ |
| Elastic Section Modulus (S) | 53.8 | 3.77 | in³ |
| Plastic Section Modulus (Z) | 68.5 | 8.14 | in³ |
| Radius of Gyration (r) | 5.24 | 0.865 | in |
Torsional Properties
| Property | Value | Unit |
|---|---|---|
| Torsional Constant (J) | 2.65 | in⁴ |
| Warping Constant (Cw) | 492 | in⁶ |
| Distance Between Flange Centroids (ho) | 14.4 | in |
| Effective Radius (rts) | 1.17 | in |
Section Profile Summary
The shear center of a channel lies outside the web (distance eâÃÂàfrom the web face). Loads applied to the top flange produce torsion unless the load plane passes through the shear center. For AISC 360 flexural design, lateral-torsional buckling must be checked with the warping constant Cw.
At 15" deep and 50 lb/ft, this is a mid-range section suitable for floor beams, roof framing, and columns in low-to-mid-rise structures.
Key Design Checks (AISC 360)
| Check | Formula | This Section |
|---|---|---|
| Plastic moment | Mp = Zx × Fy | 3,425 kip-in |
| Deflection | Δ = 5wLâÃÂô/(384EIx) | Use Ix = 404 in⁴ |
| Torsion | St. Venant = GJ/L | J = 2.65 in⁴ |
| Column buckling | KL/r âÃÂàFcr | r_x = 5.24 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: Library stack beam — c15x50
Scenario: Library stack area — dead load includes shelving and books. Simply supported channel, 35 ft span, 7 ft tributary width. Service loads: 85 psf dead + 60 psf live (1015 plf total).
Given:
- Span L = 35 ft (420 in)
- Total service load w = 1015 plf
- Live load portion w_L = 420 plf
- Section c15x50: Ix = 404 in⁴, Sx = 53.8 in³, Zx = 68.5 in³
- Steel: ASTM A992, Fy = 50 ksi, E = 29,000 ksi
- Design moment strength: φMn = 0.9 × Zx × Fy = 257 kip-ft
Step 1 — Live load deflection check:
Δ_LL = 5 w_L LâÃÂô / (384 E Ix)
Δ_LL = 5 × (420/12) × (420)âÃÂô / (384 × 29,000,000 × 404)
Δ_LL = 1.21 in
Step 2 — Allowable deflection (IBC Table 1604.3, L/240):
Δ_allow = L / 240 = 420 / 240 = 1.75 in
Step 3 — Dead + live deflection:
Δ_total = 2.93 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 = 257 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.