C9X15 Steel C-shape — Section Properties

Dimensions

Property Value Unit
Depth (d) 9 228.6 mm
Flange Width (bf) 2.49 6.32 cm
Flange Thickness (tf) 0.413 10.5 mm
Web Thickness (tw) 0.285 7.2 mm
Area (A) 4.4 in² 28.4 cm²
Weight 15 lb/ft 22.3 kg/m

Elastic Section Properties

Property Strong Axis (X-X) Weak Axis (Y-Y) Unit
Moment of Inertia (I) 51 1.91 in⁴
Elastic Section Modulus (S) 11.3 1.01 in³
Plastic Section Modulus (Z) 13.6 2.04 in³
Radius of Gyration (r) 3.4 0.659 in

Torsional Properties

Property Value Unit
Torsional Constant (J) 0.208 in⁴
Warping Constant (Cw) 31 in⁶
Distance Between Flange Centroids (ho) 8.59 in
Effective Radius (rts) 0.825 in

Section Profile Summary

The shear center of a channel lies outside the web (distance e₀ from 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 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 680 kip-in
Deflection Δ = 5wL⁴/(384EIx) Use Ix = 51 in⁴
Torsion St. Venant = GJ/L J = 0.208 in⁴
Column buckling KL/r → Fcr r_x = 3.4 in

Design Notes

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 — c9x15

Scenario: Library stack area — dead load includes shelving and books. Simply supported channel, 21 ft span, 7 ft tributary width. Service loads: 85 psf dead + 60 psf live (1015 plf total).

Given:

Step 1 — Live load deflection check:

Δ_LL = 5 w_L L⁴ / (384 E Ix)

Δ_LL = 5 × (420/12) × (252)⁴ / (384 × 29,000,000 × 51)

Δ_LL = 1.24 in

Step 2 — Allowable deflection (IBC Table 1604.3, L/240):

Δ_allow = L / 240 = 252 / 240 = 1.05 in

Step 3 — Dead + live deflection:

Δ_total = 3.00 in

Step 4 — Design check:

⚠ Live load deflection exceeds L/240 — consider a deeper section, reduce tributary width, or shorten the span.

The required flexural strength at ultimate is approximately w_u L²/8. With factored loads 1.2D + 1.6L, verify φMn = 51 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

Design Resources


Educational reference only. Verify all section properties against the current AISC 360 Manual and mill certificates before design. Results are PRELIMINARY — NOT FOR CONSTRUCTION.