C4X4.5 Steel C-shape — Section Properties

Dimensions

Property Value Unit
Depth (d) 4 101.6 mm
Flange Width (bf) 1.52 3.86 cm
Flange Thickness (tf) 0.296 7.5 mm
Web Thickness (tw) 0.125 3.2 mm
Area (A) 1.34 in² 8.6 cm²
Weight 4.5 lb/ft 6.7 kg/m

Elastic Section Properties

Property Strong Axis (X-X) Weak Axis (Y-Y) Unit
Moment of Inertia (I) 3.53 0.265 in⁴
Elastic Section Modulus (S) 1.77 0.253 in³
Plastic Section Modulus (Z) 2.05 0.495 in³
Radius of Gyration (r) 1.62 0.445 in

Torsional Properties

Property Value Unit
Torsional Constant (J) 0.031 in⁴
Warping Constant (Cw) 0.778 in⁶
Distance Between Flange Centroids (ho) 3.7 in
Effective Radius (rts) 0.506 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 4" 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 102.5 kip-in
Deflection Δ = 5wL⁴/(384EIx) Use Ix = 3.53 in⁴
Torsion St. Venant = GJ/L J = 0.031 in⁴
Column buckling KL/r → Fcr r_x = 1.62 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: Assembly hall floor beam — c4x4_5

Scenario: Public assembly space — higher live load for movable seating/standing. Simply supported channel, 10 ft span, 8 ft tributary width. Service loads: 60 psf dead + 100 psf live (1280 plf total).

Given:

Step 1 — Live load deflection check:

Δ_LL = 5 w_L L⁴ / (384 E Ix)

Δ_LL = 5 × (800/12) × (120)⁴ / (384 × 29,000,000 × 3.53)

Δ_LL = 1.76 in

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

Δ_allow = L / 240 = 120 / 240 = 0.50 in

Step 3 — Dead + live deflection:

Δ_total = 2.81 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 = 8 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.