MC13X31.8 Steel MC-shape — Section Properties
Dimensions
| Property | Value | Unit |
|---|---|---|
| Depth (d) | 13 | 330.2 mm |
| Flange Width (bf) | 4 | 10.16 cm |
| Flange Thickness (tf) | 0.61 | 15.5 mm |
| Web Thickness (tw) | 0.375 | 9.5 mm |
| Area (A) | 9.35 in² | 60.3 cmÃÂò |
| Weight | 31.8 lb/ft | 47.3 kg/m |
Elastic Section Properties
| Property | Strong Axis (X-X) | Weak Axis (Y-Y) | Unit |
|---|---|---|---|
| Moment of Inertia (I) | 239 | 11.4 | in⁴ |
| Elastic Section Modulus (S) | 36.7 | 3.79 | in³ |
| Plastic Section Modulus (Z) | 43.4 | 7.69 | in³ |
| Radius of Gyration (r) | 5.05 | 1.1 | in |
Torsional Properties
| Property | Value | Unit |
|---|---|---|
| Torsional Constant (J) | 0.937 | in⁴ |
| Warping Constant (Cw) | 380 | in⁶ |
| Distance Between Flange Centroids (ho) | 12.4 | in |
| Effective Radius (rts) | 1.34 | in |
Section Profile Summary
Channels are efficient for bracing, girts, and stair stringers where loads align near the shear center. At 31.8 lb/ft, this channel is appropriate for secondary framing in industrial and commercial structures.
At 13" deep and 31.8 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 | 2,170 kip-in |
| Deflection | Δ = 5wLâÃÂô/(384EIx) | Use Ix = 239 in⁴ |
| Torsion | St. Venant = GJ/L | J = 0.937 in⁴ |
| Column buckling | KL/r âÃÂàFcr | r_x = 5.05 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: Warehouse mezzanine beam — mc13x31_8
Scenario: Mezzanine beam in a warehouse — storage live load governs design. Simply supported channel, 22 ft span, 5 ft tributary width. Service loads: 30 psf dead + 125 psf live (775 plf total).
Given:
- Span L = 22 ft (264 in)
- Total service load w = 775 plf
- Live load portion w_L = 625 plf
- Section mc13x31_8: Ix = 239 in⁴, Sx = 36.7 in³, Zx = 43.4 in³
- Steel: ASTM A992, Fy = 50 ksi, E = 29,000 ksi
- Design moment strength: φMn = 0.9 × Zx × Fy = 163 kip-ft
Step 1 — Live load deflection check:
Δ_LL = 5 w_L LâÃÂô / (384 E Ix)
Δ_LL = 5 × (625/12) × (264)âÃÂô / (384 × 29,000,000 × 239)
Δ_LL = 0.48 in
Step 2 — Allowable deflection (IBC Table 1604.3, L/240):
Δ_allow = L / 240 = 264 / 240 = 1.10 in
Step 3 — Dead + live deflection:
Δ_total = 0.59 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 = 163 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.