W24X84 Steel Beam — Section Properties
Dimensions
| Property | Value | Unit |
|---|---|---|
| Depth (d) | 24.10 | in (612.1 mm) |
| Flange Width (bf) | 9.02 | in (229.1 mm) |
| Flange Thickness (tf) | 0.77 | in |
| Web Thickness (tw) | 0.47 | in |
| Area (A) | 24.70 | in² (159.4 cmÃÂò) |
| Weight | 84 | lb/ft (125 kg/m) |
Elastic Section Properties
| Property | Strong Axis (X-X) | Weak Axis (Y-Y) | Unit |
|---|---|---|---|
| Moment of Inertia (I) | 2,370 | 94.40 | in⁴ |
| Elastic Section Modulus (S) | 196 | 20.90 | in³ |
| Plastic Section Modulus (Z) | 224 | 32.60 | in³ |
| Radius of Gyration (r) | 9.79 | 1.95 | in |
Torsional Properties
| Property | Value | Unit |
|---|---|---|
| Torsional Constant (J) | 3.70 | in⁴ |
| Warping Constant (Cw) | 12,800 | in⁶ |
| Distance Between Flange Centroids (ho) | 23.30 | in |
| Effective Radius (rts) | 2.37 | in |
Section Profile Summary
With Ix = 2,370 in⁴, this wide flange is well-suited for long-span floor beams and transfer girders where stiffness controls the design.
At 24.1" deep, this section is frequently specified for primary floor beams, girders, and moment frame columns in commercial and institutional buildings.
Key Design Checks (AISC 360)
| Check | Formula | This Section |
|---|---|---|
| Plastic moment | Mp = Zx × Fy | 11,200 kip-in |
| Deflection | Δ = 5wLâÃÂô/(384EIx) | Use Ix = 2,370 in⁴ |
| Torsion | St. Venant = GJ/L | J = 3.7 in⁴ |
| Column buckling | KL/r âÃÂàFcr | r_x = 9.79 in |
Design Notes
- Compactness: Most W-shapes in ASTM A992 satisfy the compact limits in AISC 360 Table B4.1b for flexure (ÃÂû âÃÂä ÃÂûp). This allows full plastic moment Mp development before local buckling occurs.
- Flange local buckling (FLB): The flange slenderness ratio bf/2tf is compared against ÃÂûpf = 0.38âÃÂÃÂ(E/Fy) âÃÂà9.15 for compact sections.
- Web local buckling (WLB): h/tw is checked against ÃÂûpw = 3.76âÃÂÃÂ(E/Fy) âÃÂà90.5 for flexure, and a more restrictive limit for uniform compression.
- Lateral-torsional buckling (LTB): Lp âÃÂà82.7 in (plastic limit). For unbraced lengths âÃÂä Lp, the full plastic moment is available. Between Lp and Lr, linear interpolation per AISC 360 Eq. F2-2 applies.
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 — w24x84
Scenario: Public assembly space — higher live load for movable seating/standing. Simply supported wide flange, 53 ft span, 8 ft tributary width. Service loads: 60 psf dead + 100 psf live (1280 plf total).
Given:
- Span L = 53 ft (636 in)
- Total service load w = 1280 plf
- Live load portion w_L = 800 plf
- Section w24x84: Ix = 2,370 in⁴, Sx = 196 in³, Zx = 224 in³
- Steel: ASTM A992, Fy = 50 ksi, E = 29,000 ksi
- Design moment strength: φMn = 0.9 × Zx × Fy = 840 kip-ft
Step 1 — Live load deflection check:
Δ_LL = 5 w_L LâÃÂô / (384 E Ix)
Δ_LL = 5 × (800/12) × (636)âÃÂô / (384 × 29,000,000 × 2,370)
Δ_LL = 2.07 in
Step 2 — Allowable deflection (IBC Table 1604.3, L/240):
Δ_allow = L / 240 = 636 / 240 = 2.65 in
Step 3 — Dead + live deflection:
Δ_total = 3.31 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 = 840 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.