W10X77 Steel Beam — Section Properties
Dimensions
| Property | Value | Unit |
|---|---|---|
| Depth (d) | 10.60 | in (269.2 mm) |
| Flange Width (bf) | 10.20 | in (259.1 mm) |
| Flange Thickness (tf) | 0.87 | in |
| Web Thickness (tw) | 0.53 | in |
| Area (A) | 22.70 | in² (146.5 cmÃÂò) |
| Weight | 77 | lb/ft (115 kg/m) |
Elastic Section Properties
| Property | Strong Axis (X-X) | Weak Axis (Y-Y) | Unit |
|---|---|---|---|
| Moment of Inertia (I) | 455 | 154 | in⁴ |
| Elastic Section Modulus (S) | 85.90 | 30.10 | in³ |
| Plastic Section Modulus (Z) | 97.60 | 45.90 | in³ |
| Radius of Gyration (r) | 4.49 | 2.60 | in |
Torsional Properties
| Property | Value | Unit |
|---|---|---|
| Torsional Constant (J) | 5.11 | in⁴ |
| Warping Constant (Cw) | 3,630 | in⁶ |
| Distance Between Flange Centroids (ho) | 9.73 | in |
| Effective Radius (rts) | 2.95 | in |
Section Profile Summary
With Ix = 455 in⁴, this wide flange is appropriate for typical beam spans in the 12âÃÂÃÂ25 ft range for commercial and institutional construction.
At 10.6" deep, this is a compact section appropriate 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 | 4,880 kip-in |
| Deflection | Δ = 5wLâÃÂô/(384EIx) | Use Ix = 455 in⁴ |
| Torsion | St. Venant = GJ/L | J = 5.11 in⁴ |
| Column buckling | KL/r âÃÂàFcr | r_x = 4.49 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 âÃÂà110.2 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: Hospital corridor beam — w10x77
Scenario: Hospital corridor — deflection limit tightened for ceiling and services. Simply supported wide flange, 21 ft span, 6 ft tributary width. Service loads: 50 psf dead + 80 psf live (780 plf total).
Given:
- Span L = 21 ft (252 in)
- Total service load w = 780 plf
- Live load portion w_L = 480 plf
- Section w10x77: Ix = 455 in⁴, Sx = 85.9 in³, Zx = 97.6 in³
- Steel: ASTM A992, Fy = 50 ksi, E = 29,000 ksi
- Design moment strength: φMn = 0.9 × Zx × Fy = 366 kip-ft
Step 1 — Live load deflection check:
Δ_LL = 5 w_L LâÃÂô / (384 E Ix)
Δ_LL = 5 × (480/12) × (252)âÃÂô / (384 × 29,000,000 × 455)
Δ_LL = 0.16 in
Step 2 — Allowable deflection (IBC Table 1604.3, L/360):
Δ_allow = L / 360 = 252 / 360 = 0.70 in
Step 3 — Dead + live deflection:
Δ_total = 0.26 in
Step 4 — Design check:
âÃÂàLive load deflection is within the L/360 limit.
The required flexural strength at ultimate is approximately w_u LÃÂò/8. With factored loads 1.2D + 1.6L, verify φMn = 366 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.