W8x31 Section Properties
The W8x31 is a wide-flange steel section weighing 31 lb/ft (46.1 kg/m) with a nominal depth of 8 inches. The W8x31 occupies a unique niche in the AISC inventory -- it is a stocky, nearly square section (bf = 8.00 in, d = 8.00 in) that serves primarily as a light column, a beam-column in low-rise frames, and a short-span beam where shallow depth is critical. Its wide flange relative to depth gives it good weak-axis properties for its weight class.
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Complete Section Properties (Imperial)
| Property | Symbol | Value | Unit |
|---|---|---|---|
| Depth | d | 8.00 | in |
| Flange Width | bf | 7.995 | in |
| Flange Thickness | tf | 0.435 | in |
| Web Thickness | tw | 0.285 | in |
| Cross-Sectional Area | A | 9.13 | in² |
| Weight per Foot | wt | 31 | lb/ft |
| Moment of Inertia (strong axis) | Ix | 110 | in⁴ |
| Elastic Section Modulus (strong axis) | Sx | 27.5 | in³ |
| Plastic Section Modulus (strong axis) | Zx | 30.4 | in³ |
| Radius of Gyration (strong axis) | rx | 3.47 | in |
| Moment of Inertia (weak axis) | Iy | 37.1 | in⁴ |
| Elastic Section Modulus (weak axis) | Sy | 9.27 | in³ |
| Plastic Section Modulus (weak axis) | Zy | 14.1 | in³ |
| Radius of Gyration (weak axis) | ry | 2.02 | in |
| Torsional Constant | J | 0.536 | in⁴ |
| Warping Constant | Cw | 530 | in⁶ |
Metric Equivalents
| Property | Symbol | Value | Unit |
|---|---|---|---|
| Depth | d | 203 | mm |
| Flange Width | bf | 203 | mm |
| Flange Thickness | tf | 11.0 | mm |
| Web Thickness | tw | 7.24 | mm |
| Cross-Sectional Area | A | 5,890 | mm² |
| Weight per Metre | wt | 46.1 | kg/m |
| Moment of Inertia (strong axis) | Ix | 45.8 x 10⁶ | mm⁴ |
| Elastic Section Modulus (strong axis) | Sx | 451 x 10³ | mm³ |
| Plastic Section Modulus (strong axis) | Zx | 498 x 10³ | mm³ |
AISC 360 Compactness Classification
For A992 steel (Fy = 50 ksi, E = 29,000 ksi):
Flange: bf/(2tf) = 7.995 / (2 x 0.435) = 9.19. Compact limit = 0.38 x sqrt(29,000/50) = 9.15. Since 9.19 > 9.15 (by a negligible margin), this flange is technically noncompact per the strict AISC criterion. However, the ratio is so close to the compact limit that the reduction in moment capacity is negligible. Per AISC 360 Table F3-1, the nominal moment for noncompact flanges is: Mn = Mp - (Mp - 0.7FySx)(lambda - lambdapf)/(lambdarf - lambdapf). With lambda = 9.19, lambdapf = 9.15, and lambdarf = 24.1, the reduction is less than 0.1%.
Web: h/tw = (8.00 - 2 x 0.935) / 0.285 = 6.13 / 0.285 = 21.5. Compact limit = 90.6. Web is compact.
Classification: Noncompact (flange, marginally) -- effectively full Mp is available for practical design purposes.
Design Capacity Summary (AISC 360 LRFD, A992 Fy = 50 ksi)
Axial Compression Capacity (phi = 0.90, K = 1.0)
| Effective Length KL | KL/ry | phi x Pn (kips) | Fcr (ksi) |
|---|---|---|---|
| 8 ft | 47.5 | 352 | 42.8 |
| 10 ft | 59.4 | 333 | 40.6 |
| 12 ft | 71.3 | 310 | 37.8 |
| 14 ft | 83.2 | 282 | 34.3 |
| 16 ft | 95.0 | 250 | 30.5 |
Flexural Capacity (phi = 0.90)
| Unbraced Length Lb | phi x Mn | Governing Limit State |
|---|---|---|
| 0 ft (full bracing) | 114 ft-kips | Yielding (Mp) |
| 6 ft | 114 ft-kips | Yielding (Lb < Lp) |
| 10 ft | 98.3 ft-kips | Inelastic LTB |
| 14 ft | 77.3 ft-kips | Inelastic LTB |
| 18 ft | 51.0 ft-kips | Elastic LTB |
Lateral bracing limits: Lp = 6.24 ft (based on ry = 2.02 in). Lr = 19.2 ft.
Shear Capacity (phi = 1.00)
phi x Vn = 1.00 x 0.6 x 50 x (8.00 x 0.285) = 68.4 kips
Common Applications for W8x31
- Columns in single-story and two-story buildings carrying moderate axial loads (150-350 kips factored). The 8-inch square footprint fits neatly within standard wall cavities.
- Short-span beams (10-15 ft) where floor-to-floor depth is severely constrained, such as mezzanines, renovations, and retrofit projects.
- Beam-columns in braced frames where combined axial and flexural demands are moderate.
- Equipment supports and platforms in industrial facilities where stiffness and compact depth are priorities.
- Lintels over wide openings in steel-framed walls where structural depth is limited to the wall cavity.
- Stair stringer beams requiring compact depth and moderate capacity.
The W8x31 is a "column-weight" section (bf approximately equals d) in the W8 family. The lighter W8x18 (bf = 5.25 in, ry = 1.23 in) and W8x24 (bf = 6.50 in, ry = 1.61 in) have narrower flanges and are classified as "beam-weight" sections. The difference in ry is dramatic: 2.02 in for the W8x31 vs 1.23 in for the W8x18, making the W8x31 vastly superior for column applications.
Available Steel Grades
| Grade | Specification | Fy (ksi) | Fu (ksi) | Status |
|---|---|---|---|---|
| A992 | ASTM A992/A992M | 50 | 65 | Current standard for W-shapes |
| A572 Gr 50 | ASTM A572/A572M | 50 | 65 | Acceptable alternate |
Comparison with Adjacent Sections
| Property | W8x24 | W8x31 | W8x35 | W8x40 |
|---|---|---|---|---|
| Weight (lb/ft) | 24 | 31 | 35 | 40 |
| d (in) | 7.93 | 8.00 | 8.12 | 8.25 |
| bf (in) | 6.495 | 7.995 | 8.020 | 8.070 |
| A (in²) | 7.08 | 9.13 | 10.3 | 11.7 |
| Ix (in⁴) | 82.7 | 110 | 127 | 146 |
| ry (in) | 1.61 | 2.02 | 2.03 | 2.04 |
The jump from W8x24 to W8x31 is significant: bf increases from 6.5 in to 8.0 in and ry jumps from 1.61 in to 2.02 in. This represents the transition from narrow-flange (beam) to wide-flange (column) sub-groups within the W8 family. The W8x35 and W8x40 offer incremental improvements in area and Ix with essentially the same ry.
Run This Calculation
Column Capacity Calculator -- check W8x31 axial compression capacity with KL/r slenderness.
Beam Capacity Calculator -- check W8x31 bending, shear, and LTB capacity.
Beam Deflection Calculator -- calculate deflection for W8x31 under loading.
Related Pages
- Section Properties Database
- W-Shape Beam Sizes -- Complete Table
- Column K-Factor Guide
- Steel Grades Reference
- A992 steel grade properties
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