S12X31.8 Steel S-shape — Section Properties
Dimensions
| Property | Value | Unit |
|---|---|---|
| Depth (d) | 12 | 304.8 mm |
| Flange Width (bf) | 5 | 12.70 cm |
| Flange Thickness (tf) | 0.544 | 13.8 mm |
| Web Thickness (tw) | 0.35 | 8.9 mm |
| Area (A) | 9.31 in² | 60.1 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) | 217 | 9.33 | in⁴ |
| Elastic Section Modulus (S) | 36.2 | 3.73 | in³ |
| Plastic Section Modulus (Z) | 41.8 | 6.44 | in³ |
| Radius of Gyration (r) | 4.83 | 1 | in |
Torsional Properties
| Property | Value | Unit |
|---|---|---|
| Torsional Constant (J) | 0.878 | in⁴ |
| Warping Constant (Cw) | 306 | in⁶ |
| Distance Between Flange Centroids (ho) | 11.5 | in |
| Effective Radius (rts) | 1.21 | in |
Section Profile Summary
This is a standard hot-rolled I-beam profile covered by AISC 360. The tabulated section properties are computed from the nominal dimensions per the governing material standard. With Ix = 217 in⁴, the strong-axis flexural stiffness is suitable for preliminary sizing of beams and beam-columns.
At 12" deep, this is a compact section suitable 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 | 2,090 kip-in |
| Deflection | Δ = 5wLâÃÂô/(384EIx) | Use Ix = 217 in⁴ |
| Torsion | St. Venant = GJ/L | J = 0.878 in⁴ |
| Column buckling | KL/r âÃÂàFcr | r_x = 4.83 in |
Design Notes
- Compactness: Verify flange and web slenderness against AISC 360 Table B4.1 classification limits for the governing load case (pure compression, pure flexure, or combined).
- Combined loading: For members under simultaneous axial force and bending, use the interaction equations in AISC 360 Section H. The governing equation depends on the ratio of required to available axial strength.
- Connection limit states: Check bolt bearing, tear-out, block shear, and weld strength at all connections. The governing connection limit state often controls the member size selection.
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: Library stack beam — s12x31_8
Scenario: Library stack area — dead load includes shelving and books. Simply supported I-beam, 23 ft span, 7 ft tributary width. Service loads: 85 psf dead + 60 psf live (1015 plf total).
Given:
- Span L = 23 ft (276 in)
- Total service load w = 1015 plf
- Live load portion w_L = 420 plf
- Section s12x31_8: Ix = 217 in⁴, Sx = 36.2 in³, Zx = 41.8 in³
- Steel: ASTM A992, Fy = 50 ksi, E = 29,000 ksi
- Design moment strength: φMn = 0.9 × Zx × Fy = 157 kip-ft
Step 1 — Live load deflection check:
Δ_LL = 5 w_L LâÃÂô / (384 E Ix)
Δ_LL = 5 × (420/12) × (276)âÃÂô / (384 × 29,000,000 × 217)
Δ_LL = 0.42 in
Step 2 — Allowable deflection (IBC Table 1604.3, L/240):
Δ_allow = L / 240 = 276 / 240 = 1.15 in
Step 3 — Dead + live deflection:
Δ_total = 1.02 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 = 157 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.