S20X75 Steel S-shape — Section Properties
Dimensions
| Property | Value | Unit |
|---|---|---|
| Depth (d) | 20 | 508.0 mm |
| Flange Width (bf) | 6.39 | 16.23 cm |
| Flange Thickness (tf) | 0.795 | 20.2 mm |
| Web Thickness (tw) | 0.635 | 16.1 mm |
| Area (A) | 22 in² | 141.9 cmÃÂò |
| Weight | 75 lb/ft | 111.6 kg/m |
Elastic Section Properties
| Property | Strong Axis (X-X) | Weak Axis (Y-Y) | Unit |
|---|---|---|---|
| Moment of Inertia (I) | 1280 | 29.5 | in⁴ |
| Elastic Section Modulus (S) | 128 | 9.25 | in³ |
| Plastic Section Modulus (Z) | 152 | 16.7 | in³ |
| Radius of Gyration (r) | 7.62 | 1.16 | in |
Torsional Properties
| Property | Value | Unit |
|---|---|---|
| Torsional Constant (J) | 4.59 | in⁴ |
| Warping Constant (Cw) | 2720 | in⁶ |
| Distance Between Flange Centroids (ho) | 19.2 | in |
| Effective Radius (rts) | 1.49 | 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 = 1,280 in⁴, the strong-axis flexural stiffness is suitable for preliminary sizing of beams and beam-columns.
At 20" deep and 75 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 | 7,600 kip-in |
| Deflection | Δ = 5wLâÃÂô/(384EIx) | Use Ix = 1,280 in⁴ |
| Torsion | St. Venant = GJ/L | J = 4.59 in⁴ |
| Column buckling | KL/r âÃÂàFcr | r_x = 7.62 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: Residential floor beam — s20x75
Scenario: Residential floor joist supporting bedrooms and living areas. Simply supported I-beam, 40 ft span, 10 ft tributary width. Service loads: 40 psf dead + 40 psf live (800 plf total).
Given:
- Span L = 40 ft (480 in)
- Total service load w = 800 plf
- Live load portion w_L = 400 plf
- Section s20x75: Ix = 1,280 in⁴, Sx = 128 in³, Zx = 152 in³
- Steel: ASTM A992, Fy = 50 ksi, E = 29,000 ksi
- Design moment strength: φMn = 0.9 × Zx × Fy = 570 kip-ft
Step 1 — Live load deflection check:
Δ_LL = 5 w_L LâÃÂô / (384 E Ix)
Δ_LL = 5 × (400/12) × (480)âÃÂô / (384 × 29,000,000 × 1,280)
Δ_LL = 0.62 in
Step 2 — Allowable deflection (IBC Table 1604.3, L/360):
Δ_allow = L / 360 = 480 / 360 = 1.33 in
Step 3 — Dead + live deflection:
Δ_total = 1.24 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 = 570 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.