What is the section modulus of S3X7.5?

Sx = 1.94 inÃÂÃÂ³, Zx = 2.35 inÃÂÃÂ³ (strong axis). Sy = 0.461 inÃÂÃÂ³, Zy = 0.821 inÃÂÃÂ³ (weak axis).

What steel grade is standard for S3X7.5?

ASTM A36 (Fy = 36 ksi) for S-shapes. Verify with mill certificate.

What is the moment of inertia of S3X7.5?

Ix = 2.91 inÃÂ¢ÃÂÃÂ´ about the strong axis and Iy = 0.578 inÃÂ¢ÃÂÃÂ´ about the weak axis. The radius of gyration is rx = 1.15 in and ry = 0.513 in.

S3X7.5 Steel S-shape — Section Properties

Dimensions

Property	Value	Unit
Depth (d)	3	76.2 mm
Flange Width (bf)	2.51	6.38 cm
Flange Thickness (tf)	0.26	6.6 mm
Web Thickness (tw)	0.349	8.9 mm
Area (A)	2.2 in²	14.2 cmÃÂÃÂ²
Weight	7.5 lb/ft	11.2 kg/m

Elastic Section Properties

Property	Strong Axis (X-X)	Weak Axis (Y-Y)	Unit
Moment of Inertia (I)	2.91	0.578	in⁴
Elastic Section Modulus (S)	1.94	0.461	in³
Plastic Section Modulus (Z)	2.35	0.821	in³
Radius of Gyration (r)	1.15	0.513	in

Torsional Properties

Property	Value	Unit
Torsional Constant (J)	0.09	in⁴
Warping Constant (Cw)	1.08	in⁶
Distance Between Flange Centroids (ho)	2.74	in
Effective Radius (rts)	0.638	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 = 2.91 in⁴, the strong-axis flexural stiffness is suitable for preliminary sizing of beams and beam-columns.

At 3" deep — one of the smallest standard sections available. Used for light-duty lintels, bracing, handrail posts, and miscellaneous structural iron.

Key Design Checks (AISC 360)

Check	Formula	This Section
Plastic moment	Mp = Zx × Fy	117.5 kip-in
Deflection	Δ = 5wLÃÂ¢ÃÂÃÂ´/(384EIx)	Use Ix = 2.91 in⁴
Torsion	St. Venant = GJ/L	J = 0.09 in⁴
Column buckling	KL/r ÃÂ¢ÃÂÃÂ Fcr	r_x = 1.15 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 — s3x7_5

Scenario: Residential floor joist supporting bedrooms and living areas. Simply supported I-beam, 10 ft span, 10 ft tributary width. Service loads: 40 psf dead + 40 psf live (800 plf total).

Given:

Span L = 10 ft (120 in)
Total service load w = 800 plf
Live load portion w_L = 400 plf
Section s3x7_5: Ix = 2.91 in⁴, Sx = 1.94 in³, Zx = 2.35 in³
Steel: ASTM A992, Fy = 50 ksi, E = 29,000 ksi
Design moment strength: φMn = 0.9 × Zx × Fy = 9 kip-ft

Step 1 — Live load deflection check:

Δ_LL = 5 w_L LÃÂ¢ÃÂÃÂ´ / (384 E Ix)

Δ_LL = 5 × (400/12) × (120)ÃÂ¢ÃÂÃÂ´ / (384 × 29,000,000 × 2.91)

Δ_LL = 1.07 in

Step 2 — Allowable deflection (IBC Table 1604.3, L/360):

Δ_allow = L / 360 = 120 / 360 = 0.33 in

Step 3 — Dead + live deflection:

Δ_total = 2.13 in

Step 4 — Design check:

ÃÂ¢ÃÂÃÂ Live load deflection exceeds L/360 — consider a deeper section, reduce tributary width, or shorten the span.

The required flexural strength at ultimate is approximately w_u LÃÂÃÂ²/8. With factored loads 1.2D + 1.6L, verify φMn = 9 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

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.