What do Ix, Sx, Zx, rx, J, and Cw mean in steel section properties?

Each section property has a specific physical meaning and design use: Ix, Iy — Moment of Inertia (in⁴ or cm⁴). Measures resistance to bending deflection — higher I means less deflection. δ = 5wL⁴/(384EI) — deflection scales as 1/I. Ix is about the strong (x-x) axis, Iy about the weak (y-y) axis. For a W24×68, Ix = 1,830 in⁴ (stiff in strong axis), Iy = 70.4 in⁴ (much weaker in weak axis, ratio Ix/Iy = 26). Sx, Sy — Elastic Section Modulus (in³ or cm³). S = I/c where c = distance from neutral axis to extreme fiber. Used for elastic stress: fb = M/S. For A36 ASD design: Fb = 0.66Fy = 24 ksi up to Lp. For W24×68: Sx = 154 in³, so allowable moment = 154 × 24/12 = 308 kip-ft. Zx, Zy — Plastic Section Modulus (in³ or cm³). The full-plastic moment capacity: Mp = Zx × Fy. Zx is always ≥ Sx because the plastic stress distribution uses the full cross-section, while the elastic stress distribution only reaches yield at extreme fibers. Shape factor ξ = Zx/Sx — for W shapes ξ = 1.12-1.18 meaning 12-18% more moment capacity plastically vs. elastically. LRFD: φMn = 0.90 × Zx × Fy. rx, ry — Radius of Gyration (in or cm). r = √(I/A). Used for column buckling: slenderness ratio KL/r. Compressive strength Fcr depends on KL/r per AISC Chapter E. A larger r means more buckling resistance. For W24×68: rx = 9.55 in (strong axis), ry = 1.87 in (weak axis, controls buckling). J — Torsional Constant (in⁴ or cm⁴). Measures resistance to uniform (St. Venant) torsion. For W shapes, J is very small (0.6-2.5 in⁴) because the open cross-section offers little torsional resistance. For HSS6×6×3/8: J = 74.5 in⁴ — HSS is ~50× better in torsion than comparable W shapes. Cw — Warping Constant (in⁶ or cm⁶). Measures resistance to warping torsion (non-uniform torsion where flanges bend laterally). Important for W shapes under torsion because warping resistance often dominates over St. Venant resistance for open sections.

How do I find section properties for a specific W-shape?

Section properties for W-shapes are published in the AISC Steel Construction Manual Tables 1-1 through 1-12 (16th Edition). The tables provide: Table 1-1 — dimensions (d, bf, tw, tf, k, T) and properties (A, Ix, Iy, Sx, Sy, rx, ry, Zx, Zy, J, Cw) for all 148 W-shapes. Table 1-2 — beam design properties including φMp, φMr, Lp, Lr for flexure. Table 1-4 — column design properties including φcPn at various KL values. Online approach: the AISC Shapes Database (free Excel file from aisc.org/shapes) contains all properties for all shapes. Our free tool at steelcalculator.app/section-properties/ provides instant search of all AISC shapes plus international sections. Example lookups: W12×26 (light beam): d = 12.22 in, bf = 6.49 in, A = 7.65 in², Ix = 204 in⁴, Sx = 33.4 in³, Zx = 37.2 in³, rx = 5.17 in, ry = 1.51 in, J = 0.353 in⁴. Common entry-level beam for spans 15-25 ft. W14×48 (medium column): d = 13.79 in, bf = 8.03 in, A = 14.1 in², Ix = 484 in⁴, rx = 5.85 in, ry = 1.91 in. Workhorse column for 2-4 story buildings. W24×68 (floor beam): d = 23.73 in, A = 20.1 in², Ix = 1,830 in⁴, Sx = 154 in³, Zx = 177 in³, rx = 9.55 in. Common floor beam for 30 ft spans at 8-10 ft spacing. For section selection: first determine required Sx or Zx from the moment demand (S_req = Mu/(φFy) for LRFD elastic, Z_req = Mu/(0.90Fy) for LRFD plastic). Then select the lightest section with adequate Sx/Zx from the tables. For deflection-critical members: required Ix = 5wL⁴/(384E×δ_allowable) for uniform load.

How do UB, IPE, and W-shape section properties compare?

UB (Universal Beam, AS 4100 Australia), IPE (European I-section, EN 1993), and W-shape (AISC, US) are all I-shaped profiles with similar geometry but different designation systems and subtle profile differences: UB sections — designated by nominal depth (mm) + mass (kg/m). Example: 310UB40.4 = 310 mm deep, 40.4 kg/m (approximately 27 lb/ft). UB sections generally have wider flanges than comparable W-shapes at the same depth, giving higher Iy/Ix ratios and better weak-axis properties. Flange thickness is typically constant (not tapered). IPE sections — designated by nominal depth (mm). Example: IPE 300 = 300 mm deep, 150 mm flange width. IPE sections have narrower flanges than comparable W or UB shapes at the same depth, making them lighter per meter of depth but with lower Iy and weaker weak-axis properties. IPE is the original European standard; HEA/HEB/HEM (wide-flange) sections supplement IPE for column applications. W-shapes — designated by nominal depth (in) × weight (lb/ft). Example: W12×26 = approximately 12 in deep, 26 lb/ft. W shapes have the widest range (148 sizes vs ~50 IPE + ~60 UB). Comparison of similar-sized sections: W8×18 (4.6 kg/m): d = 8.14 in (207 mm), bf = 5.25 in (133 mm), Ix = 61.9 in⁴ (2,580 cm⁴). IPE 200 (22.4 kg/m): h = 200 mm, b = 100 mm, Ix = 1,943 cm⁴. 150UB14 (14 kg/m): D = 150 mm, B = 75 mm, Ix = 7.86 × 10⁶ mm⁴ = 786 cm⁴. For US projects: use W-shapes per AISC. For Australian projects: use UB/UC per AS 4100. For European projects: use IPE/HEA/HEB per EN 1993. The section properties tools should use the appropriate database for the selected design code. Our section properties tool supports all four code databases.

What is the torsional constant J and why is it important?

The torsional constant J measures a cross-section's resistance to uniform (St. Venant) torsion — the twisting deformation where plane sections remain plane and the torque is resisted by shear stresses circulating around the section. For W-shapes (open sections): J = Σ(bt³)/3 approximately, where b = width and t = thickness of each plate element (flanges + web). J values are very small: W24×68: J = 1.49 in⁴, W12×26: J = 0.353 in⁴. This means W-shapes are extremely weak in torsion — a small torque produces large twist. For HSS (closed sections): J = 4A₀²/∮(ds/t) where A₀ = enclosed area. HSS6×6×3/8: J = 74.5 in⁴ — approximately 50× the torsional stiffness of a similar-depth W-shape. This is why HSS is preferred for torsional loading. Why J matters: (1) Torsion from eccentric loads — a beam loaded on one flange only (e.g., crane runway beam) experiences torsion. The resulting twist and warping stresses can be significant. (2) Lateral-torsional buckling (LTB) — the elastic LTB moment Mcr depends on √(I²y × Cw/J) + GJ. Higher J reduces LTB sensitivity. (3) Spandrel beams — support facade loads eccentrically and experience torsion. (4) Curved beams — the curvature introduces torsion even under gravity loads. (5) Stability during erection — beams are susceptible to twisting when unbraced. For torsion-critical applications: use HSS sections, box sections, or provide torsional bracing (lateral bracing of both flanges at intervals). AISC Design Guide 9 covers torsional analysis of structural steel members. For most building beams with symmetric loading and adequate lateral bracing from the floor/roof diaphragm, torsion is minimal and J is not a governing design parameter — but for crane runways, spandrels, and curved members, torsion must be explicitly checked.

How does the radius of gyration (r) control column design?

The radius of gyration r = √(I/A) is the single most important property for column design because it appears in the slenderness ratio KL/r, which determines the column buckling strength Fcr per AISC 360 Chapter E: Elastic buckling stress: Fe = π²E/(KL/r)². Critical stress Fcr: if KL/r ≤ 4.71√(E/Fy) [= 113 for Fy=50]: Fcr = 0.658^(Fy/Fe) × Fy (inelastic buckling). If KL/r > 113: Fcr = 0.877 × Fe (elastic buckling). For a given column length L and end fixity K: doubling r halves the slenderness ratio, which dramatically increases Fcr (super-linear in the elastic range because Fcr ∝ 1/(KL/r)²). Example: 12 ft column (K=1.0): W12×26: rx = 5.17 in, KL/rx = 27.9 (very short, no buckling reduction), ry = 1.51 in, KL/ry = 95.4 (controls). Fe = π²×29000/95.4² = 31.4 ksi, Fy/Fe = 50/31.4 = 1.59, Fcr = 0.658^1.59 × 50 = 25.7 ksi. φPn = 0.90 × 25.7 × 7.65 = 177 kips. W14×48: ry = 1.91 in, KL/ry = 75.4. Fe = π²×29000/75.4² = 50.3 ksi, Fcr = 0.658^0.994 × 50 = 33.0 ksi. φPn = 0.90 × 33.0 × 14.1 = 419 kips — 2.4× the capacity with only 84% more weight, demonstrating the importance of ry. Column selection principle: for a given area (= weight), maximize r, especially ry. This is why W14 sections are preferred for columns — their deeper flanges and wider profile give higher ry than W10 or W12 of the same weight. W14 is the optimal column depth because ry peaks at d/bf ≈ 1.7-2.0. HSS square: equal rx = ry, no weak axis — rx = ry = 0.39×B for thin-walled squares. For HSS6×6×3/8: r = 2.36 in, better than W12×26's ry = 1.51 in despite similar weight. This is why HSS is popular for columns — equal buckling resistance in all directions.

Steel Section Properties — W, HSS, UB, IPE, HEA Lookup

Section properties are the geometric values that determine how a structural steel member resists loads. The most important are moment of inertia (Ix, Iy), section modulus (Sx, Sy), plastic modulus (Zx, Zy), radius of gyration (rx, ry), and torsional constant (J).

This page provides quick-reference property tables for the most commonly used steel sections. For the complete database of 500+ shapes, use the section properties tool.

Key Section Properties Explained

Property	Symbol	Units	What It Determines
Moment of inertia	Ix, Iy	in⁴, cm⁴	Deflection and stiffness
Elastic section modulus	Sx, Sy	in³, cm³	Allowable bending stress (elastic)
Plastic section modulus	Zx, Zy	in³, cm³	Plastic moment capacity (LRFD)
Radius of gyration	rx, ry	in, cm	Column buckling (KL/r)
Torsional constant	J	in⁴, cm⁴	Torsional resistance
Warping constant	Cw	in⁶, cm⁶	Warping torsion resistance
Cross-sectional area	A	in², cm²	Axial capacity
Self-weight	—	lb/ft, kg/m	Dead load contribution

Top 20 Most Popular W-Shapes (AISC)

Shape	d (in)	bf (in)	A (in²)	Ix (in⁴)	Iy (in⁴)	Sx (in³)	Zx (in³)	rx (in)	ry (in)	J (in⁴)
W4x13	4.16	4.060	3.83	11.3	3.86	5.46	6.28	1.72	1.00	0.151
W6x15	5.99	5.990	4.43	29.1	9.32	9.72	11.0	2.56	1.45	0.201
W8x18	8.14	5.250	5.26	61.9	7.97	15.2	17.5	3.43	1.23	0.210
W8x31	8.00	8.000	9.12	110	42.5	27.5	30.4	3.47	2.16	0.536
W10x22	10.17	5.750	6.49	118	11.4	23.2	26.6	4.27	1.33	0.239
W10x30	10.47	5.810	8.84	170	16.7	32.4	36.6	4.38	1.37	0.376
W12x26	12.22	6.490	7.65	204	17.3	33.4	37.2	5.17	1.51	0.353
W12x40	11.94	8.005	11.7	310	44.1	51.9	57.0	5.14	1.94	0.906
W14x22	13.74	5.000	6.49	199	7.00	29.0	33.2	5.54	1.04	0.207
W14x30	13.84	6.730	8.85	291	19.6	42.0	47.2	5.73	1.49	0.456
W14x48	13.79	8.030	14.1	484	51.4	70.2	78.0	5.85	1.91	1.09
W16x36	15.86	6.985	10.6	448	24.5	56.5	64.0	6.50	1.52	0.545
W18x40	17.90	6.015	11.8	612	18.4	68.4	78.0	7.21	1.25	0.410
W18x55	18.11	7.530	16.2	890	40.0	98.3	112	7.41	1.57	0.876
W21x44	20.66	6.500	13.0	761	20.8	73.7	84.0	7.67	1.27	0.473
W21x57	21.06	6.555	16.7	1,030	28.5	97.8	114	7.85	1.31	0.636
W24x55	23.57	7.005	16.2	1,350	29.1	114	134	9.13	1.34	0.631
W24x68	23.73	8.960	20.1	1,830	70.4	154	177	9.55	1.87	1.49
W27x84	26.71	9.960	24.7	2,850	106	213	244	10.7	2.07	2.12
W30x99	29.65	10.458	29.1	3,990	128	269	312	11.7	2.10	2.48

Source: AISC Steel Construction Manual, 16th Edition.

Popular Square HSS Sections

Shape	B×B (in)	t (in)	A (in²)	Ix (in⁴)	Sx (in³)	rx (in)	J (in⁴)
HSS2x2x1/4	2×2	0.250	1.76	0.796	0.796	0.673	1.29
HSS3x3x3/16	3×3	0.187	2.05	2.49	1.66	1.10	4.12
HSS4x4x1/4	4×4	0.250	3.59	7.44	3.72	1.44	12.2
HSS5x5x3/8	5×5	0.375	6.59	22.7	9.07	1.86	37.8
HSS6x6x3/8	6×6	0.375	8.01	44.7	14.9	2.36	74.5
HSS8x8x3/8	8×8	0.375	10.8	101	25.3	3.06	169
HSS10x10x3/8	10×10	0.375	13.7	198	39.6	3.80	331
HSS12x12x1/2	12×12	0.500	22.0	455	75.8	4.55	762

Popular Rectangular HSS Sections

Shape	B×D (in)	t (in)	Ix (in⁴)	Iy (in⁴)	Sx (in³)	Sy (in³)
HSS4x2x1/4	4×2	0.250	3.13	1.08	1.56	1.08
HSS6x4x3/8	6×4	0.375	14.7	8.00	4.90	4.00
HSS8x4x3/8	8×4	0.375	28.3	9.37	7.08	4.69
HSS8x6x3/8	8×6	0.375	45.0	29.1	11.3	9.70
HSS10x6x3/8	10×6	0.375	72.0	32.1	14.4	10.7
HSS12x6x1/2	12×6	0.500	136	48.0	22.7	16.0
HSS14x6x3/8	14×6	0.375	120	36.0	17.1	12.0

Popular UB Sections (AS 4100)

Shape	D (mm)	B (mm)	Ix (×10⁶ mm⁴)	Iy (×10⁶ mm⁴)	Zx (×10³ mm³)	Sx (×10³ mm³)
150UB14	150	75	7.86	0.82	105	122
200UB18.2	198	99	16.7	2.76	169	192
250UB25.7	254	102	36.5	4.47	287	327
310UB32	298	101	55.0	4.98	369	418
310UB40.4	306	102	72.6	5.60	475	537
360UB44.7	352	127	108	12.5	615	698
410UB53.6	403	140	159	17.3	791	895
460UB67.1	459	153	225	24.2	980	1,120
530UB82	528	158	318	26.9	1,204	1,366
610UB101	603	178	447	37.3	1,482	1,680

Popular IPE Sections (EN 1993)

Shape	h (mm)	b (mm)	Ix (cm⁴)	Iy (cm⁴)	Wpl,x (cm³)	Wel,x (cm³)
IPE 80	80	46	80.1	3.62	25.3	20.0
IPE 100	100	55	171	7.94	45.9	34.2
IPE 120	120	64	318	14.5	72.6	53.0
IPE 140	140	73	541	23.9	110	77.3
IPE 160	160	82	869	37.4	159	109
IPE 180	180	91	1,317	55.6	222	146
IPE 200	200	100	1,943	80.5	307	194
IPE 220	220	110	2,773	115	417	252
IPE 240	240	120	3,893	159	555	324
IPE 270	270	135	5,790	243	759	429
IPE 300	300	150	8,356	365	1,020	557
IPE 330	330	160	11,777	481	1,317	714
IPE 360	360	170	16,273	622	1,695	904
IPE 400	400	180	23,128	856	2,308	1,156
IPE 450	450	190	33,742	1,182	3,194	1,500
IPE 500	500	200	48,200	1,576	4,324	1,928
IPE 550	550	210	67,122	2,044	5,719	2,441
IPE 600	600	220	92,081	2,639	7,479	3,069

Frequently Asked Questions

What is the difference between Sx and Zx? Sx is the elastic section modulus (I/c), used for allowable stress design. Zx is the plastic section modulus, used for LRFD plastic design. Zx is always larger than Sx. For a compact W-shape, Zx/Sx ≈ 1.12-1.18.

How do I look up section properties for any W-shape? Use the free section properties tool to search all 148 AISC W-shapes, 73 HSS shapes, and international sections. Enter the designation (e.g., W12x26) to get all properties instantly.

What is the torsional constant J used for? J measures a section's resistance to twisting. For W-shapes, J is very small (0.1-3 in⁴), which is why open sections are poor in torsion. For HSS sections, J is much larger, making them ideal for torsion-critical applications.

What is the radius of gyration? r = √(I/A). It measures how far the area is spread from the centroid. A larger r means the section is more resistant to buckling. For column design, the slenderness ratio KL/r uses r for the weakest axis.

How do UB and W-shape section properties compare? UB sections (AS 4100, Australia) and W-shapes (AISC, US) have similar profiles but different designations. A 310UB40 is roughly equivalent to a W12x27. Use the section comparison tool for side-by-side comparison.

Where can I find the full AISC section properties database? The full database is in the AISC Steel Construction Manual, Tables 1-1 through 1-12. Our section properties tool provides all values online for free.

Section Properties Database — Full searchable database of 500+ shapes
Moment of Inertia Calculator — Ix, Iy formulas and examples
Steel Beam Sizes — W, UB, IPE, HEA dimension charts
Section Comparison Tool — Side-by-side shape comparison
Beam Capacity Calculator — Uses Sx, Zx in flexure checks
Column Capacity Calculator — Uses rx, ry in buckling checks

Disclaimer

This is a calculation tool, not a substitute for professional engineering certification. All results must be independently verified by a licensed Professional Engineer (PE), Chartered Professional Engineer (CPEng), or Structural Engineer before use in construction, fabrication, or permit documents. The user is responsible for accuracy of all inputs and verification of all outputs.