Structural Steel Sections

Section library, properties & EN 1993-1-1 combined stress check

EN 1993-1-1103 sections

103 sections

Section	Type	h (mm)	b (mm)	A (cm²)	Iy (cm⁴)	Wy,el (cm³)	iy (cm)	Mass (kg/m)
IPE 80	IPE	80	46	7.64	80.1	20	3.24	6
IPE 100	IPE	100	55	10.3	171	34.2	4.07	8.1
IPE 120	IPE	120	64	13.2	318	53	4.9	10.4
IPE 140	IPE	140	73	16.4	541	77.3	5.74	12.9
IPE 160	IPE	160	82	20.1	869	109	6.58	15.8
IPE 180	IPE	180	91	23.9	1,320	146	7.42	18.8
IPE 200	IPE	200	100	28.5	1,940	194	8.26	22.4
IPE 220	IPE	220	110	33.4	2,770	252	9.11	26.2
IPE 240	IPE	240	120	39.1	3,890	324	9.97	30.7
IPE 270	IPE	270	135	45.9	5,790	429	11.2	36.1
IPE 300	IPE	300	150	53.8	8,360	557	12.5	42.2
IPE 330	IPE	330	160	62.6	11,770	713	13.7	49.1
IPE 360	IPE	360	170	72.7	16,270	904	15	57.1
IPE 400	IPE	400	180	84.5	23,130	1160	16.5	66.3
IPE 450	IPE	450	190	98.8	33,740	1500	18.5	77.6
IPE 500	IPE	500	200	116	48,200	1930	20.4	90.7
IPE 550	IPE	550	210	134	67,120	2440	22.3	106
IPE 600	IPE	600	220	156	92,080	3070	24.3	122
HEA 100	HEA	96	100	21.2	349	72.8	4.06	16.7
HEA 120	HEA	114	120	25.3	606	106	4.89	19.9
HEA 140	HEA	133	140	31.4	1,033	155	5.73	24.7
HEA 160	HEA	152	160	38.8	1,673	220	6.57	30.4
HEA 180	HEA	171	180	45.3	2,510	294	7.45	35.5
HEA 200	HEA	190	200	53.8	3,692	389	8.28	42.3
HEA 220	HEA	210	220	64.3	5,410	515	9.17	50.5
HEA 240	HEA	230	240	76.8	7,763	675	10.1	60.3
HEA 260	HEA	250	260	86.8	10,450	836	11	68.2
HEA 280	HEA	270	280	97.3	13,670	1010	11.9	76.4
HEA 300	HEA	290	300	112	18,260	1260	12.8	88.3
HEA 320	HEA	310	300	124	22,930	1480	13.6	97.6
HEA 340	HEA	330	300	133	27,690	1680	14.4	105
HEA 360	HEA	350	300	143	33,090	1890	15.2	112
HEA 400	HEA	390	300	159	45,070	2310	16.8	125
HEA 450	HEA	440	300	178	63,720	2900	18.9	140
HEA 500	HEA	490	300	198	86,970	3550	20.9	155
HEB 100	HEB	100	100	26	450	89.9	4.16	20.4
HEB 120	HEB	120	120	34	864	144	5.04	26.7
HEB 140	HEB	140	140	43	1,509	215	5.93	33.7
HEB 160	HEB	160	160	54.3	2,492	311	6.78	42.6
HEB 180	HEB	180	180	65.3	3,831	426	7.66	51.2
HEB 200	HEB	200	200	78.1	5,696	570	8.54	61.3
HEB 220	HEB	220	220	91	8,091	736	9.43	71.5
HEB 240	HEB	240	240	106	11,260	938	10.3	83.2
HEB 260	HEB	260	260	118	14,920	1150	11.2	93
HEB 280	HEB	280	280	131	19,270	1380	12.1	103
HEB 300	HEB	300	300	149	25,170	1680	13	117
HEB 320	HEB	320	300	161	30,820	1930	13.8	127
HEB 340	HEB	340	300	171	36,660	2160	14.6	134
HEB 360	HEB	360	300	181	43,190	2400	15.4	142
HEB 400	HEB	400	300	198	57,680	2880	17.1	155
RHS 50×30×3	RHS	30	50	4.44	6.2	4.1	1.18	3.5
RHS 60×40×3	RHS	40	60	5.64	14.3	7.2	1.59	4.4
RHS 80×40×4	RHS	40	80	8.96	23	11.5	1.6	7
RHS 100×50×4	RHS	50	100	11.36	47.4	19	2.04	8.9
RHS 120×60×5	RHS	60	120	17	101.4	33.8	2.44	13.3
RHS 150×100×6	RHS	100	150	28.56	466.3	93.3	4.04	22.4
RHS 200×100×6	RHS	100	200	34.56	599	119.8	4.16	27.1
RHS 200×150×8	RHS	150	200	53.44	1,935.6	258.1	6.02	42
SHS 40×3	SHS	40	40	4.44	10.2	5.1	1.52	3.5
SHS 50×3	SHS	50	50	5.64	20.8	8.3	1.92	4.4
SHS 60×4	SHS	60	60	8.96	47.1	15.7	2.29	7
SHS 80×5	SHS	80	80	15	141.3	35.3	3.07	11.8
SHS 100×5	SHS	100	100	19	286.6	57.3	3.88	14.9
SHS 120×6	SHS	120	120	27.36	594.3	99	4.66	21.5
SHS 150×6	SHS	150	150	34.56	1,196.5	159.5	5.88	27.1
SHS 200×8	SHS	200	200	61.44	3,781.4	378.1	7.85	48.2
CHS 33.7×3	CHS	34	34	2.89	3.4	2	1.09	2.3
CHS 48.3×3.2	CHS	48	48	4.53	11.6	4.8	1.6	3.6
CHS 60.3×3.6	CHS	60	60	6.41	25.9	8.6	2.01	5
CHS 76.1×4	CHS	76	76	9.06	59.1	15.5	2.55	7.1
CHS 88.9×4	CHS	89	89	10.67	96.3	21.7	3	8.4
CHS 114.3×5	CHS	114	114	17.17	256.9	45	3.87	13.5
CHS 139.7×5	CHS	140	140	21.16	480.5	68.8	4.77	16.6
CHS 168.3×6	CHS	168	168	30.59	1,008.7	119.9	5.74	24
CHS 219.1×8	CHS	219	219	53.06	2,959.6	270.2	7.47	41.6
W4×13	AISC_W	106	103	24.4	470	88.7	4.39	19.4
W6×9	AISC_W	152	100	17.97	731	96.2	6.38	13.4
W6×15	AISC_W	152	152	28.11	1,190	156.6	6.51	22.3
W8×18	AISC_W	207	134	33.54	2,554	246.7	8.73	26.8
W8×31	AISC_W	203	203	57.69	4,476	441	8.81	46.1
W10×22	AISC_W	259	147	41.44	4,889	377.5	10.86	32.7
W10×33	AISC_W	247	202	63.1	7,110	575.7	10.62	49.1
W12×26	AISC_W	310	165	48.86	8,405	542.3	13.12	38.8
W12×40	AISC_W	303	203	73.95	12,508	825.6	13.01	59.5
W14×22	AISC_W	349	125	40.51	7,929	454.4	13.99	32.7
W14×48	AISC_W	351	203	84.62	18,562	1057.7	14.81	71.4
W16×26	AISC_W	399	140	49.05	12,340	618.5	15.86	38.8
W18×35	AISC_W	450	152	65.39	20,816	925.1	17.84	52.2
W18×50	AISC_W	457	190	93.62	32,862	1438.2	18.74	74.4
W21×44	AISC_W	549	165	84.45	37,992	1384	21.21	65.5
W24×55	AISC_W	598	178	97.08	53,085	1775.4	23.38	81.7
W24×76	AISC_W	608	222	123.4	74,138	2438.8	24.51	113
W27×84	AISC_W	686	254	146.53	113,445	3307.4	27.83	125
W30×90	AISC_W	762	267	149.94	143,860	3775.9	30.98	134
W33×118	AISC_W	851	292	203.79	238,854	5613.5	34.24	176
W36×135	AISC_W	912	305	233.33	314,003	6886	36.68	201
S3×5.7	AISC_S	76	59	10.49	103	27.1	3.13	8.5
S4×7.7	AISC_S	102	66	13.62	240	47.1	4.2	11.5
S5×10	AISC_S	127	73	17.43	470	74.1	5.2	14.8
S6×12.5	AISC_S	152	80	21.32	827	108.8	6.23	18.6
S8×18.4	AISC_S	203	89	29.84	2,014	198.4	8.21	27.4
S10×25.4	AISC_S	254	102	42.65	4,388	345.5	10.14	37.7
S12×31.8	AISC_S	305	111	52.85	7,712	505.7	12.08	47.4

Preview

IPE 200

Height h200mm

Width b100mm

Web tw5.6mm

Flange tf8.5mm

Area A28.5cm²

Iy1,940cm⁴

Mass22.4kg/m

Steel Sections Calculator — Section Properties, Unity Checks & LTB (EN 1993-1-1)

Governing standard: EN 1993-1-1· EN 1993-1-1:2005 (Eurocode 3, Part 1-1) · §6.2 cross-section resistance · §6.3.2.3 lateral-torsional buckling (Method 2, curve b) · §6.2.9 M-N interaction

How EN 1993-1-1 works — the method explained

The MechanixCalc steel sections calculator provides tabulated section properties and full cross-section resistance checks to EN 1993-1-1 (Eurocode 3, Part 1-1). Select any section from a built-in library of IPE, HEA, HEB, RHS, SHS, CHS and AISC W & S profiles, define the steel grade (S235 to S460), enter the span and loads, and the tool instantly returns the bending, shear and axial unity checks, the lateral-torsional buckling (LTB) reduction factor and buckling moment resistance, the M-N interaction check, and the mid-span deflection against the L/300 serviceability limit.

It is designed for structural and civil engineers who need to select and verify steel members quickly to the Eurocode — checking a floor beam, crane girder, column, hollow section strut or any structural frame member — and who need to hand a reviewer a complete, standards-cited calculation rather than a back-of-envelope lookup. The section library is searchable and filterable by profile type, and up to three sections can be compared side-by-side in a radar chart and efficiency table.

What this calculator does

EN 1993-1-1 section classification (Class 1–4) for flanges and webs of IPE, HEA, HEB, RHS, SHS, CHS and AISC W & S profiles
Bending, shear and axial unity checks per Eurocode 3 §6.2 (elastic and plastic resistances with γ_M0 = 1.0)
Lateral-torsional buckling (LTB) check with χ_LT reduction factor and design buckling moment resistance M_b,Rd (EC3 §6.3.2.3 Method 2, curve b)
M-N interaction diagram for combined bending and axial load per EN 1993-1-1 §6.2.9 (Class 1/2 linear boundary)
Mid-span deflection under UDL and point load, checked against the L/300 serviceability limit
Side-by-side section comparison with radar chart (Iy, Iz, Wy,el, mass, height) and material-efficiency index (Wy,el / mass)
Branded PDF engineering report with the full Eurocode method, section sketch and all intermediate results shown

Method & formulas

Section classification (EN 1993-1-1 §5.5)

Eurocode 3 classifies each element of the cross-section (flange outstand and web) based on the ratio of the element's compression width c to its thickness t. The slenderness limits are scaled by the factor ε = √(235 / fy), which corrects for steel grade — higher-strength steels have a lower ε and therefore stricter limits. A Class 1 section can form a full plastic hinge; Class 2 can reach plastic moment but cannot sustain it for moment redistribution; Class 3 can reach the elastic moment in extreme fibre; and a Class 4 section undergoes local buckling before any yield, requiring effective-section reduction.

The calculator evaluates both the flange outstand (c/t_f) and the web (c/t_w) and reports the governing class, which determines whether the elastic modulus W_el or plastic modulus W_pl is used in the resistance formulas.

Slenderness correction factor

ε = √(235 / fy)

where ε = Eurocode 3 slenderness factor (dimensionless); fy = yield strength of the steel grade (MPa). ε = 1.0 for S235, ≈ 0.924 for S275, ≈ 0.814 for S355.

Flange outstand class limits (rolled I-section)

c / tf ≤ 9ε → Class 1; ≤ 10ε → Class 2; ≤ 14ε → Class 3

where c = flange outstand = (b/2 − tw/2 − r) (mm); tf = flange thickness (mm); tw = web thickness (mm); r = root fillet radius (mm); b = total flange width (mm).

Cross-section resistance checks (EN 1993-1-1 §6.2)

For Class 1 and 2 sections the plastic modulus W_pl is used for the bending resistance; for Class 3 the elastic modulus W_el governs. The shear resistance uses the shear area A_v (the load-carrying web area) derived per §6.2.6 depending on section type. The axial plastic resistance is N_pl,Rd = A · fy / γ_M0. Unity checks (η = action / resistance) are computed for bending, shear and axial force individually, and the combined M-N interaction is checked graphically against the §6.2.9 simplified boundary.

Bending resistance (Class 1/2, elastic γ_M0 = 1.0)

M_c,Rd = W_pl · fy / γ_M0

where M_c,Rd = design moment resistance (kN·m); W_pl = plastic section modulus about strong axis (mm³); fy = yield strength (MPa); γ_M0 = 1.0 (partial factor for cross-section resistance, EN 1993-1-1 §6.1).

Shear resistance

V_pl,Rd = Av · fy / (√3 · γ_M0)

where V_pl,Rd = design plastic shear resistance (kN); Av = shear area (mm²) per §6.2.6; fy = yield strength (MPa); √3 appears from the von Mises yield criterion.

Lateral-torsional buckling (EN 1993-1-1 §6.3.2.3)

When an unrestrained I-section beam is loaded in bending it can buckle laterally before reaching the cross-section moment resistance. Eurocode 3 §6.3.2.3 Method 2 quantifies this via the non-dimensional LTB slenderness λ̄_LT = √(W_y · fy / M_cr), where M_cr is the elastic critical moment. The χ_LT reduction factor (buckling curve b, imperfection factor α_LT = 0.34) then scales the cross-section resistance to give the design buckling moment resistance M_b,Rd. The LTB check is expressed as a unity ratio η_LTB = M_Ed / M_b,Rd ≤ 1.

The elastic critical moment M_cr is calculated from the Saint-Venant torsional stiffness (GI_t), the warping stiffness (EI_w) and the weak-axis flexural stiffness (EI_z) of the section, over the laterally unrestrained length L_cr.

Elastic critical moment (uniform moment, C1 = 1)

M_cr = C1 · (π²·E·Iz / L_cr²) · √(Iw/Iz + L_cr²·G·It / (π²·E·Iz))

where M_cr = elastic critical moment (kN·m); E = 210 000 MPa (Young's modulus); G = 80 770 MPa (shear modulus); Iz = second moment of area about weak axis (mm⁴); It = Saint-Venant torsion constant (mm⁴); Iw = warping constant = Iz·(h−tf)²/4 (mm⁶); L_cr = laterally unrestrained length (mm); C1 = 1.0 for uniform moment (conservative).

LTB reduction factor (buckling curve b, α_LT = 0.34)

χ_LT = 1 / (Φ_LT + √(Φ_LT² − λ̄_LT²)) ≤ 1; Φ_LT = 0.5·[1 + α_LT·(λ̄_LT − 0.2) + λ̄_LT²]

where χ_LT = LTB reduction factor (≤ 1); λ̄_LT = √(Wy·fy / M_cr) = non-dimensional LTB slenderness; α_LT = 0.34 (EC3 Table 6.3, buckling curve b for rolled I-sections with h/b > 2); Φ_LT = intermediate factor.

Worked example

Check an IPE 300 beam in S355 steel, simply supported over a span of 5 m, carrying a uniformly distributed load of 10 kN/m (serviceability). Determine the bending unity check (elastic), the shear unity check and the mid-span deflection against the L/300 limit. (Assume full lateral restraint so LTB does not govern.)

Given

SectionIPE 300 (Wy,el = 557 cm³, Wy,pl = 628 cm³, Iy = 8 360 cm⁴, A = 53.8 cm²)
Steel gradeS355 (fy = 355 MPa)
Span L5 m (simply supported)
UDL w10 kN/m (applied load)
Lateral restraintFull (LTB not critical)

Result

Section classClass 1 (fully plastic, both flange and web)
Plastic moment resistance M_c,Rd222.9 kN·m
Design moment M_Ed31.25 kN·m
Bending unity check η_M0.140 (PASS)
Shear unity check η_V0.047 (PASS)
Mid-span deflection δ4.63 mm (L/300 limit = 16.7 mm — PASS)

Section classification: ε = √(235 / 355) = √0.662 = 0.814. For IPE 300: c/tf = (150/2 − 7.1/2 − 15) / 10.7 = (75 − 3.55 − 15) / 10.7 = 56.45 / 10.7 = 5.28. Limit for Class 1 flange: 9ε = 9 × 0.814 = 7.32 > 5.28 → Class 1 flange.
Web: c/tw = (300 − 2 × 10.7 − 2 × 15) / 7.1 = (300 − 21.4 − 30) / 7.1 = 248.6 / 7.1 = 35.0. Limit for Class 1 web: 72ε = 72 × 0.814 = 58.6 > 35.0 → Class 1 web. Overall section: Class 1.
Bending resistance (plastic, Class 1): M_c,Rd = W_pl · fy / γ_M0 = 628 cm³ × 355 MPa / 1.0 = 628 × 10³ mm³ × 355 N/mm² / 10⁶ = 222.9 kN·m.
Design bending moment: M_Ed = w · L² / 8 = 10 × 5² / 8 = 31.25 kN·m. Bending unity check: η_M = M_Ed / M_c,Rd = 31.25 / 222.9 = 0.140 ≤ 1.0 → PASS.
Shear area (rolled I-section per EC3 §6.2.6): Av ≈ A − 2·b·tf + (tw + 2r)·tf = 53.8 − 2 × 15.0 × 10.7/100 + (0.71 + 2 × 1.5) × 10.7/100 cm² ≈ 53.8 − 32.1 + 3.96 ≈ 25.7 cm². Shear resistance: V_pl,Rd = Av × fy / (√3 × γ_M0) = 25.7 cm² × 355 N/mm² / (1.732 × 1.0) / 10 = 527 kN. Design shear: V_Ed = w · L / 2 = 10 × 5 / 2 = 25 kN. Unity check: η_V = 25 / 527 = 0.047 ≤ 1.0 → PASS (shear is not critical for this span and load).
Mid-span deflection: δ = 5 · w · L⁴ / (384 · E · Iy) = 5 × 10 × (5 000)⁴ / (384 × 210 000 × 8 360 × 10 000) mm = 5 × 10 × 6.25×10¹⁴ / (384 × 210 000 × 8.36×10⁷) = 3.125×10¹⁶ / 6.742×10¹⁵ = 4.63 mm. Limit: L/300 = 5 000 / 300 = 16.7 mm. Check: 4.63 mm ≤ 16.7 mm → PASS.

Illustrative example — recompute against your own geometry, loading and load combinations. The calculator also checks LTB for laterally unrestrained spans; the worked example above assumes full lateral restraint.

Frequently asked questions

Which standard does the steel sections calculator use?

Cross-section resistance checks (bending, shear, axial, M-N interaction) follow EN 1993-1-1:2005 (Eurocode 3, Part 1-1), §6.2. Section classification uses §5.5. Lateral-torsional buckling is evaluated to §6.3.2.3 Method 2 (buckling curve b, α_LT = 0.34). The deflection check uses the Euler-Bernoulli beam formula and is compared to the L/300 serviceability limit. The governing standard and clause references are shown in the generated PDF report.

Which section profiles are in the library?

The built-in library includes European hot-rolled I-profiles (IPE, HEA, HEB), rectangular hollow sections (RHS), square hollow sections (SHS), circular hollow sections (CHS) and American AISC wide-flange (W) and standard beam (S) shapes. Properties are from EN 10365 (European profiles) and ASTM A6/AISC v16 (American shapes). You can filter by type and search by name.

Does the calculator check lateral-torsional buckling?

Yes — for open I/H-sections (IPE, HEA, HEB and AISC W/S shapes) the LTB check is performed per EC3 §6.3.2.3 Method 2. Enter the laterally unrestrained length L_cr; the tool computes the elastic critical moment M_cr from the section torsional and warping properties, the non-dimensional slenderness λ̄_LT, the χ_LT reduction factor (curve b) and the design buckling moment resistance M_b,Rd. For hollow sections (RHS, SHS, CHS) LTB is not critical and the cross-section resistance governs directly.

Can I compare multiple sections?

Yes — the Compare tab lets you select up to three sections simultaneously and shows a radar chart normalised to the maximum in each property (Iy, Iz, Wy,el, height, mass), a side-by-side property table, and an efficiency index (Wy,el / mass) to identify the most material-efficient profile for your load case. The M-N interaction diagram is also shown for the currently selected section.

Is the steel sections calculator free?

Yes — the Steel Sections tool is fully free with no login required. You can access section properties and all EN 1993-1-1 checks immediately. A free 30-minute preview of the wider MechanixCalc suite is available with no sign-up, and a free 14-day account trial (no credit card required) unlocks every paid calculator. The branded PDF engineering report and saved calculations are part of a paid plan.

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