Section
A = 8446 mm²Iy = 231.3×10⁶ mm⁴Iz = 13.18×10⁶ mm⁴Wel,y = 1156×10³ mm³Wpl,y = 1307×10³ mm³iz = 39.5 mmIt = 51.1 cm⁴Iw = 0.490×10¹² mm⁶
Material
fy = 355.0 MPafu = 510.0 MPaE = 210000 MPaG = 80770 MPa
Span & bracing
Lb = L = 6.00 m (single unbraced segment)
C1 = 1.136 — AISC F1-1 quarter-point formula on the factored diagram
Loads (unfactored)
Point loads (kN @ m)
UDLs (kN/m)
Applied moments (kN·m)
Factored effects — 1.35G + 1.5Q
MEd = 162.0 kN·mVEd = 108.0 kNC1 = 1.136
Deflection limits (editable)
Defaults: L/360 live, L/250 total. Practice varies — set your project's limits.
Steel Beam Design
IPE400 · S355 · EN 1993-1-1Bending — Mc,RdPASS
MEd
162.0kN·m
Mc,Rd
464.0kN·m
Utilization34.9%
Shear — Vpl,RdPASS
VEd
108.0kN
Vpl,Rd
875.0kN
Utilization12.3%
LTB — Mb,RdPASS
MEd
162.0kN·m
Mb,Rd
212.9kN·m
Utilization76.1%
λ̄LT = 1.334, χLT = 0.459
Bending + shearPASS
MEd
162.0kN·m
Mc,Rd
464.0kN·m
Utilization34.9%
VEd ≤ 0.5·Vpl,Rd — no reduction required
Deflection — live (L/360)PASS
δ live
5.21mm
limit
16.67mm
Utilization31.3%
Deflection — total (L/250)PASS
δ total
8.69mm
limit
24.00mm
Utilization36.2%
Governing checkLTB76.1%ALL CHECKS PASS
Checks
| Check | Demand | Capacity | Util. | Status |
|---|---|---|---|---|
| Classification | Class 1–3 | Class 1 | — | PASS |
| Bending | 162.0 kN·m | 464.0 kN·m | 34.9% | PASS |
| Shear | 108.0 kN | 875.0 kN | 12.3% | PASS |
| LTBGOVERNS | 162.0 kN·m | 212.9 kN·m | 76.1% | PASS |
| Deflection, live (L/360) | 5.21 mm | 16.67 mm | 31.3% | PASS |
| Deflection, total (L/250) | 8.69 mm | 24.00 mm | 36.2% | PASS |
Related calculators
⋈Connection Design
Bolted shear (single/double angle, shear tab), bolted moment (flush/extended end-plate) and welded steel connections — bolt shear, bearing, block shear, prying action and fillet weld group capacity per EN 1993-1-8 and AISC 360.
◫Section Properties
Area, centroid, moment of inertia, section modulus, radius of gyration, plastic modulus and torsion constant — pick a standard steel section or enter a custom rectangle, I/W, channel, angle, T, circular or hollow shape.
⌐Frame Analysis
Arbitrary-geometry 2D rigid frame analysis — graphical or accessible table geometry input, direct stiffness method with member self-loads, and combined bending/shear/axial checks per EC3 and AISC 360.
Steel Beam Design v1.0Validated against 15 benchmark cases →Learn: Understanding shear force and bending moment diagrams →Learn: Reading a beam deflection result: what's actually acceptable? →Learn: Lateral-torsional buckling (LTB), explained simply →Learn: Section classification (compact/non-compact/slender or Class 1–4): why it changes which formula applies →Learn: Why steel design leans on tables (section properties) more than concrete does →Learn: Load paths: how a load actually gets from a slab to the foundation →Learn: Characteristic values vs design values: what "characteristic strength" actually means statistically →Learn: ULS vs SLS: the two questions every structural check is really asking →
Classification — EN 1993-1-1 Table 5.2▼
Table 5.2Material coefficient
ε = √(235 / fy)
ε = √(235 / 355)
ε = 0.814
Table 5.2Flange (outstand in compression)
c = (b − tw − 2r)/2; limits 9ε | 10ε | 14ε
c/tf = 64.7/13.5 = 4.79 vs 7.32 | 8.14 | 11.39
Flange: Class 1
Table 5.2Web (internal, in bending)
c = h − 2tf − 2r; limits 72ε | 83ε | 124ε
c/tw = 331.0/8.6 = 38.49 vs 58.6 | 67.5 | 100.9
Web: Class 1
§5.5.2(6)Section class = least favourable element class
max(flange, web)
max(1, 1)
Section: Class 1
Bending — §6.2.5▼
§6.2.5(2)Section modulus for Class 1
Class 1/2 → plastic modulus
Wpl,y = 1307.0 × 10³ mm³
Wpl,y = 1307000 mm³
§6.2.5(2)Design resistance for bending
Mc,Rd = Wpl,y · fy / γM0
Mc,Rd = 1307000 × 355 / 1
Mc,Rd = 464.0 kN·m
§6.2.5(1)Cross-section bending check
MEd / Mc,Rd ≤ 1.0
162.0 / 464.0
Ratio = 0.349 → OK
Shear — §6.2.6▼
§6.2.6(3)aShear area, rolled I-section
Av = A − 2b·tf + (tw + 2r)·tf ≥ η·hw·tw
Av = 8446 − 2×180×13.5 + (8.6 + 2×21)×13.5 = 4269; min 3849
Av = 4269 mm²
§6.2.6(2)Plastic shear resistance
Vpl,Rd = Av · (fy/√3) / γM0
Vpl,Rd = 4269 × (355/√3) / 1
Vpl,Rd = 875.0 kN
§6.2.6(6)Web shear buckling check
hw/tw ≤ 72ε/η, else EN 1993-1-5 §5 governs
43.4 vs 48.8
OK — no shear buckling check needed
§6.2.6(1)Shear check
VEd / Vpl,Rd ≤ 1.0
108.0 / 875.0
Ratio = 0.123 → OK
Lateral-torsional buckling — §6.3.2▼
§6.3.2.2Moment-distribution factor (k = kw = 1, load at shear centre)
C1 taken as the AISC F1-1 Cb of the factored diagram (or manual)
Lcr = 6000 mm
C1 = 1.136
§6.3.2.2Elastic critical moment
Mcr = C1·(π²EIz/Lcr²)·√(Iw/Iz + Lcr²·G·It/(π²EIz))
Iz = 13.18×10⁶ mm⁴, It = 51.1×10⁴ mm⁴, Iw = 0.4900×10¹² mm⁶
Mcr = 260.9 kN·m
§6.3.2.2Non-dimensional slenderness
λ̄LT = √(Wy·fy / Mcr)
λ̄LT = √(1307000 × 355 / 260900852)
λ̄LT = 1.334
Table 6.5Buckling curve (rolled section)
h/b ≤ 2 → curve b, else c
h/b = 2.22
Curve c → αLT = 0.49
§6.3.2.3(1)Reduction factor (f-factor refinement omitted — conservative)
ΦLT = 0.5·[1 + αLT(λ̄LT − 0.4) + 0.75·λ̄LT²]; χLT = 1/(ΦLT + √(ΦLT² − 0.75·λ̄LT²)) ≤ min(1, 1/λ̄LT²)
ΦLT = 1.3956
χLT = 0.4589
§6.3.2.1(3)Design buckling resistance moment
Mb,Rd = χLT · Wy · fy / γM1
Mb,Rd = 0.4589 × 1307000 × 355 / 1
Mb,Rd = 212.9 kN·m
§6.3.2.1(1)LTB check
MEd / Mb,Rd ≤ 1.0
162.0 / 212.9
Ratio = 0.761 → OK
Bending + shear — §6.2.8▼
Deflection (SLS)▼
Elastic deflections from the beam analysis (unfactored SLS loads)
δ from double integration of M(x)/EI
EI = 48573 kN·m²
δ_dead = 3.47 mm, δ_live = 5.21 mm, δ_total = 8.69 mm
EN 1990 A1.4.3Deflection limits (editable — verify against project spec)
Live: L/360; Total: L/250
L = 6000 mm
Limits: 16.67 mm (live), 24.00 mm (total)
EN 1990 A1.4.3Serviceability check
δ_live ≤ L/360 and δ_total ≤ L/250
5.21 vs 16.67; 8.69 vs 24.00
Live: OK; Total: OK
Step-by-step values are shown in SI (kN, kN·m, mm, MPa) regardless of the display-unit toggle.