Calculations › RHS/SHS Beam
RHS/SHS Beam
EN 1993-1-1
EN 1993-1-1 RHS/SHS beam — bending, shear, LTB, deflection
Example inputs
Section100x100x5SHS
Steel gradeS275
Span (mm)4000 mm
Ultimate UDL (kN/m)10 kN/m
Characteristic UDL (kN/m)7 kN/m
National annexUK
Results
RHS/SHS Beam — 100x100x5SHS
S275 · 4000mm span · EN 1993-1-1
Results
✓ CROSS SECTION PASS
util 0.331.00EN 1993-1-1 §5.5 Table 5.2
| ε = √(235/fy) = √(235/fy) | 0.924 | — | EN 1993-1-1 §5.5 |
| c_web / t (web) = (h−3t)/t | 17 | — | |
| c_flange / t (flange) = (b−3t)/t | 17 | — | |
| Web class | 1 | — | |
| Flange class | 1 | — | |
| Section class | 1 | — |
✗ BENDING FAIL
util 1.0720.00EN 1993-1-1 §6.2.5
| Section class | 1 | — | |
| fy yield strength | 275 | N/mm² | EN 1993-1-1 Table 3.1 |
| MEd design moment = wEd × L² / 8 | 20 | kNm | |
| Wpl,y plastic modulus | 67.75 | cm³ | |
| MRd moment resistance = Wpl,y × fy / γM0 | 18.63 | kNm | EN 1993-1-1 §6.2.5 |
✓ SHEAR PASS
util 0.1320.00EN 1993-1-1 §6.2.6
| VEd design shear = wEd × L / 2 | 20 | kN | |
| Av shear area = A × h / (h+b) | 950 | mm² | EN 1993-1-1 §6.2.6(3) |
| VRd shear resistance = Av × fy / (√3 × γM0) | 150.83 | kN | EN 1993-1-1 §6.2.6 |
✗ LTB FAIL
util 1.1020.00EN 1993-1-1 §6.3.2
| Mcr elastic critical moment = (π/L)√(EIzGIt+(πE/L)²IzIw) | 358.54 | kNm | EN 1993-1-1 §6.3.2 |
| λ̄LT slenderness = √(Wpl,y fy / Mcr) | 0.228 | — | |
| αLT imperfection factor | 0.76 | — | EN 1993-1-1 Table 6.5, curve d |
| φLT = 0.5[1 + αLT(λ̄LT − 0.2) + λ̄LT²] | 0.537 | — | |
| χLT reduction factor = 1/(φLT+√(φLT²−λ̄LT²)) | 0.978 | — | EN 1993-1-1 §6.3.2.2 |
| Mb,Rd buckling resistance = χLT × Wpl,y × fy / γM1 | 18.22 | kNm |
✗ DEFLECTION FAIL
util 2.9138.77EN 1993-1-1 §NA
| Iy second moment of area | 286.6 | cm⁴ | |
| δ deflection = 5wkL⁴ / (384EI) | 38.77 | mm | |
| δ_limit L/300 = L / 300 | 13.33 | mm |
Try it yourself
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