38
Bending and Axial Compression (N, My, Mz) Geometrie: Length: Z-Axis Buckling Length: 6 m Y-Axis Buckling Length: 6 m Torsional Buckling Length: 6 m Section Properties Section IPE300 31.84 35.25 2.3 3.77 A G b h [kg/m] [cm] [cm] [cm] [cm] [cm] [cm] 53.80 33.67 25.67 42.20 15.00 30.00 0.71 1.07 8360.00 604.00 12.50 3.35 Warping constant [cm] 557 81 628 125 0 0 314 30 20 12.94 125900 125934 S235,275,355,420 S235,275,355,420 S460 S460 1.52 LT buckling curve: r a b a0 a0 b 1.5 0.21 0.34 0.13 0.34 Analysis model: Design Value: Normal Force (Tension (-)) kN Design Value: Normal Force (Compression (+)) 273 kN Design Value: Bending Moment (Y-Y Axis) 67.5 kNm Design Value: Bending Moment (Z-Z Axis) 0 kNm Design Value: Torsional Moments kNm Design Value : Shear Force Vz 37.5 kN Design Value : Shear Force Vy 0 kN Partial Factors resistance of cross-sections 1 resistance of members to buckling 1 resistance of cross-sections in tension to 1.25 fracture Web: Flange: Stress Distribution: sigma_1 16.32 kN/cm² 5.07 kN/cm² sigma_2 -16.32 kN/cm² 5.07 kN/cm² Material Grades S235 235.00 N /mm² 1.00 -1.00 0.83 Classification of Cross Section: Compression: Web: d / tw = 35.0 2 Flange: c /tf = 5.28 1 2 Bending Web: d / tw = 35.0 1 Flange: c /tf = 5.28 1 1 Elastic stress distribution Web: d / tw = 35.0 1 Flange: c /tf = 7.01 1 1 Resistance of Cross-Section Plastic shear resistance: 348.28 kN Plastic shear resistance: 456.83 kN Bending resistance: 147.58 kNm Bending resistance: 29.43 kNm Compression resistance: 1264.30 kN Consideration of shear buckling: Verification for Bending, Shear and Axial Force (no Buckling) 147.58 kNm 29.43 kNm 144.94 kNm 28.90 kNm n= 0.22 a= 0.40 Compression: = 0.22 < 1 Pass! Bending: = 0.46 < 1 Pass! = 0.00 < 1 Pass! Shear: = 0.11 < 1 Pass! Av,y Av,z tw tf l Iy Iz iy iz [cm 2 ] [cm 2 ] [cm 2 ] [cm 4 ] [cm 4 ] Wel,y Wel,z Wpl,y Wpl,z Weff,y Weff,z S,y S,z I,T i,p I,W [cm 3 ] [cm 3 ] [cm 3 ] [cm 3 ] [cm 3 ] [cm 3 ] [cm 3 ] [cm 3 ] [cm 4 ] [cm 6 ] Buckling curve about y-y axis: Buckling curve about z-z axis: Buckling curve about y-y axis: Buckling curve about z-z axis: Bending and Axial Force: M, N γM0 = γM1 = γM2 = fy,k = e = y = a = Classification for compression Classification for bending Bending and Compression Classification for bending & compression Vpl,z,Rd =(Av,z*fy/Sqrt(3))/γM0 Vpl,y,Rd =(Av,y*fy/Sqrt(3))/γM0 Mpl,y,Rd =(Wpl,y*fyM0 Mpl,z,Rd =(Wpl,z*fyM0 Npl,Rd =(A*fyM0 (hw/tw < 72*eps/1,2 don't consider shear buckling! Checking VEz,d < 0,5 *Vpl,z,Rd Mpl,y,V,Rd = Checking VEy,d < 0,5 *Vpl,y,Rd Mpl,z,V,Rd = Checking NEd < 0,25 *Npl,Rd and NEd < 0,5 *hw * tw * fy/1,0 Mpl,y,N,Vz,Rd = Checking NEd < 0,25 *Npl,Rd and NEd < 0,5 *hw * tw * fy/1,0 Mpl,z,N,Vy,Rd = Checking NEd/Npl,Rd Checking ME,yd/Mpl,y,Rd Checking ME,zd/Mpl,z,Rd Checking VEz,d/Vpl,z,Rd

14 03 Flexural Buckling EC3

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Page 1: 14 03 Flexural Buckling EC3

Bending and Axial Compression(N, My, Mz)

Geometrie: Length:Z-Axis Buckling Length: 6 m

Y-Axis Buckling Length: 6 m

Torsional Buckling Length: 6 mSection PropertiesSection IPE300

31.84 35.25 2.3 3.77A G b h

[kg/m] [cm] [cm] [cm] [cm] [cm] [cm]

53.80 33.67 25.67 42.20 15.00 30.00 0.71 1.07 8360.00 604.00 12.50 3.35

Warping constant

[cm]

557 81 628 125 0 0 314 30 20 12.94 125900 125934

S235,275,355,420 S235,275,355,420 S460 S460 1.52

LT buckling curve: r

a b a0 a0 b 1.5

0.21 0.34 0.13 0.34

Analysis model:

Design Value: Normal Force (Tension (-)) kN

Design Value: Normal Force (Compression (+)) 273 kN

Design Value: Bending Moment (Y-Y Axis) 67.5 kNm

Design Value: Bending Moment (Z-Z Axis) 0 kNm

Design Value: Torsional Moments kNm

Design Value : Shear Force Vz 37.5 kN

Design Value : Shear Force Vy 0 kN

Partial Factorsresistance of cross-sections 1

resistance of members to buckling 1

resistance of cross-sections in tension to 1.25

fracture

Web: Flange:

Stress Distribution: sigma_1 16.32 kN/cm² 5.07 kN/cm²

sigma_2 -16.32 kN/cm² 5.07 kN/cm²

Material Grades S235235.00 N /mm²

1.00-1.000.83

Classification of Cross Section:

Compression: Web: d / tw = 35.0 2

Flange: c /tf = 5.28 1

2

Bending Web: d / tw = 35.0 1

Flange: c /tf = 5.28 1

1

Elastic stress distributionWeb:

d / tw =35.0 1

Flange:c /tf =

7.01 1

1

Resistance of Cross-SectionPlastic shear resistance: 348.28 kN

Plastic shear resistance: 456.83 kN

Bending resistance: 147.58 kNm

Bending resistance: 29.43 kNm

Compression resistance: 1264.30 kN

Consideration of shear buckling:

Verification for Bending, Shear and Axial Force (no Buckling)147.58 kNm

29.43 kNm

144.94 kNm

28.90 kNm n= 0.22 a= 0.40

Compression: = 0.22 < 1 Pass!

Bending: = 0.46 < 1 Pass!

= 0.00 < 1 Pass!

Shear: = 0.11 < 1 Pass!

Av,y Av,z tw tf l Iy Iz iy iz

[cm2] [cm2] [cm2] [cm4] [cm4]

Wel,y Wel,z Wpl,y Wpl,z Weff,y Weff,z S,y S,z I,T i,p I,W

[cm3] [cm3] [cm3] [cm3] [cm3] [cm3] [cm3] [cm3] [cm4] [cm6]

Buckling curve about y-y axis:

Buckling curve about z-z axis:

Buckling curve about y-y axis:

Buckling curve about z-z axis:

Bending and Axial Force: M, N

γM0 =

γM1 =

γM2 =

fy,k =

e =

y =

a =

Classification for compression

Classification for bending

Bending and Compression

Classification for bending & compression

Vpl,z,Rd =(Av,z*fy/Sqrt(3))/γM0

Vpl,y,Rd =(Av,y*fy/Sqrt(3))/γM0

Mpl,y,Rd =(Wpl,y*fy/γM0

Mpl,z,Rd =(Wpl,z*fy/γM0

Npl,Rd =(A*fy/γM0

(hw/tw < 72*eps/1,2

don't consider shear buckling!

Checking VEz,d < 0,5 *Vpl,z,Rd Mpl,y,V,Rd =

Checking VEy,d < 0,5 *Vpl,y,Rd Mpl,z,V,Rd =

Checking NEd < 0,25 *Npl,Rd and NEd < 0,5 *hw * tw * fy/1,0 Mpl,y,N,Vz,Rd =

Checking NEd < 0,25 *Npl,Rd and NEd < 0,5 *hw * tw * fy/1,0 Mpl,z,N,Vy,Rd =

Checking NEd/Npl,Rd

Checking ME,yd/Mpl,y,Rd

Checking ME,zd/Mpl,z,Rd

Checking VEz,d/Vpl,z,Rd

Page 2: 14 03 Flexural Buckling EC3

Shear: = 0.00 < 1 Pass!

Bending, Axial Force and Shear:= 0.22 < 1 Pass!

Stability Verifications:

Norminal Buckling Length: = 6.00 m

= 6.00 m

Elastic Critical Force for buckling mode: = 4813.10 kN

= 347.74 kN

= 93.90

= 0.51

= 1.91

= 0.66

= 2.61

= 0.92

= 0.23

Verification against Buckling: = 1164.12 kN

= 288.00 kN

= 288.00 kN

= 0.95 < 1 Pass!

Verification againstLateral Torsional Buckling:

(Bending)y

h /bf

1.132 2.00 <= 2 b 0.34 1.04

0.00 1.13

= 10258 kNcm

= 1.20

= 1.18

= 0.58

Lateral torsional buckling = 85.53 kNm

Resistance = 0.79 <= 1 Pass!

Verification againstLateral Torsional Buckling:(Bending and axial Compression)

(1) -1 = 0.9

(1) 0 = 0.9

(1) -1 = 0.9

= 0.97= 1.26= 0.72= 2.09

= 1.00 <= 1 Pass!

= 1.52 > 1 Fail!

(1) 0.9

(2)(3)(4)(5)(6)(7)(8)(9) -0,8*as > 0,4

(10)(11)(12)

Checking VEy,d/Vpl,y,Rd

(ME,y,d/Mpl,y,N,Vz,Rd)^2 + (MEz,d/Mpl,z,N,Vy,Rd )^(b+n)

Lycr

Lzcr

Ny,cr

Nz,cr

l1

ly

lz

Fy

Fz

cy

cz

Nb,y,Rd

Nb,z,Rd

Nb,Rd

Checking NEd/Nb,Rd

C1

Buckling Curve

a LT

Calculating Mcr

Calculating lLT

Calculating FLT

Calculating cy,LT

Calculating Mb,Rd cy,LT *Wy*fy/gM,1 =

Checking MEd/Mb,Rd

Calculating Cmy

Calculating Cmz

Calculating CmLT

Calculating Kyy

Calculating Kyz

Calculating Kzy

Calculating Kzz

NE,d/(cy *NRk) + kyy* (MyE,d+DMy,Ed)/(cLT*My,Rk) + kyz*(MzE,d+DMz,Ed)/(Mz,Rk)

NE,d/(cz *NRk) + kzy* (MyE,d+DMy,Ed)/(cLT*My,Rk) + kzz*(MzE,d+DMz,Ed)/(Mz,Rk)

0,6+0,4*f>0,4

0,2+0,8*as >0,4

0,1-0,8*as >0,4

0,1(1-Y)-0,8*as >0,4

0,095-0,05*ah

0,095+0,05*ah

0,95+0,05*ah (1+2Y)

0,2(1-Y)-0,8*as >0,4

0,90+0,1*ah

0,90+0,05*ah (1+2Y)

Page 3: 14 03 Flexural Buckling EC3

Fahnenblechanschluss(Anschlüsse für Qz und N)

Achtung: Fahnenblechanschlüsse sind in aussteifenden Systemen bzw. Bauteilen nicht zulässigEingabedaten:

Schrauben HV M20- 4.6

Lochdurchmesser 22 mm

Grenzabscherkraft 68.5 [kN]

Grenzzugkraft 62.3 [kN]

Anzahl der vertikalen Schraubenreihe 2Anzahl der horizontalen Schraubenreihe 2

FahnenblechBlechdicke Fahnenblech 12 mmStahlsorte Fahnenblech S235

Streckgrenze Fahnenblech 240 N/mm²

218.18 N/mm²

Abstand der vertikalen Schraubenreihe x 80 80 mmAbstand der horizontalen Schraubenreihe y 60 60 mm

Abstand System-Anschlussprofil 80 mm

Randabstand Fahnenblech x Richtung a 50 50 mmRandabstand Fahnenblech y Richtung b 45 45 mm

Anschlussprofil IPE500

Flanschdicke (Standardprofile) 16 mm

Flanschdicke (Schweißprofile) mmStahlsorte Anschlussprofil S235

Streckgrenze Anschlussprofil 240 N/mm²

218.18 N/mm²

Flanschdicke für die Berechnung 16.00 mm

Profilhöhe (Standardprofile) h 500 mmProfilhöhe (Schweißprofil) h mmFlanschdicke für die Berechnung h 500.00 mm

Stegdicke (Standardprofile) t 10.2 mmStegdicke (Schweißprofil) t mmStegdicke für die Berechnung t 10.20 mm

Randabstand Anschlussprofil x - Richtung 50 50 mm

Randabstand Anschlussprofil y - Richtung 60 60 mmAnschluss an OG Abfangprofil ( ja = 1, nein = 0) 0

dL

VaR,d

NR,d

fy,k

fy,d

eT

tf

tf

fy,k

fy,d

tf

e1

e2

Page 4: 14 03 Flexural Buckling EC3

Abfangprofil IPE300

Stegdicke (Standardprofile) 7.1 mm

Stegdicke (Schweißprofil) mm

Stegdicke für die Berechnung 7.10 mmSteifer oder durchgebundener Anschluss ( ja = 1, nein = 0) 0Stahlsorte Abfangprofil S355

Streckgrenze Abfangprofil 360 N/mm²

327.27 N/mm²

Lochleibungsbeanspruchbarkeit

Schrauben: 400 N/mm²240 N/mm²

Anschußblech 360 N/mm²240 N/mm²

e = 45 mm

= 0.66

= 2.5 mm

= 60 mmt = 12 mm

= 101.65 kN

Randabstand (mm)

= -0.74

= -41 kN

tw

tw

tw

fy,k

fy,d

fu,b,k

fy,b,k

fu,k

fy,k

αb

k1

e3

Fb,Rd

e1

α1

Vl,R,d

Page 5: 14 03 Flexural Buckling EC3

Steel

E G g[N/mm²] [N/mm²] [N/mm²] [N/mm²] [1/K] [kN/mm³]

S235 240 360 210000 81000 1.20E-05 7.85E-08S355 360 510 210000 81000 1.20E-05 7.85E-08

Schraubenanzahl123

Bolts Effective Area

d A[mm] [-] [mm] [mm²] [mm²] [mm]

M16-8.8 16 8.8 16 201 157 30M20-8.8 20 8.8 20 314 245 37M16-10.9 16 10.9 16 201 157 30M20-10.9 20 10.9 20 314 245 37

janein

Schaft in der Scherfuge Gewinde in der Scherfuge

Bolt dL fyk fubk dschM12 - 10.9 61.3 56.5 13 900 1000 12M12 - 5.6 28 30.8 13 300 500 12M12 - 8.8 49 49.3 13 640 800 12M12- 4.6 22.4 24.7 13 240 400 12M16 - 10.9 114 101 18 900 1000 16M16 - 5.6 49.8 54.8 18 300 500 16M16 - 8.8 91.3 87.7 18 640 800 16M16- 4.6 39.9 43.9 18 240 400 16M20 - 10.9 178 157 22 900 1000 20M20 - 5.6 77.9 85.6 22 300 500 20M20 - 8.8 143 137 22 640 800 20M20- 4.6 62.3 68.5 22 240 400 20M22 - 10.9 220 190 24 900 1000 22M22 - 5.6 94.2 104 24 300 500 22M22 - 8.8 176 166 24 640 800 22M22- 4.6 75.4 82.9 24 240 400 22M24 - 10.9 257 226 26 900 1000 24M24 - 5.6 112 123 26 300 500 24M24 - 8.8 205 197 26 640 800 24M24- 4.6 89.7 98.6 26 240 400 24M27 - 10.9 334 287 30 900 1000 27M27 - 5.6 142 156 30 300 500 27M27 - 8.8 267 250 30 640 800 27

Yield Strength

Tensile Strength

Elastiv Modulus

Shear Modulus

Coefficient of Thermic Expansion

Specific Weight

fy,k fu,k aT

Thread Diameter

Strength Class

Shank Diameter

Shank Area

Washer Diameter

ds As dW

NR,d VaR,d

Page 6: 14 03 Flexural Buckling EC3

M27- 4.6 114 125 30 240 400 27M30 - 10.9 408 354 33 900 1000 30M30 - 5.6 175 193 33 300 500 30M30 - 8.8 326 309 33 640 800 30M30- 4.6 140 154 33 240 400 30M36 - 10.9 594 509 39 900 1000 36M36 - 5.6 252 278 39 300 500 36M36 - 8.8 475 444 39 640 800 36M36- 4.6 202 222 39 240 400 36

Strength Class

2[N/mm²] [N/mm²] 4

64.6 240 400 85.6 300 500 108.8 640 800 1210.9 900 1000 14

16182022242628

SchweißnähteKehlnahtDoppelkehlnahtV-NahtHV-NahtY-NahtHY-NahtDV-NahtDHV-NahtDY-NahtDHY-Naht

Yield Strength

Tensile Strength

Number of Bolts

fy,b,k fu,b,k

Page 7: 14 03 Flexural Buckling EC3

M_16_8M_20_8

M_16_10M_20_10

SLP-Verbindung: Scher-Lochleibungsverbindung ohne LochspielSL-Verbindung: Scher-Lochleibungsverbindung mit Lochspiel

Gewinde in der Scherfuge

As (cm²) A cm² (Schaft in der Scherfuge)33.7 0.84 0.55 1.1323 0.84 0.6 1.13

36.8 0.84 0.6 1.1318.4 0.84 0.6 1.1362.8 1.57 0.55 2.0142.8 1.57 0.6 2.0168.5 1.57 0.6 2.0134.3 1.57 0.6 2.0198 2.45 0.55 3.14

66.8 2.45 0.6 3.14107 2.45 0.6 3.1453.5 2.45 0.6 3.14121 3.03 0.55 3.882.6 3.03 0.6 3.8132 3.03 0.6 3.866.1 3.03 0.6 3.8141 3.53 0.55 4.5296.3 3.53 0.6 4.52154 3.53 0.6 4.5277 3.53 0.6 4.52

184 4.59 0.55 5.73125 4.59 0.6 5.73200 4.59 0.6 5.73

validity parameter

VaR,d α,a

Page 8: 14 03 Flexural Buckling EC3

100 4.59 0.6 5.73224 5.61 0.55 7.07153 5.61 0.6 7.07245 5.61 0.6 7.07122 5.61 0.6 7.07327 8.17 0.55 10.18223 8.17 0.6 10.18357 8.17 0.6 10.18178 8.17 0.6 10.18

Page 9: 14 03 Flexural Buckling EC3

Preference List of Chinese Welded Steel Sections & WIDE FLANGE BEAMSStandard Sectional Dimension Moment of Inertia

H B A m Ix Iy

mm kg/m

- 0 0 0.0 0.0 0 0 0 0 0HWS350*175*10*16 350 175 10.0 16.0 6 87.8 68.9 18309 1431HWS350*200*10*16 350 200 10.0 16.0 6 95.8 75.2 20542 2135HWS350*250*10*16 350 250 10.0 16.0 6 111.0 87.8 25008 4169HWS350*300*10*16 350 300 10.0 16.0 6 127.0 100.0 29473 7202HWS350*300*10*18 350 300 10.0 18.0 7 139.0 109.0 32369 8102HWS350*350*10*16 350 350 10.0 16.0 6 143.0 113.0 33939 11435HWS350*350*10*18 350 350 10.0 18.0 7 157.0 124.0 37334 12865HWS350*350*12*20 350 350 12.0 20.0 8 177.0 139.0 41140 14296HWS400*200*10*16 400 200 10.0 16.0 6 100.0 79.1 27759 2136HWS400*200*10*18 400 200 10.0 18.0 7 108.0 85.1 30304 2403HWS400*200*10*20 400 200 10.0 20.0 7 116.0 91.1 32794 2669HWS400*250*10*16 400 250 10.0 16.0 6 116.0 91.7 33661 4169HWS400*250*10*18 400 250 10.0 18.0 7 126.0 99.2 36876 4690HWS400*250*10*20 400 250 10.0 20.0 7 136.0 107.0 40021 5211HWS400*300*10*16 400 300 10.0 16.0 6 132.0 104.0 39562 7203HWS400*300*10*18 400 300 10.0 18.0 7 144.0 113.0 43447 8103HWS400*300*10*20 400 300 10.0 20.0 7 156.0 122.0 47248 9003HWS400*300*12*20 400 300 12.0 20.0 8 163.0 128.0 48025 9005HWS450*250*10*16 450 250 10.0 16.0 6 121.0 95.6 43774 4170HWS450*250*10*18 450 250 10.0 18.0 7 131.0 103.0 47927 4690HWS450*250*10*20 450 250 10.0 20.0 7 141.0 111.0 52001 5211HWS450*250*12*22 450 250 12.0 22.0 8 158.0 125.0 57112 5735HWS450*250*12*25 450 250 12.0 25.0 8 173.0 136.0 62910 6516HWS450*300*10*16 450 300 10.0 16.0 6 137.0 108.0 51312 7203HWS450*300*10*18 450 300 10.0 18.0 7 149.0 117.0 56330 8103HWS450*300*10*20 450 300 10.0 20.0 7 161.0 126.0 61253 9003HWS450*300*12*20 450 300 12.0 20.0 8 169.0 133.0 62402 9005HWS450*300*12*25 450 300 12.0 25.0 8 198.0 155.0 74212 11255HWS500*250*10*16 500 250 10.0 16.0 6 126.0 99.5 55410 4170HWS500*250*10*18 500 250 10.0 18.0 7 136.0 107.0 60621 4691HWS500*250*10*20 500 250 10.0 20.0 7 146.0 115.0 65744 5212HWS500*250*12*22 500 250 12.0 22.0 8 164.0 129.0 72359 5735HWS500*250*12*25 500 250 12.0 25.0 8 179.0 141.0 79685 6516HWS500*300*10*16 500 300 10.0 16.0 6 142.0 112.0 64783 7203HWS500*300*10*18 500 300 10.0 18.0 7 154.0 121.0 71081 8103HWS500*300*10*20 500 300 10.0 20.0 7 166.0 130.0 77271 9003HWS500*300*12*22 500 300 12.0 22.0 8 186.0 147.0 84934 9906HWS500*300*12*25 500 300 12.0 25.0 8 204.0 160.0 93800 11256HWS600*300*10*16 600 300 10.0 16.0 6 152.0 120.0 97144 7204HWS600*300*10*18 600 300 10.0 18.0 7 164.0 129.0 106435 8104HWS600*300*10*20 600 300 10.0 20.0 7 176.0 138.0 115594 9004HWS600*300*12*22 600 300 12.0 22.0 8 198.0 156.0 127488 9908HWS600*300*12*25 600 300 12.0 25.0 8 216.0 170.0 140700 11257HWS700*300*10*18 700 300 10.0 18.0 7 174.0 137.0 150008 8105HWS700*300*10*20 700 300 10.0 20.0 7 186.0 146.0 162718 9005HWS700*300*10*25 700 300 10.0 25.0 8 215.0 169.0 193822 11255

Sectional Area

Unit Weight

t1 t2r / hf

cm2 cm4

Page 10: 14 03 Flexural Buckling EC3

HWS700*300*12*22 700 300 12.0 22.0 8 210.0 165.0 179979 9909HWS700*300*12*25 700 300 12.0 25.0 8 228.0 179.0 198400 11259HWS700*300*12*28 700 300 12.0 28.0 8 245.0 193.0 216484 12609HWS700*300*12*30 700 300 12.0 30.0 9 256.0 202.0 228354 13509HWS700*300*12*35 700 300 12.0 35.0 9 285.6 224.2 257173 15750HWS800*300*10*18 800 300 10.0 18.0 7 184.0 145.0 202302 8106HWS800*300*10*20 800 300 10.0 20.0 7 196.0 154.0 219141 9006HWS800*300*10*25 800 300 10.0 25.0 8 225.0 177.0 260468 11256HWS800*300*12*22 800 300 12.0 22.0 8 222.0 175.0 243005 9910HWS800*300*12*25 800 300 12.0 25.0 8 240.0 188.0 267500 11260HWS800*300*12*28 800 300 12.0 28.0 8 257.0 202.0 291606 12610HWS800*300*12*30 800 300 12.0 30.0 9 268.0 211.0 307462 13510HWS800*300*12*35 800 300 12.0 35.0 9 297.6 233.6 346145 15750HWS900*300*10*20 900 300 10.0 20.0 7 206.0 161.7 285325 9000HWS900*300*12*20 900 300 12.0 20.0 8 223.2 175.2 295926 9000HWS900*300*12*22 900 300 12.0 22.0 8 234.7 184.3 317114 9900HWS900*300*12*25 900 300 12.0 25.0 8 252.0 197.8 348522 11250HWS900*300*12*28 900 300 12.0 28.0 8 269.3 211.4 379482 12600HWS900*300*14*30 900 300 14.0 30.0 9 297.6 233.6 409754 13500HWS900*300*16*35 900 300 16.0 35.0 10 342.8 269.1 469056 15750HWS1000*300*10*20 1000 300 10.0 20.0 7 206.0 161.7 285325 9000HWS1000*300*12*20 1000 300 12.0 20.0 8 223.2 175.2 295926 9000HWS1000*300*12*22 1000 300 12.0 22.0 8 234.7 184.3 317114 9900HWS1000*300*12*25 1000 300 12.0 25.0 8 252.0 197.8 348522 11250HWS1000*300*12*28 1000 300 12.0 28.0 8 269.3 211.4 379482 12600HWS1000*300*12*30 1000 300 12.0 30.0 9 280.8 220.4 399875 13500HWS1000*300*14*35 1000 300 14.0 35.0 9 326.2 256.1 495927 15750HWS1000*300*14*40 1000 300 14.0 40.0 10 354.8 278.5 508086 18000HWS1000*300*16*35 1000 300 16.0 35.0 11 342.8 269.1 469056 15750HWS1000*300*16*40 1000 300 16.0 40.0 11 371.2 291.4 517276 18000HWS1100*300*12*20 1100 300 12.0 20.0 8 247.2 194.1 469022 9000HWS1100*300*12*22 1100 300 12.0 22.0 8 258.7 203.1 501246 9900HWS1100*300*12*25 1100 300 12.0 25.0 8 276.0 216.7 549122 11250HWS1100*300*12*28 1100 300 12.0 28.0 8 293.3 230.2 596447 12600HWS1100*300*14*30 1100 300 14.0 30.0 9 325.6 255.6 646439 13500HWS1100*300*14*35 1100 300 14.0 35.0 9 354.2 278.0 722953 15750HWS1100*300*16*40 1100 300 16.0 40.0 11 403.2 316.5 815654 18000H148*100*6*9 148 100 6 9 11 26.84 21.1 1020 151H150*75*5*7 150 75 5 7 8 17.85 14 666 49.5H150*150*7*10 150 150 7 10 11 40.14 31.5 1640 563H194*150*6*9 194 150 6 9 13 39.01 30.6 2690 507H198*99*4.5*7 198 99 4.5 7 11 23.18 18.2 1580 114H200*100*5.5*8 200 100 5.5 8 11 27.16 21.3 1840 134H200*200*8*12 200 200 8 12 13 63.53 49.9 4720 1600H200*204*12*12 200 204 12 12 13 71.53 56.2 4980 1700H208*202*10*16 208 202 10 16 13 83.69 65.7 6530 2200H244*175*7*11 244 175 7 11 16 56.24 44.1 6120 984H244*252*11*11 244 252 11 11 16 82.06 64.4 8790 2940H248*124*5*8 248 124 5 8 12 32.68 25.7 3540 255H248*249*8*13 248 249 8 13 16 84.7 66.5 9930 3350H250*125*6*9 250 125 6 9 12 37.66 29.6 4050 294H250*250*9*14 250 250 9 14 16 92.18 72.4 10800 3650H250*255*14*14 250 255 14 14 16 104.7 82.2 11500 3880H294*200*8*12 294 200 8 12 18 72.38 56.8 11300 1600

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H294*302*12*12 294 302 12 12 18 107.7 84.5 16900 5520H298*149*5.5*8 298 149 5.5 8 13 40.8 32 6320 442H298*201*9*14 298 201 9 14 18 83.36 65.4 13300 1900H298*299*9*14 298 299 9 14 18 110.8 87 18800 6240H300*150*6.5*9 300 150 6.5 9 13 46.78 36.7 7210 508H300*300*10*15 300 300 10 15 18 119.8 94 20400 6750H300*305*15*15 300 305 15 15 18 134.8 106 21500 7100H304*301*11*17 304 301 11 17 18 134.8 106 23400 7730H310*305*15*20 310 305 15 20 18 165.3 130 28150 9460H310*310*20*20 310 310 20 20 18 180.8 142 29390 9940

1 2 3 4 5 6 7 8 9 10

Page 12: 14 03 Flexural Buckling EC3

Preference List of Chinese Welded Steel Sections & WIDE FLANGE BEAMSRadius of Gyration Modulus of Section Stability parameters for upper notched beam

ix iy Zx Zy S235 S355

cm 0 0.5 1 0

0 0 0 014.4 4.0 1046 16314.6 4.7 1173 21315.0 6.1 1429 33315.2 7.5 1684 48015.2 7.6 1849 54015.4 8.9 1939 65315.4 9.1 2133 73515.2 9.0 2350 81616.6 4.6 1387 21316.7 4.7 1515 24016.8 4.8 1639 26617.0 6.0 1683 33317.1 6.1 1843 37517.1 6.2 2001 41617.3 7.4 1978 48017.3 7.5 2172 54017.4 7.6 2362 60017.1 7.4 2401 60019.0 5.9 1945 33319.1 6.0 2130 37519.2 6.1 2311 41619.0 6.0 2538 45819.0 6.1 2796 52119.3 7.3 2280 48019.4 7.4 2503 54019.5 7.5 2722 60019.2 7.3 2773 60019.3 7.5 3298 75020.9 5.8 2216 33321.1 5.9 2424 37521.2 6.0 2629 41621.0 5.9 2894 45821.0 6.0 3187 52121.3 7.1 2591 48021.4 7.3 2843 54021.5 7.4 3090 60021.3 7.3 3397 66021.4 7.4 3752 75025.2 6.9 3238 48025.4 7.0 3547 54025.6 7.2 3853 60025.3 7.1 4249 66025.5 7.2 4690 75029.3 6.8 4285 54029.5 7.0 4649 60030.0 7.2 5537 750

cm3

Nd / Vz,d Nd / Vz,d Nd / Vz,d Nd / Vz,d

Page 13: 14 03 Flexural Buckling EC3

29.2 6.9 5142 66029.4 7.0 5668 75029.7 7.2 6185 84029.8 7.3 6524 90030.0 7.4 7348 133.1 6.6 5057 54033.4 6.8 5478 60034.0 7.1 6511 75033.0 6.7 6075 66033.3 6.8 6687 75033.6 7.0 7290 84033.8 7.1 7686 90034.1 7.3 8654 137.2 6.6 6341 60036.4 6.4 6576 60036.8 6.5 7047 66037.2 6.7 7745 75037.5 6.8 8433 84037.1 6.7 9106 90037.0 6.8 10423 60037.2 6.6 6341 60036.4 6.4 6576 60036.8 6.5 7047 66037.2 6.7 7745 75037.5 6.8 8433 84037.7 6.9 8886 90037.5 6.9 10212 1,05037.8 7.1 11291 1,20037.0 6.8 10423 1,05037.3 7.0 11495 1,20043.6 6.0 8528 60044.0 6.2 9114 66044.6 6.4 9984 75045.1 6.6 10844 84044.6 6.4 11753 90045.2 6.7 13145 1,05045.0 6.7 14830 1,2006.17 2.37 138 30.1 100% 100% 100% 100%6.11 1.66 88.8 13.2 100% 100% 100% 100%6.39 3.75 219 75.1 100% 100% 100% 100%8.3 3.61 277 67.6 100% 100% 100% 100%

8.26 2.21 160 23 100% 100% 100% 100%8.24 2.22 184 26.8 100% 100% 100% 100%8.62 5.02 472 160 100% 100% 100% 100%8.35 4.88 498 167 100% 100% 100% 100%8.83 5.13 628 218 100% 100% 100% 100%10.4 4.18 502 113 100% 100% 100% 100%10.3 5.98 720 233 100% 100% 100% 100%10.4 2.79 285 41.1 100% 91% 82% 94%10.8 6.29 801 269 100% 100% 100% 100%10.4 2.79 324 47 100% 100% 100% 100%10.8 6.29 867 292 100% 100% 100% 100%10.5 6.09 919 304 100% 100% 100% 100%12.5 4.71 771 160 100% 100% 100% 100%

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12.5 7.16 1150 365 100% 100% 100% 100%12.4 3.29 424 59.3 100% 78% 70% 85%12.6 4.77 893 189 100% 100% 100% 100%13 7.5 1270 417 100% 100% 100% 100%

12.4 3.29 481 67.7 100% 93% 83% 99%13.1 7.51 1360 450 100% 100% 100% 100%12.6 7.26 1440 466 100% 100% 100% 100%13.2 7.57 1540 514 100% 100% 100% 100%13.2 7.6 1810 620 100% 100% 100% 100%12.8 7.5 1890 642 100% 100% 100% 100%

11 12 13 14 15 16 17 18

Page 15: 14 03 Flexural Buckling EC3

Stability parameters for upper notched beam Stability parameters for double notched beam

S355 S235 S355

0.5 1 0 0.5 1 0 0.5

Nd / Vz,d Nd / Vz,d Nd / Vz,d Nd / Vz,d Nd / Vz,d Nd / Vz,d Nd / Vz,d

Page 16: 14 03 Flexural Buckling EC3

100% 100% 100% 100% 100% 100% 100%100% 100% 100% 100% 100% 100% 100%100% 100% 100% 100% 100% 100% 100%100% 100% 100% 100% 100% 100% 100%93% 83% 100% 100% 100% 100% 100%

100% 94% 100% 100% 100% 100% 100%100% 100% 100% 100% 100% 100% 100%100% 100% 100% 100% 100% 100% 100%100% 100% 100% 100% 100% 100% 100%100% 100% 100% 100% 100% 100% 100%100% 100% 100% 100% 100% 100% 100%76% 68% 100% 100% 100% 100% 91%

100% 100% 100% 100% 100% 100% 100%93% 83% 100% 100% 100% 100% 100%

100% 100% 100% 100% 100% 100% 100%100% 100% 100% 100% 100% 100% 100%100% 89% 100% 100% 100% 100% 100%

Page 17: 14 03 Flexural Buckling EC3

100% 100% 100% 100% 100% 100% 100%65% 58% 100% 94% 87% 89% 79%

100% 100% 100% 100% 100% 100% 100%100% 100% 100% 100% 100% 100% 100%78% 69% 100% 100% 100% 100% 91%

100% 100% 100% 100% 100% 100% 100%100% 100% 100% 100% 100% 100% 100%100% 100% 100% 100% 100% 100% 100%100% 100% 100% 100% 100% 100% 100%100% 100% 100% 100% 100% 100% 100%

19 20 21 22 23 24 25

Page 18: 14 03 Flexural Buckling EC3

Stability parameters for double notched beam

S355

1

Nd / Vz,d

Page 19: 14 03 Flexural Buckling EC3

100%100%100%100%100%100%100%100%100%100%100%85%

100%100%100%100%100%

Page 20: 14 03 Flexural Buckling EC3

100%73%

100%100%85%

100%100%100%100%100%

26

Page 21: 14 03 Flexural Buckling EC3

CROSS SECTION PROFILES

1 2 3 4 5 6 7 8 9

A G b h

[kg/m] [cm] [cm] [cm] [cm]

HE1000A 347 193.67 184.71 272.0 30 99 1.65 3.1HE1000B 400 225.31 212.44 314.0 30 100 1.9 3.6

HE1000M 444 252.31 234.8 349.0 30.2 100.8 2.1 4

HE100A 21.2 16.85 7.52 16.7 10 9.6 0.5 0.8HE100B 26 21.08 9 20.4 10 10 0.6 1

HE100M 53.2 45.28 18 41.8 10.6 12 1.2 2

HE120A 25.3 20.05 8.42 19.9 12 11.4 0.5 0.8HE120B 34 27.6 10.95 26.7 12 12 0.65 1.1

HE120M 66.4 55.98 21.15 52.1 12.6 14 1.25 2.1

HE140A 31.4 24.76 10.11 24.7 14 13.3 0.55 0.85HE140B 43 34.93 13.12 33.7 14 14 0.7 1.2

HE140M 80.6 67.49 24.5 63.2 14.6 16 1.3 2.2

HE160A 38.8 30.06 13.24 30.4 16 15.2 0.6 0.9HE160B 54.3 43.44 17.64 42.6 16 16 0.8 1.3

HE160M 97.1 80.42 30.86 76.2 16.6 18 1.4 2.3

HE180A 45.3 35.46 14.52 35.5 18 17.1 0.6 0.95HE180B 65.3 52.4 20.29 51.2 18 18 0.85 1.4

HE180M 113 93.56 34.4 88.9 18.6 20 1.45 2.4

HE200A 53.8 41.59 18.05 42.3 20 19 0.65 1HE200B 78.1 62.43 24.85 61.3 20 20 0.9 1.5

HE200M 131 107.95 40.75 103.0 20.6 22 1.5 2.5

HE220A 64.3 50.15 20.63 50.5 22 21 0.7 1.1HE220B 91 73.01 27.88 71.5 22 22 0.95 1.6

HE220M 149 122.71 44.87 117.0 22.6 24 1.55 2.6

HE240A 76.8 59.74 25.14 60.3 24 23 0.75 1.2HE240B 106 84.7 33.24 83.2 24 24 1 1.7

HE240M 200 165.74 60.48 157.0 24.8 27 1.8 3.2

HE260A 86.8 67.36 28.74 68.2 26 25 0.75 1.25HE260B 118 94.4 37.15 93.0 26 26 1 1.75

HE260M 220 181.76 67.25 172.0 26.8 29 1.8 3.25

HE280A 97.3 75.36 31.78 76.4 28 27 0.8 1.3HE280B 131 104.42 40.73 103.0 28 28 1.05 1.8

HE280M 240 197.94 71.86 189.0 28.8 31 1.85 3.3

HE300A 113 87.02 37.75 88.3 30 29 0.85 1.4HE300B 149 118.18 47.35 117.0 30 30 1.1 1.9

HE300M 303 251.88 90.45 238.0 31 34 2.1 3.9

HE320A 124 96.24 40.76 97.6 30 31 0.9 1.55HE320B 161 127.43 51.43 127.0 30 32 1.15 2.05

HE320M 312 257.28 94.8 245.0 30.9 35.9 2.1 4

HE340A 133 102.47 44.48 105.0 30 33 0.95 1.65HE340B 171 133.68 56.19 134.0 30 34 1.2 2.15

HE340M 316 257.28 98.8 248.0 30.9 37.7 2.4 4

HE360A 143 108.7 49.2 112.0 30 35 1 1.75HE360B 181 139.94 60.96 142.0 30 36 1.25 2.25

HE360M 319 256.48 102.6 250.0 30.8 39.5 2.1 4

Av,y Av,z tw tfl

[cm2] [cm2] [cm2]

Page 22: 14 03 Flexural Buckling EC3

HE400A 159 118.18 57.35 125.0 30 39 1.1 1.9HE400B 198 149.47 70.2 155.0 30 40 1.35 2.4

HE400M 326 255.68 110.4 256.0 30.7 43.2 2.1 4

HE450A 178 130.43 65.75 140.0 30 44 1.15 2.1HE450B 218 161.74 79.68 171.0 30 45 1.4 2.6

HE450M 335 255.68 119.4 263.0 30.7 47.8 2.1 4

HE500A 198 142.68 75.18 155.0 30 49 1.2 2.3HE500B 239 174.02 90.18 187.0 30 50 1.45 2.8

HE500M 344 254.88 129.2 270.0 30.6 52.4 2.1 4

HE550A 212 148.94 83.96 166.0 30 54 1.25 2.4HE550B 254 180.3 100.01 199.0 30 55 1.5 2.9

HE550M 354 254.88 139.2 278.0 30.6 57.2 2.1 4

HE600A 226 155.2 92.75 178.0 30 59 1.3 2.5HE600B 270 186.59 110.85 212.0 30 60 1.55 3

HE600M 364 254.08 150 285.0 30.5 62 2.1 4

HE650A 242 161.47 103.55 190.0 30 64 1.35 2.6HE650B 286 192.88 121.7 225.0 30 65 1.6 3.1

HE650M 374 254.08 160 293.0 30.5 66.8 2.1 4

HE700A 260 168.02 116.5 204.0 30 69 1.45 2.7HE700B 306 199.48 136.72 241.0 30 70 1.7 3.2

HE700M 383 253.28 169.8 301.0 30.4 71.6 2.1 4

HE800A 286 174.75 139 224.0 30 79 1.5 2.8HE800B 334 206.31 161.57 262.0 30 80 1.75 3.3

HE800M 404 253.11 194 317.0 30.3 81.4 2.1 4

HE900A 321 187.36 163.8 252.0 30 89 1.6 3HE900B 371 218.97 188.48 291.0 30 90 1.85 3.5

HE900M 424 252.31 214.8 333.0 30.2 91 2.1 4

I100 10.6 7.2 4.72 8.34 5 10 0.45 0.68I120 14.2 9.45 6.45 11.1 5.8 12 0.51 0.77I140 18.2 12 8.32 14.3 6.6 14 0.57 0.86I160 22.8 14.85 10.54 17.9 7.4 16 0.63 0.95I180 27.9 18.01 13 21.9 8.2 18 0.69 1.04I200 33.4 21.47 15.6 26.2 9 20 0.75 1.13I220 39.5 25.22 15.8 31.1 9.8 22 0.81 1.22I240 46.1 29.29 21.75 36.2 10.6 24 0.87 1.31I260 53.3 33.63 25.41 41.9 11.3 26 0.94 1.41I280 61 38.22 29.43 47.9 11.9 28 1.01 1.52I300 69 42.83 33.75 54.2 12.5 30 1.08 1.62I330 77.7 47.97 38.34 61 13.1 32 1.15 1.73I340 86.7 53.12 43.26 68 13.7 34 1.22 1.83I360 97 59.15 48.83 76.1 14.3 36 1.3 1.95I380 107 64.84 54.34 84 14.9 38 1.37 2.05I400 118 71.11 60.37 92.4 15.5 40 1.44 2.16I450 147 87.87 76.19 115.4 17 45 1.62 2.43I475 163 96.98 85 128 17.8 47.5 1.71 2.56I500 179 106.38 93.68 140.5 18.5 50 1.8 2.7I550 212 127.22 109.1 166.4 20 55 1.9 3I600 132 79.66 67.58 104 16.3 42.5 1.53 2.3I600 254 148.65 135.68 199.4 21.5 60 2.16 3.24I80 7.57 5.26 3.3 5.94 4.2 8 0.39 0.59

IPE100 10.3 6.73 5.06 8.1 5.5 10 0.41 0.57IPE120 13.2 8.57 6.3 10.4 6.4 12 0.44 0.63IPE140 16.4 10.62 7.62 12.9 7.3 14 0.47 0.69IPE160 20.1 12.84 9.67 15.8 8.2 16 0.5 0.74

Page 23: 14 03 Flexural Buckling EC3

IPE180 23.9 15.32 11.2 18.8 9.1 18 0.53 0.8IPE200 28.5 17.99 14.02 22.4 10 20 0.56 0.85IPE220 33.4 21.3 15.91 26.2 11 22 0.59 0.92IPE240 39.1 24.83 19.13 30.7 12 24 0.62 0.98IPE270 45.9 28.97 22.09 36.1 13.5 27 0.66 1.02IPE300 53.8 33.67 25.67 42.2 15 30 0.71 1.07IPE330 62.6 38.71 30.8 49.1 16 33 0.75 1.15IPE360 72.7 45.26 35.11 57.1 17 36 0.8 1.27IPE400 84.5 51.15 42.73 66.3 18 40 0.86 1.35IPE450 98.8 58.34 50.82 77.6 19 45 0.94 1.46IPE500 116 67.18 60.35 90.7 20 50 1.02 1.6IPE550 134 76.14 71.93 106.0 21 55 1.11 1.72IPE600 156 87.92 83.8 122.0 22 60 1.2 1.9IPE80 7.64 5.12 3.57 6.0 4.6 8 0.38 0.52

Welded Sections

Page 24: 14 03 Flexural Buckling EC3

10 11 12 13 14 15 16 17 18

[cm] [cm]

553800 14000 40 6.35 11190 934 12820 1414.48644700 16280 40.1 6.38 12890 1090 14860 1716.27722300 18460 40.3 6.45 14330 1220 16560 1939.68

349 134 4.06 2.51 72.8 26.8 83 41.14450 167 4.16 2.53 89.9 33.5 104.2 51.42

1140 399 4.63 2.74 190 75.3 236 116.31

606 231 4.89 3.02 106 38.5 119.4 58.85864 318 5.04 3.06 144 52.9 165.2 80.97

2020 703 5.51 3.25 288 112 350 171.63

1030 389 5.73 3.52 155 55.6 173.4 84.851510 550 5.93 3.58 216 78.5 246 119.783290 1140 6.39 3.77 411 157 494 240.51

1670 616 6.57 3.98 220 76.9 246 117.632490 889 6.78 4.05 311 111 354 169.965100 1760 7.25 4.26 566 212 674 325.46

2510 925 7.45 4.52 294 103 324 156.493830 1360 7.66 4.57 426 151 482 231.017480 2580 8.13 4.77 748 277 884 425.19

3690 1340 8.28 4.98 389 134 430 203.825700 2000 8.54 5.07 570 200 642 305.81

10640 3650 9 5.27 967 354 1136 543.22

5410 1950 9.17 5.51 515 178 568 270.598090 2840 9.43 5.59 736 258 828 393.88

14600 5010 9.89 5.79 1220 444 1420 678.55

7760 2770 10.1 6 675 231 744 351.6911260 3920 10.3 6.08 938 327 1054 498.4224290 8150 11 6.39 1800 657 2120 1005.93

10450 3670 11 6.5 836 282 920 430.1714920 5130 11.2 6.58 1150 395 1282 602.2531310 10450 11.9 6.9 2160 780 2520 1192.47

13670 4760 11.9 7 1010 340 1112 518.1319270 6590 12.1 7.09 1380 471 1534 717.5739550 13160 12.8 7.4 2550 914 2960 1396.68

18260 6310 12.7 7.49 1260 421 1384 641.1725170 8560 13 7.58 1680 571 1868 870.1459200 19400 14 8 3480 1250 4080 1913.18

22930 6990 13.6 7.49 1480 466 1628 709.7430820 9240 13.8 7.57 1930 616 2140 939.168130 19710 14.8 7.95 3800 1280 4440 1950.72

27690 7440 14.4 7.46 1680 496 1850 755.9536660 9690 14.6 7.53 2160 646 2400 985.7276370 19710 15.6 7.9 4050 1280 4720 1952.71

33090 7890 15.2 7.43 1890 526 2080 802.2843190 10140 15.5 7.49 2400 676 2680 1032.4984870 19520 16.3 7.83 4300 1270 4980 1942.35

Iy Iz iy iz Wel,y Wel,z Wpl,y Wpl,z Weff,y

[cm4] [cm4] [cm3] [cm3] [cm3] [cm3] [cm3]

Page 25: 14 03 Flexural Buckling EC3

45070 8560 16.8 7.34 2310 571 2560 872.8657680 10820 17.1 7.4 2880 721 3240 1104.04

104100 19340 17.9 7.7 4820 1260 5580 1934.13

63720 9470 18.9 7.29 2900 631 3220 965.5379890 11720 19.1 7.33 3550 781 3980 1197.66

131500 19340 19.8 7.59 5500 1260 6340 1939.2

86970 10370 21 7.24 3550 691 3940 1058.51107200 12620 21.2 7.27 4290 842 4820 1291.65161900 19150 21.7 7.46 6180 1250 7100 1932.02

111900 10820 23 7.15 4150 721 4620 1106.9136700 13080 23.2 7.17 4970 872 5600 1341.14198000 19160 23.6 7.35 6920 1250 7940 1937.31

141200 11270 25 7.05 4790 751 5360 1155.66171000 13530 25.2 7.08 5700 902 6420 1391.06237400 18980 25.6 7.22 7660 1240 8780 1930.38

175200 11720 26.9 6.97 5470 782 6140 1204.79210600 13980 27.1 6.99 6480 932 7320 1441.41281700 18980 27.5 7.13 8430 1240 9660 1935.67

215300 12180 28.8 6.84 6240 812 7040 1256.74256900 14440 29 6.87 7340 963 8320 1495.04329300 18800 29.3 7.01 9200 1240 10540 1928.78

303400 12640 32.6 6.65 7680 843 8700 1312.26359100 14900 32.8 6.68 8980 994 10220 1553.13442600 18630 33.1 6.79 10870 1230 12480 1930.39

422100 13550 36.3 6.5 9480 903 10820 1414.48494100 15820 36.5 6.53 10980 1050 12580 1658.34570400 18450 36.7 6.6 12540 1220 14440 1928.88

171 12.2 4.01 1.07 34.2 4.88 39.8 8.99328 21.5 4.81 1.23 54.7 7.41 63.6 13.71573 35.2 5.61 1.4 81.9 10.7 95.4 19.84935 54.7 6.4 1.55 117 14.8 136 27.57

1450 81.3 7.2 1.71 161 19.8 186.8 37.062140 117 8 1.87 214 26 250 48.523060 162 8.8 2.02 278 33.1 324 62.124250 221 9.59 2.2 354 41.7 412 78.055740 288 10.4 2.32 442 51 514 95.667590 364 11.1 2.45 542 61.2 632 114.639800 451 11.9 2.56 653 72.2 762 135.15

12510 555 12.7 2.67 782 84.7 914 158.8215700 674 13.5 2.8 923 98.4 1080 184.1519610 818 14.2 2.9 1090 114 1276 214.324010 975 15 3.02 1260 131 1482 245.0629210 1160 15.7 3.13 1460 149 1714 279.8245850 1730 17.7 3.43 2040 203 2400 380.1156480 2090 18.6 3.6 2380 235 2800 439.6468740 2480 19.6 3.72 2750 268 3240 501.7899180 3490 21.6 4.02 3610 349 4240 648.4836970 1440 16.7 3.3 1740 176 2040 329.95

139000 4670 23.4 4.3 4630 434 5460 817.5377.8 6.29 3.2 0.91 19.5 3 22.8 5.5171 15.9 4.07 1.24 34.2 5.79 39.4 9.15318 27.7 4.9 1.45 53 8.65 60.8 13.58541 44.9 5.74 1.65 77.3 12.3 88.4 19.25869 68.3 6.58 1.84 109 16.7 123.8 26.1

Page 26: 14 03 Flexural Buckling EC3

1320 101 7.42 2.05 146 22.2 166.4 34.61940 142 8.26 2.24 194 28.5 220 44.612770 205 9.11 2.48 252 37.3 286 58.113890 284 9.97 2.69 324 47.3 366 73.925790 420 11.2 3.02 429 62.2 484 96.958360 604 12.5 3.35 557 80.5 628 125.22

11770 788 13.7 3.55 713 98.5 804 153.6816270 1040 15 3.79 904 123 1020 191.123130 1320 16.5 3.95 1160 146 1308 22933740 1680 18.5 4.12 1500 176 1702 276.3848200 2140 20.4 4.31 1930 214 2200 335.8867120 2670 22.3 4.45 2440 254 2780 400.5492080 3390 24.3 4.66 3070 308 3520 485.65

80.1 8.49 3.24 1.05 20 3.69 23.2 5.82

Page 27: 14 03 Flexural Buckling EC3

19 20 21 22 23 24 25 26S235,275,355,420 S235,275,355,420

[cm]

6410 348.75 825.0 40.50 32074000 a b7430 405 1260.0 40.60 37637000 a b8280 456.02 1710 40.81 43015000 a b41.5 10 5.3 4.77 2581 b c52.1 12.5 9.29 4.87 3375 b c118 28.09 68.5 5.38 9925 b c

59.7 14.4 6.0 5.75 6472 b c82.6 19.8 13.9 5.90 9410 b c175 41.67 92 6.40 24790 b c

86.7 20.83 8.2 6.72 15060 b c123 29.4 20.1 6.93 22480 b c247 58.62 120 7.42 54330 b c123 28.8 12.3 7.68 31410 b c177 41.6 31.4 7.90 47940 b c337 79.22 163 8.41 108100 b c162 38.47 14.9 8.71 60210 b c241 56.7 42.3 8.92 93750 b c442 103.79 204 9.43 199300 b c215 50 21.1 9.66 108000 b c321 75 59.5 9.93 171100 b c568 132.61 260 10.43 346300 b c284 66.55 28.6 10.70 193300 b c414 96.8 76.8 10.96 295400 b c710 166 316 11.46 572700 b c372 86.4 41.7 11.75 328500 b c527 122.4 103.0 11.96 486900 b c

1060 246.02 630 12.72 1152000 b c460 105.63 52.6 12.78 516400 b c641 147.88 124.0 12.99 753700 b c

1260 291.79 722 13.76 1728000 b c556 127.4 62.4 13.81 785400 b c767 176.4 144.0 14.02 1130000 b c

1480 342.14 810 14.79 2520000 b c692 157.5 85.6 14.74 1200000 b c934 213.75 186.0 15.05 1688000 b c

2040 468.49 1410 16.12 4386000 b c814 174.38 108.0 15.53 1512000 b c

1070 230.63 226.0 15.74 2069000 b c2220 477.4 1510 16.80 5004000 b c

925 185.63 128.0 16.22 1824000 b c1200 241.88 258.0 16.43 2454000 b c2360 477.4 1510 17.49 5585000 a b1040 196.88 149.0 16.92 2177000 b c1340 253.13 293.0 17.21 2883000 b c2490 474.32 1510 18.08 6137000 a b

Weff,z S,y S,z I,T i,p I,W Buckling curve about y-y axis:

Buckling curve about z-z axis:

[cm3] [cm3] [cm3] [cm4] [cm6]

[-] [-]

Page 28: 14 03 Flexural Buckling EC3

1280 213.75 190.0 18.33 2942000 a b1620 270 357.0 18.63 3817000 a b2790 471.24 1520 19.49 7410000 a b1610 236.25 245.0 20.26 4146000 a b1990 282.5 442.0 20.46 5258000 a b3170 471.24 1530 21.20 9252000 a b1970 258.75 310.0 22.21 5643000 a b2410 315 540.0 22.41 7018000 a b3550 468.18 1540 22.95 11187000 a b2310 270 353.0 24.09 7189000 a b2800 326.25 602.0 24.28 8856000 a b3970 468.18 1560 24.72 13516000 a b2680 281.25 399.0 25.98 8978000 a b3210 337.5 669.0 26.18 10965000 a b4390 465.13 1570 26.60 15908000 a b3070 292.5 450.0 27.79 11027000 a b3660 348.75 741.0 27.99 13363000 a b4830 465.13 1580 28.41 18650000 a b3520 303.75 515.0 29.60 13352000 a b4160 360 833.0 29.80 16064000 a b5270 462.08 1590 30.13 21398000 a b4350 315 599.0 33.27 18290000 a b5110 371.25 949.0 33.47 21840000 a b6240 459.05 1650 33.79 27775000 a b5410 337.5 739.0 36.88 24962000 a b6290 393.75 1140.0 37.08 29461000 a b7220 456.02 1680 37.29 34746000 a b19.9 2.13 1.6 4.15 268 a b31.8 3.24 2.71 4.96 685 a b47.7 4.68 4.32 5.78 1540 a b

68 6.5 6.57 6.59 3138 a b93.4 8.74 9.58 7.40 5924 a b125 11.44 13.5 8.22 10520 a b162 14.65 18.6 9.03 17760 a b206 18.4 25 9.84 28730 a b257 22.51 33.5 10.66 44070 a b316 26.91 44.2 11.37 64580 a b381 31.64 56.8 12.17 91850 a b457 37.11 72.5 12.98 128800 a b540 42.93 90.4 13.79 176300 a b638 49.84 115 14.49 240100 a b741 56.89 141 15.30 318700 a b857 64.87 170 16.01 419600 a b

1200 87.78 267 18.03 791100 a b1400 101.39 329 18.95 1067000 a b1620 115.51 402 19.95 1403000 a b2120 150 544 21.97 2389000 a b1020 76.39 216 17.02 587500 a b2730 187.21 813 23.79 3821000 a b11.4 1.3 0.87 3.33 87.5 a b19.7 2.16 1.2 4.25 351 a b30.4 3.23 1.7 5.11 890 a b44.2 4.6 2.5 5.97 1980 a b61.9 6.22 3.6 6.83 3960 a b

Page 29: 14 03 Flexural Buckling EC3

83.2 8.28 4.8 7.70 7430 a b110 10.63 7.0 8.56 12990 a b143 13.91 9.1 9.44 22670 a b183 17.64 12.9 10.33 37390 a b242 23.24 16.0 11.60 70580 a b314 30.09 20.2 12.94 125900 a b402 36.8 28.3 14.15 199100 a b510 45.88 37.5 15.47 313600 a b654 54.67 51.4 16.97 490000 a b851 65.88 67.1 18.95 791000 a b

1100 80 89.7 20.85 1249000 a b1390 94.82 124.0 22.74 1884000 a b1760 114.95 166.0 24.74 2846000 a b11.6 1.38 0.7 3.41 118.0 a b

Page 30: 14 03 Flexural Buckling EC3

27 28 29 30 31 32 33 #REF!S 460 S 460

r

a0 a0 c 3a0 a0 c 3a0 a0 c 3a a b 1.2a a b 1.2a a b 1.2a a b 1.2a a b 1.2a a b 1.2a a b 1.2a a b 1.2a a b 1.2a a b 1.5a a b 1.5a a b 1.5a a b 1.5a a b 1.5a a b 1.5a a b 1.8a a b 1.8a a b 1.8a a b 1.8a a b 1.8a a b 1.8a a b 2.1a a b 2.1a a b 2.1a a b 2.4a a b 2.4a a b 2.4a a b 2.4a a b 2.4a a b 2.4a a b 2.7a a b 2.7a a b 2.7a a b 2.7a a b 2.7a a b 2.7a a b 2.7a a b 2.7a0 a0 b 2.7a a b 2.7a a b 2.7a0 a0 b 2.7

Buckling curve

about y-y axis:

Buckling curve

about z-z axis:

LT buckling

curve:

[-] [-] [-]

Page 31: 14 03 Flexural Buckling EC3

a0 a0 b 2.7a0 a0 b 2.7a0 a0 b 2.7a0 a0 b 2.7a0 a0 b 2.7a0 a0 b 2.7a0 a0 b 2.7a0 a0 b 2.7a0 a0 b 2.7a0 a0 b 2.7a0 a0 b 2.7a0 a0 b 2.7a0 a0 b 2.7a0 a0 b 2.7a0 a0 c 2.7a0 a0 c 2.7a0 a0 c 2.7a0 a0 c 2.7a0 a0 c 2.7a0 a0 c 2.7a0 a0 c 2.7a0 a0 c 3a0 a0 c 3a0 a0 c 3a0 a0 c 3a0 a0 c 3a0 a0 c 3

a0 a0 b 0.45

a0 a0 c 0.51

a0 a0 c 0.57

a0 a0 c 0.63

a0 a0 c 0.69

a0 a0 c 0.75

a0 a0 c 0.81

a0 a0 c 0.87

a0 a0 c 0.94

a0 a0 c 1.01

a0 a0 c 1.08

a0 a0 c 1.15

a0 a0 c 1.22

a0 a0 c 1.3

a0 a0 c 1.37

a0 a0 c 1.44

a0 a0 c 1.62

a0 a0 c 1.71

a0 a0 c 1.8

a0 a0 c 1.9

a0 a0 c 1.53

a0 a0 c 2.16

a0 a0 b 0.39

a0 a0 b 0.7

a0 a0 b 0.7

a0 a0 b 0.7

a0 a0 b 0.9

Page 32: 14 03 Flexural Buckling EC3

a0 a0 b 0.9

a0 a0 b 1.2

a0 a0 b 1.2

a0 a0 b 1.5

a0 a0 b 1.5

a0 a0 b 1.5

a0 a0 c 1.8

a0 a0 c 1.8

a0 a0 c 2.1

a0 a0 c 2.1

a0 a0 c 2.1

a0 a0 c 2.4

a0 a0 c 2.4

a0 a0 b 0.5

Page 33: 14 03 Flexural Buckling EC3

Compression: NBending Moment: Only MBending and Axial Force: M, N

Page 34: 14 03 Flexural Buckling EC3

Standard and Steel Grade

EN 10025-2 fy (N/mm²) fu (N/mm²) fy (N/mm²) fu (N/mm²)

S235 235 360 215 360S275 275 430 255 410S355 355 510 335 470

t< 40 mm 40mm < t < 80 mm