Ec9_ex92_Beam column_RHS.mcd Axial force and bending moment Page 1 of 3

Transverse force FEd 8 kN⋅:=

Bending moment My.EdFEd lc⋅

4:= My.Ed 7.6 kN m⋅=

Classification of the cross section in axial compression

Web βwhy 2 tf⋅−

tw:= βw 28= ε

250 MPa⋅

fo:= ε 1.336=

[1] Tab. 6.2 β1w 11 ε⋅:= β2w 16 ε⋅:= β3w 22 ε⋅:=

classc if βw β1w> if βw β2w> if βw β3w> 4, 3,( ), 2,( ), 1,( ):= classc 3=

[1] 6.3.1 Ae A:= A η 1.0:=

Classification of the cross section in y-y axis bending

Web βw 0.4hy 2 tf⋅−

tw⋅:= βw 11.2=

Example 9.2 Beam-column with rectangular hollow section

N

l c

l c/2l c/2

F

N

by

h y

z

z

yy

twt f

Dimensions and material propertiesMPa 106 Pa⋅≡Length lc 3800 mm⋅:=kN 1000 newton⋅≡

Thickness tw 6 mm⋅:= tf 6 mm⋅:=

Width hy 180 mm⋅:= hi hy 2 tf⋅−:= hi 168 mm=

by 120 mm⋅:= bi by 2 tw⋅−:= bi 108 mm=

[1] Table 3.2b Alloy: EN AW-6060 T6 EP t < 15 mm fo 140 MPa⋅:= fu 170 MPa⋅:=

BC "A":= E 70000 MPa⋅:= γM1 1.1:= γM2 1.25:=

Forces and moment

Axial force NEd 110 kN⋅:=

T Höglund aluMATTER 2007-07-29

Ec9_ex92_Beam column_RHS.mcd Axial force and bending moment Page 2 of 3

[1] Tab. 5.1 β1f 11 ε⋅:= β2f 16 ε⋅:= β3f 22 ε⋅:=

[1] 5.4.5 classf if βf β1w> if βf β2f> if βf β3f> 4, 3,( ), 2,( ), 1,( ):= classf 3=

Classification of the total cross-section in z-z axis bending:

classz if classf classw> classf, classw,( ):= classz 3=

Cross section constants

A by hy⋅ bi hi⋅−:= A 3.456 103× mm2

=

Iyby hy

3⋅

12

bi hi3

⋅

12−:= Iy 1.565 107

× mm4= Iz

hy by3

⋅

12

hi bi3

⋅

12−:=

iz 49 mm=izIzA

:=iy 67.3 mm=iyIyA

:=

αz 1:=classz 3=αy 1.208=αyWpl.y

Wel.y:=classy 2=[1] 5.6.2.1

Wpl.y 2.1 105× mm3

=Wpl.yby hy

2⋅

4

bi hi2

⋅

4−:=

Wel.z 1.4 105× mm3

=Wel.zIz 2⋅

by:=Wel.y 1.738 105

× mm3=Wel.y

Iy 2⋅

hy:=

Iz 8.28 106× mm4

=

classf 2=classf if βf β1w> if βf β2f> if βf β3f> 4, 3,( ), 2,( ), 1,( ):=[1] 5.4.5

β3f 22 ε⋅:=β2f 16 ε⋅:=β1f 11 ε⋅:=[1] Tab. 5.1

βf 18=βfby 2 tw⋅−

tf:=Flange

classw 1=classw if βw β1w> if βw β2w> if βw β3w> 4, 3,( ), 2,( ), 1,( ):=[1] 5.4.5

β3w 22 ε⋅:=β2w 16 ε⋅:=β1w 11 ε⋅:=[1] Tab. 5.1

βf 28=βfhy 2 tf⋅−

tw:=Flange

classw 1=classw if βw β1w> if βw β2w> if βw β3w> 4, 3,( ), 2,( ), 1,( ):=[1] 5.4.5

β3w 22 ε⋅:=β2w 16 ε⋅:=β1w 11 ε⋅:=[1] Tab. 5.1

βw 7.2=βw 0.4by 2 tw⋅−

tf⋅:=Web

Classification of the cross section in z-z axis bending

classy 2=classy if classf classw> classf, classw,( ):=

Classification of the total cross-section in y-y axis bending:

T Höglund aluMATTER 2007-07-29

Ec9_ex92_Beam column_RHS.mcd Axial force and bending moment Page 3 of 3

ψc χz ψ⋅:= ψc if ψc 0.8< 0.8, ψc,( ):= ψc 0.8=

Cross weld in mid section

[1] Tab. 5.2 HAZ softening factor ρhaz 0.65:=

[1] 5.9.4.5 ωoρhaz fu⋅ γM1⋅

fo γM2⋅:= ωo 0.695= ωx ωo:=

My.Rd αy Wel.y⋅foγM1⋅:= My.Rd 26.721 kN m⋅= My.Ed 7.6 kN m⋅=

Mz.Rd αz Wel.z⋅foγM1⋅:= Mz.Rd 17.572 kN m⋅= Mz.Ed 0 kN⋅ m⋅:=

χmin χy:= χmin 0.779=

Flexural buckling check

[1] 5.9.4.2 (4)NEd

χmin ωx⋅ NRd⋅

⎛⎜⎝

⎞⎟⎠

ψc1ωo

My.Ed

My.Rd

⎛⎜⎝

⎞⎟⎠

1.7 Mz.Ed

Mz.Rd

⎛⎜⎝

⎞⎟⎠

1.7

+⎡⎢⎢⎣

⎤⎥⎥⎦

0.6

⋅+ 0.939= < 1,0 OK !

Flexural buckling

TALAT (5.6) λylcπ iy⋅

η fo⋅

E⋅:= λy 0.804= λz

lcπ iz⋅

η fo⋅

E⋅:= λz 1.105=

[1] 5.8.4.1 φy 0.5 1 0.20 λy 0.1−( )⋅ λy2

+⎡⎣

⎤⎦+⎡

⎣⎤⎦⋅:= φz 0.5 1 0.20 λz 0.1−( )⋅ λz

2+⎡

⎣⎤⎦+⎡

⎣⎤⎦⋅:=

χy1

φy φy2

λy2

−+

:= χy 0.779= χz1

φz φz2

λz2

−+

:= χz 0.586=

[1] Table 5.5 k1 1:= k2 1:=

NRdA fo⋅

γM1:= NRd 439.9 kN=

Exponents in interaction formula

[1] 5.9.4.2 (4) ψ αz αy⋅:= ψ if ψ 2> 2, ψ,( ):= ψ 1.208=

T Höglund aluMATTER 2007-07-29