This 3-page document provides an example problem for designing a beam-column with a rectangular hollow cross section subjected to axial force and bending moments. It includes dimensions, material properties, classifications of the cross section, cross section properties, buckling checks, and a summary that the design is acceptable with a factor of safety of 0.939.

1. TALAT Lecture 2301
Design of Members
Axial force and bending moment
Example 9.2 : Beam-column with rectangular hollow
section
4 pages
Advanced Level
prepared by Torsten Höglund, Royal Institute of Technology, Stockholm
Date of Issue: 1999
 EAA - European Aluminium Association
TALAT 2301 – Example 9.2 1

2. Example 9.2 Beam-column with rectangular hollow section
Dimensions and material properties
MPa 10 . Pa
6
Length lc 3800 . mm
kN 1000 . newton
Thickness tw 6 . mm tf 6 . mm
Width hy 180 . mm hi hy 2 .t f h i = 168 mm
by 120 . mm bi by 2 .t w b i = 108 mm
[1] Table 3.2b Alloy: EN AW-6060 T6 EP t < 15 mm f 0.2 140 . MPa fu 170 . MPa
[1] (5.4), (5.5) fo f 0.2 fa fu E 70000 . MPa γ M1 1.1 γ M2 1.25
Forces and moment
Axial force N Ed 110 . kN
Transverse force F Ed 8 . kN
F Ed . l c
Bending moment M y.Ed M y.Ed = 7.6 kN . m
4
Classification of the cross section in axial compression
hy 2 .t f 250 . MPa
Web β w β w 28
= ε ε = 1.336
tw fo
[1] Tab. 5.1 β 1w 11 . ε β 2w 16 . ε β 3w 22 . ε
class c if β w β 1w , if β w > β 2w , if β w > β 3w , 4 , 3 , 2 , 1
> class c = 3
[1] 5.8.4.1 Ae A η 1.0
TALAT 2301 – Example 9.2 2

3. Classification of the cross section in y-y axis bending
hy 2 .t f
Web β w 0.4 . β w 11.2
=
tw
[1] Tab. 5.1 β 1w 11 . ε β 2w 16 . ε β 3w 22 . ε
[1] 5.4.5 class w if β w β 1w , if β w > β 2w , if β w > β 3w , 4 , 3 , 2 , 1
> class w = 1
by 2 .t w
Flange β f β = 18
f
tf
[1] Tab. 5.1 β 1f 11 . ε β 2f 16 . ε β 3f 22 . ε
[1] 5.4.5 class f if β > β 1w , if β f > β 2f , if β f > β 3f , 4 , 3 , 2 , 1
f class f = 2
Classification of the total cross-section iny-y axis bending:
class y if class f > class w , class f , class w class y = 2
Classification of the cross section in z-z axis bending
by 2 .t w
Web β w 0.4 . β w 7.2
=
tf
[1] Tab. 5.1 β 1w 11 . ε β 2w 16 . ε β 3w 22 . ε
[1] 5.4.5 class w if β w β 1w , if β w > β 2w , if β w > β 3w , 4 , 3 , 2 , 1
> class w = 1
hy 2 .t f
Flange β f β = 28
f
tw
[1] Tab. 5.1 β 1f 11 . ε β 2f 16 . ε β 3f 22 . ε
[1] 5.4.5 class f if β > β 1w , if β f > β 2f , if β f > β 3f , 4 , 3 , 2 , 1
f class f = 3
Classification of the total cross-section inz-z axis bending:
class z if class f > class w , class f , class w class z = 3
Cross section constants
b y .h y b i.h i A = 3.456 . 10 mm
3 2
A
b y .h y b i.h i h y .b y h i.b i
3 3 3 3
I y = 1.565 . 10 mm I z = 8.28 . 10 mm
7 4 6 4
Iy Iz
12 12 12 12
I y .2 I z.2
W el.y = 1.738 . 10 mm W el.z = 1.4 . 10 mm
5 3 5 3
W el.y W el.z
hy by
b y .h y b i.h i
2 2
W pl.y = 2.1 . 10 mm
5 3
W pl.y
4 4
W pl.y
[1] 5.6.2.1 class y = 2 α y α y = 1.208 class z = 3 α z 1
W el.y
Iy Iz
iy i y = 67.3 mm iz i z = 49 mm
TALAT 2301 – A
Example 9.2 3 A

4. Flexural buckling
lc η .f o lc η .f o
TALAT (5.6) λ y . λ y 0.804
= λ z . λ z 1.105
=
π .i y E π .i z E
φ y 0.5 . 1 0.20 . λ y φ z 0.5 . 1 0.20 . λ z
2 2
[1] 5.8.4.1 0.1 λ y 0.1 λ z
1 1
χ y χ y = 0.779 χ z χ z = 0.586
2 2 2 2
φ y φ y λ y φ z φ z λ z
[1] Table 5.5 k1 1 k2 1
A .f o
N Rd N Rd = 439.9 kN
γ M1
Exponents in interaction formula
[1] 5.9.4.2 (4) ψ α z.α y ψ if ( ψ > 2 , 2 , ψ ) ψ = 1.208
ψ c χ z.ψ ψ c if ψ c < 0.8 , 0.8 , ψ c ψ c 0.8
=
Cross weld in mid section
[1] Tab. 5.2 HAZ softening factor ρ haz 0.65
ρ haz . f u . γ M1
[1] 5.9.4.5 ω o ω o 0.695
= ω x ω o
f o . γ M2
fo
M y.Rd α y . W el.y. M y.Rd = 26.721 kN . m M y.Ed = 7.6 kN . m
γ M1
fo
M z.Rd α .z el.z.
W M z.Rd = 17.572 kN . m M z.Ed 0 . kN . m
γ M1
χ min χ y χ min = 0.779
Flexural buckling check
ψc 1.7 1.7 0.6
N Ed 1 . M y.Ed M z.Ed
[1] 5.9.4.2 (4) = 0.939 < 1,0 OK !
χ min x . N Rd
.ω ω o M y.Rd M z.Rd
TALAT 2301 – Example 9.2 4