Talat Lecture 2301: Design Of Members Example 5.5: Axial Force Resistance Of Laced Column
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TALAT Lecture 2301
Design of Members Axial Force Example 5.5 : Axial force resistance of laced column 3 pages Advanced Level prepared by Torsten Höglund, Royal Institute of Technology, Stockholm
Date of Issue: 1999 EAA - European Aluminium Association TALAT 2301 – Example 5.5
1
Example 5.5. Axial force resistance of laced column Width
400 . mm
b
Longitudinal members d o Lacing bd
5.4.3
10 . mm
5 .m
Axial force
N Ed
2
2
200 . MPa
E 70000 . MPa γ M1 1.0
kN 1000 . newton 6 MPa 10 . Pa
d = 640.3 mm lc = 10 a
b
270 . kN
Slenderness parameters do π.
Al
2
di
do π.
A l = 392.699 mm
4
4
I l = 3.191 . 10 mm 4
64
λ =l 1.888
4 .A l 4 .I l
A = 1.571 . 10 mm 3
4 .A l.
b
I = 6.296 . 10 mm 7
I
2
4
i = 200.2 mm
A
lc 1 fo . . λ o E i π
Lacing
Ad
id
2
2
Effective length l c
Id
4
i l = 9.014 mm
Al
2 .a . 1 . f o λ l E il π A
2
4
di
Il
i
Composite member
td
lc
I
Effective length d
40 . mm
Effective length
il
Four main member
20 . mm
a
Il
Effective length 2 . a
di
d
2
Single main member
30 . mm
500 . mm
a
fo
λ o= 0.425
b d .t d b d .t d
A d = 400 mm
2
3
I d = 3.333 . 10 mm 3
12 Id
i d = 2.9 mm
Ad f o .A .d
4
d . 1 . fo λ d E id π
λ d= 3.774
3
λ c
2
λ o
TALAT 2301 – Example 5.5
λ c= 0.466
E .A d .a .b
2
2
5.8.4
Flexural buckling, buttoned strut
Table 5.5 and 5.6
α
0.2
(5.33)
φ
0.5 . 1
λ o
0.1
k1
α . λ
1
λ o
k2 2
λ
λ
1
fo
φ 2
φ
λ
5.8.4
Flexural buckling, single longitudinal member
Table 5.5 and 5.6
α
(5.33)
φ
λ o
0.5 . 1
0.1
k1
α . λ
χ .k 1 .k 2 .
1
λ o fo
.A
N l.Rd
5.8.4
Flexural buckling, lacing
TALAT (5.22)
qχ
l c. 1
λ (5.33)
5.8.3 (1)
φ
N Ed
1
2
χ
λ
λ l 1
φ 2
φ
λ
= 2.46
q χ = 1.022 kN . m
2
c
0.9 . A . f o
Nl
V χ.
d
1
N l.Rd = 19.4 kN
Vχ
q χ .l c 2
0.02 . N b.Rd = 5.757 kN
b
χ = 0.248
2
l
0.015 . N Ed .λ
λ
k2
φ
5.8.3 (1)
γ M1
χ = 0.916
N b.Rd = 287.8 kN
N b.Rd
0.2
= 0.645
2
.A
5.8.3 (1)
γ M1
λ c = 0.466
1
χ φ
χ .k 1 .k 2 .
λ c
V χ = 2.555 kN N l = 4.091 kN
λ d 0.5 . 1
N l.Rd
α . λ
χ .k 1 .k 2 .
TALAT 2301 – Example 5.5
λ o fo
γ M1
λ
2
1
χ φ
.A
φ
φ 2
λ
= 7.989
N l.Rd = 5.3 kN
d
3
χ = 0.067
2
< N l OK !
Design of Members Axial Force Example 5.5 : Axial force resistance of laced column 3 pages Advanced Level prepared by Torsten Höglund, Royal Institute of Technology, Stockholm
Date of Issue: 1999 EAA - European Aluminium Association TALAT 2301 – Example 5.5
1
Example 5.5. Axial force resistance of laced column Width
400 . mm
b
Longitudinal members d o Lacing bd
5.4.3
10 . mm
5 .m
Axial force
N Ed
2
2
200 . MPa
E 70000 . MPa γ M1 1.0
kN 1000 . newton 6 MPa 10 . Pa
d = 640.3 mm lc = 10 a
b
270 . kN
Slenderness parameters do π.
Al
2
di
do π.
A l = 392.699 mm
4
4
I l = 3.191 . 10 mm 4
64
λ =l 1.888
4 .A l 4 .I l
A = 1.571 . 10 mm 3
4 .A l.
b
I = 6.296 . 10 mm 7
I
2
4
i = 200.2 mm
A
lc 1 fo . . λ o E i π
Lacing
Ad
id
2
2
Effective length l c
Id
4
i l = 9.014 mm
Al
2 .a . 1 . f o λ l E il π A
2
4
di
Il
i
Composite member
td
lc
I
Effective length d
40 . mm
Effective length
il
Four main member
20 . mm
a
Il
Effective length 2 . a
di
d
2
Single main member
30 . mm
500 . mm
a
fo
λ o= 0.425
b d .t d b d .t d
A d = 400 mm
2
3
I d = 3.333 . 10 mm 3
12 Id
i d = 2.9 mm
Ad f o .A .d
4
d . 1 . fo λ d E id π
λ d= 3.774
3
λ c
2
λ o
TALAT 2301 – Example 5.5
λ c= 0.466
E .A d .a .b
2
2
5.8.4
Flexural buckling, buttoned strut
Table 5.5 and 5.6
α
0.2
(5.33)
φ
0.5 . 1
λ o
0.1
k1
α . λ
1
λ o
k2 2
λ
λ
1
fo
φ 2
φ
λ
5.8.4
Flexural buckling, single longitudinal member
Table 5.5 and 5.6
α
(5.33)
φ
λ o
0.5 . 1
0.1
k1
α . λ
χ .k 1 .k 2 .
1
λ o fo
.A
N l.Rd
5.8.4
Flexural buckling, lacing
TALAT (5.22)
qχ
l c. 1
λ (5.33)
5.8.3 (1)
φ
N Ed
1
2
χ
λ
λ l 1
φ 2
φ
λ
= 2.46
q χ = 1.022 kN . m
2
c
0.9 . A . f o
Nl
V χ.
d
1
N l.Rd = 19.4 kN
Vχ
q χ .l c 2
0.02 . N b.Rd = 5.757 kN
b
χ = 0.248
2
l
0.015 . N Ed .λ
λ
k2
φ
5.8.3 (1)
γ M1
χ = 0.916
N b.Rd = 287.8 kN
N b.Rd
0.2
= 0.645
2
.A
5.8.3 (1)
γ M1
λ c = 0.466
1
χ φ
χ .k 1 .k 2 .
λ c
V χ = 2.555 kN N l = 4.091 kN
λ d 0.5 . 1
N l.Rd
α . λ
χ .k 1 .k 2 .
TALAT 2301 – Example 5.5
λ o fo
γ M1
λ
2
1
χ φ
.A
φ
φ 2
λ
= 7.989
N l.Rd = 5.3 kN
d
3
χ = 0.067
2
< N l OK !
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