Talat Lecture 2301: Design Of Members Example 7.1: Concentrated Force
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TALAT Lecture 2301
Design of Members Concentrated Load Example 7.1 : Concentrated force 4 pages Advanced Level prepared by Torsten Höglund, Royal Institute of Technology, Stockholm
Date of Issue: 1999 EAA - European Aluminium Association
TALAT 2301 – Example 7.1
1
Example 7.1. Concentrated force
Dimensions and material properties Beam:
Purlin (p):
Section height:
h
570 . mm
Section height:
hp
180 . mm
Flange width:
b
160 . mm
Flange width:
bp
12 . mm
Flange thickness:
tf
16 . mm
Flange thickness:
t fp
12 . mm
Web thickness:
tw
5 . mm
Web thickness:
t wp
5 . mm
Fillet radius:
r
4 . mm
Fillet radius:
rp
5 . mm
Overall length:
L
10 . m
Distance between purlins: c p
1.2 . m
Table 3.2b
Alloy: EN AW-6082 T6 EP/O t > 5 mm
f 0.2
(5.4), (5.5)
fo
E
f 0.2
fa
Partial safety factors: S.I. units
TALAT 2301 – Example 7.1
fu
260 . MPa
fu
310 . MPa
70000 . MPa
γ M11.10
kN 1000 . newton
kNm kN . m
2
MPa 1000000 . Pa
Concentrated force resistance of beam 5.12.8
bf hw
Figure 5.24 and above
(5.109)
Figure 5.24
(5.110)
(5.111)
(5.108)
f of
fo
f ow
2 .t f
h
Parameter m 1
g
r p. 2
ss
t wp
m2
Effective loaded lengthly
ly
Design resistance
2 .g
g = 2.9 mm
2 . t fp
s s = 34.9 mm m 1 = 32
if
ss
f ow
hw
2
k F = 6.01
a 4 . t f . h w . f ow
ss
2 k F .E .t w
2 .t f . 1
m1
> 0.2 , 0.02 .
hw tf
2
,0
, t w .l y . γ M1
f ow
m 2 = 22.6 l y = 303.3 mm
m2
k F . l y . f ow . E 1 2. . . 0.57 t w hw γ M1
F Rd = 101.7 kN
, F Rd
F Rd = 101.7 kN
M1
Flange induced buckling Elastic moment resistance utilised
(5.115)
rp . 2
2.
6
F Rd
γ
L
f ow . t w
kF
Parameter m 2
a
f of . b f
m1
Buckling coefficient
if F Rd> t w . l y .
fo
h w = 538 mm
Length of stiff bearing
F Rd
5.12.9
b
LS =
hw tw
= 107.6
TALAT 2301 – Example 7.1
RS =
k
0.55
. k .E . h w t w = 151.8 f of b .t f
3
f of
fo
LS < RS
OK!
Concentrated force resistance of purlin (upward) 5.12.8
bf h wp
Figure 5.24 and above
(5.109)
Figure 5.24
(5.110)
(5.111)
(5.108)
bp hp
f of
fo
f ow
2 . t fp
h wp = 156 mm
Length of stiff bearing
Parameter m 1
TALAT 2301 – Example 7.1
ss
tw
m2
if
ly
Design resistance
if F Rd> t wp . l y .
r. 2
kF
Effective loaded lengthly
F Rd
g
m1
Buckling coefficient
Parameter m 2
fo
F Rd
10 m
r . 2 2 .g
g = 2.3 mm
2 .t f
s s = 41.7 mm
f of . b f
m 1 = 2.4
f ow . t wp 2.
6 ss
h wp
2
kF=6
ap
4 . t fp . h wp . f ow 2 k F . E . t wp
ss
2 . t fp . 1
0.57 . t
f ow
γ
ap
, t wp . l y . γ M1
4
wp
2.
f ow M1
m1
> 0.2 , 0.02 .
t fp
h wp
2
,0
m 2 = 3.4 l y = 123.4 mm
m2
k F . l y . f ow . E 1 .
, F Rd
h wp
γ M1
F Rd = 120.4 kN
F Rd = 120.4 kN
Design of Members Concentrated Load Example 7.1 : Concentrated force 4 pages Advanced Level prepared by Torsten Höglund, Royal Institute of Technology, Stockholm
Date of Issue: 1999 EAA - European Aluminium Association
TALAT 2301 – Example 7.1
1
Example 7.1. Concentrated force
Dimensions and material properties Beam:
Purlin (p):
Section height:
h
570 . mm
Section height:
hp
180 . mm
Flange width:
b
160 . mm
Flange width:
bp
12 . mm
Flange thickness:
tf
16 . mm
Flange thickness:
t fp
12 . mm
Web thickness:
tw
5 . mm
Web thickness:
t wp
5 . mm
Fillet radius:
r
4 . mm
Fillet radius:
rp
5 . mm
Overall length:
L
10 . m
Distance between purlins: c p
1.2 . m
Table 3.2b
Alloy: EN AW-6082 T6 EP/O t > 5 mm
f 0.2
(5.4), (5.5)
fo
E
f 0.2
fa
Partial safety factors: S.I. units
TALAT 2301 – Example 7.1
fu
260 . MPa
fu
310 . MPa
70000 . MPa
γ M11.10
kN 1000 . newton
kNm kN . m
2
MPa 1000000 . Pa
Concentrated force resistance of beam 5.12.8
bf hw
Figure 5.24 and above
(5.109)
Figure 5.24
(5.110)
(5.111)
(5.108)
f of
fo
f ow
2 .t f
h
Parameter m 1
g
r p. 2
ss
t wp
m2
Effective loaded lengthly
ly
Design resistance
2 .g
g = 2.9 mm
2 . t fp
s s = 34.9 mm m 1 = 32
if
ss
f ow
hw
2
k F = 6.01
a 4 . t f . h w . f ow
ss
2 k F .E .t w
2 .t f . 1
m1
> 0.2 , 0.02 .
hw tf
2
,0
, t w .l y . γ M1
f ow
m 2 = 22.6 l y = 303.3 mm
m2
k F . l y . f ow . E 1 2. . . 0.57 t w hw γ M1
F Rd = 101.7 kN
, F Rd
F Rd = 101.7 kN
M1
Flange induced buckling Elastic moment resistance utilised
(5.115)
rp . 2
2.
6
F Rd
γ
L
f ow . t w
kF
Parameter m 2
a
f of . b f
m1
Buckling coefficient
if F Rd> t w . l y .
fo
h w = 538 mm
Length of stiff bearing
F Rd
5.12.9
b
LS =
hw tw
= 107.6
TALAT 2301 – Example 7.1
RS =
k
0.55
. k .E . h w t w = 151.8 f of b .t f
3
f of
fo
LS < RS
OK!
Concentrated force resistance of purlin (upward) 5.12.8
bf h wp
Figure 5.24 and above
(5.109)
Figure 5.24
(5.110)
(5.111)
(5.108)
bp hp
f of
fo
f ow
2 . t fp
h wp = 156 mm
Length of stiff bearing
Parameter m 1
TALAT 2301 – Example 7.1
ss
tw
m2
if
ly
Design resistance
if F Rd> t wp . l y .
r. 2
kF
Effective loaded lengthly
F Rd
g
m1
Buckling coefficient
Parameter m 2
fo
F Rd
10 m
r . 2 2 .g
g = 2.3 mm
2 .t f
s s = 41.7 mm
f of . b f
m 1 = 2.4
f ow . t wp 2.
6 ss
h wp
2
kF=6
ap
4 . t fp . h wp . f ow 2 k F . E . t wp
ss
2 . t fp . 1
0.57 . t
f ow
γ
ap
, t wp . l y . γ M1
4
wp
2.
f ow M1
m1
> 0.2 , 0.02 .
t fp
h wp
2
,0
m 2 = 3.4 l y = 123.4 mm
m2
k F . l y . f ow . E 1 .
, F Rd
h wp
γ M1
F Rd = 120.4 kN
F Rd = 120.4 kN
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