8/6/2019 Prediction of Buckling Load of Steel Racking Frame Using Non Destructive Method
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8/6/2019 Prediction of Buckling Load of Steel Racking Frame Using Non Destructive Method
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Steel deckCoil/Drum
Bracing
channel
Adjustable beam
Frame upright
Slotted timber deck
Typical pallet racking system [3,4]
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8/6/2019 Prediction of Buckling Load of Steel Racking Frame Using Non Destructive Method
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LURIE,1952 – Investigated the relation of instability to
s ruc ura s ness exper men a an ana y ca wor .
–
beams subjected to compressive axial load.
LEE,1965 – Developed a linear relationship
2
Ideal Equation1=⎟⎟ ⎠
⎜⎜⎝
+o
L
cr f
f
P
P
8/6/2019 Prediction of Buckling Load of Steel Racking Frame Using Non Destructive Method
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8/6/2019 Prediction of Buckling Load of Steel Racking Frame Using Non Destructive Method
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Numerical AnalysisNumerical Analysis ExperimentalExperimentalTheoreticalTheoretical
One DimensionalOne Dimensional Three SpecimensThree Specimens
Two Dimensional FrameTwo Dimensional Frame
8/6/2019 Prediction of Buckling Load of Steel Racking Frame Using Non Destructive Method
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8/6/2019 Prediction of Buckling Load of Steel Racking Frame Using Non Destructive Method
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ONE DIMENSIONAL
Description Location Average1 2 3 4 5
Width (mm) 25.34 25.34 25.38 25.33 25.36 25.35
Thickness (mm) 1.56 1.59 1.59 1.58 1.59 1.58
Length (mm) 457.7 - - - - 457.7
Specimen 2
LocationDescription Average
1 2 3 4 5
Width (mm) 25.24 25.20 25.20 25.18 25.24 25.21
Thickness (mm) 1.98 1.97 1.98 1.96 1.94 1.97
engt (mm) . - - - - .
Specimen 3
Description
Location
Average1 2 3 4 5
Width (mm) 25.41 25.38 25.36 25.37 25.36 25.38
Thickness (mm) 3.19 3.19 3.20 3.21 3.22 3.20
Length (mm) 711.0 - - - - 711.0
8/6/2019 Prediction of Buckling Load of Steel Racking Frame Using Non Destructive Method
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ONE DIMENSIONAL
8/6/2019 Prediction of Buckling Load of Steel Racking Frame Using Non Destructive Method
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ONE DIMENSIONAL
Buckling Load Natural Frequency
- -
e r i m
e n t
( N ) S A S
( N ) o r e t i c a l
( N ) r e n t i a l
( % )
e r i m
e n t
( N ) S A S
( N ) o r e t i c a l
( N ) r e n t i a l
( % )
E x p L
T h e
D i f f
E x p L
T h e
D i f f
Specimen 1 90 82.05 82.63 0.70 8.943 17.65 17.65 0
pec men . . . . . . .
Specimen 3 238.75 282.8 282.8 0 13.90 14.86 14.81 0.34
Table 1: Bucklin load and Natural Fre uenc for s ecimens
8/6/2019 Prediction of Buckling Load of Steel Racking Frame Using Non Destructive Method
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ONE DIMENSIONAL
Buckling Load Natural Frequency
1 2 [1-2]/1% 1 2 [3-2]/2%
r e t i c
a l
) A S ) r e n t i a l
) r e t i c
a l
) A S ) r e n t i a l
)
T h e o (
L U (
D i f f e (
T h e o (
L U (
D i f f e (
Simply supported column 89.66 89.67 0.011 54.075 54.23 0.29
Cantilever column 22.42 22.42 0 19.26 19.32 0.3
One pin ended and other fixedended
183.51 183.5 0.005 84.89 84.71 0.26
Table 2 : Buckling load and Natural Frequency for columns with various end conditions
8/6/2019 Prediction of Buckling Load of Steel Racking Frame Using Non Destructive Method
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Axial load versus calculated squared-frequency using LUSAS for columns
ONE DIMENSIONAL
160
180
200
Simply supported column
Cantilever column
One pin ended and other
120
140
L o a d ( N )
P
60
80
100
A x i a l P
0
20
40
0 1000 2000 3000 4000 5000 6000 7000 8000
Squared-frequency ( Hz2)
Figure 1 : Axial load versus calculated squared-frequency determined using LUSAS for columns with various support conditions
8/6/2019 Prediction of Buckling Load of Steel Racking Frame Using Non Destructive Method
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Dimensionless plot of axial load versus calculated squared-frequency using LUSAS for columns
ONE DIMENSIONAL
y = -1.0007x + 1.0156
R2
= 0.9998
0.90
1.00
Simply supported column
Cantilever column
y = -0.9971x + 0.9972
R2
= 1
0.60
0.70
.
a l l o a
d ( P / P c r )
fixed column
y = -0.9948x + 0.9997
R2
= 1
0.30
0.40
0.50
R a t i o o f t o t a l a x i
0.10
0.20
.
0.000 0.100 0.200 0.300 0.400 0.500 0.600 0.700 0.800 0.900 1.000
Ratio of frequency squared (f/fo)
Figure 2 : Relationships between non-dimensional load versus squared frequency for different support conditions
8/6/2019 Prediction of Buckling Load of Steel Racking Frame Using Non Destructive Method
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TWO DIMENSIONAL FRAME
H=Hs=1.5m
EI1=20.44 GNmm2
EI1 EI1
EI1
mmmmmmmmmm
Lb=2.7m
Second moment of Second moment of
Figure 3 : Details of the Single steel racking 2D frame used for study
SHS (mm)
mens on
( m )
rea
( m2 ) area about y axis,Iyy ( m4 )
area about z axis,Izz ( m4 )
40x40x3.0 As shown 4.34x10-4 9.78x10-8 9.78x10-8
Table 3 : Section properties for a simple racking frame
8/6/2019 Prediction of Buckling Load of Steel Racking Frame Using Non Destructive Method
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TWO DIMENSIONAL FRAMEAxial load versus calculated squared-frequency using LUSAS for a simple racking frame
50
55
60
35
40
45
L o a d ( k N / m )
y = -0.3105x + 52.565
R2
= 0.9657
15
20
25 A x i a l
0
5
10
0 20 40 60 80 100 120 140 160 180
Squared-frequency ( Hz2)
Figure 4 : Axial load versus calculated squared-frequency determined using LUSAS for a simple steel racking 2D frame
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Dimensionless plot of axial load versus calculated squared-frequency
TWO DIMENSIONAL FRAME
0.8
0.9
1
y = -1.3849x + 1.3174
R2
= 0.96570.6
0.7
a l l o
a d ( P / P
c r ) Ideal Equation
0.3
0.4
0.5
N o n - d i m e n s i o
0
0.1
0.2
0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00
Non-dimensional squared frequency (f/fo)2
Figure 5 : Comparison non-dimensional versus squared frequency determined using LUSAS and the ideal equation
8/6/2019 Prediction of Buckling Load of Steel Racking Frame Using Non Destructive Method
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TWO DIMENSIONAL FRAME
Buckling Load Natural Frequency
1 2 [1-2]/1% 1 2 [3-2]/2%
Theoretical LUSASDifferential
Theoretical LUSAS Differential (N) (N)
(%)
(N) (N)
(%)
Single storey racking42.17 39.99 5.17 13.77 13.44 2.4
Table 4 :Comparison of buckling and natural frequency using different methods for a Simple racking frame
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8/6/2019 Prediction of Buckling Load of Steel Racking Frame Using Non Destructive Method
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Dimensionless plot of axial load versus calculated squared-frequency
THREE DIMENSIONAL FRAME
using LUSAS for racking 3D frames
0.9
1
Single Bay Three storeyMultibay three storey
y = -1.0111x + 1.0147
R2
= 0.9999
0.6
0.7
.
l l o a
d ( P / P
c r )
y = -1.0069x + 1.0088
R2
= 1
0.3
0.4
0.5
N o n - d i m e n s i o n
0
0.1
0.2
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Non-dimensional squared frequency (f/fo)2
Figure 7 : Comparison non-dimensional versus squared frequency determined
using LUSAS and the ideal equation for 3D steel racking frame
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A strut regardless of the type of end support
con on sa s e e ea equa on
between axial load and squared frequency which are
not in good agreement with the ideal equation
The 3D frame agreed closely with the ideal
equation