Prediction of Buckling Load of Steel Racking Frame Using Non Destructive Method

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]





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





Numerical AnalysisNumerical Analysis ExperimentalExperimentalTheoreticalTheoretical

One DimensionalOne Dimensional Three SpecimensThree Specimens

Two Dimensional FrameTwo Dimensional Frame





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



ONE DIMENSIONAL



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



ONE DIMENSIONAL


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



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



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



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



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



Dimensionless plot of axial load versus calculated squared-frequency


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





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





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





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

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Prediction of Buckling Load of Steel Racking Frame Using Non Destructive Method