Interactive Buckling of Cold-Formed Steel Sections Applied ... 2011/Presentations/Day1... ·...
Transcript of Interactive Buckling of Cold-Formed Steel Sections Applied ... 2011/Presentations/Day1... ·...
Interactive Buckling of
Cold-Formed Steel Sections
Applied in
Pallet Rack Upright Members
D. Dubina, V. Ungureanu, A. Crisan “Politehnica” University of Timişoara
Peculiarities of cold-formed thin-walled
sections
• Cold forming technologies modify the properties of
base material and induces specific residual stresses
• Thin walled sections (class 4, usually) are : • highly sensitive to local and sectional instability modes
• highly sensitive to geometrical imperfections
• characterized by interaction of local and overall buckling
modes
Conclusion : stability analysis of such members
would need for a specific treatment , compared with
conventional hot-rolled sections !
Simple Instabilities
L D F T FT
L – Local Buckling
D – Distortional Buckling
F – Flexural Buckling
T – Torsional Buckling
FT – Flexural-Torsional
buckling
Coupled Instabilities
L + D F + L F+D FT+L FT+D
L – Local Buckling
D – Distortional Buckling
F – Flexural Buckling
T – Torsional Buckling
FT – Flexural-Torsional
buckling
Erosion Concept
Nu=Ncr – y
I: Weak interaction (WI), ψ0.1
II: Moderate interaction (MI), 0.1 ψ 0.3
III: Strong interaction (SI), 0.3 ψ 0.5
IV: Very Strong interaction (VSI), ψ>0.5
Thin walled
members
Coupled Instabilities – design methods
EUROCODE3 (EN1993-1-1)
Ayrton-Perry model
Buckling
curves a0 a b c d
a 0.13 0.21 0.34 0.49 0.76
,1
eff yb Rd
M
A fN
22
11
eff y
cr
A f
N
AISI – AS/NZ4600
0.85n c e n cP A F
Axial load Pn is:
2
2
2
1.5, 0.658
0.6581.5,
c
c
c n y
c n y
yc
e
for F f
for F f
f
F
Ae is the effective area at Fn
Fe minimum critical stress (F, T, FT)
Coupled Instabilities – ECBL approach
0
1
N=N/Npl
= (Q.Npl/Ncr)
0.5
QDy
QD
Sectional instability:
ND=QD M
QD QD-0.1 QD QD+0.1 QD
N(y,QD)=QD-y
0.2
Coupled instability:
N(y,QD)
Results/numerical simulations
NEULER=1/2
DD
y
NQ
A f
2
1- 1- 0.2
D
D
Q
Q
ya
y
1. Defining the sectional capacity
2. Determining the coupling point (M)
3. Definition of the coupling interval ( ± 10%)
4. Computation of coupling erosion (yD)
5. Determination of a imperfection factor based on
the design value of the erosion factor (yD)
EN 15512:2009 Steel static storage systems - Adjustable pallet
racking systems - Principles for structural design
Annex A (normative) Testing
A.1 Materials tests
A.1.1 Tensile test
A.1.2 Bend tests
A.2 Tests on components and connections
A.2.1 Stub column compression test
A.2.2 Compression tests on uprights - Checks for the effects of
distortional buckling
A.2.3 Compression tests on uprights - Determination of buckling curves
A.2.4 Bending tests on beam end connectors
A.2.5 Looseness tests on beam end connectors
A.2.6 Shear tests on beam end connectors and connector locks
A.2.7 Tests on floor connections
A.2.8 Tests for the shear stiffness of upright frames
A.2.9 Bending tests on upright sections
A.2.10 Bending tests on beams
A.2.11 Tests on upright splices
Experimental Program
EN15512:2009
a. Stub column tests
b. Upright buckling tests
Additional:
c. Distortional buckling tests
d. Interactive buckling tests
Experimental Program
Distortional buckling specimens
LBA – analysis
PERFORATED – teq (Davies or experimental)
Experimental Program – buckling length
Interactive buckling tests
ECBL Approach – (Distortional + Flexural)
Experimental Program – buckling length
0
1
N=N/Npl
QDy
QD
Sectional instability:
ND=QD M
QD
N(y,QD)=QD-y
0.2
NEULER=1/2
,y
QD cr CUPLAREcr
A fL
N
RS125x3.2mm RS95x2.6mm
fy=461.41 N/mm2
fu=538.90 N/mm2
E=207464 N/mm2
fy=465.18 N/mm2
fu=537.40 N/mm2
E=202941 N/mm2
Anet/Abrut = 0.806 Anet/Abrut = 0.760
Experimental Program
437.16kN 390.75kN
STUB column test results
18 specimens 6 – brut section @ 510mm 12 – net section @ 510mm
336.85kN 273.79kN
18 specimens 6 – brut section @ 410mm 12 – net section @ 410mm
RS125 RS95
354.95kN 324.77kN
UPRIGHT Test Results
RS125 RS95
15 specimens 5 – brut section @ 1200mm 10 – net section @ 1200mm
15 specimens 5 – brut section @ 1200mm 10 – net section @ 1200mm
264.28kN 202.00kN
Remark:
The test for distortion according with EN15512 is realized for
an upright section of a length equal with the length between
two subsequent nodes. However, depending on the cross-
section dimensions this length can be offend larger than
distortional critical length and the obtained test result can
be the one corresponding to the interaction distortional-
global.
Suggestion:
For the consistency of the testing procedure compression
and bending tests for specimens of critical distortional
length would be necessary!
417,37kN 348,32kN
Distortional buckling results
10 specimens 5 – brut section @ 670mm 5 – net section @ 710mm
RS125 RS95
6 specimens 3 – brut section @ 590mm 3 – net section @ 610mm
309,4kN 257,84kN
302,29kN 269,71kN
Interactive buckling results
RS125 RS95
16 specimens
7 – brut section 3 @ 2110mm 3 @ 2310mm 3 @ 2510mm
9 – net section 3 @ 2110 mm 3 @ 231 0mm 3 @ 2510 mm
18 specimens
9 – brut section 3 @ 1510mm 3 @ 1610mm 3 @ 1760mm
9 – net section @ 1510mm @ 1610mm @ 1760mm 225,73kN 197,36kN
Calibration of a imperfection factor
,
,,
1
2
1
2
1 1 0.2
D exp ii
DD
y
exp iexp i
y
n
m ii
d d
Dd
d D
N N
NN
A f
NN
A f
n
N
N
y
y y
y y
ya
y
ND – considered sectional strength Nexp,i – experimental failure force for
specimen i A – cross-sectional area fy – yield strength yi – erosion for specimen i ym – mean value of erosion yd – design value of erosion – standard deviation a – imperfection coefficient
(calibrated value)
Experimental – net sections
0
100
200
300
400
500
0 1000 2000 3000 4000 5000
Axia
l Fo
rce [
kN
]
Length [mm]
RS125N
EN15512
ECBL N
ECBL B
TESTS
0
100
200
300
0 500 1000 1500 2000 2500 3000 3500 4000
Axia
l Fo
rce [
kN
]
Length [mm]
RS95N
EN15512
ECBL B
ECBL N
TESTS
0
100
200
300
400
0 1000 2000 3000 4000
Axia
l lo
ad
[kN
]
Length [mm]
RS95N
TESTS
Brut moment of inertia
Net moment of inertia
M110
0
100
200
300
400
500
0 1000 2000 3000 4000 5000
Axia
l Lo
ad
[kN
]
Length [mm]
RS125NTESTS
Brut moment of inertia
Net moment of inertia
M110
Experimental – net sections
0
100
200
300
400
500
0 1000 2000 3000 4000 5000
Axia
l Lo
ad
[kN
]
Length [mm]
RS125NTESTS
Brut moment of inertia
Net moment of inertia
M110
0
100
200
300
400
0 1000 2000 3000 4000
Axia
l lo
ad
[kN
]
Length [mm]
RS95N
TESTS
Brut moment of inertia
Net moment of inertia
M111
0
100
200
300
400
500
0 1000 2000 3000 4000 5000
Axia
l Lo
ad
[kN
]
Length [mm]
RS125NTESTS
Brut moment of inertia
Net moment of inertia
M111
Experimental – net sections
0
100
200
300
400
500
0 1000 2000 3000 4000 5000
Axia
l Lo
ad
[kN
]
Length [mm]
RS125NTESTS
Brut moment of inertia
Net moment of inertia
M110
• Numerical model calibration
• Software: ABAQUS/CAE 6.7.1
• Elements: S4R
• Mesh: 5x5mm
• End assemblies:
RIGID BODY with PINNED NODES
• 2 steps analysis:
1. LBA > buckling modes
2. GMNIA > ultimate capable force
Numerical simulations – Sensitivity study
Numerical simulations – Sensitivity study
0
1
N=N/Npl
QDy
QD
Sectional instability:
ND=QD M
QD
N(y,QD)=QD-y
0.2
NEULER=1/2
Profile ND,cr [kN] Npl [kN] QD
RS125N 370.48 483.16 0.767
RS95N 340.78 286.69 1.00*
+
LBA =>
DD
y
NQ
A f
D+ distortional buckling mode scaled with ( t)
D- distortional buckling mode scaled with (-t) F+ flexural buckling mode scaled with ( L/750)
F- flexural buckling mode scaled with (-L/750)
Ecc_Y load eccentricity in Y direction
Ecc_Z load eccentricity in Z direction
Numerical simulations – Sensitivity study
Numerical simulations – CPR
RS125B RS125N RS95B RS95N
D+ F+ y 0.387 0.395 0.490 0.504
a 0.259 0.273 0.587 0. 639
D+ F+
Ecc_-2
y 0.405 0.422 0.547 0.560
a 0.294 0.327 0.824 0.893
• Small increase in y => significant increase in a
• Considering all imperfections => too conservative
• Loading eccentricity => great influence when coupled with initial bow imperfection (same sense)
Numerical simulations – RS125
1 23 4
5
6
Cth (D+FT)
Cth (D+F)
Cpr (ND,cr+F)
0
200
400
600
800
1000
1200
100 1000 10000
Ax
ial lo
ad
[k
N]
Length [mm]
RS125N
D
FT
F
Squash Load
ND,cr
GMNIA
TESTS
1 23 4
5
6
Cth (D+FT)
Cth (D+F)
Cpr (ND,CR+F)
0
200
400
600
800
1000
1200
100 1000 10000
Ax
ial lo
ad
[k
N]
Length [mm]
RS125B
D
FT
F
Squah Load
ND,cr
GMNIA
TESTS
Numerical simulations – RS95
1 2 34
5
6
Cth (D+FT)
Cth (D+F)
Cpr (Npl+F)
0
200
400
600
800
100 1000 10000
Ax
ial lo
ad
[k
N]
Length [mm]
RS95N
D
FT
F
ND,cr
Squash Load
GMNIA
TESTS
1 23 4
5
6
Cth (D+FT)
Cth (D+F)
Cpr (Npl+F)
0
200
400
600
800
100 1000 10000
Ax
ial lo
ad
[k
N]
Length [mm]
RS95B
D
FT
F
ND,cr
Squash Load
GMNIA
TESTS
Numerical simulations – buckling curves
0
100
200
300
400
500
0 1000 2000 3000 4000 5000
Axia
l Lo
ad
[kN
]
Length [mm]
RS125NTESTS
Brut moment of inertia
Net moment of inertia
M110
0
100
200
300
400
500
0 1000 2000 3000 4000 5000
Axia
l Lo
ad
[kN
]
Length [mm]
RS125NTESTS
Brut moment of inertia
Net moment of inertia
M110
LBA > Ncr,D
GMNIA > NU,D
Numerical simulations – buckling curves
0
100
200
300
400
0 1000 2000 3000 4000
Axia
l lo
ad
[kN
]
Length [mm]
RS95N
TESTS
Brut moment of inertia
Net moment of inertia
M110
0
100
200
300
400
0 1000 2000 3000 4000
Axia
l lo
ad
[kN
]
Length [mm]
RS95N
TESTS
Brut moment of inertia
Net moment of inertia
M110
LBA > Ncr,D
GMNIA > NU,D
0
100
200
300
400
500
0 1000 2000 3000 4000 5000
Axia
l Lo
ad
[kN
]
Length [mm]
RS125NTESTS
Brut moment of inertia
Net moment of inertia
M110
0
100
200
300
400
500
0 1000 2000 3000 4000 5000
Axia
l Lo
ad
[kN
]
Length [mm]
RS125NTESTS
Brut moment of inertia
Net moment of inertia
M110
Concluding remarks
• The ECBL concept can be used to adapt the European buckling curves for the case of perforated cold formed members
• It is very important to correctly define: • the sectional capacity • the global buckling mode (F, T, FT) (the corresponding coupling length)
• Reduced number of experimental/numerical tests
• Experimental
• Short length specimens (sectional capacity) – 3 tests
• Relevant tests for interactive buckling – 3 x 3 tests
Concluding remarks
• The critical combination of imperfections can be
determined based on ECBL approach
• The partial safety coefficient M1 can be properly determined applying Annex D of EN1990
• EN15512, even if is based on the brut section properties, is to conservative for usual lengths
• The effect of perforations can not be ignored for global calculations