Interactive Buckling of Cold-Formed Steel Sections Applied ... 2011/Presentations/Day1... ·...

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Interactive Buckling of Cold-Formed Steel Sections Applied in Pallet Rack Upright Members D. Dubina, V. Ungureanu, A. Crisan Politehnica” University of Timişoara

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

Thank you