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1

Metwally Abu-Hamd

Professor of Steel Structures

Cairo University, EgyptCairo University

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Outline

1- INTRODUCTION

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2- COMPRESSION FLANGE LOCAL BUCKLING

3- WEB BEND BUCKLING

4- WEB SHEAR BUCKLING

5- EFFECT OF EDGE CONDITIONS

6- CONCLUSIONS

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Applications: Short\Medium Span Bridges

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Design Considerations

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Design Limit States:1- Flexural Strength:

1-1) Compression Flange Local Buckling

1-2) Compression Flange Lateral Torsional Buckling

1-4) Tension Flange Yield

1-3) Web Bend Bulking

2- Shear Strength:

2-2) Web yield in Shear

2-1) Web Shear Bulking

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Local Buckling Modes

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Local Buckling Consideration

Depending on the width-to-thickness ratio of the plategirder components, AISC and AASHTO LRFD Design

Specifications classify structural steel elements into:

6

Section\Element Classification (AISC\AASHTO):

1- Compact: < p

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2- Non-compact: p > > r

3- Slender: > r

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Local Buckling Resistance

7

Fn or Mn

Inelastic Buckling

(non-compact)

Elastic Buckling

(Slender)

Inelastic Buckling(Compact)

lp

lr

l

Fyr or Mr

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/CSA)3Section Classification (EC

Eurocode EC3 and the Canadian StandardCAN/CSA-S16-01 classify structural steel elements

into four classes: Class 1, 2, 3, and 4 according to:

8

1- Element Slenderness Ratio

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2- Performance requirements for resistance to

bending moments.

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Moment

LocalBuckling

Mpl

9

fy

Plastic momenton gross section

Moment

LocalBuckling

Mpl

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1Class

Moment

LocalBuckling

Mel

Mpl

Moment

LocalBuckling

Mel

Mpl

3Class 4Class

Canadian)\Section Classification (European

2Class

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Local Buckling Strength

Class 1Class 2

Class 3

Euler Buckling Stress

0,5 0,6 0,9

1

1,0 l p

N fpu

y=

10

k4.28

/5.0

ltb

cr

y

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Design Considerations

Codes give comparable resultsfor Compact (Classes 1,2) andNon-Compact (Class 3)

Elements.

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Same Codes differ considerably

in the treatment of Slender(Class 4) Elements:

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AISC\ AASHTO EC3

Reducing thedesign bending

compressive stressto the critical

buckling stress

Reducing the crosssection to an

effective sectionaccording to theeffective width

concept

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Design Considerations

This paper presents a comparative study of localbuckling effects in American and European Codes.

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AASHTO Critical Stress Approach\AISC

Where k

is theplate buckling factor, which depends on

the stress distribution and the edge support conditions.

13

2

2

2

)1(12

b

tE

kFcr

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The Elastic Buckling stress of a compressed plate, Fcr, is:

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Buckling Behaviour-Post

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AverageStress

F

Average Axial Strain

uniform stress prior to

Straight line indicates

buckling b

Low b/t

Fy

cr

High b/t

strength

Post buckling

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Buckling Behaviour-Post

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Effective Section Approach3EC

Cross-sections with class 4 elementsare replaced by an effective cross-section taken as the gross sectionminus holes where the buckles mayoccur.

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Designed in a similar manner toclass 3 sections using elastic cross-sectional resistance limited byyielding in the extreme fibers

Effective widths of compressionelements are calculated using areduction factor which isdependent on the normalised plateslenderness

Non-effective Zones

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Comparison of Slenderness Limits

Considerable variations between

American and European Codes

17

Code Compact Non-compact

1- Compression Flange Local Buckling:

AISC/AASHTO 9.24 16.33

EC3 8.25 11.55

2- Web Bend Buckling:

AISC/AASHTO 91.43 138.61

EC3 68.5 102.34

3- Web Shear Buckling:

AISC/AASHTO 59.81/60.90 74.49/76.12

EC3 49.32 77.01

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18

0.00

0.20

0.40

0.60

0.80

1.00

1.20

1.40

6 8 10 12 14 16 18 20 22 24

Flange Slenderness f

EC3

EC

3:=68.5

AISC/AASHTO:p=9

.24

Flange Slenderness f

EC3

EC

3:=68.5

AISC/AASHTO:p=9

.24

AAS

HTO:r=13.6

2

AISC

(SW):r=16.3

4

AISC(

CW):r=18.4

7

Comparison of Flange Buckling Stress

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Fcr/Fy

EC

3:r=11.5

5

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EC3 gives much higher results because ofconsiderations of Post-Buckling

19

0.00

0.50

1.00

1.50

2.00

2.50

16 17 18 19 20 21 22 23 24

Flange Slenderness f

Fn/Theory

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Comparison of Flange Buckling Stress

AASHTO

AISC (CW)

AISC (SW)

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0.00

0.20

0.40

0.60

0.80

1.00

1.20

1.40

50

70

90

110

130

150

170

190

210

Web Slenderness (D/t)

Fcr/F

y

EC3:p=68.5

EC

3:r=102.3

AISC/AASHTO:r=138

.6

Comparison of Web Bend Buckling Stress

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AISC/AASHTO:p=91.4

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0

0.2

0.4

0.6

0.8

30 60 90 120 150 180

Web Slenderness (D/t)

Vn/Vp

EC3:p=49.3

AISC/AA

SHTO:ix=60

Comparison of Web Shear Buckling Stress

Stiffened Webs)-(Un

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Comparison of Web Shear Buckling Stress

Stiffened Webs)-(Un

22

0

0.5

1

1.5

2

2.5

3

3.5

140 160 180 200 220

Fn/Theory

Web Slenderness (D/t)

AASHTO

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0.0

0.2

0.4

0.6

0.8

30 60 90 120 150 180

Comparison of Web Shear Buckling Stress

)1=(Stiffened Web,

Web Slenderness (D/t)

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Vn/Vp

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Comparison of Web Shear Buckling Stress

)1=(Stiffened Web,

24

0

0.5

1

1.5

2

2.5

80 100 120 140 160 180

Web Slenderness (D/t)

AISC/AASHTO

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Effect of Edge Conditions

Numerical analysis ( Finite Element/ Finite Strip)may be used to study the effect of real edge

conditions (EC3:EN 1993-1-5).

CUFSM (Schafer and Adany) was used in thepresent study.

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The parameters varied in the study are:1)Web plate height of 1000, 1500, and 2000 mm, and

2) Flange plate width of 250, 300,400,500 mm.

The corresponding web and flange plate thicknesseswere selected to cover the following combinations:

a) Slender flangewith compact, non-compact, and

slender web,

b) Slender webwith compact, non-compact, and slenderflange.

Steel: Fy=345 Mpa, E = 204000 MPa.

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Effect of Edge Conditions

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Flange Buckling Coefficient

27

0.00

0.40

0.80

1.20

1.60

14 16 18 20 22

Simple: k = 0.43

Fixed: k = 1.28

Flange Slenderness f

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BucklingCoefficientk

f

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0

10

20

30

40

100 120 140 160 180 200 220

Bu

cklingCoefficientk

w

Web Slenderness w

Simple: k=23.9

Fixed k=39.6

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Web Bend Buckling Coefficient

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29

0

10

20

30

40

0 5 10 15 20 25

Flange Slenderness f

Simple: k=23.9

Fixed k=39.6

BucklingCoeffic

ientk

w

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Web Bend Buckling Coefficient

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Web Bend Buckling Coefficient

30

0

10

20

30

40

5 10 15 20 25 30BucklingCoefficientk

w

Ratio (w /f)

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Cairo University