2 Local Buckling and Section Classification - 2011

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Local Buckling &

Section Classification

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Introduction

ClassesofCrossSections

MaximumWidthtoThicknessRatiosforCompressionPartsInternalCompressionPartsOutstandCompressionPartsAngles&TubularSections

EffectiveCrossSectionforClass4Sections

Class3Web+Class1or2Flange

Examples

ExampleSC

1(Section

classification

for

combined

bending

and

compression)

ExampleSC2(EffectiveareaofaClass4compressionmember)ExampleSC3(SectionwithClass3webandClass1flanges)

Outline

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Steel members are generally composed of thin elements for structuralefficiency.

The slender elements are prone to local instabilities under compressivestress, even before the yield strength is reached.

The effects of local buckling are accounted for in EC3 by classifying thecross-section into Classes 1, 2, 3 or 4.

Cross-section classification is made by comparing actual width-to-thickness ratios of the plate elements with a set of limiting values.

The classification of the overall cross-section is taken as the leastfavourable of the constituent elements.

IntroductionCE5509 RLiew

Local BucklingWhen the section is not standard section but fabricatedfrom thin elements, the section element may bucklelocally before fy is reached due to slenderness

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Local Buckling and Section Classification

Factors Influencing Local Buckling

Boundary conditionsinternal elements or outstands

Local Slenderness d/t internal element (eg. web) b/T outstand (eg. flange)

Youngs modulus Yield strength Stress distribution Strain (deformation) requirement Residual stresses

b

t

5

Elements to be classified

For a Hot finished RHScf= (b-2r - tw)/2 cw=h-2(tf+ r)

Universal Beam

cf= b-2(tw+r) cw=h-2(t + r)

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cf

hcw

b

tWeb

Flange

Outstand

cf

Internal element

cw


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Classes of Cross-Sections

Why classify ?

Class 1

Rotation, Moment

Mpl

Mel

Rotational capacity

Class 2

Class 3

Class 4

MM

Neutral

axis

Neutralaxis

Bending stress distributions at maximum moment capacity

Class 2

fy

Class 3

fy

Class 4

fy

Class 1

fy

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StrainStress

fy

Classes of Cross-Sections

Class 1Cross sections with both plastic moment capacity and plastic hinge rotation

capacity.M

c,Rd

= fy

Wpl

/M0

Class 2Cross-sections with plastic moment capacity but limited plastic hinge

rotation capacity.Mc,Rd= fyWpl /M0

Class 3Cross-sections in which the stress in the extreme compression fibre canreach the yield strength, but only the elastic moment capacity can bedeveloped.

Mc,Rd= fyWel /M0

Class 4Cross-sections in which local buckling will occur before the attainment of

yield stress.Mc,Rd= fyWeff/M0

Class 1

Rotation, Moment

MplMel

Rotational capacity

Class 2

Class 3

Class 4

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Maximum Width to Thickness Ratiosfor Compression Parts

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Internal COMPRESSION Parts

ClassPart subjectto bending

Part subj ect tocompression

Part subject to Stress distributionb end in g an d co mp res si on (c om pr es si on +v e)

1

2

3

Max Width-to-Thickness Ratios for Compression Parts

Web

InternalFlange

EN 1993-1-1 (Table 5.2)

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Consider the case ofI orH section subjected to compression and major axis bending, wherethe neutral axis lies within the web.

+

The ratio of the tensile stress to the compressive stress

at the extreme fibers, , can be calculated as follows:

The ratio of the compressed width to the total width

of the element, , can be calculated as follows:

+

tf

tw

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ClassPart subject to Stress distributioncompression (compression +ve)

Part subject to bending and compression

Tip in Stress distribution

compression (compression +ve)

Tip in Stress distribution

tension (compression +ve)

1

2

3

Outstand COMPRESSION Parts


OutstandFlange

Determination ofBuckling Factork

c

+ 12

c

+ 12 -

=2/1 1 0 -1 1 -3

k

0.43 0.57 0.85 0.57 - 0 .21+ 0.072

c

+ 21

c

+ 21

-

=2/1 1 1 0 0 0 -1 -1

k

0.43 0.578/(+ 0.34) 1.70 1.7 -5+ 17.12 23.8

21 21

EN 1993-1-1 (Table 5.2)

EN 1993-1-5 (Table 4.2)

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Class Section in compression

1

2

3

Angles(not in continuous contact with other components)


Tubular Sections

Class Section in bending and/or compression

1

2

3

EN 1993-1-1 (Table 5.2)

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Effective Cross-Sectionfor Class 4 Sections

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Effective Cross-Section for Class 4 SectionsEN 1993-1-5 Clause 4.4

Stepsindeterminingthereductionfactorforplatebuckling

Determine the stress distribution

AdditionalrulesforelementsofIsectionandBoxGirder

For flange elements, use the gross cross-sectional area to determine the stress distribution.

For web elements, use the effective area of the compression flange and the gross area of the web todetermine the stress distribution.

Determine stress ratio 2/1 and buckling factork

This depends on whether it is internal or external compression element.

The effective area Aeff should be determined assuming that the cross section is subjectonly to uniform axial compression.

The effective section modulus Weff should be determined assuming the cross section is subjectonly to bending moment.For biaxial bending, effective se ction moduli should be determined about both main axes.

whereAc and bc are respectively the area of the section and the width of the element in compression.

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2

1

2

1

InternalCompressionElements

1 0 1k 4.0 7.81 23.9

Common values of

OutstandCompressionElements

1

212

2

1

2

1

1 0 1k 0.43 0.57 0.85

Common values of

Tipunderlarger compressivestress

1 0 1k 0.43 1.70 23.8

Common values of

Tipundersmaller compressivestress

k1 0 8.2/(1.05 + )

0 1 7.81 6.29+ 9.782

1 3 5.98(1 2)

k1 3 0.57 0.21+ 0.072

k1 0 0.578/(+ 0.34)

0 1 1.7 5+ 17.12

Stress ratio and buckling factork

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Calculatebw for websb for internal flange elements (except RHS)

b 3t for flanges of RHS

c for outstand flanges

h for angles

Calculate

Internalcompressionelements

Outstandcompressionelements

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21

2

1

InternalCompressionElements

OutstandCompressionElements

1

2

12 2

1

2

1

Tipunderlarger compressivestress Tipundersmaller compressivestress

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Effective Width for Class 4 Elements

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Cold formed steel sections

These sections aremade from thin- steelsheets.

They are prone tolocal buckling.

Effective sectionproperties are needed.

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SSEN 1993-1-3


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Class 3 Web + Class 1 or 2 Flange

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Class 3 Web + Class 1 or 2 Flange

EN 1993-1-1 (Cl 5.5.2(11) & Cl 6.2.2.4)

Cross-sections with Class 3 webs and Class 1 or 2 flanges can be classified as

effective Class 2 cross-sections with the compressed portion of the web being

replaced by a part of 20tw adjacent to the compression flange (measured from the base

of the root radius for rolled section and the base of the weld for welded section), with

another part of 20tw adjacent to the plastic neutral axis of the effective cross-section.

b

20tw

h

tw

20twCompression

Tension

Plastic neutral axis

fy

fy

+

Neglectedineffectivearea

20tw

20tw

tw

b

40tw


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Implications for Design

Class 1. Plastic mustbe used in plasticdesign, can sustain high strain. Can beusedwithoutrestriction in normaldesign

Class 2 Compact can be used with theplastic modulus in bending

Class3 Semi-compact when inbending the elastic modulus or aneffective plastic modulus mustbe used

Class 4 Slender Effective sectionproperties must be used

Section and Design Tables

Steel building design:Design data,Publication P363, TheSteel Construction

Institute and the

British Constructional

Steelwork Association

UK, 2009.

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Based on Steel buildingdesign: Design data

n limit =NE,d/ Npl,Rd

Class 2 limit

Class 3 limit

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General Guidancewhen using the Deign TablesSteel building design: Design data, Publication P-363, jointly published by

The Steel Construction Institute and the British Constructional SteelworkAssociation UK, 2009 (IVLE).

None of the universal beam and column sections ingrade S275 and S355 are class 4 under bending only.

None of the universal columns can be class 4 underpure compression; but some universal beams andhollow sections can be class 4. Sections that can beclass 4 under pure compression are marked with * in

the design tables. None of the UC or UB sections l isted in the design

tables are slender due to the flange being class 4.Under combined axial compression and bending, thesection would be Class 2 or Class 3 up to given n =NEd/N pl,Rd limits.


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Summary of design procedure

1 Select, from experience, a suitable sectionbased on the factored load effects

2Determine the section classification

3 If necessary calculate effective plasticmodulus for Class 3 (semi-compact) sections

4 If necessary calculate effective sectionproperties for class 4(slender sections)

5 Proceed with design procedures suitable for

the section classification

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Examples

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Design Strengthtw = 7.7mm, tf= 10.9mm.

Maximum thickness = 10.9mm < 16mm (EN 10025-2)

For S275 steel, fy = 275N/mm2

Example SC-1: Section classification fo r combined bending and compression

A member is to be designed to carry combined bending and axial load. In the presence of a

major axis (y-y) bending moment and an axial compression of 300kN, determine the cross-

section classification of a 406x178x54UB in grade S275 steel.

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Section Classification

First, classify the cross-section under the most severe loading condition of pure compression todetermine whether anything is to be gained by more precise calculations.

Cross-section classification under pure compression

Classification of Flange

= (235 /fy)0.5 = 0.92

Flange is Class 1.

Classification of Web

Web is Class 4.

Under pure compression, the overall cross-section is therefore Class 4.Material efficiency are therefore to be gained by using a more precise approach.

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Cross-section classification under combined loading

Flange classification remains the same as Class 1.

Classification of Web

Web is Class 2.

Under combined loading, the overall cross-section is therefore Class 2.

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Page C-149n =300/1900=0.16


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Example 2

S275 steel 457x152x52 UBGrade S275

A) Subject to bending about

its major axis

B) Subject to 800kN axial load

and bending about its major

axis

C) Subject to 1500kN axial

load and bending about its

major axis

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Class 2 if n < 0.169 or

NEd < 0.169 x 1830 = 309kN

Class 3 if n < 0.586 or

F < 0.586 x 1830 = 1073 kN

Page C-147

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a) Pure bending about its major axis

S275 steel 457x152x52 UB Grade S275

A) Subject to bending about its major axis

n = 0, therefore class 2

B) Subject to 800kN axial load and bending about its major axis

n = 800/1830 = 0.437 > 0.169 class 3

C) Subject to 1500kN axial load and bending about its major axis

n = 1500/1830 = 0.82>0.586 class 4

Npl,Rd =fyAeffMel,Rd = fyWeff

Npl,Rd =fyA

Mpl,Rd = fyWpl,Rd

Npl,Rd =fyA

Mel,Rd = fyWel,Rd

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Summary

For optimum design of welded section, thedesigner has the following choices

1. Eliminate local buckling by ensuringwidth-to-thickness ratio is sufficientlysmall

2. If higher width-to-thickness is used, usestiffeners to reduce plate width

3. Determine section capacity allowing forlocal buckling


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Q1 What happen when the limiting plateslenderness ratios are exceeded?

Cross section strength cannot be fully developed.

i.e., cross section strength is governed by local bucklinginstead of yielding.

Q2 How can we prevent local buckling of a plate

component?

Ensure that b/t ratio is compact. Provide plate stiffener

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Q3 What effect does a slender andunstiffened element have on the strengthof compression member as opposed tothat of a non-slender element?

Slender element reduces the compression

resistance of the compression memberbecause of local buckling effect


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Quiz

Which of the followings are considered to bean internal elements?

1. leg of an angle

2. flange of a channel

3. Web of a I section

4. Wall of HSS


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Q5 Determine the section classification ofthe following sections with S355 steel:

UC 254 x 254 x 89 S275 subject to axial load.

Answer: at least class 2

UC 203 x 203 x 46 S355 subject to bending.


UB 457 x 152 x 60 S355 subject to bending.


UB 457 x 152 x 60 S355 subject to axial force1500kN.

Answer: class 4

2 Local Buckling and Section Classification - 2011

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