2-localbuckling

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apter 2: Local Buckling and Section Classificcation 15/08/20

R Liew

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Chapter 2: Member design

Section 1: Local Buckling & Section Classification

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Local Buckling

M

M


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Local Buckling and Section

Classification

Failure modes for UB in compression

Overall yielding in compression

Overall buckling as a strut Local buckling of flange toes

Local buckling of web

b

D

t

T

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Local Buckl ing and Section Classif ication

Factors Influencing LocalBuckling

Boundary conditionsinternal elements or outstands

Local Slenderness

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

Youngs modulus

Yield stress

Stress distribution

Strain (deformation) requirement

Residual stresses

2

2

2

crb

t

)1(12

Ek

=

b

t


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Why classify ?

ME

PM

Class 1

Class 4

Class 2

Class 3

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Stress blocks

Class 1 & 2 Class 3 Class 4

y y < y


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Elements to be classified

b=B-3t d=D-3tFor a Hot finished RHS

b

B

D td

b = B/2

T

r

d=D-2(T + r)Universal Beam

Outstand

Web

b

Dd

B

tWeb

Flange

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Table 11: Limiting width tothickness ratios for

sections other than CHS or RHS

(Flanges)

5

4

32

9

28

b/T

b/T

Outstand element of

compression flange

Internal element of

compression flange

Class 3Class 2Class 1

Limiting valuesRatioCompression element b

D

t

T


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But 40But 40But 40

d/t

r1 +ve

Web Generally

not applicabled/tWeb subject to

axialcompression


12010080d/tWeb (bending)

Limiting valuesRatioCompression

element

Table 11: UB and UC Webs

11

80

r+

15.11

100

r+

221

120

r+

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Table 12:Limiting width tothickness ratios for Hot

Finished RHS

(Flanges)

4032 62-.5d/t

2880-d/t

b/tCompressionflange in

bending

40Not applicableb/tAxialcompression


Limiting valuesRatioCompression

element

b

d

B

t

Flange


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able 12: Hot-finished RHS Webs

but 40but 40

d/tWeb Generally

but 40not applicabled/tWeb in axialcompression

1208064d/tWeb (bending)


Limiting valuesRatioCompressionelement

16.01

64

r+

11

80

r+

221

120

r+

d

tWeb

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Notes to the table1. The term =(275/py)

1/2 is used to accommodate

varying design strengths.

2. For I and H sections but 1


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Implications for Design

Class 1. Plastic must be used in plasticdesign, can sustain high strain. Can beused without restriction in normal design

Class 2Compact can be used with theplastic modulus in bending

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

Class 4 Slender Effective sectionproperties must be used

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Class 3 (Semi-compact sections)either elastic section modulus or effective

section modulus (Seff)may be used for

bending calculations. For I and H

sections:

+=

1

1t/d

)ZS(ZS2

w2

w3

2

w3

xxxeff,x

+

1

1/)(

2

3

3

,

f

f

f

xxxeffxTbZSZS

but

+=

1

1/)(

2

3

3

,

f

f

f

yyyeffy

TbZSZS

2f

= limiting value of b/T for a class 2 compact flange2w

= limiting value of d/t for a class 2 compact web

3f

= limiting value of b/T for a class 3 semi-compact flange3w

= limiting value of d/t for a class 3 semi cmpact web


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Slender sections

Effective cross section subject to purecompression for determining Aeff

tt

20t

Rolled I Section Hot finis hed RHS

20t

20t

20t

20t

20t

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Slender sections Effective cross section subject to pure

moment for determining Zeff

t

Minor axis bending

t

20t

Major axis bending

D

20t

20t

20t

20t 20t


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Effective section with slender

web under pure bending

+

+

=

cw

tw

yw

twcw

ffe

f

f

p

ff

tb

11

120

Non effective Zone

0.4b

0.6b

Elastic Neutral axis

eff

eff

f

f

cw

tw

Elastic neutral axis

of gross section of effective section

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Classification of the cross-section

should be based upon the

combined effects of the axial and

bending actions.

Effective section with slender

web subject to combined axialforce and moment??


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Design Table

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General Guidancewhen using the Deign Tables in the Handout

None of the universal beam and column sections ingrade S275 and S355 are slender under bendingonly.

None of the universal columns can be slenderunder compression only, but some universal beamsand hollow sections can be slender. Sections thatcan be slender under axial compression are

marked with * in the design tables. None of the sections listed in the design tables are

slender due to the flange being slender. Undercombined axial compression and bending, thesection would be compact or semi-compact up togiven F/Pz 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 (Table 11

& 12)

3 If necessary calculate effective plastic

modulus for Class 3 (semi-compact) sections

4 If necessary calculate effective section

properties for class 4(slender sections)

5 Proceed with design procedures suitable forthe section classification

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Example1

b

B

D td

T

r

S275 steel 457x152x52 UB

Grade 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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T 41.2 Web Not Class 1

d/t limit = 100 / (1+1.5r1) but 40 for Class 2,100 / (1+1.5r1) = 100 / (1 +1.5 x 0.94) = 41.553.6 > 41.5 Web Not Class 2

b

td

T


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

major axis . . . Continued . . . .

Classification

d/t limit = 120 / (1+2r2) but 40 for Class 3,r2 = Fc / Agpyw = 800 x 10 / (66.6 x 275) = 0.44

120 / (1+2r2) = 120 / (1 + 2 x 0.44) = 63.853.6 < 63.8 Web = Class 3

Section is Class 3 Semi-Compact

Pc =pcAg Mc = pySx,effor pyZx

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Semi compact

F = 0.619 x 1830 = 1133kN

Compact

F = 0.268 x 1830 = 490 kN

Since F = 800kN

< 1133kN, it is semi

compact


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

major axis

ClassificationOutstand element of compression flange,

b/T limit = 9 for Class 1 (Plastic),Since 6.99 < 9 Flange = Class 1

d/t limit = 120 / (1+2r2) but 40 for Class 3,r2 = Fc / Agpyw = 1500 x 10 / (66.6 x 275) = 0.82

120 / (1+2r2) = 120 / (1 + 2 x 0.82) = 45.553.6 > 45.5 Web = Class 4

Section is Class 4 SlenderPc =pcAeff

Mc = pyZx,eff

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Example 2

Consider a 400x150x6.3

hot finished RHS

GradeS355

subject to bending about

its major axis

b

D

d

B

t


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88.0355275275 ===

py

t < 16mm therefore py = 355 N/mm2

From section tables b/t = 20.8 and d/t = 60.5

From table 12 the limit fora class 2 flange is,

32 but less than or equal to 62-0.5d/t32 = 28.16 and 62-0.5d/t = 24.31 Flange is class 2

From table 12 the d/t limit for a class 2 rolled web

with the neutral axis at mid depth is 80 =70.4Web is class 2

Therefore section is class 2 when subject to bending

Classify the section under minor axis bending.

b

D

d

B

t

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Web now becomes the flange and the flange the web.

Flange is now class 4 (slender) under pure bending i.e. b/t=60.3 >40.

An effective section modulus is therefore required about the y-y axis.

Taking an excluded area equally disposed about the centroid of the

section in one flange only the effective section modulus can then be

calculated.20t =111 20t = 111

b=381

d=130y yRevised

X

x

A B

Example 3: Classify the same section in Example 2under minor axis bending


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Calculate the revised neutral axis position

Take the moment of areas about A-BWhere Aeff= Ag - Aex =67.3 10 =57.3cm

2

Thus

The revised inertia of the section

Ieff=

Ieff= 2955x104 0.331x104-711x104 = 2244x104 mm4

The revised elastic modulusZeff= Ieff/(D-x) = 2244x10

4/(150-62.5) = 256 cm2

mmx

xxxxX 5.62

1003.57

)15.3150(100101003.6775=

=

{ }2

2

g g ex ex

DI A X I A x(D x t / 2)

2

+ +

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Summary

For optimum design of welded section, the

designer has the following choices

1. Eliminate local buckling by ensuring

width-to-thickness ratio is sufficiently

small

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

3. Determine section capacity allowing for

local buckling


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Q1 What happen when the limiting

plate slenderness ratios are exceeded?

Cross section strength cannot be fully

developed.

i.e., cross section strength is governed by

local buckling instead of yielding.

Q2 How can local buckling of a plate component beprevented?

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

so that b/t is less than the limiting b/t

Questions


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Q3 What effect does a slender and

unstiffened element has on the strength of

compression member as opposed to that

of a non-slender element?

Slender element reduces the compression

resistance of the compression member

because of local buckling effect

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Q4

Which of the followings are considered to be

an 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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Reading assignments

BS 5950:Part 1Code:

Clauses 3.5 & 3.6

Reference : Chapter 2: Section 1

2-localbuckling

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