4 Compression Members - 2011 New

7/25/2019 4 Compression Members - 2011 New

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Compression Members


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Introduction

Resistance of Cross-SectionsSections not prone to local buckling

Sections prone to local buckling

Buckling Resistance of MembersSections not prone to local buckling

Sections prone to local buckling

Reduction Factor for Buckling ResistanceElastic Critical Force & Buckling LengthNon-Dimensional Slenderness for Flexural BucklingBuckling Curve of Perfect ColumnBuckling Curves of Imperfect ColumnsSelection of Buckling Curve and Imperfection Factor

Design Procedure

ExamplesExample CM-1 (UC with intermediate restraint under compression)Example CM-2 (CHS under compression)

Outline


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Introduction

Compression members are structural components that are subject to

axial compression loads only. These generally refer to compressed pin-ended struts found in trusses,

lattice girders or bracing members.

Most real columns are subjected to significant bending moments in

addition to the axial loads, due to the eccentricities of axial load and thepresence of transverse forces. They are referred to as beam-columnsand are covered in a separate chapter.

Compression members must be checked for

resistance of cross-sections buckling resistance of members


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Resistance of Cross Section


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Class 1, 2 and 3 cross-sections areunaffected by local buckling.

Design resistance of cross-sectionNc,Rdequals the plastic resistanceNpl,Rd.

Resistance of Cross-Sections

Sections NOT PRONE to local buckling

Class 4 sections suffers from local bucklingwhich prevents the attainment of squash load.

Design resistance of cross-sectionNc,Rdlimited to local buckling resistance.

Sections PRONE to local buckling

EN 1993-1-1 Clause 6.2.4 (1)

The design value of the compression forceNEdat each cross-sectionshall satisfy:

RdcEd NN ,

EN 1993-1-1 Clause 6.2.4 (2)

0M

y

RdcAfN

=,0M

yeff

RdcfAN

=,

If Class 4 section is unsymmetrical, it has to bedesigned as beam-columndue to the additionalmomentarising from eccentricity of the

centroidal axis.

M0= 1.00

42tc /

14tc /

Internal element

Outstand elementNon slender


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Buckling Resistance of Member


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Elastic Buckling of Columns

2

2cr

EI

L

Euler Buckling Load

Ncr =L

2

crcr 2

cr

N Ef

A (L / i)

= =

Buckling stress

I = i2A

i = radius of gyration


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=21

2

E

fy

f

fy

Failure byCross section yielding

Failure by elastic buckling

Euler elastic buckling

Buckling Curve of Perfect Column

1

where is the column slenderness.i

Lcr=

2

2

2

22

2

2

E

L

Ei

AL

EI

A

Nf

crcr

crcr ====

Whenfcr=fy, =1

yf

E

=1

is the radius of gyration.I

Ai =

i

Lcr=


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0.0

0.2

0.4

0.6

0.8

1.0

0 1 2 3 4

f/fy

Factors Influence the Buckling of Columns

/1

=0

Euler buckling curve

1. Effective length of Column

2. Residual Stresses

3. Member initial out-of-straightness4. Types of cross section

5. Local buckling of component plate

Practical Region

Inelastic buckling

Elastic buckling

Imperfectcolumns


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= L / 1000

Initial out of straightness

+260 N/mm

-125 N/mm

+55 N/mm

Rolled Section

C

T

C C

C C

T

2

2

2

CC

T

CC

T

C

T

TWeb Distribution

Welded section

Factors that affect overall buckling of columns

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Design buckling resistanceNb,Rdshould betaken as:

Buckling Resistance of Members

Sections NOT PRONE to local buckling

Design buckling resistanceNb,Rdshould betaken as:

Sections PRONE to local buckling

EN 1993-1-1 Clause 6.3.1.1 (1)

The design value of the compression forceNEdshall be checked against the design

buckling resistance:

RdbEd NN ,

EN 1993-1-1 Clause 6.3.1.1 (2)

1M

y

Rdb

AfN

=,

1M

yeff

Rdb

fAN

=,

If Class 4 section is unsymmetrical, it has to bedesigned as beam-column.

Holes for fasteners at the column ends need NOT

to be taken into account in determiningAandAeff.

M1= 1.00

/ /


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Reduction Factor for Buckling Resistance

EN 1993-1-1 Clause 6.3.1.2

1.0but +=

22

1

]0.2)(0.5[1 2 ++=where

imperfection factor (refer to Table 6.1 & 6.2)

non-dimensional slenderness

sections-cross4Classfor

sections-cross3and21,Classforcr

y

N

Af=

cr

yeff

N

fA=

For , or for , the buckling resistance check

can be ignored and only cross sectional checks apply.

0.2 0.04cr

Ed

N

N

14/8/2013

2

2

cr

crL

EIN

=


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Buckling length

Lcr= effective length in BS5950

No guidance given in EC3

NCCI

Use same factors as BS5950 Applied to system length, L

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Elastic Critical Force & Buckling Length

I Second moment of area which is determined based on thegross cross sectional propertiesfor all classes of cross-sections.

Lcr

Buckling length in thebuckling plane considered.2

2

cr

crL

EIN

=

Nominal buckl ing lengthsLcrfor compression members

Non-sway mode

Sway mode

where


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Non-Dimensional Slenderness for Flexural Buckling

2 2

1

1

( / )

/

y y y

cr

cr cr

ycr

Af Af fAL

N EI L I E

fL

i E

= = =

= =

2 2

1

( / )

eff y eff y eff y

cr

cr cr

eff ycr

A f A f A fAL

N EI L A I E

A fL

i A E

= = =

=

For Class 1, 2 and 3cross-sections,

For Class 4cross-sections,

= Lcr/i 1= (E/fy)0.5


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0.0

0.2

0.4

0.6

0.8

1.0

0 1 2 3 4

f/fy

Buckling Curves of Imperfect Columns

/1

=0.13 =0.21 =0.34 =0.49 =0.76

=0

Euler buckling curve


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Buckling curve a0 a b c d

Imperfection factor 0.13 0.21 0.34 0.49 0.76

Table 6.2: Selection of buckling curve for a cross-section Table 6.1: Imperfection factors fo r buck ling curves

Selection of Buckling Curve and Imperfection Factor

Imperfections can be attributed to the following:

initial out-of-straightness

eccentricity of applied loads

material variations

residual stresses

Typical residual stress p rofil e in a hot-rolled I-section

Residual compressive stressResidual tensile stress


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Design Procedure


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For each axis of buckling, determine

buckling lengthLcr

Limiting slenderness1

non-dimensional slenderness

appropriate strut curve(a0, a, b, c or d)from Table 6.2

imperfection factorfrom Table 6.1

buckling reduction factor

Design Procedure

Check ifNb,Rd>NEd. Else, repeat steps.

Use the smaller value ofto determine buckling resistanceNb,Rd.

Determine design axial forceNEd.

Select a trial section such thatNEd

/A


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Examples


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Example CM-1: Universal column with intermediate restraint under compression

Determine the maximum compression load that can be taken by a 5m column using

203x203x60UC in S275 steel. Both ends of the column are pin supported about both y-y and

z-z axes. A lateral restraint, that is aligned to the y-y axis, is provided at mid-height.N

N

2.5m

2.5m

AA

Section AA

z z

y

y


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Yield Strength

tw= 9.4mm, tf= 14.2mm.

Maximum thickness = 14.2mm < 16mm (EN 10025-2)

For S275 steel,fy= 275N/mm2

Section Classification

= (235/fy)0.5= 0.92

Classification of flange

Flange is Class 1 (Plastic).

Classification of web

Web is Class 1 (Plastic).

8.320.92996.20 === */ ff

tc

30.40.92*333317.1 === ww tc /

Section is Class 1 (PLASTIC).


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Resistance of CrossSection

2101kN1.0

10*)(275)10*(76.4 32

0

====

M

y

RdplRdc

AfNN

,,

Flexural Buckling abouty-yaxis

Use buckling curveb= 0.34

86.8210000/275 === yfE/1

0.643

86.8

1

8.96

5001=

==

1

,

y

ycr

y

i

L

&1.21.02205.8

209.6


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Flexural Buckling aboutz-zaxis

Use buckling curvec= 0.49

0.55486.81

5.202501 =

==

1

,

z

zcrz

iL

100mm&1.2


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Example CM-2: Circular hollow section under compression

A circular hollow section (CHS) member is to be used in a 4m long column which is pinned at

both ends. The design axial compression,NEd, is 2400kN. Assess the suitability of a hot-rolled

244.5x10 CHS in grade 355 steel for this application.

Yield Strength

t= 10.0mm


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Resistance of CrossSection

2400kN2616kN1.0

10*)(355)10*(73.7 32

0

>===

M

y

Rdc

AfN

,

Buckling Resistance of Member

Use buckling curvea= 0.21

76.4210000/355 === yfE/1

0.631

76.4

1

8.30

4001=

==

1

i

Lcr

2400kNkN210*1.0

355*)10*(73.7*0.854 3

2


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Effective length Lcrof

compression members


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Effective length of

column in frame

Lcr=KL

K

L

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Projects to Illustrate theConcept of Steel Design

Prof. Richard Liew

Dept of Civil & EnvironmentalNational University of Singapore

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Buckling of compression members Axial compressioncauses failure by buckling(out-of-plane

deflection) in slender members.

Buckling about major(x-x) axis. Buckling about minor(y-y) axis.

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Members with intermediate lateral restraints


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Pin connected space frame


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Pin-connected space frame


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Adequate Bracing during

Construction

1

1

2

3

6

4

5

Sequence of erection

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Cantilever Structure

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Cantilever trusses

1

1

2

3

6

4

5

49


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Lateral bracing for

cantilever trusses

1

1 2

3

6

4

5

Purlin

Cantilever trussFly bracing

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Question

y

y

z z

Lcr,y= ?

Lcr,z= ?

4 Compression Members - 2011 New

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