5 Compression Members

7/30/2019 5 Compression Members

1/48

1

Compression Members

23/8/2012


2/48

2

Introduction

ResistanceofCrossSectionsSectionsnotpronetolocalbuckling

Sectionspronetolocalbuckling

BucklingResistanceofMembersSectionsnotpronetolocalbuckling

Sectionspronetolocalbuckling

ReductionFactorforBucklingResistance

Elastic

Critical

Force

&

Buckling

LengthNonDimensionalSlendernessforFlexuralBucklingBucklingCurveofPerfectColumnBucklingCurvesofImperfectColumnsSelectionofBucklingCurveandImperfectionFactor

DesignProcedure

ExamplesExampleCM1(UCwithintermediaterestraintundercompression)ExampleCM2(CHSundercompression)

Outline23/8/2012


3/48

3

Introduction

Compression members are structural components that are subject toaxial 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 inaddition to the axial loads, due to the eccentricities of axial load and the

presence 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

23/8/2012


4/48

4

Resistance of Cross-Section

23/8/2012


5/48

5

Class 1, 2 and 3 cross-sections are

unaffected by local buckling.Design resistance of cross-sectionNc,Rdequals the plastic resistanceNpl,Rd.

Resistance of Cross-Sections

SectionsNOTPRONEtolocalbuckling

Class 4 sections suffers from local buckling

which prevents the attainment of squash load.Design resistance of cross-sectionNc,Rdlimited to local buckling resistance.

SectionsPRONEtolocalbuckling

EN 1993-1-1 Clause 6.2.4 (1)

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

EN 1993-1-1 Clause 6.2.4 (2)

IfClass4sectionisunsymmetrical,ithastobedesignedasbeamcolumn duetotheadditionalmoment arisingfromeccentricityofthe

centroidalaxis.

M0 = 1.00

23/8/2012


6/48

6

Buckling Resistance of Member

23/8/2012


7/48

7

Elastic Buckling of ColumnsEuler Buckling Load

Ncr=L

Buckling stress

I =i2 A

i = radius of gyration


8/48

8

f

fy

Failureby

Crosssectionyielding

Failurebyelasticbuckling

Euler elastic buckling

BucklingCurveofPerfectColumn

1

where is the column slenderness.

Whenfcr=fy, = 1

is the radius of gyration.


9/48

9

f/fy

FactorsInfluencetheBucklingofColumns

/1

=0

Euler buckling curve

1. Effective length of Column

2. Residual Stresses

3. Member initial out-of-straightness

4. Types of cross section

5. Local buckling of component plate

Practical Region

Inelastic buckling

Elastic buckling

Imperfect

columns


10/48

= 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

10


11/48

11

Design buckling resistanceNb,Rdshould betaken as:

Buckling Resistance of Members

SectionsNOTPRONEtolocalbuckling

Design buckling resistanceNb,Rdshould betaken as:

SectionsPRONEtolocalbuckling

EN 1993-1-1 Clause 6.3.1.1 (1)

The design value of the compression forceNEdshall be checked against the designbuckling resistance:

EN 1993-1-1 Clause 6.3.1.1 (2)

IfClass4sectionisunsymmetrical,ithastobedesignedasbeamcolumn.

HolesforfastenersatthecolumnendsneedNOT

tobe

taken

into

account

in

determining A and Aeff.

M1 = 1.00

23/8/2012


12/48

12

ReductionFactor forBucklingResistanceEN 1993-1-1 Clause 6.3.1.2

where

imperfection factor (refer to Table 6.1 & 6.2)

non-dimensional slenderness

For ,orfor , thebucklingresistancecheck

canbe

ignored

and

only

cross

sectional

checks

apply.

23/8/2012


13/48

Buckling lengthLcr = effective length in BS5950

No guidance given in EC3

NCCI

Use same factors as BS5950 Applied to system length, L

13

23/8/2012


14/48

14

ElasticCriticalForce&BucklingLength

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

Lcr Buckling length in the buckling plane considered.

Nominal buckling lengthsLcr for compression membersNonswaymode Swaymode

where

23/8/2012


15/48

15

NonDimensionalSlendernessforFlexuralBuckling

ForClass 1, 2 and 3 cross-sections,

ForClass 4 cross-sections,

23/8/2012


16/48

16

f/fy

BucklingCurvesofImperfectColumns

=0.13=0.21=0.34

=0.49=0.76

=0

23/8/2012

Euler buckling curve


17/48

17

Buckling curve a0 a b c d

Imperfection factor 0.13 0.21 0.34 0.49 0.76

Table 6.2: Selection of buckl ing curve for a cross-section Table 6.1: Imperfection factors for buckl ing curves

SelectionofBucklingCurveandImperfectionFactor

Imperfectionscanbeattributedtothefollowing:

initialoutofstraightness

eccentricityof

applied

loads

materialvariations

residualstresses

Typical residual stress profile in a hot-rolled I-section

Residual compressive stress

Residual tensile stress

23/8/2012


18/48

18

Design Procedure

23/8/2012


19/48

19

For each axis of buckling, determine

buckling lengthLcr Limiting slenderness

1 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 thatNEdM0 /A


20/48

20

Examples

23/8/2012


21/48

21

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

Determine the maximum compression load that can be taken by a 5m column using203x203x60UC 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

23/8/2012


22/48

22

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).

Section is Class 1 (PLASTIC).

23/8/2012


23/48

23

Resistance of CrossSection

Flexural Buckl ing abouty-y axis

Use buckling curveb = 0.34



23/8/2012


24/48

24

Flexural Buckl ing aboutz-z axis

Use buckling curvec = 0.49



Buckl ing Resistance of Member

23/8/2012

Minor axis buckling (z-axis) control!


25/48

27/9/00

.25

Lcr,y = 5m

Nby,Rd = 1710kN

Page C-13203x203x60UC in

S275 steel

Lcr,z = 2.5m

Nbz,Rd = 1710kN


26/48

26

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 atboth 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 < 16mm (EN 10025-2)

For S355 steel,fy = 355N/mm2

Section Classification

= (235/fy)0.5 = 0.814

d/t= 244.5/10.0 = 24.5 502 = 33.1

Section is Class 1.

23/8/2012


27/48

27

Resistance of CrossSection

Buckling Resistance of Member

Use buckling curvea = 0.21

The chosen cross-section, 244.5x10 CHS, in grade S355 steel is not acceptable.

Try 244.5x12.5 CHS, in grade S355


28/48

23/8/2012

28

Page D-15

hot-hrolled 244.5x10

CHS in grade 355

Le =4m

Nbz,Rd = 2300kN

2400kN

adequate

NEd, is 2400kN


29/48

29

Typical effective length

factor for use in

column design

=KL

K

L


30/48

30

Effective length factor for continuous columns based on

stability analysis

31


31/48

31


32/48


33/48


34/48

35

Pi t d f


35/48

Pin-connected space frame


36/48


37/48

Adequate Bracing duringConstruction

Sequence of erection

11

2

3

6

45


38/48


39/48


40/48

Cantilever Structure

40


41/48

41


42/48

42


43/48

43


44/48

44


45/48

45


46/48

46


47/48

Cantilever trusses

11

2

3

6

45

47


48/48

Lateral bracing for

cantilever trusses

1

1

2

3

6

4

5

Purlin

Cantilever trussFly bracing

48

5 Compression Members

Documents

Transcript of 5 Compression Members