FINAL - SKILLS - Design of Built-up Columns - V3

SKILLS Project SKILLS Project

BUILT-UP COLUMNS

Special features for the design of built-up columns

Design procedure

Design of closely spaced built-up members

LEARNING OUTCOMES

3

Introduction

Constructional details

Calculation

General

Laced built-up columns

LIST OF CONTENTS

Battened built-up columns

Closely spaced built-up members

General

Simplified method

Worked example

Conclusion

4

INTRODUCTION

2 types of built-up columns:

INTRODUCTION

Laced built-up columns Battened built-up columns

6

INTRODUCTION

1000

11

55

Type 2

1000

Type 1

1000

20

00

Type 3

7

Built-up column Shear stiffness [kN]

Type 1 615000

Type 2 288000

Type 3 73000

L 100x10

HEA 400

8x 1000 20x400

Shear stiffness of a panel:

INTRODUCTION

LFSv

=

F

8

L

F

Advantages

Reduction of mass

Increasing of flexural stiffness

Architectural effect

Disadvantages

INTRODUCTION

Disadvantages

Costs of joints

Costs of protection against corrosion

9

Modelling using design software

One bar-type element using effective section properties

Area A = Area of the chords

Inertia about strong axis = Ieff

Inertia about weak axis = 2 x Iy,chord

Shear stiffness Sv

INTRODUCTION

v

Advantage: Rapidity of the modelling process

Sets of elements using common section properties

Advantage: Knowledge of internal forces and moments of the

elements of the built-up column

10

CONSTRUCTIONAL DETAILS

Field of application

Pinned at both ends

Parallel chords

Equal modules of lacings or battens

At least 3 modules per member


At least 3 modules per member

12


A Corresponding lacing

system

B Mutually opposed lacing

system

A BA B

1 2 2 1 1 2 2 1

2 2

1 1

2 2

1 1

13

Treillis sur

face A

Treillis sur

face B

Treillis sur

face A

Treillis sur

face B


14

N-Shape V-Shape X-Shape


Types of section

Chords:

I-shape

Channels

Web members (laced systems)

15

Web members (laced systems)

Angles

Web members (battened systems)

Plates

CALCULATION

CALCULATION GENERAL

Design steps

Mechanical properties of the built-up section

Critical axial force of the built-up column

Maximum global bending moment

Maximum axial force

Maximum transverse force

17


Verification of the components

CALCULATION GENERAL

Mechanical properties of the built-up section

Built-up columns with lacings:

Effective second moment of area:

ch0eff AhI25,0= EN 1993-1-1 6.4.2.1

h0

18

Ach Area of the chord

Ich Second moment of area of the chord

H0 Distance between the chords

h0

Ich, Ach

CALCULATION GENERAL

Shear stiffness Sv: EN 1993-1-1 6.4.1

System

Ad

Av

a

Ad

a

Ad

a

19

SV

n is the number of planes of lacings

Ad and Av refer to the cross sectional area of the bracings

3

20d

2dahnEA

3

20d

dahnEA

+ 3

V

0d3

20d

1dAhAd

ahnEA

h0h0h0

CALCULATION GENERAL

Built-up columns with battens:

Effective second moment of area:

chch0eff IAhI 25,0 2 += EN 1993-1-1 6.4.3.1

Criterion Efficiency factor

20

150 0

75 < < 150

75 1,0

Where:

752 =

0iL

=ch

10 2A

Ii = chch0 IAhI 25,02

1 +=

CALCULATION GENERAL

Built-up columns with battens:

Shear stiffness:

2

2

2

221

24a

EI

a

hnII

a

EIS ch0

b

ch

chv

+

= EN 1993-1-1 6.4.3.1

h0

21

Ib: second moment of area of

the batten

b h0

Ich, Ach

Ib

CALCULATION GENERAL

Maximum global bending moment

MeN I+

Critical axial force:

2

2

LEIN effcr

=

22

eff

ch0EdEdEdch, 2

5,0I

AhMNN +=

V

Ed

cr

Ed

Ed0Ed

1SN

NN

MeNMI

Ed

+= EN 1993-1-1 6.4.1

EN 1993-1-1 6.4.1

Maximum compression axial force in a chord

CALCULATION GENERAL


Compression and imperfection

Attention: In case of a bending moment caused by external

LMV EdEd pi=

( )0Ed =IMEN 1993-1-1 6.4.1

23

Attention: In case of a bending moment caused by external

loads, this formula is not applicable.

Transverse force due to external loads has to

be accounted for.

CALCULATION LACED BUILT-UP COLUMN

Verification of the components

Flexural buckling of the chord:

Buckling length:

1Rdb,

Ed, NNch

EN 1993-1-1 6.3.1.1

24

Buckling length:

in plane buckling: I or H sections: 0,9 a

other sections : 1,0 a

out of plane buckling: distance between lateral supports


Flexural buckling of the compressed web members (angle

sections):

Buckling length and slenderness ratio:

welded connection/at least 2 bolts per joint

1Rdb,

Ed NN EN 1993-1-1 6.3.1.1

25

welded connection/at least 2 bolts per joint

1 bolt per joint

LL =cr

LL =cr

veff,vmin 7,035,0 +==

vmin =

EN 1993-1-1 BB 1.2


z

uvh

26

y

z

y

u vh


Verification of the web members diagonals in tension:

Welded joints:

1Rdt,

Ed NN

0M

yRdpl,Rdt,

AfNN ==

EN 1993-1-1 6.2.3

27

Bolted joints: According to connection type

Category A connections: Bearing type

Category B connections: Slip resistant at service limit state

Category C connections: Slip resistant at ultimate limit state

0M


Category A, B and C connections:

( )Rdu,Rdpl,Rdt, ,NNMinN =

0M

yRdpl,

AfN =

EN 1993-1-1 6.2.3

EN 1993-1-1 6.2.3

28

1 Bolt 2 Bolts 3 Bolts or more

( )2M

u02Rdu,

5,00,2

tfdeN =2M

unet2Rdu,

fAN =2M

unet3Rdu,

fAN =

EN 1993-1-8 3.10.3


Constants 2 and 3:

Pitch p1 2,5 d0 5,0 d0

2 bolts 2 0,4 0,73 bolts or more 3 0,5 0,7

EN 1993-1-8 3.10.3

29

d0

e1

e2

e1

e2

p1 e1 p1 p1


Additional verification for category C connections:

0M

ynetRdnet,

fAN = EN 1993-1-1 6.2.3

EdRdnet, NN

30

Where: t: is the thickness of the leg

n: is the number of vertically aligned holes

d0: is the diameter of the hole

0grossnet tndAA =

CALCULATION BATTENED BUILT-UP COLUMN

Verification of the chord

Flexural buckling perpendicular to the battens

Buckling length = distance between lateral supports

Chord subjected to axial force

31

1Rdb,

Ed, NNch EN 1993-1-1 6.3.1.1


Flexural buckling in the plane of the battens:

Buckling length = distance between battens

Chord subjected to axial force and local bending moment

1Rk

Edch,yy

Rky

Edch, +

M

MkN

N1

Rk

Edch,zy

Rkz

Edch, +

M

MkN

N

32

+ Verification of the end sections

1M1M 1M1M

EN 1993-1-1 6.3.3


Verification of the web members battens

Transverse force:

1Rdc,

Edbatten, V

V

( )0M

y

Rdpl,Rdc,

3

fA

VVv

== EN 1993-1-1 6.2.6

33

Bending moment/Lateral Torsional buckling:

0M

1Rdb,

Edbatten, M

M

1M

yyLTRdb,

f

WM =EN 1993-1-1 6.3.2.1


Axial force and moment in the

chord:

Shear force and moment in

4EdEdch,aVM =

eff

ch0EdEdEdch, 2

5,0I

AhMNN +=

VEd a/2

a/2

h0

a/2

VEd a/2

VEd a/4 VEd a/4

34

Shear force and moment in

the battens:

0EdEdbatten, h

aVV =

2EdEdbatten,aVM =

h0

VEd a/h0

a/2

h0

a/2

VEd/2

VEd/2 VEd/2

VEd/2

VEd a/h0

CLOSELY SPACED BUILT-UP MEMBERS

CLOSELY SPACED BUILT-UP MEMBERS GENERAL

Case 1: Connected through packing plates

36

Case 2: Connected by pairs of battens

CLOSELY SPACED BUILT-UP MEMBERS GENERAL

Calculation

Shear stiffness is set to infinity if maximum spacing for

joints are respected

Case Maximum spacing

1 15i

EN 1993-1-1 6.4.4

37

Buckling verification as a single member

If maximum spacing is not respected

Shear deformation has to be accounted for

1

2

min15i

min70i

CLOSELY SPACED BUILT-UP MEMBERS SIMPLIFIED METHOD

Simplified calculation for sections composed of 2 equal

leg angles (Reference [3])

when the spacing is > 15 imin.

h0

z

38

a atp

yy

z


Scope of application

Spacing of the packing plates a: 15imin 50 imin

Number of packing plates: 2 5

Width of the legs b: 50 mm 200 mm

39

Thickness of the legs t: 0,1b

Thickness of the packing plates: 0,8t 2t

Non dimensional slenderness about z-z: 1,80


Procedure

Second moment of area about z-z axis:

Critical axial force about z-z axis:

chch20z' 25,0 IAhI +=

z'2EIN pi=

40

Non dimensional slenderness about z-z axis:

2z'

cr,z' LEIN pi=

cr,z'

ychz'

2N

fA=


Effective non dimensional slenderness about z-z axis

Number of packing

platesS235 S355

2 39,077,018,0 2 ++ 66,018,086,0 2 +

:eff

41

2

3

4

5

39,077,018,0 z'2z' ++

41,052,032,0 z'2z' ++

48,017,056,0 z'2z' ++

53,005,069,0 z'2z' +

66,018,086,0 z'2z' +

66,016,066,0 z'2z' +

67,021,065,0 z'2z' +

70,031,069,0 z'2z' +


Second moment of area about y-y axis:

Critical axial force about y-y axis:

chy' 2II =

2y'cr,

'

2

y'cr, LEI

N ypi

=

42

Non dimensional slenderness about y-y axis:

y'cr,L

y'cr,

ychy'

2N

fA=


Choice of the determining non dimensional

slenderness:

Determination of the reduction factor with:

),( y'effmax Max=

34,0=

43

Resistance criterion:

34,0=

1M

ychEd

)2(

fAN

WORKED EXAMPLE

WORKED EXAMPLE GEOMETRY

Height: 10m

Loading:

Axial force: 900 kN

Bending moment: 450 kN.m

NEd=900 kN

MEd = 450 kN.m

45

WORKED EXAMPLE GEOMETRY

1

2

800

800

12

50

46

1. Chords: HEA 240

2. Posts: Equal leg angles 80 x 80 x 8

3. Diagonals: Equal leg angles 90 x 90 x 9

2

3

12

50

WORKED EXAMPLE SECTION PROPERTIES

Chords HEA 240 S355

Posts Equal leg angles L 80 x 80 x 8 S355

2ch cm8,76=A

cm05,10y =i cm0,6=zi

2cm27,12=VA

cm125=a

cm800 =h

47

Diagonals Equal leg angles L 90 x 90 x 9 S355

cm27,12=VA

cm43,2== zy ii cm06,3=ui cm56,1=vi

2cm52,15=DA

cm73,2== zy ii cm44,3=ui cm75,1=vi

cm800 =h

cm148=d

WORKED EXAMPLE BUILT-UP COLUMN

Effective second moment of area of the built-up column

Critical axial force

ch2

0eff 5,0 AhI =442

eff cm2457601076808005,0 == I

2EIpi

EN 1993-1-1 6.4.2.1

48

2eff

2

cr LEIN pi=

kN509371010000

10245760210000 32

42

cr =pi

=N

EN 1993-1-1 6.4.1

WORKED EXAMPLE BUILT-UP COLUMN

Shear stiffness

+

=

3V

30d3

20d

v

1dAhAd

ahnEAS

800125015522100002 32

EN 1993-1-1 6.4.2.1

49

kN13407510

14801227800155211480

800125015522100002 3

3

33

2

v =

+

=

S

WORKED EXAMPLE INTERNAL FORCES AND MOMENTS

Maximum global bending moment:

Imperfection:

Global bending moment:

mm20500

100000 ==e

MeN I+ EN 1993-1-1 6.4.1

50

V

Ed

cr

Ed

Ed0EdEd

1SN

NN

MeNMI

+=

kNm7,47910

134100900

509379001

1045020900 33=

+=

EdM

EN 1993-1-1 6.4.1


Maximum compressive axial force of the chord

Class of the section:

Class 1

Maximum axial force in the chord

AhMN EN 1993-1-1 6.4.1

EN 1993-1-1 5.6 Table 5.2

51

eff

ch0EdEdEdch, 22 I

AhMNN +=

kN6,10491024576027680800479700

2900

4Edch, =

+=N

EN 1993-1-1 6.4.1


Maximum shear force

Shear force due to axial force and imperfection

Shear force due to external loading

V

Ed

cr

Ed

0EdEd1Ed,

1

1

SN

NNL

eNL

MV

== pipi

52


Maximum shear force

V

Ed

cr

Ed

EdEd2Ed,

1

1

SN

NNL

ML

MV

I

==

2Ed,1Ed,Ed VVV +=


Maximum shear force

Shear force due to axial force and imperfection


kNV 80,5

134100900

509379001

110000

209001Ed, =

= pi

53


Maximum shear force

kNV 12,46

134100900

509379001

110000

10450 32Ed, =

=

kNV 92,5112,4680,5Ed =+=

WORKED EXAMPLE BUCKLING OF THE CHORDS

Out-of-plane (strong axis) buckling of the chords

Non dimensional slenderness

5,995,100

10000y

ycr,y === i

L

06,7681,09,939,931 ===

54

Buckling curve

31,106,765,99

1

yy ===

b curve buckling100mmt

1,2h/b

f

==k

73

end bolts:

= 1,,

u

ubdb f

fMin

0

2d 3d

e=

0

5,28,17,118454,11 ==ik

74,0183

40de =

=

WORKED EXAMPLE CATEGORY A CONNECTION

Ratio fub/fu:

b :

( ) 74,01;22,1;74,0Minb ==

22,1490600

u

ub==

ff

74

Bearing resistance Fb,Rd in the transverse direction:

kN19,751025,1

91649074,08,1 3Rd,b, =

=

trF


Bearing resistance of the bolt group (Reference [4]):

2

Rdb,tr,

02

Rdlg,b,

1Rdb,

1

+

=

FF

nN

( )6e

=

75

( ) 110 16

pne

+=

( ) 09,145126,246

0 =+

=

kN3,105

19,7509,1

5,811

222Rdb,

=

+

=N


kN0,52kN48

kN3,105kN48

Rd,Edv, SNF

Rdb,Edv, NF

76

WORKED EXAMPLE BLOCK TEARING

Block tearing resistance

0M

nvy

2M

ntuRdeff,2, 3

5,0AfAfF +=

NEd

(2)

EN 1993-1-8 3.10.2

77

(1) Shear plane

(2) Tension plane

(1)

WORKED EXAMPLE BLOCK TEARING

Tension Area

Shear Area

Block tearing resistance

222nt cm79,2109182

110940 == A

( ) 222nv cm6,3109185,21094540 =+= A

78

Resistance criterion

kN5,128100,13

3603551025,1

2794905,0 33Rdeff,2, =

+

=

F

kN5,128kN48

CONCLUSION

The buckling verification of a built-up member is based on a

calculation that takes into account an equivalent geometric

imperfection (L/500) and 2nd order effects.

Then the resistance of each component has to be checked

(cross-section resistance, buckling resistance, resistance of

CONCLUSION

(cross-section resistance, buckling resistance, resistance of

connections)

A simplified procedure is proposed for built-up members

with closely spaced chords.

80

REFERENCES

EN 1993-1-1 Eurocode 3 Design of steel structures Part 1-1:General rules and rules for buildings

EN 1993-1-8 Eurocode 3 Design of steel structures Part 1-8:Design of joints.

A.Bureau/P.-L. Chouzenoux. Mthode simplifie pour la vrification de barres comprimes composes de deux cornires assembles

REFERENCES

de barres comprimes composes de deux cornires assembles dos--dos.

Simplified method for the verification of compressed built-up

members composed of two closely spaced angles.

Revue Construction Mtallique n4/2010. CTICM.

J.-P. Jaspart, J.-F. Demonceau, S. Renkin, M.L. Guillaume, European Recommendation for the Design of Simple Joints in Steel Structures, ECCS, Publication n126, 2009

82

Documents

FINAL - SKILLS - Design of Built-up Columns - V3