skills m01e design builtupcolumns

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SKILLS Project

October 2013



BUILT-UP COLUMNS



Special features for the design of built-up columns

Design procedure

Design of closely spaced built-up members

3

LEARNING OUTCOMES



Introduction

Constructional details

Calculation

General

Laced built-up columns Battened built-up columns

Closely spaced built-up members

General

Simplified method

Worked example

Conclusion

4

LIST OF CONTENTS



INTRODUCTION



2 types of built-up columns:

6

INTRODUCTION

Laced built-up columns Battened built-up columns



7

INTRODUCTION

Built-up column Shear stiffness [kN]

Type 1 615000

Type 2 288000

Type 3 73000

L 100x10

1000

1 1 5 5

Type 2

HEA 400

8x 1000

1000

Type 1

20x400

1000

2 0 0 0

Type 3



Shear stiffness of a panel:

8

INTRODUCTION

LF Sv

F

L

F



Advantages

Reduction of mass

Increasing of flexural stiffness

Architectural effect

Disadvantages

Costs of joints

Costs of protection against corrosion

9

INTRODUCTION



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

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

INTRODUCTION



CONSTRUCTIONAL DETAILS



Field of application

Pinned at both ends

Parallel chords

Equal modules of lacings or battens At least 3 modules per member

12




13


A – Corresponding lacing

system

B – Mutually opposed lacing

system

A B A B

Treillis sur

face A

Treillis sur

face B

Treillis sur

face A

Treillis sur

face B

1 2 2 1 1 2 2 1

2 2

1 1

2 2

1 1



14


N-Shape V-Shape X-Shape



15


Types of section

Chords:

I-shape

Channels Web members (laced systems)

Angles

Web members (battened systems)

Plates



CALCULATION



17

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

Verification of the components



18


Mechanical properties of the built-up section

Built-up columns with lacings:

Effective second moment of area:

Ach Area of the chord

Ich Second moment of area of the chord

H0 Distance between the chords

ch0eff AhI 25,0 EN 1993-1-1 § 6.4.2.1

h0

Ich, Ach



19


Shear stiffness Sv: EN 1993-1-1 § 6.4.1

System

SV

n is the number of planes of lacings

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

3

20d

2d

ahnEA3

20d

d

ahnEA

3V

0d3

20d

1

d A

h Ad

ahnEA

h0

Ad

Av

a

h0

Ad

a

h0

Ad

a



20


Built-up columns with battens:

Effective second moment of area:

chch0eff I AhI 25,0 2 EN 1993-1-1 § 6.4.3.1

Criterion Efficiency factor

l ≥ 150 0

75 < l < 150

l ≤ 75 1,0

Where:

752

l

0i

Ll

ch

10

2 A

I i chch0 I AhI 25,0

21



21


Built-up columns with battens:

Shear stiffness:

Ib: second moment of area of

the batten

2

2

2

2

21

24

a

EI

a

h

nI

I a

EI S ch

0

b

ch

chv

π

EN 1993-1-1 § 6.4.3.1

h0

Ich, Ach

Ib



22


Maximum global bending moment

eff

ch0EdEdEdch,

25,0

I

AhM N N

V

Ed

cr

Ed

Ed0Ed

1S

N

N

N

M eN M

I

Ed

EN 1993-1-1 § 6.4.1

EN 1993-1-1 § 6.4.1

Maximum compression axial force in a chord

Critical axial force:

2

2

L

EI N eff

cr

π



23


Maximum transverse force

Compression and imperfection

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.

L

M V EdEd

0Ed I M

EN 1993-1-1 § 6.4.1



24

CALCULATION – LACED BUILT-UP COLUMN

Verification of the components

Flexural buckling of the chord:

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

1Rdb,

Ed, N

N ch EN 1993-1-1 § 6.3.1.1



25


Flexural buckling of the compressed web members (angle

sections):

Buckling length and slenderness ratio:

welded connection/at least 2 bolts per joint

1 bolt per joint

1Rdb,

Ed N

N

LL cr

LL cr

veff,vmin 7,035,0 l l l

vmin l l

EN 1993-1-1 BB § 1.2

EN 1993-1-1 § 6.3.1.1



26


z

y

z

y

u

u v

v

h

h



27


Verification of the web members – diagonals in tension:

Welded joints:

Bolted joints: According to connection type

Category A connections: Bearing type

Category B connections: Slip resistant at service limit stateCategory C connections: Slip resistant at ultimate limit state

1Rdt,

Ed N

N

0M

y

Rdpl,Rdt,

Af N N

EN 1993-1-1 § 6.2.3



28


Category A, B and C connections:

Rdu,Rdpl,Rdt, ,N N MinN

0M

yRdpl,

Af N

1 Bolt 2 Bolts 3 Bolts or more

2Mu02Rdu,

5,00,2

tf d eN

2M

unet2

Rdu,

f A

N 2M

unet3

Rdu,

f A

N

EN 1993-1-1 § 6.2.3

EN 1993-1-1 § 6.2.3

EN 1993-1-8 § 3.10.3



29


Constants 2 and 3:

Pitch p1 ≤ 2,5 d0 ≥ 5,0 d0

2 bolts 2 0,4 0,7

3 bolts or more 3 0,5 0,7

EN 1993-1-8 § 3.10.3

d0

e1

e2

e1

e2

p1 e1 p1 p1



30


Additional verification for category C connections:

Where: t: is the thickness of the legn: is the number of vertically aligned holes

d0: is the diameter of the hole

0M

ynetRdnet,

f AN

0grossnet tnd A A

EN 1993-1-1 § 6.2.3

EdRdnet, N N

O O



31

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

1Rdb,

Ed, N

N ch EN 1993-1-1 § 6.3.1.1

CALCULATION BATTENED BUILT UP COLUMN



32


• Flexural buckling in the plane of the battens:

Buckling length = distance between battens

Chord subjected to axial force and local bending moment

+ Verification of the end sections

1

1M

Rk

Edch,yy

1M

Rky

Edch,

M

M k

N

N 1

1M

Rk

Edch,zy

1M

Rkz

Edch,

M

M k

N

N

EN 1993-1-1 § 6.3.3




33


Verification of the web members – battens

Transverse force:

Bending moment/Lateral Torsional buckling:

1Rdc,

Edbatten, V

V

0M

y

Rdpl,Rdc,

3

f A

V V

v

1Rdb,

Edbatten, M M

1M

yyLTRdb,

f

W M EN 1993-1-1 § 6.3.2.1

EN 1993-1-1 § 6.2.6




34


Axial force and moment in the

chord:

Shear force and moment in

the battens:

0EdEdbatten,h

aV V

2EdEdbatten,

aV M

4EdEdch,

aV M

eff

ch0EdEdEdch,

25,0

I

AhM N N

V Ed a/2

a/2

h0

a/2

V Ed a/2

V Ed a/4 V Ed a/4

V Ed a/h0

a/2

h0

a/2

V Ed/2

V Ed/2 V Ed/2

V Ed/2

V Ed a/h0



CLOSELY SPACED BUILT-UP MEMBERS

CLOSELY SPACED BUILT UP MEMBERS GENERAL



36

CLOSELY SPACED BUILT-UP MEMBERS – GENERAL

Case 1: Connected through packing plates

Case 2: Connected by pairs of battens

CLOSELY SPACED BUILT UP MEMBERS GENERAL



37

CLOSELY SPACED BUILT-UP MEMBERS – GENERAL

Calculation

Shear stiffness is set to infinity if maximum spacing for

joints are respected

Buckling verification as a single member If maximum spacing is not respected

Shear deformation has to be accounted for

Case Maximum spacing

1

2

min15i

min70i

EN 1993-1-1 § 6.4.4

CLOSELY SPACED BUILT UP MEMBERS SIMPLIFIED METHOD



38

CLOSELY SPACED BUILT-UP MEMBERS – SIMPLIFIED METHOD

Simplified calculation for sections composed of 2 equal

leg angles (Reference [3])

when the spacing is > 15 i min.

a a

h0

tp

y’ y’

z’

z’




39


Scope of application

Spacing of the packing plates a: 15i min … 50 i min

Number of packing plates: 2 … 5

Width of the legs b: 50 mm … 200 mm

Thickness of the legs t : 0,1b

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

Non dimensional slenderness about z’-z’: ≤ 1,80




40


Procedure

Second moment of area about z’-z’ axis:

Critical axial force about z’-z’ axis:

Non dimensional slenderness about z’-z’ axis:

chch20z' 25,0 I AhI

2

z'2

cr,z'L

EI N

cr,z'

ychz'

2

N

f Al




41


Effective non dimensional slenderness about z’-z’ axis

Number of packing

platesS235 S355

2

3

4

5

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

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

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

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

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

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

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

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

:eff l




42


Second moment of area about y’-y’ axis:

Critical axial force about y’-y’ axis:

Non dimensional slenderness about y’-y’ axis:

chy' 2I I

2y'cr,

'2

y'cr, L

EI N

y

y'cr,

ychy'

2

N

f A

l




43


Choice of the determining non dimensional

slenderness:

Determination of the reduction factor with:

Resistance criterion:

),( y'eff max l l l Max

34,0

1M

ychEd

)2(

f AN



WORKED EXAMPLE

WORKED EXAMPLE – GEOMETRY



45


Height: 10m

Loading:

Axial force: 900 kN

Bending moment: 450 kN.m

NEd=900 kN

MEd

= 450 kN.m




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

1

2

3

800

800

1 2 5 0

1 2 5 0

WORKED EXAMPLE – SECTION PROPERTIES



47

WORKED EXAMPLE – SECTION PROPERTIES

Chords HEA 240 – S355

Posts Equal leg angles L 80 x 80 x 8 – S355

Diagonals Equal leg angles L 90 x 90 x 9 – S355

2

ch cm8,76 Acm05,10y i cm0,6z i

2cm27,12V A

cm43,2 z y i i cm06,3ui cm56,1v i

2cm52,15D A

cm73,2 z y i i cm44,3ui cm75,1v i

cm125a

cm800 h

cm148d

WORKED EXAMPLE – BUILT-UP COLUMN



48


Effective second moment of area of the built-up column

Critical axial force

ch

2

0eff 5,0 AhI 442

eff cm2457601076808005,0 I

2

eff 2

cr L

EI N

kN5093710

10000

10245760210000 3

2

42

cr

N

EN 1993-1-1 § 6.4.2.1

EN 1993-1-1 § 6.4.1




49

WORKED EXAMPLE BUILT-UP COLUMN

Shear stiffness

3V

30d3

20dv

1d A

h Ad

ahnEAS

kN13407510

14801227

800155211480

800125015522100002 3

3

33

2

v

S

EN 1993-1-1 § 6.4.2.1

WORKED EXAMPLE – INTERNAL FORCES AND MOMENTS



50

WORKED EXAMPLE INTERNAL FORCES AND MOMENTS

Maximum global bending moment:

Imperfection:

Global bending moment:

mm20500

100000 e

V

Ed

cr

Ed

Ed0EdEd

1S

N

N

N

M eN M

I

kNm7,47910

134100

900

50937

9001

1045020900 33

Ed M

EN 1993-1-1 § 6.4.1




51


Maximum compressive axial force of the chord

Class of the section:Class 1

Maximum axial force in the chord

eff

ch0EdEdEdch,

22 I

AhM N N

kN6,1049102457602

7680800479700

2

9004Edch,

N

EN 1993-1-1 § 6.4.1

EN 1993-1-1 §5.6 Table 5.2




52


Maximum shear force

Shear force due to axial force and imperfection

Shear force due to external loading

Maximum shear force

V

Ed

cr

Ed

EdEd2Ed,

1

1

S

N

N

N L

M

L

M V

I

V

Ed

cr

Ed

0EdEd1Ed,

1

1

S

N

N

N L

eN

L

M V

2Ed,1Ed,Ed V V V




53


Maximum shear force

Shear force due to axial force and imperfection

Shear force due to external loading

Maximum shear force

kN V 12,46

134100

900

50937

9001

1

10000

10450 3

2Ed,

kN V 80,5

134100

900

50937

9001

1

10000

209001Ed,

kN V 92,5112,4680,5Ed

WORKED EXAMPLE – BUCKLING OF THE CHORDS



54

WORKED EXAMPLE BUCKLING OF THE CHORDS

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

Non dimensional slenderness

Buckling curve

5,995,100

10000

y

ycr,y i

Ll

06,7681,09,939,931 l

31,106,76

5,99

1

yy

l

l l

bcurvebuckling100mmt

1,2h/b

f

EN 1993-1-1 § 6.3.1.3

EN 1993-1-1 § 6.3.1.2




Reduction factor

0

0,1

0,2

0,3

0,4

0,5

0,6

0,7

0,8

0,9

1

1,1

0 0,2 0,4 0,6 0,8 1 1,2 1,4 1,6 1,8 2 2,2 2,4 2,6 2,8 3

a0

a

b

c

d

55


42,0y




56


Design buckling resistance

Resistance criterion

1M

ychyRdy,b,

f AN

kN1145100,1

355768042,0 3Rdy,b,

N

192,01145

6,1049

Rdy,b,

Edch, N

N

EN 1993-1-1 § 6.3.1.1




57


In-plane (weak axis) buckling of the chords

Non dimensional slenderness

Buckling curve

Reduction factor

75,1860

12509,0

z

cr,zz

i

Ll

25,0

06,76

75,18

1

zz

l

l l

ccurvebuckling

100mmt

1,2h/b

f

97,0z

EN 1993-1-1 § 6.3.1.3

EN 1993-1-1 § 6.3.1.2




58



1M

ychRd,b,

f AN z

z

kN2645100,1

355768097,0 3Rd,b,

z N

140,02645

6,1049

Rd,b,

Edch, z N

N

WORKED EXAMPLE – BUCKLING OF THE WEB MEMBERS



Buckling of the diagonals

Class of the section

Section is of class 4

et

59

EN 1993-1-1 §5.6 Table 5.2 5,112

t

hb 15

t

h

15,1281,015109

90

3,95,1110902

9090





Calculation of the effective areaLocal buckling coefficient

Non dimensional slenderness and reduction factor

60

0,4 k EN 1993-1-5 §4.4 Table 4.1

748,022,0481,04,28

9/90

4,28

/

l

k

t h p

0,1 EN 1993-1-5 §4.4 (4.3)




61


Maximum compression axial force per diagonal

Slenderness

0

EdEdEdd,

cos

nh

d V

n

V N

kN488002

14809,51Edd,

N

57,845,17

1480

vv i d

l




62

Effective non dimensional slenderness

Reduction factor (buckling curve b)


veff,v 7,035,0 l l 13,111,17,035,0eff,v l

52,0v

kN5,286100,1

355155252,0 3Rdb,v, N

EN 1993-1-1 BB § 1.2




63


Buckling of the posts (class 4, = 1,0)

kN9,51EdEdp, V N

712,0822,0 veff,v l

kN N 310Rdb,v,

161,0310

190

Rdb,v,

Edp, N

N

117,05,286

48Rdb,v,

Edd, N N

WORKED EXAMPLE – WEB MEMBERS IN TENSION



64

Category A connection

mm401 e

mm402 e

mm451 p

2 M16 6.8




65

Diagonals in tension

Axial force

Tension resistance (Category A connection)

Resistance of the gross section

kN48cosEd

Edt, n

V N

Rdu,Rdpl,Rdt, ,N N MinN

0M

yRdpl,

Af N

kN551100,1

3551552 3Rdpl,

N

EN 1993-1-1 § 6.2.3




66

Resistance of the net section:

Net section area:

Reduction factor:

Resistance of the net section:

2M

net2Rdu,

uf AN EN 1993-1-8 § 3.10.3

ntd A A 0grossnet

222net cm9,13101189101552 A

kN21825,1

49013904,0Rdu,

N

4,02 EN 1993-1-8 § 3.10.3 Table 3.8




67

Tension resistance (Category A connection)


122,0218

48

Rdt,

Edt, N

N

kN218kN218kN,551MinRdt, N

WORKED EXAMPLE – CATEGORY A CONNECTION



68

Resistance criteria

Shear resistance F v,Rd per bolt:

Rdv,Edv, F F

Rdb,Edv, F F

2M

ubvRdv,

Af F

kN7,371025,1

1576005,0 3Rdv,

F

EN 1993-1-8 § 3.4.2

EN 1993-1-8 § 3.6.1




69

Shear resistance of the bolt group:

Consideration of the eccentricity (Reference [4]):

Shear resistance:

kN N 0,527,3769,02RdS,

11 1

61

1

pn

e

69,0

4512

6,2461

1

Rdv,1RdS, F nN




70

Bearing resistance F b,Rd:

Longitudinal direction

k 1 : edge bolts:

end bolts:

inner bolts:

2M

ub1Rdb,

dt f k

F

5,27,18,20

2

1 d

ek

1,,

u

ubdbf

f Min

0

1

d 3d

e

4

1

d3 0

1d p

EN 1993-1-8 § 3.6.1 Table 3.4

EN 1993-1-8 § 3.6.1




71

k 1 : edge bolts:

b : end bolt:

inner bolt:

5,25,47,118408,2e1 k

74,0183

40de

58,04

1

183

45di




72

Ratio f ub/f u:

b :

Bearing resistance F b,Rd in the longitudinal direction:

58,01;22,1;58,0;74,0Minb

kN5,8110

25,1

91649058,05,2 3Rdlg,b,

F

22,1490

600

u

ub f

f




73

Transverse direction:

k 1 : edge bolts:

inner bolts:

end bolts:

5,27,18,2 0

1

1 d

e

k

1,,

u

ubdbf

f Min

0

2d

3d

e

5,27,14,1

0

11

d

pk

5,25,47,118

408,2e1 k

5,28,17,118

454,11 i k

74,0183

40de




74

Ratio f ub/f u:

b :

Bearing resistance F b,Rd in the transverse direction:

74,01;22,1;74,0Minb

kN19,751025,1

91649074,08,1 3Rd,b,

tr F

22,1490

600

u

ub f

f




75

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

2

Rdb,tr,

0

2

Rdlg,b,

1Rdb,

1

F F

nN

110

16 pne

09,1

4512

6,2460

kN3,105

19,75

09,1

5,81

1

2

22Rdb,

N




76

kN0,52kN48

kN3,105kN48

Rd,Edv, SN F

Rdb,Edv, N F

WORKED EXAMPLE – BLOCK TEARING



77

Block tearing resistance

(1) Shear plane

(2) Tension plane

0M

nvy

2M

ntuRdeff,2,

35,0

Af Af F

NEd

(1)

(2)

EN 1993-1-8 § 3.10.2

WORKED EXAMPLE – BLOCK TEARING



78

Tension Area

Shear Area

Block tearing resistance


222

nt cm79,2109182

1

10940

A

222nv cm6,3109185,21094540 A

kN5,128100,13

36035510

25,1

2794905,0 33Rdeff,2,

F

kN5,128kN48



CONCLUSION

CONCLUSION



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

calculation that takes into account an equivalent geometricimperfection (L/500) and 2nd order effects.

Then the resistance of each component has to be checked

(cross-section resistance, buckling resistance, resistance ofconnections)

A simplified procedure is proposed for built-up members

with closely spaced chords.

80



REFERENCES

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. Méthode simplifiée pour la vérification

de barres comprimées composées de deux cornières assembléesdos-à-dos.

Simplified method for the verification of compressed built-up

members composed of two closely spaced angles.

Revue Construction Métallique n°4/2010. CTICM.

J.-P. Jaspart, J.-F. Demonceau, S. Renkin, M.L. Guillaume, EuropeanRecommendation for the Design of Simple Joints in Steel Structures,ECCS, Publication n°126, 2009

82



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The project was funded with support from the European Commission. This module reflects only the views of the

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contained therein.

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skills m01e design builtupcolumns

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