SKILLS Project - CTICMskills.cticm.org/.../020813/SKILLS_M01E_Design_of_built-up_columns… · 2...

SKILLS Project

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

11

55

Type 2

HEA 400 8x 1000

1000

Type 1

20x400

1000

20

00

Type 3

Shear stiffness of a panel:

8

INTRODUCTION

LFSv

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 AhI2

5,0 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

1dA

hAd

ahnEA

h0

Ad

Av

a

h0

Ad

a

h0

Ad

a

20


Built-up columns with battens:

Effective second moment of area:

chch0eff IAhI 25,02

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

2A

Ii chch0 IAhI 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

Ia

EIS 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

AhMNN

V

Ed

cr

Ed

Ed0Ed

1S

N

N

N

MeNM

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

EIN 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

MV Ed

Ed

0Ed IM

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

Nch 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 lll

vmin ll

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 state

Category C connections: Slip resistant at ultimate limit state

1Rdt,

Ed N

N

0M

yRdpl,Rdt,

AfNN

EN 1993-1-1 § 6.2.3

28


Category A, B and C connections:

Rdu,Rdpl,Rdt, ,NNMinN

0M

yRdpl,

AfN

1 Bolt 2 Bolts 3 Bolts or more

2M

u02Rdu,

5,00,2

tfdeN

2M

unet2Rdu,

fAN

2M

unet3Rdu,

fAN

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 leg n: is the number of vertically aligned holes d0: is the diameter of the hole

0M

ynetRdnet,

fAN

0grossnet tndAA

EN 1993-1-1 § 6.2.3

EdRdnet, NN

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

Nch EN 1993-1-1 § 6.3.1.1

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

Mk

N

N1

1M

Rk

Edch,zy

1M

Rkz

Edch,

M

Mk

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

fAVV v

1Rdb,

Edbatten,

M

M

1M

yyLTRdb,

fWM

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

aVV

2EdEdbatten,

aVM

4EdEdch,

aVM

eff

ch0EdEdEdch,

25,0

I

AhMNN

VEd a/2

a/2

h0

a/2

VEd a/2

VEd a/4 VEd a/4

VEd a/h0

a/2

h0

a/2

VEd/2

VEd/2 VEd/2

VEd/2

VEd a/h0

CLOSELY SPACED BUILT-UP MEMBERS

36

CLOSELY SPACED BUILT-UP MEMBERS – GENERAL

Case 1: Connected through packing plates

Case 2: Connected by pairs of battens

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

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 imin.

a a

h0

tp

y’ y’

z’

z’

39


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

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 IAhI

2

z'2

cr,z'L

EIN

cr,z'

ychz'

2

N

fAl

41


Effective non dimensional slenderness about z’-z’ axis

Number of packing plates

S235 S355

2

3

4

5

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

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

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

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

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

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

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

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

:effl

42


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

Critical axial force about y’-y’ axis:

Non dimensional slenderness about y’-y’ axis:

chy' 2II

2y'cr,

'2

y'cr,L

EIN

y

y'cr,

ychy'

2

N

fAl

43


Choice of the determining non dimensional slenderness:

Determination of the reduction factor with:

Resistance criterion:

),( y'effmax lll Max

34,0

1M

ychEd

)2(

fAN

WORKED EXAMPLE

45

WORKED EXAMPLE – GEOMETRY

Height: 10m

Loading:

Axial force: 900 kN

Bending moment: 450 kN.m

NEd=900 kN

MEd = 450 kN.m

46

WORKED EXAMPLE – GEOMETRY

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

1250

12

50

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

2ch cm8,76A

cm05,10y i cm0,6zi

2cm27,12VA

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

2cm52,15DA

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

cm125a

cm800 h

cm148d

48

WORKED EXAMPLE – BUILT-UP COLUMN

Effective second moment of area of the built-up column

Critical axial force

ch2

0eff 5,0 AhI

442eff cm2457601076808005,0 I

2

eff2

crL

EIN

kN509371010000

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

20d

v

1dA

hAd

ahnEAS

kN13407510

14801227

800155211480

800125015522100002 3

3

33

2

v

S

EN 1993-1-1 § 6.4.2.1

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

MeNM

I

kNm7,47910

134100

900

50937

9001

1045020900 33

EdM

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

AhMNN

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

NL

M

L

MV

I

V

Ed

cr

Ed

0EdEd1Ed,

1

1

S

N

N

NL

eN

L

MV

2Ed,1Ed,Ed VVV

53


Maximum shear force

Shear force due to axial force and imperfection

Shear force due to external loading

Maximum shear force

kNV 12,46

134100

900

50937

9001

1

10000

10450 3

2Ed,

kNV 80,5

134100

900

50937

9001

1

10000

209001Ed,

kNV 92,5112,4680,5Ed

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

ll

b curve buckling100mmt

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,

fAN

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

25,006,76

75,18

1

zz

l

ll

c curve buckling100mmt

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,

fAN

zz

kN2645100,1

355768097,0 3Rd,b,

zN

140,02645

6,1049

Rd,b,

Edch,

zN

N

Buckling of the diagonals

Class of the section

Section is of class 4

et

59

WORKED EXAMPLE – BUCKLING OF THE WEB MEMBERS

EN 1993-1-1 §5.6 Table 5.2 5,112

t

hb15

t

h

15,1281,015109

90

3,95,1110902

9090


Calculation of the effective area

Local buckling coefficient

Non dimensional slenderness and reduction factor

60


0,4k EN 1993-1-5 §4.4 Table 4.1

748,022,0481,04,28

9/90

4,28

/

l

k

thp

0,1 EN 1993-1-5 §4.4 (4.3)

61



Maximum compression axial force per diagonal

Slenderness

0

EdEdEdd,

cos

nh

dV

n

VN

kN488002

14809,51Edd,

N

57,845,17

1480

vv

i

dl

62


Effective non dimensional slenderness

Reduction factor (buckling curve b)


veff,v 7,035,0 ll

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, VN

712,0822,0 veff,v l

kNN 310Rdb,v,

161,0310

190

Rdb,v,

Edp,

N

N

117,05,286

48

Rdb,v,

Edd,

N

N

64

WORKED EXAMPLE – WEB MEMBERS IN TENSION

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

VN

Rdu,Rdpl,Rdt, ,NNMinN

0M

yRdpl,

AfN

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,

ufAN EN 1993-1-8 § 3.10.3

ntdAA 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

68

WORKED EXAMPLE – CATEGORY A CONNECTION

Resistance criteria

Shear resistance Fv,Rd per bolt:

Rdv,Edv, FF

Rdb,Edv, FF

2M

ubvRdv,

AfF

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:

kNN 0,527,3769,02RdS,

11 1

61

1

pn

e

69,0

4512

6,2461

1

Rdv,1RdS, FnN

70


Bearing resistance Fb,Rd:

Longitudinal direction

k1 : edge bolts:

end bolts:

inner bolts:

2M

ub1Rdb,

dtfkF

5,27,18,20

21

d

ek

1,,

u

ubdb

f

fMin

0

1d

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


k1 : edge bolts:

b : end bolt:

inner bolt:

5,25,47,118

408,2e1 k

74,0183

40de

58,04

1

183

45di

72


Ratio fub/fu:

b :

Bearing resistance Fb,Rd in the longitudinal direction:

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

kN5,811025,1

91649058,05,2 3Rdlg,b,

F

22,1490

600

u

ub f

f

73


Transverse direction:

k1 : edge bolts:

inner bolts:

end bolts:

5,27,18,20

11

d

ek

1,,

u

ubdb

f

fMin

0

2d

3d

e

5,27,14,10

11

d

pk

5,25,47,118

408,2e1 k

5,28,17,118

454,11 ik

74,0183

40de

74


Ratio fub/fu:

b :

Bearing resistance Fb,Rd in the transverse direction:

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

kN19,751025,1

91649074,08,1 3Rd,b,

trF

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

FF

nN

110

1

6

pn

e

09,1

4512

6,2460

kN3,105

19,75

09,1

5,81

1

2

22Rdb,

N

76


kN0,52kN48

kN3,105kN48

Rd,Edv, SNF

Rdb,Edv, NF

77

WORKED EXAMPLE – BLOCK TEARING

Block tearing resistance

(1) Shear plane

(2) Tension plane

0M

nvy

2M

ntuRdeff,2,

3

5,0

AfAfF

NEd

(1)

(2)

EN 1993-1-8 § 3.10.2

78

WORKED EXAMPLE – BLOCK TEARING

Tension Area

Shear Area

Block tearing resistance


222nt cm79,210918

2

110940 A

222nv cm6,3109185,21094540 A

kN5,128100,13

36035510

25,1

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 connections)

A simplified procedure is proposed for built-up members with closely spaced chords.

80

CONCLUSION

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 assemblées dos-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, European Recommendation for the Design of Simple Joints in Steel Structures, ECCS, Publication n°126, 2009

82

REFERENCES

SKILLS training modules have been developed by a consortium of organisations whose logos appear at the bottom of this slide. The material is under a creative commons license

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

authors, and the Commission cannot be held responsible for any use which may be made of the information contained therein.

http://creativecommons.org/licenses/by-nd/3.0/deed.es_ES

SKILLS Project - CTICMskills.cticm.org/.../020813/SKILLS_M01E_Design_of_built-up_columns… · 2...

Documents

Transcript of SKILLS Project - CTICMskills.cticm.org/.../020813/SKILLS_M01E_Design_of_built-up_columns… · 2...