skills m08 e_portalframes_singlestoreybuildings

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SKILLS Project October 2013

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Page 1: Skills m08 e_portalframes_singlestoreybuildings

SKILLS Project

October 2013

Page 2: Skills m08 e_portalframes_singlestoreybuildings

PORTAL FRAMES IN SINGLE STOREY BUILDINGS

Page 3: Skills m08 e_portalframes_singlestoreybuildings

Structural elastic analysis including second order effects and imperfections

Design procedure of portal frames

Design procedure of roof bracing and vertical bracing

3

LEARNING OUTCOMES

Page 4: Skills m08 e_portalframes_singlestoreybuildings

Introduction

Presentation of industrial steel buildings

Examples

Global Analysis

General

Second order effects

Frame imperfection

Rigidity of joints

Design Procedure of portal frames

Structural stability of frames

Stability of columns and rafters

Vertical Bracing

Roof Bracing

Conclusion 4

LIST OF CONTENTS

Page 5: Skills m08 e_portalframes_singlestoreybuildings

INTRODUCTION

Page 6: Skills m08 e_portalframes_singlestoreybuildings

6

INTRODUCTION

Typical design of single storey

steel buildings

Page 7: Skills m08 e_portalframes_singlestoreybuildings

7

INTRODUCTION

Purlins

Page 8: Skills m08 e_portalframes_singlestoreybuildings

8

INTRODUCTION

Haunched portal frames

Page 9: Skills m08 e_portalframes_singlestoreybuildings

9

INTRODUCTION

Roof bracing

Photo APK

Page 10: Skills m08 e_portalframes_singlestoreybuildings

10

INTRODUCTION

Vertical bracing

Photo APK

Page 11: Skills m08 e_portalframes_singlestoreybuildings

11

INTRODUCTION

Photo APK – JP Muzeau

Page 12: Skills m08 e_portalframes_singlestoreybuildings

12

INTRODUCTION

Page 13: Skills m08 e_portalframes_singlestoreybuildings

GLOBAL ANALYSIS

Page 14: Skills m08 e_portalframes_singlestoreybuildings

Methods of structural analysis

Elastic analysis

Material is supposed to behave perfectly linear elastic

Plastic analysis

Material non linearity is taken into account

Redistribution of internal forces and moments

14

GLOBAL ANALYSIS

EN 1993-1-1 § 5.4

Page 15: Skills m08 e_portalframes_singlestoreybuildings

Effects to be taken into account when significant

Effects of deformed geometry (2nd order effects)

Imperfections

Stiffness of joints

Ground-structure interaction

15

GLOBAL ANALYSIS

EN 1993-1-1 § 5.1

Page 16: Skills m08 e_portalframes_singlestoreybuildings

16

GLOBAL ANALYSIS

First order and second order analysis

First order analysis: performed on the non deformed structure

Second order analysis: performed including effects of deformed geometry

Page 17: Skills m08 e_portalframes_singlestoreybuildings

Effects of deformed geometry/Second order effects

17

GLOBAL ANALYSIS

V

H

MI

h

First order analysis of the structure gives:

hHM I

EI

hHI

3

3

I

Page 18: Skills m08 e_portalframes_singlestoreybuildings

Effects of deformed geometry/Second order effects

18

GLOBAL ANALYSIS

Second order analysis of the structure gives:

iterative calculation of II necessary

IIII VhHM

EI

hVhH

IIII

3

2

n1n

V H

MII

II

Page 19: Skills m08 e_portalframes_singlestoreybuildings

Effects of deformed geometry/Second order effects

19

GLOBAL ANALYSIS

Supposing: And:

With:

cr

2

2

1

1

31

1

3

V

V

EI

VhEI

hhH III

IIIIn1n I

EI

hhH

3

2

2cr

3

h

EIV

V H

MII

II

EI

hVhH

IIII

3

2

n1n

Page 20: Skills m08 e_portalframes_singlestoreybuildings

20

GLOBAL ANALYSIS

Effects of deformed geometry/Second order effects

Substituting:

cr

III

V

V

1

1

crcr

V

V

cr

11

1

III

cr

11

1

III MM

V H

MII

II

Page 21: Skills m08 e_portalframes_singlestoreybuildings

21

GLOBAL ANALYSIS

Global and local second order effects

Global 2nd order effects – P-D-effects

Concerns the deformation

of the whole structure

Local 2nd order effects – P--effects

Concerns the deformation between member ends

Generally covered by member checks EN 1993-1-1 § 6.3

D P

P

Page 22: Skills m08 e_portalframes_singlestoreybuildings

Summarizing the effects of deformed geometry

Taking the deformation of the structure into account generally leads to higher internal forces (shear force) and moments for portal frames.

The lesser the rigidity of the structure is, the higher are the deformation and therefore the 2nd order effects.

cr is representative for the influence of 2nd order effects (high values of cr stand for little influence of 2nd order effects )

22

GLOBAL ANALYSIS

Page 23: Skills m08 e_portalframes_singlestoreybuildings

Second order effects in EN-1993-1-1

First order analysis is permitted if:

for elastic analysis

for plastic analysis

23

GLOBAL ANALYSIS

10cr

15cr

EN 1993-1-1 § 5.2.1

If criterion is not respected 2nd order effects have to be accounted for

Page 24: Skills m08 e_portalframes_singlestoreybuildings

Accounting for second order effects in EN-1993-1-1

2nd order analysis (buckling length = member length) or

1st order analysis followed by amplification of sway effects (buckling length = member length) or

1st order analysis (buckling length according to sway buckling mode)

2nd order analysis (buckling length = member length)

24

GLOBAL ANALYSIS

103 cr

3cr

Page 25: Skills m08 e_portalframes_singlestoreybuildings

Amplification of sway effects

Amplification factor:

Sway effects: Horizontal loads (e.g. wind)

Effects due to imperfection

Effects due to geometry of the structure

25

GLOBAL ANALYSIS

cr

11

1

Page 26: Skills m08 e_portalframes_singlestoreybuildings

Calculation of cr

Simplified formula:

if roof slop is swallow: < 26°

if axial force in the rafter is small: or

26

GLOBAL ANALYSIS

EdH,Ed

Edcr

h

V

H

Ed

y3,0

N

Af crEd 09,0 NN

EN 1993-1-1 § 5.2.1 (4)

h

H,Ed

VEd

HEd

Page 27: Skills m08 e_portalframes_singlestoreybuildings

Practical calulation of cr for portal frames

27

GLOBAL ANALYSIS

VEd Hunit

unit

unitEd

unitcr

h

V

H

VEd

0,5 Hunit 0,5 Hunit 0,25 Hunit 0,5 Hunit 0,25 Hunit

VEd

column.meanunit column.meanunit

h

Page 28: Skills m08 e_portalframes_singlestoreybuildings

IMPERFECTIONS

Page 29: Skills m08 e_portalframes_singlestoreybuildings

Structural imperfections

Due to: lack of verticality

lack of straightness

eccentricities in joints

residual stresses

inhomogeneity of material

Physical imperfection are replaced by equivalent geometric imperfection

29

GLOBAL ANALYSIS

Page 30: Skills m08 e_portalframes_singlestoreybuildings

Equivalent geometric imperfection

Global initial sway imperfection

Local bow imperfection

30

GLOBAL ANALYSIS

f f

e0 e0

Page 31: Skills m08 e_portalframes_singlestoreybuildings

Global sway imperfection

f0: Basic value

h: Reduction factor for the height of the columns

but

m: Reduction factor for the number of columns per row

m is the number of columns carrying at least 50% of the average vertical load of the column row considered

31

GLOBAL ANALYSIS

mh0 ff

200/10 f

h

2h 1

3

2h

m

115,0m

EN 1993-1-1 § 5.3.2

Page 32: Skills m08 e_portalframes_singlestoreybuildings

Direction of sway imperfection

Every possible direction has to be considered, but only one direction in a time

32

GLOBAL ANALYSIS

f f f f

f f f f

Page 33: Skills m08 e_portalframes_singlestoreybuildings

System of equivalent forces replacing out-of-plumb

33

GLOBAL ANALYSIS

f

NEd

NEd

NEd

NEd

fNEd

fNEd

Page 34: Skills m08 e_portalframes_singlestoreybuildings

System of equivalent forces replacing out-of-plumb

34

GLOBAL ANALYSIS

f f

fNEd fNEd

fNEd fNEd

Page 35: Skills m08 e_portalframes_singlestoreybuildings

Possibility of disregarding global frame imperfection

Relatively high horizontal loads

Frame stability check with equivalent column method

(buckling length of columns are based on overall sway buckling mode)

35

GLOBAL ANALYSIS

EdEd 15,0 VH EN 1993-1-1 § 5.3.2

EN 1993-1-1 § 5.2.2

Page 36: Skills m08 e_portalframes_singlestoreybuildings

Local bow imperfection

Local 2nd order effects are generally included in the member verification formulas of EN 1993-1-1 §6.3

Local bow imperfection has to be considered for slender members under high compression axial force

36

GLOBAL ANALYSIS

Page 37: Skills m08 e_portalframes_singlestoreybuildings

If frame is sensitive to 2nd order effects, local bow imperfection has to be applied on:

compressed members that have at least one moment resistant joint and

whose reduced slenderness

is calculated supposing a pin ended column:

And

37

GLOBAL ANALYSIS

Ed

y5,0

N

Af EN 1993-1-1 § 5.3.2

cr

N

fA y EI

LN

2

cr

Page 38: Skills m08 e_portalframes_singlestoreybuildings

Value of local bow imperfection

38

GLOBAL ANALYSIS

e0

Buckling curve Elastic analysis Plastic analysis

e0/L e0/L

a0 1/350 1/300

a 1/300 1/250

b 1/250 1/200

c 1/200 1/150

d 1/150 1/100

EN 1993-1-1 § 5.3.2

Page 39: Skills m08 e_portalframes_singlestoreybuildings

System of equivalent forces replacing local bow imperfection

39

GLOBAL ANALYSIS

NEd

NEd

4NEde0,d/L

4NEde0,d/L

8NEde0,d/L2 e0

NEd

NEd

L

Page 40: Skills m08 e_portalframes_singlestoreybuildings

System of equivalent forces replacing local bow imperfection

40

GLOBAL ANALYSIS

e0 e0

4NEd e0,d/L

4NEd e0,d/L 4NEd e0,d/L

4NEd e0,d/L

8NEde0,d/L2 8NEde0,d/L2 L

Page 41: Skills m08 e_portalframes_singlestoreybuildings

STIFFNESS OF JOINTS

Page 42: Skills m08 e_portalframes_singlestoreybuildings

Rigid joint

42

GLOBAL ANALYSIS

Examples of Joints

Nominally pinned joint

Page 43: Skills m08 e_portalframes_singlestoreybuildings

Classification of joints by stiffness

43

GLOBAL ANALYSIS

Joint A M

f

Joint B

Joint C

EN 1993-1-8 § 5.2.2

Page 44: Skills m08 e_portalframes_singlestoreybuildings

Classification boundaries

44

GLOBAL ANALYSIS

Joint A M

f

Joint B

Joint C

beam

beam5,0L

EI

beam

beamb

L

EIk

Rigid joints

Semi-rigid joints

Nominally pinned joints

EN 1993-1-8 § 5.2.2.5

Page 45: Skills m08 e_portalframes_singlestoreybuildings

Value of kb for the classification of joints

kb = 8 : frames where the bracing system reduces the horizontal displacement by at least 80%

kb = 25 : other frames, provided that in every storey

Kb/Kc ≥ 0,1

Kb: mean value of Ib/Lb for all beams at the top

of the storey

Kc: mean value of Ic/Lc for all columns of the storey

Ic/b: second moment of area of a column/beam

Lc/b: height/length of a column/beam

45

GLOBAL ANALYSIS

Page 46: Skills m08 e_portalframes_singlestoreybuildings

Practical comments

The designer will probably choose the assumption of rigid rafter-to-column joints.

The designer will probably choose the assumption of either pinned or rigid column bases.

The assumptions will have to be checked afterwards.

46

GLOBAL ANALYSIS

Page 47: Skills m08 e_portalframes_singlestoreybuildings

DESIGN PROCEDURE OF PORTAL FRAMES

Page 48: Skills m08 e_portalframes_singlestoreybuildings

Structural stability of frames

cr ≥ 10 :

1st Method:

1st order analysis without imperfections

Column in-plane stability check using buckling length according to sway buckling mode

2nd Method:

1st order analysis with global imperfection

Column in-plane stability check using member length

48

DESIGN PROCEDURE OF PORTAL FRAMES

EN 1993-1-1 § 5.2.2

Page 49: Skills m08 e_portalframes_singlestoreybuildings

Structural stability of frames

cr < 3 :

Check if introduction of local imperfection is necessary

if necessary:

2nd order analysis with global imperfection if necessary

Column in-plane stability check = check of resistance of section

49

DESIGN PROCEDURE OF PORTAL FRAMES

EN 1993-1-1 § 5.2.2

Page 50: Skills m08 e_portalframes_singlestoreybuildings

Structural stability of frames

cr < 3 :

Check if introduction of local imperfection is necessary

if not necessary:

2nd order analysis with global imperfection if necessary

Column in-plane stability check using member length

50

DESIGN PROCEDURE OF PORTAL FRAMES

EN 1993-1-1 § 5.2.2

Page 51: Skills m08 e_portalframes_singlestoreybuildings

Structural stability of frames

3 ≤ cr < 10 :

Check if introduction of local imperfection is necessary

if necessary:

2nd order analysis with global imperfection if necessary

Column in-plane stability check = check of section resistance

51

DESIGN PROCEDURE OF PORTAL FRAMES

EN 1993-1-1 § 5.2.2

Page 52: Skills m08 e_portalframes_singlestoreybuildings

Structural stability of frames

3 ≤ cr < 10 :

Check if introduction of local imperfection is necessary

if not necessary:

1st Method:

1st order analysis without imperfections

Column in-plane stability check using buckling length according to sway buckling mode

Verification of joints and rafters including second order effects (amplification of sway effects)

52

DESIGN PROCEDURE OF PORTAL FRAMES

EN 1993-1-1 § 5.2.2

Page 53: Skills m08 e_portalframes_singlestoreybuildings

Structural stability of frames

3 ≤ cr < 10 :

Check if introduction of local imperfection is necessary

if not necessary:

2nd Method:

1st order analysis with global imperfection if necessary

Amplification of sway effects

Column in-plane stability check using member length

53

DESIGN PROCEDURE OF PORTAL FRAMES

EN 1993-1-1 § 5.2.2

Page 54: Skills m08 e_portalframes_singlestoreybuildings

Buckling length = Member length :

Buckling length according to sway buckling mode :

54

DESIGN PROCEDURE OF PORTAL FRAMES

Lcr

Lcr

Page 55: Skills m08 e_portalframes_singlestoreybuildings

DESIGN PROCEDURE OF PORTAL FRAMES

55

Geometry + Boundary conditions + Loads

Calculation of cr

cr < 3 3 ≤ cr < 10 cr ≥ 10

Slide 57

Slide 59

Slide 58

Page 56: Skills m08 e_portalframes_singlestoreybuildings

DESIGN PROCEDURE OF PORTAL FRAMES

56

Geometry + Boundary conditions + Loads

Calculation of cr

cr ≥ 10

In plane stability check of columns using buckling length according to global buckling mode

1st order analysis

In plane stability check of columns using member length

Global imperfection

Page 57: Skills m08 e_portalframes_singlestoreybuildings

DESIGN PROCEDURE OF PORTAL FRAMES

57

Geometry + Boundary conditions + Loads

Calculation of cr

cr < 3

Global imperfection if necessary: EN 1993-1-1 § 5.3.2 (4)

2nd order analysis

In plane stability check of columns using member length

Local imperfection if necessary: EN 1993-1-1 § 5.3.2 (6)

In plane stability check of columns = resistance check of section

Necessary Not necessary

Page 58: Skills m08 e_portalframes_singlestoreybuildings

Geometry + Boundary conditions + Loads

Calculation of cr

3 ≤ cr < 10

Local imperfection if necessary: EN 1993-1-1 § 5.3.2 (6)

2nd order analysis

In plane stability check of columns using buckling length according to sway buckling

mode

Amplification of sway effects

1st order analysis

In plane stability check of columns using member

length

DESIGN PROCEDURE OF PORTAL FRAMES

58

Global imperfection if necessary: EN 1993-1-1 § 5.3.2 (4)

In plane stability check of columns = resistance

check of section

Not necessary Necessary

Necessary Not necessary

Page 59: Skills m08 e_portalframes_singlestoreybuildings

STABILITY OF COLUMNS AND RAFTERS

Page 60: Skills m08 e_portalframes_singlestoreybuildings

Stability of columns and rafters

Columns and rafters are subjected to axial forces and moments

Use of interaction formula

60

DESIGN PROCEDURE OF PORTAL FRAMES

1

1

,

,,

1

,

,,

1

D

D

M

Rkz

EdzEdzyz

M

RkyLT

EdyEdyyy

M

Rky

Ed

M

MMk

M

MMk

N

N

1

1

,

,,

1

,

,,

1

D

D

M

Rkz

EdzEdzzz

M

RkyLT

EdyEdyzy

M

Rkz

Ed

M

MMk

M

MMk

N

N

EN 1993-1-1 § 6.3.3

Page 61: Skills m08 e_portalframes_singlestoreybuildings

Simplification for common frames

Columns and rafters are not subjected to out-of-plane moments

Columns and rafters are usually double symmetric sections

61

DESIGN PROCEDURE OF PORTAL FRAMES

1

1

,

,

1

M

RkyLT

Edyyy

M

Rky

Ed

M

Mk

N

N

1

1

,

,

1

M

RkyLT

Edyzy

M

Rkz

Ed

M

Mk

N

N

Page 62: Skills m08 e_portalframes_singlestoreybuildings

ROOF BRACING

Page 63: Skills m08 e_portalframes_singlestoreybuildings

63

ROOF BRACING

Photo APK

Page 64: Skills m08 e_portalframes_singlestoreybuildings

64

ROOF BRACING

Rafters

Purlins transmitting horizontal loads to roof bracing

Roof bracing

Page 65: Skills m08 e_portalframes_singlestoreybuildings

Ground view of roof bracing

65

ROOF BRACING

6 Rafters Roof bracing

Purlins transmitting horizontal loads to roof bracing

Page 66: Skills m08 e_portalframes_singlestoreybuildings

Idealisation of roof bracing

66

ROOF BRACING

m rafters whose flanges are subjected to the axial force NEd

(including rafters acting as upper and lower flange of roof bracing)

Roof bracing

Horizontal loads transmitted by purlins

Fexterior NEd

NEd

NEd

NEd

NEd

NEd

NEd

NEd

Page 67: Skills m08 e_portalframes_singlestoreybuildings

Imperfection for roof bracing

67

ROOF BRACING

m rafters whose flanges are subjected to the axial force NEd and that are subjected to imperfection e0

Roof bracing

Horizontal loads due to imperfection e0 and axial forces NEd and to Fexterior

EN 1993-1-1 § 5.3.3

Fexterior NEd

NEd

NEd

NEd

NEd

NEd

NEd

NEd

e0

e0

e0

e0

Page 68: Skills m08 e_portalframes_singlestoreybuildings

Imperfection for roof bracing

68

ROOF BRACING

EdRafter,Section

upFlange

Section

EdRafter,Ed N

A

A

h

MN

500

m0

Le

m

115,0m

Fexterior NEd

NEd

NEd

NEd

NEd

NEd

NEd

NEd

e0

e0

e0

e0

Roof bracing

Horizontal loads due to imperfection e0 and axial forces NEd and to Fexterior

Page 69: Skills m08 e_portalframes_singlestoreybuildings

Calculation of roof bracing

Use of geometric imperfection and 2nd order analysis

Use of equivalent forces and 1st order analysis

69

ROOF BRACING

Fexterior NEd

NEd

NEd

NEd

NEd

NEd

NEd

NEd

e0

e0

e0

e0

Page 70: Skills m08 e_portalframes_singlestoreybuildings

Equivalent load concept

g: deflection of the roof bracing due to exterior load Fexterior and equivalent load qd

iterative calculation of qd

1 or 2 iterations sufficient

70

ROOF BRACING

2

g0d 8

L

eNq Ed

qdL/4

qd

qdL/2 qdL/2

qdL/8 qdL/8 qdL/4 qdL/4

Fexterior

L

Page 71: Skills m08 e_portalframes_singlestoreybuildings

VERTICAL BRACING

Page 72: Skills m08 e_portalframes_singlestoreybuildings

72

VERTICAL BRACING

Photo APK

Page 73: Skills m08 e_portalframes_singlestoreybuildings

Design procedure

Calculation of cr

1st order or 2nd order theory

Determination of horizontal loads

Wind

Loads due to global imperfection if necessary

Calculation of internal forces and moments

Verification of stability in bracing plane

Verification of out of bracing plane stability as before

73

VERTICAL BRACING

Page 74: Skills m08 e_portalframes_singlestoreybuildings

Calculation of cr for vertical bracings

74

VERTICAL BRACING

meantotal

unit

h

V

Hcr

V V V V

Hunit

h

Vtotal

Page 75: Skills m08 e_portalframes_singlestoreybuildings

In-plane loads on vertical bracing

Ntot: Sum of axial forces of all columns stabilized by bracing

H: External horizontal loads

V: Vertical loads on columns

f: Sway imperfection

75

VERTICAL BRACING

Ntotf + H

Ntotf

V V

Page 76: Skills m08 e_portalframes_singlestoreybuildings

CONCLUSION

Page 77: Skills m08 e_portalframes_singlestoreybuildings

Generally 2nd order effects and imperfections have to be accounted for in the design of portal frames.

Depending on the value of cr different calculation methods can be adopted.

For portal frames it is convenient to account for global imperfection and global 2nd order effects in the global analysis.

77

CONCLUSION

Page 78: Skills m08 e_portalframes_singlestoreybuildings

Local 2nd order effects are generally included in the member verification formulas of EN 1993-1-1 §6.3.

Physical imperfections are replaced by either equivalent geometric imperfections or equivalent loads.

Bracing systems are subjected to external horizontal loads and loads due to their function as stabilizing elements.

78

CONCLUSION

Page 79: Skills m08 e_portalframes_singlestoreybuildings

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.