Apollo Bridge

Architect: Ing. Miroslav Maťaščík - Alfa 04 a.s., Bratislava

Design: Dopravoprojekt a.s., Bratislava

Apollo Bridge

Architect: Ing. Miroslav Maťaščík - Alfa 04 a.s., Bratislava

Design: DOPRAVOPROJEKT a.s., Bratislava

Aluminium & Cold-Formed Steel

in Scia Engineer

User Meeting Salzburg 5 november 2010 ing. Peter Van Tendeloo – Product Development Engineer

1

Contents

1. National Annex for Steel and Aluminium

2. Aluminium according to EN 1999-1-1

3. Cold-formed steel according to EN 1993-1-3

4. Small improvements in Steel

5. Benchmarks EN 1993

2

National Annex

1. National Annex for Steel and Aluminium

3

National Annex

4

National Annex

- What has been implemented?

- Which method is supported?

- How exactly is this parameter used?

-…

=> Theoretical Backgrounds

5

National Annex

6

Aluminium

2. Aluminium according to EN 1999-1-1

7

Aluminium

General design differences between Steel and Aluminium:

Steel Aluminium

- Welds are strong points - Welds weaken the material

- Classification for combined effects - Separate classification per component

- Effective width - Effective thickness

- Buckling curve depending on section - Buckling curve depending on material

(only slightly on material)

8

Aluminium

Effect of welds

Material properties according to art. 3.2.2

Theory

9

Aluminium

Effect of welds

Material properties according to art. 3.2.2

Scia Engineer

10

Aluminium

Classification

Classification according to art. 6.1.4

Theory – Definition of cross-section parts

11

Aluminium

Classification

Classification according to art. 6.1.4

Theory – Definition of slenderness limits

12

Aluminium

Classification

Classification according to art. 6.1.4

Scia Engineer – Definition of initial shape & welds

13

Aluminium

Classification

Classification according to art. 6.1.4

Scia Engineer – Slenderness limits and classification for N-

14

Aluminium

Effective section

Effective section according to art. 6.1.4

Theory – Reduction factors

The following reduction factors are calculated:

1. Local Buckling: Reduction factor ,c

2. Distortional Buckling: Reduction factor

3. HAZ effects: Reduction factor ,HAZ

Additional reduction for

distortional buckling:

15

Aluminium

Effective section

Effective section according to art. 6.1.4

Theory – Local Buckling ,c

16

Aluminium

Effective section

Effective section according to art. 6.1.4 & TALAT Lecture 2301

Theory – Distortional Buckling

17

Aluminium

Effective section

Effective section according to art. 6.1.4 & TALAT Lecture 2301

Theory – Distortional Buckling

18

Aluminium

Effective section

Effective section according to art. 6.1.4

Theory – Welding Effects ,HAZ

MIG:

TIG:

19

Aluminium

Effective section

Effective section according to art. 6.1.4

Theory – Effective section

Additional reduction for

distortional buckling:

20

Aluminium

Effective section

Effective section according to art. 6.1.4

Scia Engineer – Effective section for N-

Section with weld in the middle of the web

21

Aluminium

Effective section

Effective section according to art. 6.1.4

Scia Engineer – Effective section for My+

Section with weld in the middle of the web

22

Aluminium

Effective section

Effective section according to art. 6.1.4

Scia Engineer – Effective sections

Initial Shape Effective shape N- Effective shape My+

23

Aluminium

Effective section

Effective section according to art. 6.1.4

Scia Engineer – Effective section properties

24

Aluminium

Effective section

Effective section according to art. 6.1.4

Scia Engineer – General Cross-section

Gross section

Used for gross-section properties

Thinwalled representation

Used for classification and effective section properties

25

Aluminium

Effective section

Effective section according to art. 6.1.4

Scia Engineer – General Cross-section

26

Aluminium

Effective section

Effective section according to art. 6.1.4

Scia Engineer – General Cross-section

27

Aluminium

Section Checks

Section Checks according to EN 1999-1-1

art. 6.2.3. Tension

art. 6.2.4. Compression

art. 6.2.5. Bending Moment

art. 6.2.6. Shear

art. 6.2.7. Torsion

art. 6.2.8. Bending and shear

art. 6.2.9. Bending and axial force

art. 6.2.10. Bending , shear and axial force

28

Aluminium

Section Checks

Bending Check according to art. 6.2.5

Theory

These are NOT National Annex Parameters !!!

29

Aluminium

Section Checks

Bending Check according to art. 6.2.5

Scia Engineer

Choice of alternative values:

30

Aluminium

Section Checks

Bending Check according to art. 6.2.5

Scia Engineer

Default Alternative

31

Aluminium

Section Checks

Shear Check according to art. 6.2.6

Theory

General theory according to art. 6.5.5

32

Aluminium

Section Checks

Shear Check according to art. 6.2.6 & 6.5.5

Scia Engineer

Section with no slender elements Section with slender elements

33

Aluminium

Section Checks

Bending and axial force according to art. 6.2.9

Theory

34

Aluminium

Section Checks

Bending and axial force according to art. 6.2.9

Theory

35

Aluminium

Section Checks

Bending and axial force according to art. 6.2.9

Scia Engineer – No Transverse weld

36

Aluminium

Section Checks

Bending and axial force according to art. 6.2.9

Scia Engineer – Input of Transverse weld

37

Aluminium

Section Checks

Bending and axial force according to art. 6.2.9

Scia Engineer – With Transverse weld

38

Aluminium

Stability Checks

Stability Checks according to EN 1999-1-1

art. 6.3.1. Members in compression

art. 6.3.2. Members in bending

art. 6.3.3. Members in bending and axial compression

art. 6.7.4.2, 6.7.6.1 Shear buckling

39

Aluminium

Stability Checks

Members in compression according to art. 6.3.1

Theory – Flexural Buckling

40

Aluminium

Stability Checks

Members in compression according to art. 6.3.1

Scia Engineer – Flexural Buckling

41

Aluminium

Stability Checks

Members in compression according to art. 6.3.1

Theory – Torsional (-Flexural) Buckling

General Theory

42

Aluminium

Stability Checks

Members in compression according to art. 6.3.1

Theory – Torsional (-Flexural) Buckling

43

Aluminium

Stability Checks

Members in compression according to art. 6.3.1

Scia Engineer – Torsional (-Flexural) Buckling

44

Aluminium

Stability Checks

Members in bending and axial compression according to art. 6.3.3

Theory

45

Aluminium

Stability Checks

Members in bending and axial compression according to art. 6.3.3

Theory - Welds

46

Aluminium

Stability Checks

Members in bending and axial compression according to art. 6.3.3

Theory – Design factors and xs distance

47

Aluminium

Stability Checks

Members in bending and axial compression according to art. 6.3.3

Scia Engineer

48

Aluminium

Stability Checks

Members in bending and axial compression according to art. 6.3.3

Scia Engineer – Determination of xs

Choice of method:

xs is the distance from the studied section to a simple support or point of contra flexure of the

deflection curve for elastic buckling of axial force only

49

Aluminium

Stability Checks

Members in bending and axial compression according to art. 6.3.3

Scia Engineer – Determination of xs

50

Aluminium

National Annex

Few countries have published an NA to EN 1999-1-1 and those who have do not diverge of the EN defaults.

51

Aluminium

Theoretical Background

- What has been implemented?

- Which method is supported?

- How exactly is this parameter used?

-…

=> Theoretical Backgrounds

52

Cold-Formed

3. Cold-Formed steel according to EN 1993-1-3

53

Cold-Formed

Materials

54

Cold-Formed

Cross-section

Example: Sadef C 200 x 3.00 S390GD + Z

Core thickness EN 1993-1-3 art. 3.2.4 due to zinc coating

Nominal thickness 3 mm

Core thickness = 2,96 mm

This thickness must be used in design !

Recalculated properties of the gross section

55

Cold-Formed

May EN 1993-1-3 be applied?

May EN 1993-1-3 be applied without additional tests?

Remark: the condition for the core thickness is a Nationally Determined Parameter !

Default EN:

Austrian National Annex:

Dutch National Annex:

German National Annex:

Scia Engineer

Choice of NA

a) Condition for the core thickness: EN 1993-1-3 art. 3.2.4(1)

56

Cold-Formed

May EN 1993-1-3 be applied?

May EN 1993-1-3 be applied without additional tests?

c) Conditions for the stiffeners: EN 1993-1-3 art. 5.2(2)

b) Conditions for the section geometry: EN 1993-1-3 art. 5.2(1)

57

Cold-Formed

May EN 1993-1-3 be applied?

May EN 1993-1-3 be applied without additional tests?

Scia Engineer

58

Cold-Formed

Effective section

The calculation of the effective section can be split in the following steps:

A) Determination of the notional width of the elements

B) Local buckling of the elements in compression

C) Distortional buckling of the stiffeners with optional iterations

D) Optional: Iterative calculation of the full cross-section

59

Cold-Formed

A) Determination of the notional width

Influence of rounded corners according to EN 1993-1-3 art. 5.1

Theory

60

Cold-Formed

A) Determination of the notional width

Influence of rounded corners according to EN 1993-1-3 art. 5.1

Scia Engineer

Generation of the initial shape

61

Cold-Formed

A) Determination of the notional width

Influence of rounded corners according to EN 1993-1-3 art. 5.1

Scia Engineer

Generation of the initial shape and calculation of the notional width

62

Cold-Formed

B) Local buckling of elements in compression

Local buckling according to EN 1993-1-5 art. 4.4

Theory

Warning: Correction sheet EN 1993-1-5:2006/AC:2009

Local buckling according to EN 1993-1-3 art. 5.5.2

63

Cold-Formed

B) Local buckling of elements in compression

Local buckling according to EN 1993-1-5 art. 4.4

Scia Engineer

Calculation of the effective width for My-

64

Cold-Formed

C) Distortional buckling of stiffeners with optional iterations

Distortional buckling according to EN 1993-1-3 art. 5.5.3

Theory

The real geometry is replaced by an equivalent system with translation spring K

65

Cold-Formed

C) Distortional buckling of stiffeners with optional iterations

Distortional buckling according to EN 1993-1-3 art. 5.5.3

Theory

The effective geometry of the stiffener and the translation spring K are used

for the calculation of the critical buckling stress cr,s of the stiffener.

Default formula for the critical buckling stress of a “beam on elastic foundation”

66

Cold-Formed

C) Distortional buckling of stiffeners with optional iterations

Distortional buckling according to EN 1993-1-3 art. 5.5.3

Theory

The critical buckling stress cr,s of the stiffener is used for the calculation of

the relative slenderness and the reduction factor d.

67

Cold-Formed

C) Distortional buckling of stiffeners with optional iterations

Distortional buckling according to EN 1993-1-3 art. 5.5.3

Theory – General procedure

68

Cold-Formed

C) Distortional buckling of stiffeners with optional iterations

Distortional buckling according to EN 1993-1-3 art. 5.5.3

Theory – General procedure

69

Cold-Formed

C) Distortional buckling of stiffeners with optional iterations

Distortional buckling according to EN 1993-1-3 art. 5.5.3

Theory – General procedure – Remark

Remark: the safety factors are Nationally Determined Parameters !

Default EN:

Austrian National Annex:

Dutch National Annex:

German National Annex:

Scia Engineer

Choice of NA

70

Cold-Formed

C) Distortional buckling of stiffeners with optional iterations

Distortional buckling according to EN 1993-1-3 art. 5.5.3

Scia Engineer

Optional iterations of the stiffeners

Distortional buckling of the stiffeners with influence on local buckling

71

Cold-Formed

D) Optional: Iterative calculation of the full cross-section

Iterations of the full cross-section according to EN 1993-1-3 art. 5.5.2

Theory

72

Cold-Formed

D) Optional: Iterative calculation of the full cross-section

Iterations of the full cross-section according to EN 1993-1-3 art. 5.5.2

Scia Engineer

Optional iterations of the full cross-section

Final effective section

Effective section properties

73

Cold-Formed

D) Optional: Iterative calculation of the full cross-section

Iterations of the full cross-section according to EN 1993-1-3 art. 5.5.2

Scia Engineer

Final effective section

74

Cold-Formed

Effective section

Scia Engineer – General Cross-section

Input of any thinwalled shape Calculation of effective section

75

Cold-Formed

Section Checks

Section Checks according to EN 1993-1-3

art. 6.1.2. Axial Tension

art. 6.1.3. Axial Compression

art. 6.1.4. Bending Moment

art. 6.1.5. Shear Force

art. 6.1.6. Torsional Moment

art. 6.1.7. Local Transverse Forces

art. 6.1.8. Combined Tension and Bending

art. 6.1.9. Combined Compression and Bending

art. 6.1.10. Combined Shear, Axial force and Bending Moment

art. 6.1.11. Combined Bending and Local Transverse Force

76

Cold-Formed

Section Checks

Bending Check according to EN 1993-1-3 art. 6.1.4

Theory

77

Cold-Formed

Section Checks

Bending Check according to EN 1993-1-3 art. 6.1.4

Scia Engineer

78

Cold-Formed

Section Checks

Shear Check according to EN 1993-1-3 art. 6.1.5

Theory

79

Cold-Formed

Section Checks

Shear Check according to EN 1993-1-3 art. 6.1.5

Scia Engineer

80

Cold-Formed

Section Checks

Local Transverse Forces Check according to EN 1993-1-3 art. 6.1.7

Theory

81

Cold-Formed

Section Checks

Local Transverse Forces Check according to EN 1993-1-3 art. 6.1.7

Scia Engineer

Default Bearing Length in the Steel Setup:

Advanced modifications through additional data:

82

Cold-Formed

Section Checks

Local Transverse Forces Check according to EN 1993-1-3 art. 6.1.7

Scia Engineer

83

Cold-Formed

Section Checks

Combined Bending and Local Transverse Force according to EN 1993-1-3 art. 6.1.11

Theory

84

Cold-Formed

Section Checks

Combined Bending and Local Transverse Force according to EN 1993-1-3 art. 6.1.11

Scia Engineer

85

Cold-Formed

Stability Checks

Stability Checks according to EN 1993-1-3

art. 6.2.2. Flexural buckling

art. 6.2.3. Torsional and Torsional-Flexural buckling

art. 6.2.4. Lateral-Torsional buckling

art. 6.2.5. Bending and axial compression

art. 6.3. Bending and axial tension

86

Cold-Formed

Stability Checks

Bending and axial compression according to EN 1993-1-3 art. 6.2.5

Theory

Note: This is not a National Annex Parameter !

87

Cold-Formed

Stability Checks

Bending and axial compression according to EN 1993-1-3 art. 6.2.5

Scia Engineer

88

Cold-Formed

Stability Checks

Bending and axial tension according to EN 1993-1-3 art. 6.3

Theory

Theory according to AISI NAS 2007 art. C5

89

Cold-Formed

Stability Checks

Bending and axial tension according to EN 1993-1-3 art. 6.3

Scia Engineer

90

Cold-Formed

Special condiderations for beams (purlins) restrained by sheeting

Theory

May EN 1993-1-3 Chapter 10 be applied?

a) Conditions for cross-section dimensions: EN 1993-1-3 art. 10.1.1(1)

b) Condition for the shear stiffness of the diaphragm: EN 1993-1-3 art. 10.1.1(6)

91

Cold-Formed

Special condiderations for beams (purlins) restrained by sheeting

Scia Engineer

May EN 1993-1-3 Chapter 10 be applied?

Calculation of the shear stiffness using test data of the manufacturer:

92

Cold-Formed

Special condiderations for beams (purlins) restrained by sheeting

Theory

Beam restrained by sheeting – Principle according to EN 1993-1-3 art. 10.1.2

The purlin, restrained by sheeting, is replaced by a beam on elastic foundation

Compare with the calculation of distortional buckling: same principle!

93

Cold-Formed

Special condiderations for beams (purlins) restrained by sheeting

Theory

Beam restrained by sheeting – Resistance of the cross-section according to EN 1993-1-3 art. 10.1.4.1

94

Cold-Formed

Special condiderations for beams (purlins) restrained by sheeting

Theory

Beam restrained by sheeting – Resistance of the cross-section according to EN 1993-1-3 art. 10.1.4.1

a) Determine the geometry of the ‘free flange’

b) Determine the equivalent horizontal loading

95

Cold-Formed

Special condiderations for beams (purlins) restrained by sheeting

Theory

Beam restrained by sheeting – Resistance of the cross-section according to EN 1993-1-3 art. 10.1.4.1

c) Determine the lateral spring stiffness

96

Cold-Formed

Special condiderations for beams (purlins) restrained by sheeting

Theory

Beam restrained by sheeting – Resistance of the cross-section according to EN 1993-1-3 art. 10.1.4.1

d) Determine the equivalent bending moment

Remark: The table only gives some values, for an exact calculation the theory of Winkler

may be used for beams on elastic foundation.

97

Cold-Formed

Special condiderations for beams (purlins) restrained by sheeting

Theory

Beam restrained by sheeting – Resistance of the cross-section according to EN 1993-1-3 art. 10.1.4.1

d) Determine the equivalent bending moment

=> See Theoretical Background for other solutions

98

Cold-Formed

Special condiderations for beams (purlins) restrained by sheeting

Scia Engineer

Beam restrained by sheeting – Resistance of the cross-section according to EN 1993-1-3 art. 10.1.4.1

Calculation of the rotational stiffness of the sheeting:

Geometry of the „free flange‟:

99

Cold-Formed

Special condiderations for beams (purlins) restrained by sheeting

Scia Engineer

Beam restrained by sheeting – Resistance of the cross-section according to EN 1993-1-3 art. 10.1.4.1

100

Cold-Formed

Special condiderations for beams (purlins) restrained by sheeting

Theory

Beam restrained by sheeting – Buckling resistance of the free flange according to EN 1993-1-3 art. 10.1.4.2

Remark: the method for LT concerns a Nationally Determined Parameter !

British National Annex:

Austrian National Annex:

Scia Engineer

Choice of NA

101

Cold-Formed

Special condiderations for beams (purlins) restrained by sheeting

Theory

Beam restrained by sheeting – Buckling resistance of the free flange according to EN 1993-1-3 art. 10.1.4.2

102

Cold-Formed

Special condiderations for beams (purlins) restrained by sheeting

Scia Engineer

Beam restrained by sheeting – Buckling resistance of the free flange according to EN 1993-1-3 art. 10.1.4.2

103

Cold-Formed

Theoretical Background

- What has been implemented?

- Which method is supported?

- How exactly is this parameter used?

-…

=> Theoretical Backgrounds

104

Small Improvements

4. Small improvements in Steel

105

Small Improvements

Scia Engineer

Table for defining the reduction of the yield strength in function of the thickness

106

Small Improvements

Scia Engineer

Re-organisation of the Steel tree

107

Small Improvements

Scia Engineer

Clear outputs of the stability checks

108

Small Improvements

Scia Engineer

Shortened outputs of the stability checks

109

Small Improvements

Scia Engineer

LTB outputs for CHS and RHS sections

CHS sections

RHS sections

110

Small Improvements

Theory

Modified Design rule for LTB of Channel sections

111

Small Improvements

Scia Engineer

Modified Design rule for LTB of Channel sections

112

Small Improvements

Theory – EN 1993-1-1 art. 5.2.2(7)

2nd order: Buckling lengths taken equal to system lengths

113

Small Improvements

Scia Engineer

2nd order: Buckling lengths taken equal to system lengths

All non-sway

l = L

114

Small Improvements

Theory – EN 1993-1-3 art. 5.5.1(7)

Cold-Formed: Manual input of buckling stresses

115

Small Improvements

Theory – EN 1993-1-3 art. 5.5.1(7)

Cold-Formed: Manual input of buckling stresses

116

Small Improvements

Theory

Cold-Formed: Manual input of buckling stresses

Calculation of Local and Distortional Buckling stresses using for example CUFSM

117

Small Improvements

Theory

Cold-Formed: Manual input of buckling stresses

Calculation of Local and Distortional Buckling stresses using for example CUFSM

118

Small Improvements

Scia Engineer

Cold-Formed: Manual input of buckling stresses

Input of Local and Distortional Buckling stresses

119

Small Improvements

Scia Engineer

Cold-Formed: Manual input of buckling stresses

120

Benchmarks

5. Benchmarks EN 1993

121

Benchmarks

122

Benchmarks

123

Benchmarks

124

Benchmarks

125

Benchmarks

126

Thank You

Thank you for your attention!