1

Chair for Metal Structures

M. Sc. Thesis

Erik Zupančič

TABLE OF CONTENTS INTRODUCTION EUROCODE 3 - ANNEX J ROTATION CAPACITY COMPONENTS NUMERICAL EXAMPLE CONCLUSIONS

ROTATION CAPACITY OF SEMI RIGID CONNECTIONS

Faculty for Civil and Geodetic Engineering at University in Ljubljana

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TABLE OF CONTENTS INTRODUCTION EUROCODE 3 - ANNEX J ROTATION CAPACITY COMPONENTS NUMERICAL EXAMPLE CONCLUSIONS

M. Sc. Thesis: Rotation capacity of semi rigid connections (by Erik Zupančič)

- INTRODUCTION

- EUROCODE 3 – ANNEX J AND ROTATION CAPACITY

- ROTATION CAPACITY

- CHARACTERISTICS OF COMPONENTS

- NUMERICAL EXAMPLE

- CONCLUSIONS

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TABLE OF CONTENTS INTRODUCTION EUROCODE 3 - ANNEX J ROTATION CAPACITY COMPONENTS NUMERICAL EXAMPLE CONCLUSIONS

M. Sc. Thesis: Rotation capacity of semi rigid connections (by Erik Zupančič)

- STATIC SYSTEM

- YESTERDAY

- Pinned connections

- Rigid connections

- TODAY

- Semi rigid connections

(rotation springs)

q

pinned

semi rigid

rigid

pinned

rigid

semi rigid

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TABLE OF CONTENTS INTRODUCTION EUROCODE 3 - ANNEX J ROTATION CAPACITY COMPONENTS NUMERICAL EXAMPLE CONCLUSIONS

M. Sc. Thesis: Rotation capacity of semi rigid connections (by Erik Zupančič)

- ENV 1993: Design of steel structures, Part 1.1: General rules for buildings, Annex J: Joints in building frames

- Classification of connections by stiffness

- Classification of connections by strength

- Characteristics of connections (diagram rotation – moment)

- Resistance of connections

- Initial rotational stiffness

- Rotation capacity

Mj

2/3 Mj

y

Cd

M

Sj

Rotationcapacity

5

TABLE OF CONTENTS INTRODUCTION EUROCODE 3 - ANNEX J ROTATION CAPACITY COMPONENTS NUMERICAL EXAMPLE CONCLUSIONS

M. Sc. Thesis: Rotation capacity of semi rigid connections (by Erik Zupančič)

- Classification of connections by stiffness

KS inij 8,

b

b

L

IEK

Ib – Second moment of area of a beam

Lb – span of a beam

1. Rigid connections: 2. Semi rigid connections: 3. Pinned connections:

1

2

3

M Braced frames Unbraced frames

KS inij 5.0,

KS inij 25,

KS inij 5.0,

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TABLE OF CONTENTS INTRODUCTION EUROCODE 3 - ANNEX J ROTATION CAPACITY COMPONENTS NUMERICAL EXAMPLE CONCLUSIONS

M. Sc. Thesis: Rotation capacity of semi rigid connections (by Erik Zupančič)

- Classification of connections by strength

M

Full strength connections

Partial strength connections

Pinned connections

Plastic hinge

Full strength

Plastic hinge

Partial strength

beamplM

beamplM25.0

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TABLE OF CONTENTS INTRODUCTION EUROCODE 3 - ANNEX J ROTATION CAPACITY COMPONENTS NUMERICAL EXAMPLE CONCLUSIONS

M. Sc. Thesis: Rotation capacity of semi rigid connections (by Erik Zupančič)

- Component method

Column web in tension

Qsd

Msd

Column flange andEnd plate in bending

Column web in shear

Column web in compression

Connection

Components of connection

FRd,i , ki

ConnectionMj , Sj

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TABLE OF CONTENTS INTRODUCTION EUROCODE 3 - ANNEX J ROTATION CAPACITY COMPONENTS NUMERICAL EXAMPLE CONCLUSIONS

M. Sc. Thesis: Rotation capacity of semi rigid connections (by Erik Zupančič)

M

a

b

c

a

b

F

F

c

c

F

F1

F3

F2

b

a

M

M2

M3

M1

Components

Connection

- Rotation capacity

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TABLE OF CONTENTS INTRODUCTION EUROCODE 3 - ANNEX J ROTATION CAPACITY COMPONENTS NUMERICAL EXAMPLE CONCLUSIONS

M. Sc. Thesis: Rotation capacity of semi rigid connections (by Erik Zupančič)

- Characteristics of components

F

Fi

2/3 Fi

Si

u uyy

- for:

Column web in compression

Column web in tension

Column flange in bending

End plate in bending

- for:

Column web in shear

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TABLE OF CONTENTS INTRODUCTION EUROCODE 3 - ANNEX J ROTATION CAPACITY COMPONENTS NUMERICAL EXAMPLE CONCLUSIONS

M. Sc. Thesis: Rotation capacity of semi rigid connections (by Erik Zupančič)

- Deformation capacity of column web in compression

- Axial force (0% Npl - 50% Npl)

- Slenderness d/tw (10 - 60)

dh

beff

F

F

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TABLE OF CONTENTS INTRODUCTION EUROCODE 3 - ANNEX J ROTATION CAPACITY COMPONENTS NUMERICAL EXAMPLE CONCLUSIONS

M. Sc. Thesis: Rotation capacity of semi rigid connections (by Erik Zupančič)

- Modelling with program ABAQUS

- Material – Results of numerical simulation

- Initial geometric imperfection – Results of numerical simulation

- Number of elements – Results of numerical simulation

- Type of elements – Results of numerical simulation

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TABLE OF CONTENTS INTRODUCTION EUROCODE 3 - ANNEX J ROTATION CAPACITY COMPONENTS NUMERICAL EXAMPLE CONCLUSIONS

M. Sc. Thesis: Rotation capacity of semi rigid connections (by Erik Zupančič)

- Numerical analysis

Sila prečno na nosilec v odvisnosti od pomika

0

200

400

600

800

1000

1200

1400

1600

0 2 4 6 8 10 12 14 16

Pomik [mm]

Sil

a [k

N]

n = 10%

n = 20%

n = 30%

n = 40%

n = 50%

n = 0%

ABAQUS

d/tw = 27.13

Displacement [mm]

Displacement - Force

For

ce [k

N]

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TABLE OF CONTENTS INTRODUCTION EUROCODE 3 - ANNEX J ROTATION CAPACITY COMPONENTS NUMERICAL EXAMPLE CONCLUSIONS

M. Sc. Thesis: Rotation capacity of semi rigid connections (by Erik Zupančič)

- Determination of expressionsDeformacija stojine stebra v tlaku eps_u

0

2

4

6

8

10

12

10 15 20 25 30 35 40 45 50 55 60

Razmerje višine in debeline stojine (d/(tw eps))

eps_

u [

%]

n = 0%n = 10%n = 20%n = 30%n = 40%n = 50%Abaqus_n0Abaqus_n10Abaqus_n20Abaqus_n30Abaqus_n40Abaqus_n50

duu

13307.2

331

201

11.07.5

2011

75.05.18

%0

w

ww

ww

u

t

dfor

t

dfor

t

d

t

dfor

t

d

n

13317.1

331

201

11.08.4

201

5.01

75.0151

34.04.9

%1.0

w

ww

www

u

t

dfor

t

dfor

t

d

t

dforn

t

d

t

d

n

Limit deformations

Slenderness

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TABLE OF CONTENTS INTRODUCTION EUROCODE 3 - ANNEX J ROTATION CAPACITY COMPONENTS NUMERICAL EXAMPLE CONCLUSIONS

M. Sc. Thesis: Rotation capacity of semi rigid connections (by Erik Zupančič)

- Deformation capacity expressions of components

duu 22

0 2

34

nnu

nfornt

d

t

d

nfort

d

ww

w

u

10.01.01

81.0551

38.028

10.001

38.028

%'

14.0

1

11

2

b

afor

n

a

b

b

afor

KKuu '

duu

13307.2

331

201

11.07.5

2011

75.05.18

%0

w

ww

ww

u

t

dfor

t

dfor

t

d

t

dfor

t

d

n

13317.1

331

201

11.08.4

201

5.01

75.0151

34.04.9

%1.0

w

ww

www

u

t

dfor

t

dfor

t

d

t

dforn

t

d

t

d

n

mu 40.0

n

mklbu 110.0

bu l 10.0

(mode 1) (mode 2) (mode 3)

Column web in compression

Column web in shear

Column web in tension

Column flange andend plate in bending

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TABLE OF CONTENTS INTRODUCTION EUROCODE 3 - ANNEX J ROTATION CAPACITY COMPONENTS NUMERICAL EXAMPLE CONCLUSIONS

M. Sc. Thesis: Rotation capacity of semi rigid connections (by Erik Zupančič)

- Numerical example (rotation capacity = ?)

20

40120

200

30

40

55

220

20

55

420

6

3

6HE

B 3

20

IPE 330

40

M

Material: S 235 Bolts: M20 (8.8)

Annex – J (resistance, initial stiffness), M. Sc. Thesis (limit displacement)

kNV Rdwp 425,

kNF Rdwcc 519,,

kNF RdT 202,

kNF RdT 229,

kNF Rdwct 366,,

kNF Rdwcc 519,, kNF Rdwcc 519,,

cmkNS /18541 cmuc 855.0Compression

Tension

End plate

Column flange

Shear

Diagrams

cmKNS /10483 cmut 25.2

cmkNS /31849 cmu 71.0

cmkNS /26473 cmu 864.0

radu 207.0radkNS /305397

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TABLE OF CONTENTS INTRODUCTION EUROCODE 3 - ANNEX J ROTATION CAPACITY COMPONENTS NUMERICAL EXAMPLE CONCLUSIONS

M. Sc. Thesis: Rotation capacity of semi rigid connections (by Erik Zupančič)

- Numerical example (rotation capacity = ?)

kNF Rdwcc 519,,

Compression

Tension

End plate Column flangeShear

202 kN

202 kN

202 kN202 kN

202 kN

Compression

End plate

Shear

Cd

cm011.0

cm019.0

cm459.0

cm864.0

rad00066.075.91

004.0

043.0

y

Cd

y

Cd

R

rad

rad

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TABLE OF CONTENTS INTRODUCTION EUROCODE 3 - ANNEX J ROTATION CAPACITY COMPONENTS NUMERICAL EXAMPLE CONCLUSIONS

M. Sc. Thesis: Rotation capacity of semi rigid connections (by Erik Zupančič)

- Conclusions

- 3D numerical model

- Initial geometric imperfection

- Material characteristics

- Column web in compression

- Expected results (bigger axial force, biger

slenderness – smaller limit displacement)

- Column web in tension

- Comparision of expressions with numerical simulation

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TABLE OF CONTENTS INTRODUCTION EUROCODE 3 - ANNEX J ROTATION CAPACITY COMPONENTS NUMERICAL EXAMPLE CONCLUSIONS

M. Sc. Thesis: Rotation capacity of semi rigid connections (by Erik Zupančič)

- Column web in shear

- Expected results (bigger axial force, smaller

ratio height/width of panel – smaller limit rotation)

- Column flange and end plate in bending

- Equivalent T – Stub (three different modes)

- Mode 1 (plastification of plate)

- Mode 2 (plastification of plate and bolt)

- Mode 3 (plastification of bolt)

- Comparision of expressions with numerical simulation

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TABLE OF CONTENTS INTRODUCTION EUROCODE 3 - ANNEX J ROTATION CAPACITY COMPONENTS NUMERICAL EXAMPLE CONCLUSIONS

M. Sc. Thesis: Rotation capacity of semi rigid connections (by Erik Zupančič)

- Component method

- Simple calculation of rotation capacity of connection

- Difficult calculation of all three characteristics of connection

- Good results (comparision of method results with test results)

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TABLE OF CONTENTS INTRODUCTION EUROCODE 3 - ANNEX J ROTATION CAPACITY COMPONENTS NUMERICAL EXAMPLE CONCLUSIONS

M. Sc. Thesis: Rotation capacity of semi rigid connections (by Erik Zupančič)

- Future work

- Method of expansion on all types of connections

- 3D numerical simulation of complete connection

- More experimental tests

- Comparision of several calculated examples with tests

- Behaviour of components and expressions

- Parametric studies of influence of components on connections

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Chair for Metal Structures

M. Sc. Thesis

Erik Zupančič

TABLE OF CONTENTS INTRODUCTION EUROCODE 3 - ANNEX J ROTATION CAPACITY COMPONENTS NUMERICAL EXAMPLE CONCLUSIONS

ROTATION CAPACITY OF SEMI RIGID CONNECTIONS

Faculty for Civil and Geodetic Engineering at University in Ljubljana