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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
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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
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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 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