Helsinki University of Technology Laboratory of Steel Structures Publications 33 Teknillisen korkeakoulun teräsrakennetekniikan laboratorion julkaisuja 31 Espoo 2007
TKK-TER-33
DESIGN OF STRUCTURAL CONNECTIONS TO EUROCODE Preview of MS Power Point presentations F. Wald
AB
TEKNILLINEN KORKEAKOULU TEKNISKA HÖGSKOLAN HELSINKI UNIVERSITY OF TECHNOLOGY TECHNISCHE UNIVERSITÄT HELSINKI UNIVERSITE DE TECHNOLOGIE D’HELSINKI
List of Lessons Lessons at Seminar Seminar
Introduction Lessons Connection Design accordi ng to EN 19931993-1-8 1-8 Prof. František Wald Czech Technical Technical University in Prague Prague
1. 2. 3. 4. 5. 6. 7. 8. 9.
Intr ntroduc oducttion ion Bases Bases of of desig designn accord according ing to EN EN 19931993-1-8 1-8 Weld Welded ed conn connec ectition onss Bolte oltedd conn connec ecttions ions Basi Basics cs of stru struct ctur ural al join joints ts Desi Design gn of of simp simple le con conne nect ctio ions ns Colum lumn bases Fire Fire desig designn of connec connectio tions, ns, EN 1993 1993-1-1-22 Seis Seismi micc desi design gn,, EN 1998 1998-1 -1-1 -1
1
Summary
List of content Timing National Annexes CeStruCo Access STEEL Summary
2
List of Content Content in EN 1993-1-8 1993-1-8 1. 2. 3. 4. 5. 6. 7.
Lessons in Window Help Format with PP Presentations
CeStruCo
Introduction Bas Basis of des design ign Connec Connectio tions ns made made with with bolt bolts, s, rivet rivetss or pins pins Weld Welded ed conn connec ectition onss Analys Analysis, is, classi classific ficati ation on and and mode modellin llingg Struct Structura urall join joints ts connec connectin tingg H or I sections Holl Hollow ow sec sectition on joi joint ntss
3
Summary
List of content Timing National Annexes CeStruCo Access STEEL Summary
4
Development of Eurocodes
Lessons in Window Help Format with PP Presentations
CeStruCo
ECCS Concept in 1978 ECCS First draft in 1984 CEN Started with Eurocodes in 1990 CEN ENV 199x-x-x in 1992 (actions nationally only) CEN EN 199x-x-x in 2005 Advantages
Weakness
5
European agreement All structural materials under one safety concept Copyrights Size (some countries only rules, some textbooks) 6
List of Lessons Lessons at Seminar Seminar
Introduction Lessons Connection Design accordi ng to EN 19931993-1-8 1-8 Prof. František Wald Czech Technical Technical University in Prague Prague
1. 2. 3. 4. 5. 6. 7. 8. 9.
Intr ntroduc oducttion ion Bases Bases of of desig designn accord according ing to EN EN 19931993-1-8 1-8 Weld Welded ed conn connec ectition onss Bolte oltedd conn connec ecttions ions Basi Basics cs of stru struct ctur ural al join joints ts Desi Design gn of of simp simple le con conne nect ctio ions ns Colum lumn bases Fire Fire desig designn of connec connectio tions, ns, EN 1993 1993-1-1-22 Seis Seismi micc desi design gn,, EN 1998 1998-1 -1-1 -1
1
Summary
List of content Timing National Annexes CeStruCo Access STEEL Summary
2
List of Content Content in EN 1993-1-8 1993-1-8 1. 2. 3. 4. 5. 6. 7.
Lessons in Window Help Format with PP Presentations
CeStruCo
Introduction Bas Basis of des design ign Connec Connectio tions ns made made with with bolt bolts, s, rivet rivetss or pins pins Weld Welded ed conn connec ectition onss Analys Analysis, is, classi classific ficati ation on and and mode modellin llingg Struct Structura urall join joints ts connec connectin tingg H or I sections Holl Hollow ow sec sectition on joi joint ntss
3
Summary
List of content Timing National Annexes CeStruCo Access STEEL Summary
4
Development of Eurocodes
Lessons in Window Help Format with PP Presentations
CeStruCo
ECCS Concept in 1978 ECCS First draft in 1984 CEN Started with Eurocodes in 1990 CEN ENV 199x-x-x in 1992 (actions nationally only) CEN EN 199x-x-x in 2005 Advantages
Weakness
5
European agreement All structural materials under one safety concept Copyrights Size (some countries only rules, some textbooks) 6
List of Eurocodes
EN 1990 1990 EN 1991 1991 EN 1992 EN 1993 1993
Euroco Eurocode de 0: Euroco Eurocode de 1: 1: Eurocode Eurocode 2: Euroco Eurocode de 3:
Eurocodes List of Actions Basis Basis of Struc Structur tural al Desig Designn Action Actionss on struct structure uress Design Design of of concr concrete ete structures structures Design Design of of steel steel structu structures res
Project team Prof. F. Bijlaard
EN 1991-1-1 1991-1-1 Actions Actions – Dead load published published 04/02 EN 1991-1-2 Actions – Fi Fire 11/02 EN 1991-1-3 Actions – Sn Snow 07/03 EN 1991-1-4 Actions – Wi Wind 04/05 EN 19 1991-1-5 Ac Actions – T em emperature 11/03 EN 1991-1-6 Actions – During erection 06/05 EN 19 1991-1-7 Ac Actions – Ex Exceptional 05/06 EN 1991-2 1991-2 Action Actionss – Transp Transport ort on bridge bridgess 09/03 09/03 EN 1991-3 Actions – Crane girders 11/06 EN 1991-4 Actions – Silos and tanks 08/05
EN 1994 1994 Eurocode Eurocode 4: Design Design of compos composite ite steel steel and and concrete concrete struc. struc. Project team Prof. D. Anderson
EN 1995 1995 EN 1996 1996 EN 1997 1997 EN 1998 1998 EN 1999
Euroco Eurocode de 5: Euroco Eurocode de 6: Euroco Eurocode de 7: 7: Eurocode Eurocode 8: Eurocode Eurocode 9:
Design Design of of timber timber struc structur tures es Design Design of mason masonry ry struct structure uress Geotec Geotechni hnica call design design Design Design of structu structures res for for earthquak earthquakee resistanc resistancee Design Design of of alumin aluminium ium structures structures 7
Structural Steel Eurocodes
EN 1993-1-1 EN 1993-1-2
B as i c r u les Fir e r es i st an c e
EN 1993-1-3 EN 19 1993-1-4 EN 1993-1-5 EN 1993-1-6 EN 1993-1-7 EN 1993-1-8 EN 1993-1-9 EN 1993-1-10 EN 1993 1993-1 -1-1 -111 EN 1993-1-12 EN 1993-2 EN 1993-3-1 EN 1993-3-2 EN 1993-4-1 EN 1993-4-2 EN 1993-4-3 EN 1993-5 EN 1993- 6
Thin walled Corrosion re resistant Plates Shells Plates 2 Con n ec t i on s Fa t i g u e B r i t t l e f r ac t u r e Tens Tensilile mem membe bers rs (cab (cable les) s) HSS Bridges Mast Chimneys Silos Tanks Pipelines Pilots Crane girders
(20 documents) Fir s t pa pac k age
05/05 04/05
05/05 05/05 05/05
Eurocode Eurocode Implementa Implementation tion - Examples Examples
ECCS TC10 comments to ENV 1993-1-1 CEN/TS250/SC3 project team, team, head Mr. Jouko Kouhi Kouhi prEN 1993-1-8 document N 1054 E 900 national comments Final draft Voting Acceptation by CEN
Czech Rep. 8/2006
National Annexes UK 12/200 12/2007; 7; France France 12/20 12/2006; 06; Polan Polandd 2010; 2010;
Chapter 6 Connections Annex J Joints Annex L Base plates Annex K Hollow section joints May 12, 1992 VTT, Finland Sept. 9, 2001 Nov. 20, 2001 April 16, 2004 May 10 11, 2005
Summary
France 12/2006; Poland 2007;
8
Development of EN 1993-1-8 From ENV 1991-1
9
Translations UK N/A;
Czech Czech Rep. Rep. 8/2006 8/2006
Eurocodes Eurocodes be adopted adopted for governme government nt construction construction UK unknown; France Not; Poland 2010; Czech Rep. 2008
Eurocodes Eurocodes be adopted adopted for non-gove non-governme rnment nt construction construction UK unknown; France Not; Poland 2010; Czech Rep. 2008
List of content Timing National Annexes CeStruCo Access STEEL Conclusions
Lessons in Window Help Format with PP Presentations
CeStruCo
National National standards standards withdrawn withdrawn UK 2010 2010;; Fran France ce 2010 2010;;
Pola Poland nd 2010 2010;;
Czec Czechh Rep. Rep. 2010 2010 11
12
National Annex for EN 1993-1-8
National Choice (Czech Rep.) Clause 1.2.6 Reference Standards, Group 6: Rivets
Alternative procedures Nationally Determined Parameters
ČSN 02 2300: Rivets, Overview (Czech national standards).
Clause 2.2 Partial safety factors, paragraph (2)
National choice is allowed in EN 1993-1-8 through (only): 1.2.6(6) Reference standard Rivets 2.2(2) Partial safety factors 3.1.1(3) Bolt classes 3.4.2(1) Hand tightening of the nut is considered adequate 5.2.1(2) Classification of joints 6.2.7.2(9) Requirements for elastic distribution of forces in bolt rows
Clause 3.1.1(3) General, paragr aph (2)
Numerical values of partial safety factors for joints are not changed, the values in Table 2.1 should be used.
All bolt classes listened in Table 3.1 may be used.
Clause 3.4.2 Tension connections, paragraph (1) If the preload is not explicitly required in design for slip resistance, the hand tightening of the nut is considered adequate without the control of preload.
Clause 5.2.1 General, paragr aph (2) No additional information on classification of joints by their stiffness and strength are given to that included in 5.2.1(2).
Clause 6.2.7.2 Beam-to-column joints with bolted end-plate connections, paragraph (9)
CeStruCo = Civil enginnering Stru ctural Co nnections
Summary
List of content Timing National Annexes CeStruCo Access STEEL Summary
The requirements for elastic distribution of forces in the bolt rows introduced 14 in (6.26) are not changed.
13
Lessons in Window Help Format with PP Presentations
CeStruCo
Aristotle University of Thessaloniki, Greece Bouwen met Staall, Netherlands Building Research Establishment Ltd., United Ki ngdom Czech Technical University (contractor), Czech Republic Luleå University of Technology, Sweden University of Coimbra, Portugal Politechnica University of Timisoara, Romania
Review KREKON Design office, Rotterdam, Netherlands Czech EXCON a.s., Prague, Czech Republic Constructional Steelwork Association Ostrava, CR
15
Textbook
European Educational Projects
ESDEP WIVISS SteelCall Stainless SteelCall SSEDTA CeStruCo NFATEC SDCWASS DIFISEK
16
Basic European educational project CD lessons Virtual office Internet/CD PP presentation + lessons Connection design Internet courses Austenitic stainless steel Fire design 17
1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13.
Introduction Bolts Welding Structural Modelling Simple Connections Moment Resistance Connections Column Bases Seismic Design Fire Design Hollow Section Joints Cold-Formed Member Joints Aluminium Connections Design Cases 18
Internet / CD Version
Lessons in Window help format Textbook in PDF file Worked examples Presentations
Lessons in Window Help Format
PowerPoint Programme „Nonlinear analyses of joints by component method“ Video film
Tools for connection design
Example of Software Example of Tables 19
PowerPoint Presentations
Prepared by RoboHelp tool at Czech Technical University in Prague
20
Software
Non-linear Analysis of Steel Connections
Based on Fire test on 8th storey building Cardington, January 16, 2003
Coimbra University Prediction of behaviour by component method with nonlinear force - deformation diagram of components 21
Video Film
22
CeStruCo on CD
Statically Stressed Bolts in Dynamically Loaded Connections prepared at Delft University
23
Educational material to support conversion of ENV 1993-1-1 to EN1993-1-8 CD / Internet lessons
www.fsv.cvut.cz/cestruco
Lessons in Window Help Format with PP Presentations
CeStruCo
24
Access STEEL – Informational tool at www.access-steel.com
Summary
List of content Timing National Annexes CeStruCo Access STEEL Summary
Lessons in Window Help Format with PP Presentations
CeStruCo
25
Access STEEL – Information System
Access STEEL - Documents
Eurocodes 1993-1-x and EN 1994-1-x for not steel specialists
26
Project Initiation Scheme Development Detailed Design Verification
Topics
For practising designers, architects and their clients
Multi-storey Buildings Single Buildings Residential Construction
Detailed design of elements Step-by-step guidance Full supporting information Worked examples Interactive worked examples
250 separate technical resources + 50 interlinked modules
English, French, German and Spanish Project of EU eContent Programme
Client's guide Concept designs Flow Charts
27
Example - Client's Guide
Fire Safety Engineering
Non-conflicting Complementary Information Workedexamples (Pasive and Interactive)
28
Example - Concept Designs
29
30
Example - Flow Charts
Example - Non-Conflicting Complementary Information
31
Example – Pasive Worked Example
32
Example – Interactive Worked Example
33
Access STEEL
34
Summary
Informational system based on hypertext engine
35
EN 1993-1-8 – Connectors and joints EN 1993-1-8 – Will be used from 2007 (mostly) CeStruCo – Educational material to EN 1993-1-8 Access STEEL – Informational tool for EC3 on internet
36
List of Lessons at Seminar 1. 2. 3. 4. 5. 6. 7. 8. 9.
Bases of Design according to EN 1993-1-8 Lessons Connection Design according to EN 1993-1-8 Prof. František Wald
Introduction Bases of design according to EN 1993-1-8 Welded connections Bolted connections Basics of structural joints Design of simple connections Column bases Fire design of connections, EN 1993-1-2 Seismic design, EN 1998-1-1
1
Topics
2
General Requirements
Bases of Design
Eccentricity at Intersections
Connection Modelling in Global Analyses
Global Analysis of Lattice Girders
Classification of Joints
Modelling of Beam-to-Column Joints
Summary
All joints should have a design resistance such that the structure is capable of satisfying all the basic design requirements given in EN 1993-1-1.
3
Partial safety factors for joints
4
Applied Forces and Moments
Resistance of members and cross-sections M0, M1, M 2 Resistance of bolts, rivets, pins, welds, plates in bearing M2 Slip resistance , M3,ser M3 Bearing resistance of an injection bolt M4 Resistance of joints in hollow section lattice girder M5 Resistance of pins at serviceability limit state M6,ser Preload of high strength bolts M7
The forces and moments applied to joints at the ultimate limit state should be determined according to the principles in EN 1993-1-1.
Recommended values
M3 = 1,25 (EN 1993-1-1 = M3,ser M7 = 1,10 M4 = M5 = M6,ser = 1,00
M2
=
M0
= 1,00,
M1
= 1,10)
Frequency bar chart Effect of actions
Resistance
5
6
Resistance of Joints
Topics
On the basis of the resistances of its basic components
Linear-elastic or elastic-plastic analysis
Fasteners with different stiffnesses
Bases of Design
Eccentricity at Intersections
Connection Modelling in Global Analyses
Global Analysis of Lattice Girders
With the highest stiffness should be designed to carry the load.
Classification of Joints
(An exception bolts and slip resistant bolts).
Modelling of Beam-to-Column Joints
Summary
7
Reduction of Resistance of Angles Connected by One Leg
Eccentricity at Intersections
(and other unsymmetrically connected members in tension)
The joints and members should be designed for the resulting moments and forces
8
Except in the case of particular types of structures - lattice girders
In the case of joints of angles or tees attached by either a single line of bolts or two lines of bolts
With 1 bolt:
N u,Rd
=
With 2 bolts:
N u,Rd
=
With 3 or more bolts:
N u,Rd
=
2,0(e2 −0,5d 0 )t f u γ M 2 β 2 Anet f u γ M 2
Centroidal axes
β 3 Anet f u
Reduction factors
Fasteners
Fasteners
Pitch
p1
< 2,5 do
> 5,0 do
2 bolts
β 2
0,4
0,7
3 bolts or more β 3
0,5
0,7
γ M 2
Setting out lines 9
Topics
Bases of Design
Eccentricity at Intersections
Connection Modelling in Global Analyses
Global Analysis of Lattice Girders
Classification of Joints
Modelling of Beam-to-Column Joints
Summary
10
Types of Joint Modelling STIFFNESS
Rigid Semi - rigid Pinned
11
RESISTANCE Full-strength
Partial-strength
Pinned
Continuous
Semi-continuous
-
Semi-continuous Semi-continuous
-
-
-
Simple
12
Elastic analysis at the Serviceability Limit State
Elastic analysis at the Ultimate Limit State
Modified stiffness S j,ini and resistance M j,Rd
Design joint properties based on the type of global analysis
Initial stiffness S j,ini and resistance M j.Rd M
M
S j,ini
M j,Rd
2 M 3 j,Rd M j,Sd
M j,Sd
S j,ini
S j,ini / η φ
φ η
is stiffness modification coefficient
13
Stiffness Modification Coefficient
η M M j,Rd M j,Sd
14
Rigid - Plastic Analysis
S j,ini
Resistance M j,Rd and deformation capacity φ Cd
S j,ini / η φ
Type of connection
M
Other types of joints (beam-to-beam joints, Beam-to-column joints beam splices, column base joints)
Welded
2
3
Bolted end-plates
2
3
Bolted flange cleats
2
3,5
Base plates
-
3
M j,Rd
φ Cd
φ
15
Elastic - Plastic Analysis
16
Joint Modelling and Frame Global Analysis
Full curve description
MODELLING
M M j,Rd
TYPE OF FRAME ANALYSIS Elastic analysis
Rigid-plastic analysis
Elastic-plastic analysis
Continuous
Rigid
Full-strength
Rigid/full strength
Semicontinuous
Semi-rigid
Partial-strength
Rigid/partial-strength Semi-rigid/full-strength Semi-rigid/partial-strength
Pinned
Pinned
Pinned
S j,ini Simple
φ Cd
φ 17
18
Topics
Global Analysis of Lattice Girders
Hollow sections
Bases of Design
Eccentricity at Intersections
Connection Modelling in Global Analyses
Secondary moments (due to rigidity of joints)
Global Analysis of Lattice Girders
Moments resulting from transverse loads
Moments resulting from eccentricities
Classification of Joints
Modelling of Beam-to-Column Joints
Summary
Assumption the members connected by pinned joints (for the distribution of axial forces)
Type of component
Source of the bending moment Secondary effects
Transverse loading
Eccentricity
Compression chord Tension chord Brace member
Yes Not if criter. is satisfied
No
Yes
Joint
No Not (if criter. is satisfied)
19
20
Secondary Moments
Moments Resulting from Transverse Loads
Moments, caused by the rotational stiffness's of the joints, may be neglected in the design of members and joints.
Momets should be taken into account in the design of the members to which they are applied
Joint geometry is within the range
Ratio of the system length to the depth of the member in the plane is not less than 6
Brace members may be considered as pin-connected to the chords. Moments resulting
from transverse loads applied to chord members need not be distributed into brace members, and vice versa.
Chords may be considered as continuous beams, with simple supports at panel points.
21
Moments resulting from Eccentricities
22
Moments resulting from Eccentricities
Centric
Negative eccentricity
Positive eccentricity 23
May be neglected in the design of tension chord members and brace members
May be neglected in the design of connections if the eccentricities are within the limits: −0,55
d 0
≤
e ≤ 0,25 d 0
−0,55
h0
≤
e ≤ 0,25 h0
e
eccentricity
d 0
diameter of the chord
h0
depth of the chord, in the plane of the lattice girder 24
Topics
Based on Resitance
Bases of Design
Eccentricity at Intersections
Connection Modelling in Global Analyses
Global Analysis of Lattice Girders
Classification of Joints
Modelling of Beam-to-Column Joints
Summary
Moment, M M b,pl,Rd
Full strength connection Partial strength connection Bending moment resistance of connected beam
Rotation, φ 25
Based on Stiffness
26
Based on Rotational Capacity
(Values for Column Bases)
Accuracy of calculation
5% Ultimate Limit State
20% Serviceability Limit State
Moment, Elastic rotation M of connected beam
Relative moment M j / M pl,Rd 1,0
E I c φ
0,4
S j.ini.c.s = 12 E I c / Lc
0,2
Semi-rigid column base 0
0,01
0,002
Semi-ductile connection Brittle connection
λ o = 1,36
φ
M
(Class 2) (Class 3)
28
Column Bases – Braced Frames
Prediction of column resistance based on the lower support bending stiffness Relative stiffness of base plate S j.ini Simplified boundary E I c / L c 50 40 30 20 10 0
M φ
Rotation, φ
Pinned column base φ , rad 0,003 27
Column Bases – Braced Frames
M
Ultimate rotation of connected beam Ductile connection (Class 1)
L c M c,pl,Rd
S j.ini.c.n = 30 E I c / Lc
0,6
0
_ φ =
Rigid column base
0,8
Deformation capacity of connected member
Accurate boundary
Prediction of column resistance based on the lower support bending stiffness is the limit S j .ini
for
λ ≤ 0 ,5
for
0 ,5 < λ < 3 ,93 is the limit S j .ini
and for 3 ,93 ≤ λ
is the limit S j .ini
>
0,
≥ 7 ( 2 λ − 1 ) E I c / Lc ,
≥
48 I c / Lc .
The limiting stiffness 12 E I c / Lc (slenderness lower than λ = 1 ,36 ) 0
2
4 6 8 10 λ 0 Relative slenderness of column
29
30
Classification of Joints
Topics
National Annex may give additional information on the classification of joints by their stiffness and strength in Cl 5.2.2.1(2) Pin is difficult to define
Bases of Design
Eccentricity at Intersections
Connection Modelling in Global Analyses
Global Analysis of Lattice Girders
Classification of Joints
Small moment resistance
Modelling of Beam-to-Column Joints
Small stiffness
Summary
High deformation/rotational capacity 31
32
Shear Panel
Modelling of Joint by Rotational Springs
Component method
M b
a
M a
φ a T
M b
φ b
Joint
Forces and moments acting on the joint
Shear panel
Shear panel
separatelly
in connections 33
Distribution of Internal Forces
z 3
z 2
N b1,Ed Mb1,Ed
Forces and moments acting on the web panel at the connections
Bases of Design
Eccentricity at Intersections
=
F t1.Rd
= F t1.Rd
=
F t2.Rd
< F t2.Rd
=
F t3.Rd
< F t3.Rd
< F t3.Rd
Connection Modelling in Global Analyses
≤
F c.Rd
F c.Rd
Global Analysis of Lattice Girders
Classification of Joints
Modelling of Beam-to-Column Joints
Summary
t2.Rd
≤
F c.Rd
Elastic-plastic distribution
34
Topics
≤
Elastic distribution
Shear forces
Vb1,Ed
F
F t1.Rd
Plastic distribution
Vb2,Ed
M b2,Ed
=
=
z 1
N b2,Ed
A bolt row in shear only
Rest of shear resistance of each bolt row
Supplement of shear resistance of each bolt row
35
36
List of Lessons at Seminar 1. 2. 3. 4. 5. 6. 7. 8. 9.
Welded Connections Lessons Connection Design according to EN 1993-1-8 Prof. František Wald
Introduction Bases of design according to EN 1993-1-8 Welded connections Bolted connections Basics of structural joints Design of simple connections Column bases Fire design of connections, EN 1993-1-2 Seismic design, EN 1998-1-1
1
Topics
Bases of design
Fillet weld
Bases of Design Fillet welds
But weld
Design model
Design independent of the direction of loading
Plug welds
Very long welds
Groove welds
Design example
Effective width of welded beam-to-column connection
Weld design for full resistance of connecting members
Welding in cold-formed zones
Design of partially penetrated butt weld
Summary
a
EN 1993-1-8 requirements Design rules + Design models
3
Fillet welds – Definition of Effective Throat Thickness a
2
4
Topics
The effective throat thickness of a fillet weld should not be less than 3 mm
Bases of design
Fillet weld Design model
Design of independent of the direction of loading
Very long welds
Example - Modelling the resistance
Effective width of welded beam-to-column connection
Weld design for full resistance of connecting members
Welding in cold-formed zones
Design of Partially Penetrated Butt Weld
Summary
Design throat thickness of flare groove welds in rectangular structural hollow section 5
6
Plane Stresses
Design Model of Fillet Welds
Huber –Misses- Henckey condition of plasticity (HMH)
Triaxial state of stress (needed exceptionally only) Plane state of stress (needed very often)
σ + σz2 - σx2 σz2 + 3τ2 ≤ (f y / γM) 2 2 x
σ z σ x
a
σ ┴ σ║ τ ┴ τ║
effective throat thickness of the fillet weld normal stresses perpendicular to the throat normal stresses parallel to the axis of weld (omitted) shear stresses perpendicular to the axis of weld shear stresses parallel to the axis of weld
σ ≤ f y / γM0 τ ≤ f y / (γM0 √3) 7
(
σ⊥ + 3 τ⊥ + τ 2
2 II
)
Standard and steel grade
≤ f u (β w γ Mw )
σ⊥ ≤ f u γ Mw Ultimate tensile strength of connected material
f u
8
Correlation factor βw for fillet welds
Design Model 2
Uniaxial state of stress (from the material tests)
βw Correlation factor
EN 10025
EN 10210
EN 10219
Correlation factor β w
S 235 S 235 W
S 235 H
S 235 H
0,80
S 275 S 275 N/NL S 275 M/ML
S 275 H S 275 NH/NLH
S 275 H S 275 NH/NLH S 275 MH/MLH
0,85
S 355 S 355 N/NL S 355 M/ML S 355 W
S 355 H S 355 NH/NLH
S 355 H S 355 NH/NLH S 355 MH/MLH
0,90
S 420 MH/MLH
1,00
S 460 NH/NLH S 460 MH/MLH
1,00
S 420 N/NL S 420 M/ML γMw partial safety factor for material of
welds 9
Topics
Bases of design
Fillet weld
Design model
Design independent of the direction of loading
Very long welds
Example - Modelling the resistance
Effective width of welded beam-to-column connection
Weld design for full resistance of connecting members
Welding in cold-formed zones
Design of Partially Penetrated Butt Weld
Summary
S 460 N/NL S 460 M/ML S 460 Q/QL/QL1
S 460 NH/NLH
10
Design Independent of the Direction of Loading N ⊥ Sd F w,Rd
F w,Sd F w,Rd V ⊥,Sd
La
V //,Sd
f vw ,d =
f u 3 β w γ Mw
F w ,Rd = a f vw ,d 11
12
Topics
Very Long Welds
Bases of design
Fillet weld
Design model
Design of independent of the direction of loading
Very long welds
Design example
Effective width of welded beam-to-column connection
Weld design for full resistance of connecting members
Welding in cold-formed zones
Design of Partially Penetrated Butt Weld
Summary
τ//
τ//
τ //
14
Bases of design
Fillet weld
β Lw
0,8 0,6 0,4 0,2
L/a 0
50
100 150 200 250 300 350 400
15
Design model
Design of independent of the direction of loading
Very long welds
Design examples
Effective width of welded beam-to-column connection
Weld design for full resistance of connecting members
Welding in cold-formed zones
Design of Partially Penetrated Butt Weld
Summary
16
Fillet Weld in Normal Shear
Two Fillet Welds in Parallel Shear
τ ΙΙ = 0
τ = F 2a l
σ⊥ = τ ⊥ = σR
From plane stress analysis is F 2a l
τ //
Topics
Reduction of design strength β Lw = 1,2 − 0,2 (Lw 150 a ) ≤ 1,0
0
τ //
Lw
Lw
1
τ//
13
Long welds
Overloading of weld ends due to the different deformation of the connected elements
(
≤ f u β w γ Mw 3
)
2
Has to be satisfied
σ⊥ + 3 τ⊥ ≤ f u (βw γ Mw ) 2
2
After substitution
(σ 17
) (σ 2 ) = (β γ 2) 2
R
σR ≤ f u
2 +3 w
2
R
Mw
2 σR 2
≤ f u (βw γ Mw ) 18
Vl
Flange - Web Weld
Connection of Cantilever V Sd = FSd.
Shear force
Welds are loaded by longitudinal shear force
τII = FSd 2 a h
Transferred by web fillets Bending moment
M
Sd
V l = V Sd S I where
= F Sd e
I
Centre of gravity, Iwe and cross section modulus W we Wwe,1 and stress is
For weld at lower flange cross section modulus
σ ⊥1 = τ ⊥1 = (M Sd
Bases of design
Fillet weld
Maximum stress is at the point of maximum shear force
19
Design model
Design of independent of the direction of loading
Very long welds
Worked Examples
Effective width of welded beam-to-column connection
Weld design for full resistance of connecting members
Welding in cold-formed zones
Design of Partially Penetrated Butt Weld
Summary
In EN 1993-1-8 Chapter 4.10
Connection to plate deformed out of its plate
21
22
Effective Width
20
Effective Width of Welded Beam-to-Column Connection
Unstiffened column flanges
a
τ II = V l 2 a ≤ f u β w γ Mw 3
)
2 W we ,2
moment of inertia
Shear stress
Topics
shear force
Sd
This longitudinal force is carried by two welds effectiv e thickness
)
2 W we ,1
For upper weld on flange is
σ ⊥2 = τ ⊥2 = (M Sd
V
S Static moment of flange to neutral axis
Transferred by the shape of .weld
Effective Width t fb
beff = t wc + 2 s + 7 t fc
Unstiffened column flanges In EN1993-1-8 Clause 6.2.4.4
F t ,fc ,Rd = (t wc + 2 s + 7 k t fc )
⎛ t 2 ⎞ ⎛ f yc ⎞ beff = t wc + 2 s + 7 ⎜ fc ⎟ ⎜ ⎟ ⎜ t fb ⎟ ⎜ f yb ⎟ ⎝ ⎠ ⎝ ⎠ t wc t fc t fb s
VSd
r c t fc
t fb f yb γ M 0
⎛ f yc t fc ⎞ ⎟ ⎜ f yb t fb ; 1⎟ ⎝ ⎠
k = min ⎜
beff
t wc
σ
thickness of column web thickness of column flange thickness of beam flange equal to fillet radius r c for hot rolled column sections 23
t wc t fc t fb s
is thickness of column web thickness of column flange thickness of beam flange is equal to fillet radius r c for hot rolled column sections
24
Weld Design for Full Resistance of Connecting Members - Loading by Normal Force
Topics
Bases of design
Fillet weld
a > 0,7
Design model
Design of independent of the direction of loading
Very long welds
Example - Modelling the resistance
Effective width of welded beam-to-column connection
Weld design for full resistance of connecting members
Throat thickness of a fillet weld used in a hollow section joints
Design of Partially Penetrated Butt Weld
Summary
τ
V Sd
τ = V Sd / (t h)
≈ 0,85
σ w
f u / γ Mw
σ = F Sd / (t h) F Sd the acting design force f u plate design strength t the thinness of connecting plate b width of connecting plate full capacity of a plate the thickness S235: ( f y / γ M 0 ) t ( 235 / 1,10 ) t
f u / γ Mw
σ
F Sd
σ ⊥
= 0,7
360 / 1,25
t
= 0,52 t ≈ 0,5 t
h
t
f y /( 3 γ M 0 ) t f u / γ Mw
= 0,85
26
Weld Design or Full Resistance of Connecting Members
the design shear force in weld full capacity of a plate the thickness S235 τ t f w / γ Mw
τ ⊥
25
τ
a > 0,85
σ t
a > 0,7
Weld Design for Full Resistance of Connecting Members - Loading by Shear Force
V Sd
Not directly in code
Loading by shear force
∼ 0,5 t
Loading by normal force
∼ 0,4 t
235 /( 1,1∗ 3 ) t = 0,36 t ≅ 0,4 t 360 / 1,25
27
Topics
Bases of design
Fillet weld
Design model
Design of independent of the direction of loading
Very long welds
Example - Modelling the resistance
Effective width of welded beam-to-column connection
Weld design for full resistance of connecting members
Welding in cold-formed zones
Design of partially penetrated butt weld
Summary
28
Welding in Cold-Formed Zones
May be carried out within a length 5 t either side of a cold-formed zone
Cold-formed zones are normalized after cold-forming but before welding r / t - ratio satisfy the relevant values: r/t ≥ 25 ≥ 10 ≥ 3,0 ≥ 2,0 ≥ 1,5
29
≥ 1,0
Maximum thickness (mm) Fully killed Aluminium-killed steel (Al ≥ 0,02 %) any any 24 12 10 6
30
V
Topics
Bases of design
Fillet weld
Butt welds
1/2 V
Fully suply the cross-section
U
Design model
Design of independent of the direction of loading
Very long welds
Example - Modelling the resistance
Effective width of welded beam-to-column connection
Weld design for full resistance of connecting members
Welding in cold-formed zones
Design of partially penetrated butt weld
Summary
For low quality is decreased design strength
Calculation as fillet weld
31
32
t anom
Design of Partially Penetrated Butt Weld
anom
a nom.1
a nom
c nom a nom.2
a = anom – 2 mm
Full penetration T joints
anom ,1 + anom ,2 t c nom ≤ 5 c nom ≤ 3 mm
t anom
a nom.1
anom
a nom
c nom a nom.2
≥ t
Partial penetration with an effective width
anom,1 + anom,2 < t .
a1 = anom,1 − 2 mm a2 = anom,2 − 2 mm
33
Topics
Bases of design
Fillet weld
Design model
Design of independent of the direction of loading
Very long welds
Example - Modelling the resistance
Effective width of welded beam-to-column connection
Weld design for full resistance of connecting members
Welding in cold-formed zones
Design of partially penetrated butt weld
Summary
34
Summary
Chapter 4 Welded connections
+
Rules for connection of open sections
Rules for connection of hollow sections
35
Component method Welded
36
List of Lessons at Seminar 1. 2. 3. 4. 5. 6. 7. 8. 9.
Bolted Connections (Connections made with bolts, rivets or pins)
Lessons Connection Design according to EN 1993-1-8 Prof. František Wald
Introduction Bases of design according to EN 1993-1-8 Welded connections Bolted connections Basics of structural joints Design of simple connections Column bases Fire design of connections, EN 1993-1-2 Seismic design, EN 1998-1-1
1
Scope of the Lecture
Material
General Design resistance of individual fasteners
2
Non-preloading bolts Single lap joints Bearing through packing Slotted holes Long joints Rivets Anchor bolts
Slip-resistant connections using 8.8 or 10.9 bolts Design for block tearing Lug angles Pin connections Injection bolts Summary
B Slip-resistant at serviceability
F v,Ed.ser ≤ F s,Rd,ser F v,Ed ≤ F v,Rd F v,Ed ≤ F b,Rd
C Slip-resistant at ultimate
F v,Ed ≤ F s,Rd F v,Ed ≤ F b,Rd F v,Ed ≤ N net,Rd
4.6
4.8
5.6
5.8
6.8
8.8
10.9
f yb (N/mm2)
240
320
300
400
480
640
900
f ub (N/mm2)
400
400
500
500
600
800
1000
3
4
Holes (ENV 1990)
Shear connections F v,Ed ≤ F v,Rd F v,Ed ≤ F b,Rd
Bolt class
Note: Bolts 12.9 are not allowed
Categories of Bolted Connections A Bearing type
Nominal values of the yield strength f yb and the ultimate tensile strength f ub for bolts
from 4.6 to 10.9 8.8 or 10.9
8.8 or 10.9
Tension connections F t,Ed ≤ F t,Rd F t,Ed ≤ Bp,Rd
from 4.6 to 10.9
E Preloaded
F t,Ed ≤ F t,Rd F t,Ed ≤ Bp,Rd
8.8 or 10.9
+1 mm for M 12
+2 mm for M 16 up M 24
+3 mm for M 27 and bigger
Extra large With loose 3 mm (M12) up 8 mm (M27)
Slotted (elongated)
D Non-preloaded
Normal
Accurate – flushed bolts
5
for bolt M20 must be the clearance Δd < 0 , 3 m m 6
Positioning of Holes for Bolts and Rivets
Maximum Values for Spacings p1
e1
Minimum values for spacings
e2
Edge and end distances are unlimited, except :
p2
End distance e1
1,2 d 0
Edge distance e2
1,2 d 0
Distance in slotted holes e3
1,5 d 0
Distance in slotted holes e4
1,5 d 0
Spacing p1
2,2 d 0
Spacing p2
2,4 d 0
for compression members in order to avoid local buckling and to prevent corrosion in exposed members and; for exposed tension members to prevent corrosion.
7
Local Buckling of Plate
Staggered Rows
in compression between the fasteners:
minimum line spacing of p2 = 1,2d 0
need not to be checked if p1 / t is smaller than 9 ε ε =
8
235 / f y
according to EN 1993-1-1 using 0,6 p1 as buckling length t thickness of the thinner outer connected part 9
Resistance in Shear in One Shear Plane
Scope of the Lecture
General Design resistance of individual fasteners
Plane of shear is going through threads of bolt: For classes 4.6 a 5.6
Non-preloading bolts Single lap joints Bearing through packing Slotted holes Long joints Rivets Anchor bolts
Slip-resistant connections using 8.8 or 10.9 bolts Design for block tearing Lug angles Pin connections Injection bolts Summary
10
Fv ,Rd = (0,6 f ub A s ) γ M2 For classes 8.8 a 10.9 Fv , Rd = (0,5 f ub A s ) γ M2
A s Core area of cross section of bolt f ub Ultimate strength of bolt
γ M2 Partial safety factor of bolt 11
12
d 0
Resistance in Shear in One Shear Plane
Resistance in Bearing Fb,. Rd = (2 ,5 α f u d t ) γ M2
Plane of shear is going through shaft of bolt
Fv , Rd = (0,6 f ub A ) γ M2
A
d e 1
p 1
where α is minimum from formulas
e1 3 d 0 ; p1 3 d 0 - 1 4 ; f ub f u ; 1,0
Full area of cross section of bolt
f ub Ultimate strength of bolt
t
minimum thickness in one direction
γ M2 Partial safety factor of bolt
d
diameter of bolt
F b.Sd
d0 diameter of hole f ub strength of bolt f u strength of material
13
Resistance in Bearing
(0,8 in oversized holes)
14
Bearing of Plate and Bolt
In oversized holes reduction 0,8
Inner bolt
Outer bolt
Load on a bolt is not parallel to the edge, the bearing resistance may be verified separately for the bolt load components parallel and normal to the end R 10
20
30 e 1 40 p 1 60 e 1 40 t w 5,6
IPE 200 L 140
P 10 - 140 x 100
VSd = 110 kN
M 20 - 5.6
t p 10
10
50
4 4
10 15
16
Bearing Resistance of Bolt Group p 1
For the holes 2: α =
e1 1,2 d 0 = = 0,4 3 d 0 3 d 0
α =
p1 3 d 0
− 0,25 =
F
Holes 1
3 d 0 3 d 0
e1 = 1,2 d 0
F
For the holes 1:
Tensile Resistance
e1
p 1 = 3 d 0
Holes 2
− 0,25 = 1 − 0,25 = 0,75
1)Total bearing resistance is based on direct summarising 2,5 d t f u 2,5 d t f u 2,5 d t f u = (2 ⋅ 0,4 + 2 ⋅ 0,75)⋅ = 2,3 ⋅ F b ,Rd = (∑α ) γ M 2
γ M 2
γ M 2
2)Total bearing resistance is based on smallest of the individual resistances 2,5 d t f u 2,5 d t f u 2,5 d t f u = (2 ⋅ 0,4 + 2 ⋅ 0,40)⋅ = 1,6 ⋅17 F b .Rd = (∑α ) γ M 2
γ M 2
γ M 2
Ft,Rd = (k 2 f ub A s ) γ M2 A s
Area of core of bolt
γ Mb
Partial safety factor
f ub
Ultimate bolt strength
k 2 = 0,90 for regular bolt head k 2 = 0,63 for countersunk bolt 18
Punching Shear Resistance
Combined Shear and Tension Experimental tensile resistance / predicted tensile resistance
F t,exp F t 1,0
Bp,Rd = 0,6 π d m t p f u / γ M2
Treads in shear plane Shank in shear plane F v,S
t p plate thickness
F v,R
+
F t,S
1 ,4
1
F t,R
0,5
d m the mean of the across points and across flats dimensions of the bolt head or the nut, whichever is smaller d m =
0
d 1 + d 2 2
d 2
Owens G.W., Cheal D.B.: Structural Steelwork Connections, Butterworths, 1989.20
19
Single Lap Connection with One Bolt Reduction of bearing resistance
F b ,Rd ≤
Scope of the Lecture
1,5 f u d t γ M 2
General Design resistance of individual fasteners
M 16 - 5.6 P5 - 60 x 840 F Sd
8
5
30 30
21
Shear and Bearing pass through Packing
Slip-resistant connections using 8.8 or 10.9 bolts Design for block tearing Lug angles Pin connections Injection bolts Summary
22
60% of resistance in circular holes (force perpendicular to the long direction of the slot )
9 d 8 d + 3 t p
22
18
18
Force, F, kN
200 180
40 40 8 16 8
β p ≤ 1,0 β
Non-preloading bolts Single lap joints Bearing through packing Slotted holes Long joints Rivets Anchor bolts
Bearing Resistance in Slotted Holes
Reduction of bolt shear resistance
β p =
0,5
0
d w d m
d 1
Experimental shear resistance predicted tensile resistance F v,exp 1,0 F t
M 16
40 40 8 16 8 M 16
p
1,0
tp
0,5
Circular holes, (test 1c-16-1-d+2)
160 140 120 100
10 35 50 25
10 35 50 25
110
110
Slotted holes, (test 5c-16-1-d+2,5)
80 60 40 20
Displacement , mm
0 0
0
0,3 d
1,0 d
1,5 d
5
10
15
20
25
30
35
40
t p 23
24
45
Long Connection
Scope of the Lecture
Reduction of shear resistance β Lf = 1 −
L j − 15d
200 d
β Lt ≤ 1,0
β Lt 1
β Lt ≥ 0,75
0,8 0,75 0,6
L j
0,4
0,2
0 0
15d
65d
L j
25
Rivet Connections
General Design resistance of individual fasteners
Slip-resistant connections using 8.8 or 10.9 bolts Design for block tearing Lug angles Pin connections Injection bolts Summary
Philosophy of design was used for bolts
General Design resistance of individual fasteners
Bolts spacing's recommendations are coming from rivets
27
Anchor Bolts
Slip-resistant connections using 8.8 or 10.9 bolts Design for block tearing Lug angles Pin connections Injection bolts Summary
when the anchor bolts act in shear 640 N/mm2
N/mm2
900
28
General Design resistance of individual fasteners
Non-preloading bolts Single lap joints Bearing through packing Slotted holes Long joints Rivets Anchor bolts
Scope of the Lecture
The nominal yield strength does not exceed otherwis not more than
26
Scope of the Lecture
(class A)
Non-preloading bolts Single lap joints Bearing through packing Slotted holes Long connections Rivets Anchor bolts
For bolts with cut threads reduction by a factor of 0,85
29
Non-preloading bolts Single lap joints Bearing through packing Slotted holes Long joints Rivets Anchor bolts
Slip-resistant connections using 8.8 or 10.9 bolts Design for block tearing Lug angles Pin connections Injection bolts Summary
30
Slip-resistant Connections using 8.8 or 10.9 Bolts
Friction Coefficient μ F p.Cd
Prestressing force
Tests
F s.Rd
Fs,. Rd = (k s n μ γ M3,ser ) F p,Cd F p,Cd is design prestressing force of bolt
EN 14399-2:2002 High strength structural bolting for preloading Part 2 : Suitability Test for Preloading
Table for class of friction surfaces
With painted surface treatments a loss of pre-load may occur over time. Class of friction surfaces
(= 0,7 f ub A s),
Slip factor µ
A blasted, metal spraying (EN 1090)
0,5
μ
friction coefficient
B blasted (EN 1090)
0,4
n
number of friction planes
C cleaned (EN 1090)
0,3
D cleaned (EN 1090)
0,2
ks
coefficient corresponding to clearance of hole 31
Hole Size Coefficient k s Description
Combined Tension and Shear k s
Normal holes
1,0
Oversized holes or short slotted holes with the axis of the slot perpendicular to the direction of load transfer
0,85
Long slotted holes with the axis of the slot perpendicular to the direction of load transfer
0,7
Short slotted holes with the axis of the slot parallel to the direction of load transfer
0,76
Long slotted holes with the axis of the slot parallel to the direction of load transfer
0,63
γ M 2 Δ F b
bolt preload F p
F b total bolt force
Δ F
F t external tensile force
δ p,ext δ b elongation of the bolt δ b,ext
δ p plate shortening
34
Block Tearing
Non-preloading bolts Single lap joints Bearing through packing Slotted holes Long joints Rivets Anchor bolts
Slip-resistant connections using 8.8 or 10.9 bolts Design for block tearing Lug angles Pin connections Injection bolts Summary
k s n μ ( F p ,C − 0,8 F t ,Ed )
33
General Design resistance of individual fasteners
F s,Rd =
F
Scope of the Lecture
32
Block tearing consists of failure in shear at the row of bolts along the shear face of the hole group accompanied by tensile rupture along the line of bolt holes on the tension face of the bolt group.
N Ed
N Ed
N Ed
35
36 N Ed
Test
FE Model
Rupture
Orbison J.G., Wagner M. E., Fri tz W.P.: Tension plane behavior in single-row bolted connections subject to block shear, Journal of 37 Constructional Steel Research, 49, 1999, s. 225 – 239.
Design Model
Topkaya C.: A finite element parametric study on block shear failure of steel tension members, Journal of Constructional Steel Research, 60 , 2004, s. 1615 – 1635, ISSN 0143-974X. 38
Worked Example - Angle P10; 1.4401
Symmetric bolt group subject to concentric loading
35
70 40
V eff,1,Rd = f u Ant / γ M2 + (1/√3) f y Anv / γ M0
240 100
35 25
70
L - 100 x 100 10 materiál 1.4401 30 + 7 x 30 +30
8 x M16; 70
60
Ant net area subjected to tension
240
Anv net area subjected to shear
In plate (staggered rows) V eff,1,Rd =
Eccentric loading
V eff,2,Rd = 39
Reduction of bearing resistance
d
e 2
t
F b ,Rd ≤
N u .Rd =
+
γ M2
1
f y
3
Anv γ M0
= =
0,5 × 530× (35 − 2 × 9) ×10 1,25 ×103
+
1 3
× 220×
(2 × 240− 6 ×18 − 2 ×9) ×10 1,1×103
= 72 + 409 = 481kN
In angle (staggered rows)
V eff,2,Rd = 0,5 f u Ant / γ M2 + (1/√3) f y Anv / γ M0
Single Lap Connection
f u Ant
0,5 f u,p Ant
+
γ M2
1 3
f y,p
Anv
= =
0,5 × 530× (60 − 189) ×10
γ M0
1,25×103
+
1 3
× 220×
(240− 3 ×18 − 9)×10 = 70 + 204 = 274kN 1,1×103
40
Single Lap Connection
1,5 f u d t γ M 2
p 1 N u .Rd =
2 ,0 ( e 2 − 0 ,5 d 0 ) t f u
γ M 2
2,50 d0 ≤ 5d ≥
p 1
γ M 2
p 1
β 2 Anet f u
p 1 N u .Rd =
p 1
β 3 Anet f u
p 1
γ M 2
Reduction factors Pitch p1
41
2 bolts β 2
0,4
0,7
3 and more bolts β 3
0,5
0,7 42
Worked Example – Fin Plate
Worked Example – Fin Plate, Shear Resistance
3 x M20, 8.8 P10 - 230 x 110 meteriál S235
HEA 200 S235
10
35
80
45 70
70
IPE 300 S235
45
230 70
70
70 45
230 70 V
Sd
50 50
45
= 100 kN
In beam web
5 50 50 60
V Rd,11 =
0 ,5 f u,b1 Ant γ M2
+
1 3
f y,b1
Anv γ M0
=
0,5 × 360 × 276 ,9 1 1171,5 + × 235 × = 199 kN 1,25 1,0 3
43
44
Scope of the Lecture
Worked Example – Fin Plate, Tying Resistance
General Design resistance of individual fasteners
45
70
70
70
70
45
50
50
In beam web N Rd,u,6 =
f u,b1 Ant γ M,u
+
1 3
f y,b1
Anv γ M0
=
360 × 681,6 1 553 ,8 + × 235 × = 298 kN 1,1 1,0 3 45
Lug Angles
Slip-resistant connections using 8.8 or 10.9 bolts Design for block tearing Lug angles Pin connections Injection bolts Summary
46
Scope of the Lecture
General Design resistance of individual fasteners
1. The lug angle to transmit a force 1,2 times the force in the outstand of the angle connected. 2. The fasteners connecting the lug angle to the outstand of the angle member should be designed to transmit a force 1,4 times the force in the outstand of the angle member. 3. The connection of a lug angle to a gusset plate or other supporting part should terminate at the end of the member connected. 4. The connection of the lug angle to the member should run from the end of the member to a point beyond the direct connection of the member to the gusset or other supporting part. 47
Non-preloading bolts Single lap joints Bearing through packing Slotted holes Long joints Rivets Anchor bolts
Non-preloading bolts Single lap joints Bearing through packing Slotted holes Long joints Rivets Anchor bolts
Slip-resistant connections using 8.8 or 10.9 bolts Design for block tearing Lug angles Pin connections Injection bolts Summary
48
Design of Pin
Pin Connections
Analysis
As bolt (shear, bearing)
As beam (bending)
Given thickness t
Combination of shear and bending
a≥
d = 30
F Ed γ M 0 2 t f y
+
2 d 0 3
: c ≥
F Ed γ M 0 2 t f y
+
d 0 3
Given geometry
F Sd d 3 = 20
t 1
t 1 = 10
t 2 c
t 1 c
t 1 = 10
c =1
c =1 t 2 = 18
F Ed γ M 0
t ≥ 0,7
M Sd
f y
49
Analysis of Pin - Shear
50
Analysis of Pin - Bending Resistance of pin in bending
Resistance of one shear area of pin in shear Fv . Rd = (0,6 A f up ) γ Mp ≥ Fv . Sd = 0,5 FSd
M
Rd
= (0,8 W el A f yp ) γ Mp ≥ M Sd = (FSd 8 ) (t + 4 c + 2 t 1 )
F Sd
F Sd f up
applied force strength of pin
γMp = 1,45
partial safety material factor
A
: d 0 ≤ 2,5 t
applied force
f yp
yield point of pin
γMp = 1,45
partial safety material factor
A
Cross sectional area of pin
t 1
cross sectional area of pin
W el = π d 3 32 cross sectional elastic modulus of pin
t 2 c
M Sd
51
Analysis of Pin – Combination of Bending and Shear Stresses due to bending and shear:
(MSd
2
t 1 c
52
Analysis of Pin - Bearing Bearing stress of plate and pin
(
2
M Rd ) + (Fv ,Sd Fv , Rd ) ≤ 1
t 1
Fb, Rd = 1,5 t d f y
t 2 c
t 1 c
)γ
Mp
pro f yp ≥ f y a 2 t 1 ≥ t
f y
yield point of plates
f yp
yield point of pin
γMp = 1,45
partial safety material factor
M Sd 53
54
Analysis of Pin - Serviceability
Scope of the Lecture
Replaceable pin the contact bearing stress should satisfy σ h,Ed ≤ f h,Rd
σ h,Ed = 0,591
E F Ed ,ser ( d 0 − d )
d 2 t
f h,Ed = 2,5 f y / γ M6,ser d
the diameter of the pin;
d 0
General Design resistance of individual fasteners
the diameter of the pin hole;
F Ed,ser the design value of the force to be transferred in bearing, under the characteristic load combination for serviceability limit states
55
Injection Bolts
Non-preloading bolts Single lap joints Bearing through packing Slotted holes Long joints Rivets Anchor bolts
Slip-resistant connections using 8.8 or 10.9 bolts Design for block tearing Lug angles Pin connections Injection bolts Summary
Bearing Strength of an Injection Bolt β σ2
β σ2
t2
σ1 σ2
t1 t2
F b,Rd,resin =
1,33 1,0
σ1
σ1 1.0
σ2 2.0
t1/ t2
Bolts of class 8.8 or 10.9
The design ultimate shear load of any bolt in a Category A Preloaded injection bolts should be used for Category B and C connections 57
Scope of the Lecture
1
σ2
γ M 4
t2 t1 t2
1,33 1,0
σ1
σ1
σ2
ß f b,resin t b, resin k t
coefficient depending of the thickness ratio1.0 2.0 t / t bearing strength of the resin effective bearing thickness of the resin 1,0 for serviceability limit state 1,2 for ultimate limit state k s 1,0 for holes with normal clearances or (1,0 - 0,1 m), for oversized holes; m the difference (in mm) between the normal and oversized hole dimensions 58
1
Connections made with bolts, rivets or pins in Chapter 3 of EN 1993-1-8
Non-preloading bolts Single lap joints Bearing through packing Slotted holes Long joints Rivets Anchor bolts
Slip-resistant connections using 8.8 or 10.9 bolts Design for block tearing Lug angles Pin connections Injection bolts Summary
k t k s d t b ,re sin β σf b ,re sin
Summary
General Design resistance of individual fasteners
56
Non-preloaded bolts
Preloaded bolts – preload (0,7 f ub)
59
Injection bolts (replacement of rivets; bolts 8.8 and 10.9) Pins (including serviceability)
60
2
List of Lessons at Seminar 1. 2. 3. 4. 5. 6. 7. 8. 9.
Basics of structural joints (Structural Joints Connecting Open Sections)
Lessons Connection Design according to EN 1993-1-8 Prof. František Wald
Introduction Bases of design according to EN 1993-1-8 Welded connections Bolted connections Basics of structural joints Design of simple connections Column bases Fire design of connections, EN 1993-1-2 Seismic design, EN 1998-1-1
1
2
Different Approaches
Scope of the Lecture
General
Experimentation
Component method
Curve fitting
Basic components
Finite element analysis
Simplified analytical models – Component Method
Assembly
Resistance
Stiffness
Rotation capacity
M
Experiment
1
M-N interaction
Summary
Rotational stiffness
Moment resistance
Rotation capacity Joint resistance M j,Rd Elastic limit 2/3 M j,Rd
hb
M
+ C3 ( kM)3 + C5 ( kM )5
ta φ
3
Moment-Rotation Characteristic
lt
Function φ = C1( kM)
Scope of the Lecture
M, moment, kNm Initial stiffness S j,ini
General
Component method
Basic components
Assembly
Experimental curve Design curve
Rotation,φ , mrad Deformation capacity φ j,Cd
4
5
Resistance
Stiffness
Rotation capacity
M-N interaction
Summary
6
Procedure
Rotational Capacity
Decomposition of joint
Component description
Joint assembly
M
Bending moment, kNm
Experimental curve
Column web in tension
Bilinear model
Connection
M j.Rd
Plastic rotational capacity
Components in tension
φ pl
Components in compression
Classification
Web panel in shear
Representation
Modelling in analyses
Column web in compression Joint
Rotational capacity of joint 0
φ el
φ u
φ Cd
φ
Rotation, mrad
7
Decomposition of Joint
8
Background References
Zoetemeijer P.: Summary of the research on bolted beam-to-column connections, TU-Delft report 26-6-90-2, Delft, 1990.
Zoetemeijer P.: Summary of the Research on B olted Beam-to-Column Connections (period 1978 - 1983), Ref. No. 6-85-M, Steven Laboratory, Delft, 1983.
Zoetemeijer P.: Proposal for Standardisation of Extended End Plate Connectio n based on Test results Test and Analysi s, Ref. No. 6-83-23, Steven Laboratory, Delft, 1983.
Unstiffened column web in shear Unstiffened column web in compression
Beam flange in compression Column flange in bending Bolt row in tension End plate in bending Unstiffened column web in tension
9
Practical Application of the Component Method
10
Spring Models
F
Design tables
Parallel configuration 1
Green book Blue book
2 2
1
Fu = F1.u + F2.u k = k1 + k2
Computer programs
Serial configuration
d
1
F
Simplified
δ = min (δ 1; δ 2)
2
1
hand calculation
Fu = min (F1.u; F2.u) 1 / k = 1 / k 1 +1 / k2
2
δ = δ 1 + δ 2 . 11
d
12
Scope of the Lecture
General
Component method
Basic components
Description of Basic Components
The structural properties of basic joint components are described in Chapter 6 of EN 1993-1-8.
e.g.
Assembly
Resistance
Stiffness
Rotation capacity
V Ed
Column web panel in shear
Column web in transverse compression
Column web in transverse tension
Column flange in bending
V Ed
F t,Ed
End-plate in bending
M-N interaction
Flange cleat in bending
Summary
etc.
F t,Ed
F t,Ed F t,Ed
13
Bolts in Tension
F t,Ed
Analytical model
F c,Ed
14
F t,Ed
End-plate in Bending Analytical model
Stiffness coefficient
δ b
=
kb kb
Resistance, see bolts
Deformation capacity - britle
=
Ft ,Ed Lb
2 E As
δ p
Ft ,Ed
A =2,0 s E δ b Lb
= k10 =1,6
Stiffness coefficient
kp
As
=
=
Ft ,Ed m 3 3 E I Ft ,Ed Ft ,Ed 3 E I E δ p
=
E Ft ,Ed m 3
=
3
2 Leff ,ini t 3 12 m3
= 0,5
Leff ,ini t 3 m3
Leff.ini = 1,7 Leff
Lb
kp
= k 4 = k5 = k6 = 0,85
15
Leff t 3 m3
16
F t,Ed
End-Plate Resistance
Failure Modes
By equivalent T-stub in tension
Mode 1 - Plate failure
Mode 2 - Plate and bolts failure
Mode 3 - Bolts failure
F n
m t B
L eff 2
B
Deformation capacity - ductile 17
18
Bolt head / washer size influence F/2
Effective Length
F/2
F/2
F/2
Q ϕ
Q
Mode 1 only
n
Q
F/4
F/4
Q/2
Q/2
F/2 F/2
u
n
F/4
F/4
Q/2
Q/2
Another failure
ϕ
m
Single bolt Bolt group
Q
C
C
19
Circular Failure
20
Bolt in Corner
⇒ F
F
F
F
F
ϕ
2 r
r=m
Virtual work on cone deformation
r=n
ϕ /2
= 2 π m
r´
δ
x
1,4
α = 8
2p
5,5
4,75
4,45
1,2
0,8 0,6
=
λ 1 =
ϕ /2 ϕ
λ 2
1,0
In EN 1993-1-8 graph only λ 2
α α
r
= α m
Leff ,op
δ
Leff ,cp
Single bolt Bolt group
dw
ϕ
Circular failure
ϕ
u
m
dw
Q
Q
m2 m+e m m+e
ϕ /2
0,4 0,2 0,0 0,0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9
α α
α
21
Bolt at Oversize
22
T stub Position e
e mx
mx Weld w e mx
e mx
bp Yield lines
23
24
λ 1
Column Column Flange Flange with Backing Backing Plates Plates
Flange Flange Cleat in Bending Bending As equivalent T-stub flange
e bp bp
Increase Increase of resista resistance nce Mode 1 only
FT,1,Rd
=
4M pl ,1,Rd
h bp bp e bp bp
+ 2M bp ,Rd m
M pl,1,Rd
= 0,25Σl eff ,1tf 2 f y / γ M 0
M bp,Rd
= 0,25Σl eff ,1t bp 2f y ,bp / γ M 0 25
Influence Influence of Gap g
Another Another Componen Components ts
0,4 ta
≤
g > 0,4 ta emin m 0,8 r a
r a
g ≤0,4 t
26
g >0,4 t
ℓeff
= 0,5b 0,5ba
see EN 1993-1-8 1993-1-8
emin m 0,5 t a
r a
a
Effective Effective length length
a
b a 27
Scope of the Lecture
General
Component method
Basic components
Design Resistance
Assembly
Resistance
Stiffness
Rotation capacity
M-N interaction
Summary
28
Welded Welded connection connection
z
Ft,Rd
M j,Rd
Fc,Rd
M j ,Rd =Ft ,Rd z
29
30
Design Resistance
Simpli Simplifie fiedd Lever Lever Arm
Bote Botedd conn connec ectition on – one one bolt bolt row row Ft.Rd
Ft.Rd z
z
Fc.Rd
M j ,Rd
=
∑F
i ti ,Rd
z
z
z
z
z
Fc.Rd
zi
31
More Bolt Bolt Rows - Firs Bolt Bolt Row (start from top) Limits by shear and compressed part
Resistence of first bolt row
Colum web in shear
Column web in compression
F
t1.Rd
t1.Rd
Column flange in bending
t1.Rd
Column web in tension
F
F
t1.Rd
F
Beam flange in compression
t1.Rd
F
F
t1.Rd
t1.Rd
F
t2.Rd
F
F
t2.Rd
F
t2.Rd
t2.Rd
Column web in tension
F
t2.Rd
End plate in bending
F
t2.Rd
Resistance of both bobt bobt rows
Column flange in bending F
t1.Rd
F
t2.Rd
F
t2.Rd
Column web in tension F
t1.Rd
F
t2.Rd
34
Scope of the Lecture
F
t2.Rd
F t3.Rd
F t3.Rd
General
Component method
Basic components
t1.Rd
F
F
F
F t3.Rd
F t3.Rd
F t3.Rd
t2.Rd
Column flange in bending,
Column web in compression
F
Column web in tension
F
t1.Rd
Resistance of second bolt row t1.Rd
More More Bolt Bolt Rows Rows - Thir Thirdd Bot Bot Row Row Taking into account bolt rows groups Etc.
Colum web in shear
F
t1.Rd
33
Limit By shear and compressed part
End plate in bending
F
t1.Rd
More More Bolt Bolt Rows Rows – Seco Second nd Bolt Bolt Row Row
Beam flange in compression
F
F
32
t2.Rd
Assembly
t2.Rd
F
F
F t3.Rd
F t3.Rd
t2.Rd
t2.Rd
Part in compression F
t1.Rd
t1.Rd
F
F t3.Rd
F t3.Rd
t2.Rd
Part in tension
F
F
t2.Rd
35
Resistance
Stiffness
Rotation capacity
M-N interaction
Summary
36
φ
Rotationa Rotationall Stiffness Stiffness Rotatinal Rotatinal stiffness stiffness
S j = M / φ δ i
Deformatio Deformationn or a component component
Shape Shape Stiffn Stiffness ess Ratio Ratio Factor Factor
=
∑δ
Joint resistance M j,Rd
φ j
=
z
Elastic limit 2/3 M j,Rd
Joint Joint with with more more springs springs S j .ini
=
M j φ j
=
Fi z
∑δ
=
i
z
i
Fi z 2 Fi E
∑
1 ki
=
E z2 1 ki
→
∑
E z2 1 μ ki
j,
Initial stiffness S
ini
Design curve Shape by stiffness ratio factor Deformation capacity φ j,Cd Rotation,φ , mrad
37
38
Equivalent stiffness
δ
k eq z1 z z 2
M j
S j ,ini
∑
More Components
ψ
⎛ M ⎞ μ = = ⎜⎜ κ Sd ⎟⎟ ≥1 S j ⎝ M j ,Rd ⎠ M, moment, kNm
Fi ki E
i
Rotation Rotation in joint
From From curve curve fittin fittingg
φ 1
φ 2
k eff =
φ 3
=
∑k
Lever Lever arm
zi
z 1
∑ k1 i
i
eff ,i
i
z1
∑k z= ∑k
eff ,i z i
2
z4
i
eff ,i z i
i
39
Scope of the Lecture
40
Rotation Rotation Capacity Capacity
General
For platic platic global global analys analyses es
Component method
For For basi basicc safe safety ty
Basic components
M M j.Rd
Assembly
Resistance
Stiffness
Plate in bending
Rotation capacity
Column web in shear shear
M-N interaction
Summary
41
φ Cd Cd
Ductile Ductile components components
0,0
φ el
φ u
φ Cd Cd
φ
Brittle Brittle components components
Bots, welds
42
Upper Limits for Material In
the US standard only
In EN 1993-1-8
F Brittle
Deem to satisfy criteria
Ductile
Welded joints
φ CD ,min = 0,015 Unstiffned Unstiffned in tension + Stiffened in compression + No shear influece
δ δ Cd,1
φ Cd ,min
δ Cd,2
F
= 0,025 hc / hb
Ductile
Boted joints
Brittle
Plate failure End plate/column flange thickness
δ δ Cd,1
t ≤ 0,36 d f ub / f y
δ 43Cd,2
Scope of the Lecture
44
M-N Interaction
General
For most portal frame connections (pitched rafters)
Component method
In EN 1993-1-8
Basic components
Assembly
Resistance
Stiffness
Rotation capacity
M-N interaction
Summary
Limit 5% of normal force resistance of connected element
Linear interaction
NSd N j ,Rd
+
MSd M j ,Rd
≤1
Component method
45
Example
VSd
46
Application of EN 1993-1-8 Procedure
M Sd NSd
N Sd M Sd 1 N j ,Rd M j ,Rd
Normal force, kN
Normal force
N j,t,M=0,Rd
N j,t,M,Rd Linear interaction
5 % error
Linear interaction
Moment,
kNm
M j.c.N
F1,t
F2,c et Component method
Moment
M j.t.N
Linear interaction
et
N j,t,M,Rd
Component method
F3,t F2,t
N j,c,M,Rd
N j,c,M=0,Rd 47
N j,c,M,Rd
F1,c
48
Component Method - Resistance
Stiffness
Centre of the part in tension F t.Rd
Simplification to two springs
Bolts
Compressed part – in centre of flage
zt M Sd
N Sd
z
Fc.t.Rd
Ft.Rd
Centre of the part in compression zc
NSd z
MSd
Neutral axis
MSd
zc
F c.Rd
Active part
Fc.Rd
As
zt
NSd
z
c.t
z z
c.b
Fc.b.Rd
Bolts and compressed part
Two compressed parts
for base plates 49
50
M - φ Diagram Praha Test
Evaluation on Tests
Moment, kNm
Normal force, kN
30
200 Test SN 1500
100
-10
20
10
0 0
Moment, kNm
Interaction -200
Prediction by component method
20 Prediction of resistance by interaction
15
SN 1000
-100
Test SN 1500
25
10
Component method
5 Rotation, rad 0 0
0,01
0,02
0,03
0,04
51
52
M - φ Diagram Coimbra Test
Evaluation on Coimbra Tests
Moment, kNm
Normal force, kN 800
Component method Interaction
400 0 0
-50
50 -400
Experiments EE7 EE6 EE1 EE2 EE3 EE4 EE5
Test EE7
120 Prediction by component method
100
Moment, kNm
80
Prediction of resistance by interaction
60 40 20 Rotation, rad 0 0 53
0,01
0,02
0,03
0,04
0,05
0,06 54
List of Lessons at Seminar 1. 2. 3. 4. 5. 6. 7. 8. 9.
Design of Simple Connections (of Open Sections) Lessons Connection Design according to EN 1993-1-8 Prof. František Wald
Introduction Bases of design according to EN 1993-1-8 Welded connections Bolted connections Basicsof structural joints Design of simple connections Column bases Fire design of connections, EN 1993-1-2 Seismic design, EN 1998-1-1
1
SSEDTALecture
2
List of Lessonsrelated to Connection Design
New and Flexible Approach to Training for Engineers in Construction
Flow Charts
Non-confli cting ComplementaryInformation
Leson16 Design of Simple Joints
Access STEEL information tool on internet
Simple connections -fin plates Simple connections - end plates Column splices for both axial load & moment Column bases (axial load only) Design model for simple end plate connections A: Detailing guidance B: Shear resistance C: Tying resistance Design model for simple fin plate connections A: Detailing B: Shear resistance C: Tying resistance Design model for simple Column splices (non-bearing) Initial sizing for non-bearing splices Design model for simple Column bases - axially loaded
Passive examples
Beamto beamfin plate connection Beamtocolumnend plateconnection Column splice(non-bearing) Column base,axially loaded Column splice(bearing)
3
4
5
6
Example – Fin Plate
Flow chart
Example – Fin Plate
Subject to shear 1
1
3
1
3
4
2
2
2
1. Fin plate 2. Supported beam 3. Column 4. Supporting beam 7
8
Example – Fin Plate
Example – Fin Plate
Mode of failure - subject to shear
Bolts in shear
V Rd,1
Fin plate in bearing
V Rd,2
Fin plate in shear (gross section)
V Rd,3
Fin plate in shear (net section)
V Rd,4
Fin plate in shear (block shear)
V Rd,5
Fin plate in bending
V Rd,6
Fin plate in buckling (LTB)
V Rd,7
Beam web in bearing
V Rd,8
Beam web in shear (gross section)
V Rd,9
Beam web in shear (net section)
V Rd,10
Beam web in shear (block shear)
V Rd,11
Supporting column web or supporting beam web (punching shear)
V Rd,12 9
10
Example – Fin Plate
Ductility requirements not guided by bolt shear failure
Example – Fin Plate
Rotation capacity requirements
Subject to tying forces
1. Given rules in initial design Depth of supported beam h b1 (mm)
Fin plate thickness t p (mm)
Fin plate width b p (mm)
Horizontal gap g h (mm)
Beam edge distance e 2,b (mm)
Fin plate edge distance e 2 (mm)
h b1 ≤ 600
10
100
10
40
50
h b1 > 600
10
120
20
40
1
1
3
1
3
4
60 bp
or
gh
hp
g
v
2. Limit of hight and calculate required rotation ≤
hb
−
φ available
2t f,b1
−
2r
> φ required
e1,b
e1 a
p1
hp
p
1
e1 e 2 e 2,b z
11
2
2
2
1. Fin plate 2. Supported beam 3. Column 4. Supporting beam
he
12
Example – Fin Plate
Summary
Mode of failure– subject to tying
Bolts in shear
NRd,u,1
Fin plate in bearing
NRd,u,2
Fin plate in tension (block tearing)
NRd,u,3
Fin plate in tension (net section)
NRd,u,4
Beam web in bearing
NRd,u,5
Beam web in tension (block tearing)
NRd,u,6
Beam web in tension (net section)
NRd,u,7
Supporting column web in bending
NRd,u,8
Design of simple connections not described in EN 1993-1-8 Tables
Green book UK Blue book Germany ECCS TC10 document (in preparation)
Access STEEL materials on internet
13
14
List of Lessons at Seminar 1. 2. 3. 4. 5. 6. 7. 8. 9.
Introduction Bases of design according to EN 1993-1-8 Welded connections Bolted connections Basicsof structural joints Design of simple connections Column bases Fire design of connections, EN1993-1-2 Seismic design, EN 1998-1-1
Thank you for your attention
15
16
Simple Joints
Structural Steelwork Eurocodes
Design of Simple Joints
Frames are traditionally analysed assuming joints to be either: – Pinned. – Rigid.
However few joints meet these ideals.
1
2
Design Considerations of Joints
EC 3 Requirement
Rigid Joints: – Expensive to fabricate and construct.
Real Pin Joints: – Also expensive
Simple Joints: – Need to be flexible
3
4
Joint Requirements
Joint Properties
EC3 states that: – “A nominally pinned connection shall be designed so that it cannot develop significant moments which might adversely affect members of the structure.”
Joints must: – Transfer actions. – Accept required rotations.
5
Joints have three principal properties: – 1. Strength: » able to transfer moments & forces. – 2. Stiffness: » have an appropriate slope on M - Ø curve. – 3.Deformability: » Have adequate rotation capacity.
6
Stiffness Requirement
Strength Requirement
S j,ini not greater than: 0,5 E Ib / Lb.
Depends upon the members connected.
where: S j,ini is the initial rotational stiffness of the connection. Ib is the second moment of area of the connected beam. Lb is the length of the connected beam.
Ensures that joint has only a small resistance compared to the connected members.
Remember that shear and any axial load must be transferred between members.
7
8
Maximum Moment Resistance
Rotation Capacity
Mpbisisfully fullyplastic plasticmoment momentofofresistance resistanceofofcolumn. beam. Mpc
Joint must not fail as a consequence of any large rotations required.
Not sufficient to consider just the detail of the connection in initial state.
Mpc
Mpc Mpb
Mpb
Mpc
Mpc
If Mpb < 2Mpc then M j,Rd = 0.25Mpb
If Mpb > 2Mpc then M j,Rd = 0.25*2*Mpc
Figure 1: Maximum moment resistance requirement for simple joints
9
10
Effect of Gap Closure
Practicalities
φ
M
Contact between beam flange and column face
M
Many joints currently assumed to operate as simple joints transfer moments in excess of EC3 limits.
Resulting designs function satisfactorily.
Supported by extensive research.
φ Figure 2 : Effect of gap closure 11
12
Beam to Column Joints Example 1
Transfer of Forces
Joints likened to links in a chain.
Strength determined by weakest link.
Principal transfers by: – Welding. – Bolting. – Riveting,(occasionally ).
Top and seat cleats (major and minor axes
Seat and stability cleats (major and minor axes)
13
14
Beam to Column Joints Example 2
Single web cleat (major axis: bolted to beam and column) Welded fin plate: (minor axis: bolted to beam, welded to column.
Beam to Column Joints Example 3
Double web cleats (minor axis: Welded to beam, bolted to column). Tab plate: (major axis: welded to beam, bolted to column).
Shear plate (major axis)
Shear plate (major axis)
15
16
Typical Beam to Beam Joint
Simple Web Angle Connection
Supporting beam Supported beam Figure 4: Beam to beam connections
Single notched angle Double notched end plateconnection connection 2.1.2 Should any tying forces need to be considered ( as is the case in the U.K.NAD). Then the connection must also be checked for such action which will involve consideration of the following potential failure modes, remembering that it will often be necessary to combine the axial and the shear forces to obtain a resultant action. 17
18
Simple Web Angle Connection
Transfer of Forces
Shear force must be transferred to column.
This involves several steps: – Beam into bolts. – Bolts into angle. – Angle into bolts. – Bolts into column flange.
a1 Lv a3 a2
19
20
Transfer of Forces
Checks Needed for Tying Forces
Web of beam into bolts: – Block shear. Web of beam into bolts: – Bearing. Shear failure in bolts. Bearing and block shear in angle legs. Shear in bolts to column flange. Bearing in bolts to column flange.
21
22
Other Detailing Guidance
Summary
Block shear in beam web (amended failure zone). Bearing in bolts to beam web. Shear in bolts. Tensile capacity of web cleats. Tensile capacity of bolts to column face.
Minimum end distance. Minimum edge distance. Maximum end and edge distances. Minimum bolt spacing. Maximum bolt spacing.
23
The philosophy of simple joints in terms of idealised and real behaviour has been introduced. The concept of joints as an assemblage of components has been put forward. Requirements for strength, stiffness and rotation capacity have been described. Examples of practical details are provided.
24
List of Lessons at Seminar Column Bases Lessons Connection Design according to EN 1993-1-8 Prof. František Wald
1.
Introduction
2.
Bases of design according to EN 1993-1-8
3.
Welded connections
4.
Boltedconnections
5.
Basics of structural joints
6.
Design of simple connections
7.
Column bases
8.
Fire design of connections, EN 1993-1-2
9.
Seismic design, EN 1998-1-1
1
Scope of the Lecture
Basis of design Components
ENV 1993-1-1 – Annex L (1992)
– Base plate in bending and bolt in tension – Base plate and concrete in compression – Anchor bolt in shear
Background Materials
Assembly
– Annex A2 – Design of Joints (1992, 1999)
COST C1 - Semirigid connections (EU project, finished 1999)
– Resistance – Stiffness – Pre-design
Classification Worked examples Summary
Fixing by Base Plate Base plate in bending and anchor bolts in tension
Component Method Baseplate and concrete in compression
Baseplate in bending anchor bolts in tension
Column web in compression Base plate in bending and concrete in compression
Anchor bolts in shear
Major components
Column flange and web in compression
Anchor bolt in shear
Scope of the Lecture
Basis of design Components
Base-plate in bending and anchor bolts in tension Column flange
– Base plate in bending and bolt in tension – Base plate in bending and concrete in compression – Anchor bolt in shear
e
Assembly – Resistance – Stiffness – Pre-design
F
m
t l eff
Classification Worked examples Summary
Base plate
F
Contact of Edge of T stub
δ b = Θ p n m
n
δ b
Θ p Q=0
Q=0
3
Lb .lim
Embedded Anchor Bolt
=
< >
8 ,82m As 3
Leff t
Lb
Force, kN 180
L bf L L be
40
160 Experiment W13/98
140
b
d
Experiment W14/97
120
24 - 355 315
Prediction
5
P6 - 40 x 50 40
100 80
50
60
10
10 6
40
P10 - 95 x 95
5
20
Lbe ≅ 8 d
0 0
0,2
0,4
0,6
0,8
1
1,2
1,4
1,6 Deformation, mm
CEB documents for anchor bolts resistance
95
95
3
e
F / B t.Rd 1
Mode 2
Mode 3
m
n
0,8 F Rd.3
F Rd.1
F Rd.2 Bt.Rd
Bt.Rd
Bt.Rd
B Q
Mode 3
a)
b)
B t.Rd
B Q
Q
Q
Mode 1
Mode 1
0,6
Mode 1*
0,4
Mode 2
c)
0,2 F Rd.1*
Endplate – contact or no contact
0 0
Base plate – no contact
0,5
1
1,5
2 4
B
2,5
eff M pl.Rd
/
B
Force, kN
350
F Rd.1*
350 Force, kN
300
Resistance
300
Simplified prediction
250
W97-12
250 Experiment
200
m = 32 Complex calculation
150
B
∗
F Rd .1
=
B
Complex calculation m = 67
150
Simplified prediction
100
100
50
50
2 Leff M ´ pl . Rd
200
W97-02
Deformation, mm
0 0
2
4
6
8
Deformation, mm
0 0
2
4
6
8
m
Effective length of T stub
Stiffness
No prying 0 ,425 L eff t 3 k p = m 3 Prying accured 0 ,85 Leff t 3 k p = m 3
As k b = 2 ,0 Lb As k b = 1,6 Lb
e m
Prying occured 2 m 4 m 1 , 25 e 1 2
2 m
Leff ,1 min 1 ; Leff , 2
1
2
No prying 1
2 m 4 m 1 , 25 e
2
4 m
Leff ,1 min 1 ; Leff , 2
1
2
B t.Rd
e
w
e e x
Effective Length for Hollow Sections
m x
(not in EN 1993-1-8) a
b p
ac b (a)
Prying 1 = 4.m x+1,25 e x m x 2 = 2 = 0,5 b p 3 x + 0,625 e x 4 = 0,5 w + 2 m 5 = e + 2 m x + 0,625 e x m x 2 e 6 =
No prying
Leff ,1 min 1 ; 2 ; 3 ; 4 ; 5 ;
Leff ,1 min 1 ; 2 ; 3 ; 4 ; 5 ;
Leff , 2 min 1 ; 3 ; 4 ;
1 2 3 4 5 6
6
m
= 4.m x+1,25 e x = 4 m x = 0,5 b p = 0,5 w + 2 m x + 0,625 e x = e + 2 m x + 0,625 e x = 2 m x 4 e
Leff , 2 min 1 ; 3 ; 4 ;
5
Leff .5
= π m
=
Leff .4
=
b 2 a
m
2
=
Leff .3
eb
m ea
(a − a c )2 + (b − bc )2 2
=
ea
2
+ eb 2
8 e a eb
m
−
ea
2
+ eb 2
(a − a c )2 + (b − bc )2
L eff = min ( Leff .1 ; Leff .2 ; Leff .3 ; Leff .4 ; Leff .5 )
5
Base plate in bending and concrete in compression
Basis of design Components
Column flange
FSd
FRd c
Assembly
tw
c
t
L
– Resistance – Stiffness – Pre-design
Leff .2
6
– Base plate in bending and bolt in tension – Base plate and concrete in compression – Anchor bolt in shear
bc
m
Leff .1 = π m
Scope of the Lecture
b
Base plate
Classification Worked examples Summary
f j
Flexible base plate
3D behaviour – concrete in crushing
M
Concrete 3D Resistancein Crushing (the same as EN1992-1-1)
a1 a
c
c c
c
c
a r
c
t
Joint coefficient
Effective width
Effective width
k j =
a 1 b1 ab
⎧a + 2 a r ⎫ ⎪5 a ⎪ ⎪ ⎪ a 1 = min ⎨ ⎬ a h + ⎪ ⎪ ⎪⎩5b1 ⎪⎭
t h
b b r
a1
≥a
⎧b + 2 br ⎫ ⎪5 b ⎪ ⎪ ⎪ b1 = min ⎨ ⎬ b1 ≥ b ⎪b + h ⎪ ⎪⎩5 a 1 ⎪⎭
b1
c
Effective width
M′ = M
Elastic resistance ensuring small deformations, to unit length
1 M ′ = 1f j c 2 2 M ′ =2 f j c
Bending moment to unit length
1 1 f 2c 2 =112t 2 f f j c j = 6t f y y 22 6
Equivalent length of cantilever c Effective width
c=t
f y 3 γ Mc0=f jt
f y 3 γ M 0 f j
2
1 22 t f ydf yd 6
Comparison to FE simulation
Contact Area
Vertical deformation at the surface, mm
c
0,0
c
}
F
Vertical deformation along the block height top of the concrete block elastic deformation of the whole block
elastic deformation δ glob
local deformation under plate
c
A
Ap
0,1
deformation at the edge δ edge
predicted value
deformation at the axis δ axis
A eq
edge
c
c
axis
Vertical deformation, mm
foot of the concrete block 0
0,1
c
Stiffness F r
Comparison to Experiments a r
F tw
1600
E c
L
F
E c
1000
k c
E
a eq . el L
1 , 5 * 0 ,85 E
a eq.el = t w + 2,5 t
E c
a eq . el L
800
1 , 275 E
Prediction based on local and global deformation,
600
a eq.str = t w + 2 c = t w + 2 t
f y 3 f j
400 M 0
c fl
Prediction based on local deformation only
200 0
x
0
E I p
δ
0,1
0,2
0,3
0,4
0,5
0,6
0,7
0,8
0,9 Deformation, mm
Grout t t g
Scope of the Lecture
t g
t g
h
L
Experiment Concrete and grout Concrete
1200
ar
t
Calculated strength
1400
0 ,85 F r
Force, kN
1800
deformation of elastic hemisphere
E c A r
o
45
t g
– Base plate in bending and bolt in tension – Base plate in bending and concrete in compression – Anchor bolt in shear
o
45
β j = 2 / 3
f c.g ≥ 0,2 f c t g ≤ 0,2 min (a ; b) t g ≥ 0,2 min (a ; b)
lower nut
packings
Basis of design Components
Assembly – Resistance – Stiffness – Pre-design
Classification Worked examples Summary
Components in Shear
Anchor Bolt in Shear Fh
Resistance in tension
Fh
Reduce resistance in tension
δ h
Resistance in bending and shear δ h
0
5.6
4.6
F v .Rd =
0 ,375 f ub As
F v .Rd =
0 ,250 f ub As
Mb
Mb
Format as bolts in shear
Resistance
Scope of the Lecture
N Rd
Basis of design Components – Base plate in bending and bolt in tension – Base plate in bending and concrete in compression – Anchor bolt in shear
r b
M Rd
M 2, N 2
= Aeff f j − ∑ F t . Rd
Basis of design Components
N M=0
Assembly – Resistance – Stiffness – Pre-design
= ∑ F t . Rd r b + Aeff f j r c .
compression
Interaction diagram
Aeff f j r c
– Base plate in bending and bolt in tension – Base plate and concrete in compression – Anchor bolt in shear
M N=0
0
F t .Rd r b
Scope of the Lecture
F t.Rd
j
Plastic design –force equilibrium Complex shape of contact area
M
M Rd
f − ∑ F t . Rd = A f eff j
∑
M1 , N 1
tension
N Rd
N Rd = Aeff M f j Rd - = F F t .t Rd . Rd r b + Aeff f j r c .
Classification Worked examples Summary
N Rd
Aeff active part
r c
∑ F t.Rd
Assembly – Resistance – Stiffness – Pre-design
M Rd
N
Classification Worked examples Summary
History of Loading MRd
N Sd
Moment Non-proportional loading
M Sd c c
Non-proportional loading Proportional loading
Moment Proportional loading
Nonlinear part of the curve
N Rd
Normal force
0
φ
Anchor bolts in tension and one flange in compression
F t
= Aeff f k j −⎪⎨ ∑ F t . Rd t
⎪ ⎩
k c
k b
k c
k c
= ∑ F t . Rd r b + Aeff f j r c .
M Rd
S j.ini Rotation
0
k p
⎧
F c
e0 NSd
c
cc
c
c
z z c
z T
Column base resistance
Plastification of one component
c
M Rd min 1
FT . Rd z z c
F c . Rd z z t
; 1
M Sd / N Sd
M Sd / N Sd
Simplified contact area
Stiffness S j
M Sd / N Sd M Sd / N Sd
E z 2 1
k t
N Rd
c
80
c c
= Aeff f j − ∑ c F t . Rd
c
cc
c
∑
F r M / 2 Rd = MSd / N Sd r / 2 M Rd / N Sd M Sd / N Sd Simplified contact area 1
r
20
k c
M 20 - 10.9
t
= Aeff f j − ∑10F t . Rd Rotation, mrad
0
k c
Rd
15
N Rd
+ Aeff f j r c .
k b
M
60
0
k ⎧ p ⎪t . Rd b ⎨k t ⎪ ⎩
400 kN HE 160 B
20
40
2 ,7
1 ,5
t = 30 25
120 100
ki
z c k c z t k t k c
Moment, kNm
x c
M Sd / N Sd = konst.
5
10
15
M Rd
= ∑ F t . Rd r b + Aeff f j r c .
20
25
30
k c
Sensitivity study, base plate thickness
N Sd
Normal force, kN
M
Sd
3 000
Lever arm is changing by the activation of one bolt row Lever arm is changing by the activation of both bolt rows 40 Simplified prediction
M 24
t 30
Base plate thickness, t, mm 2 000
Components
HE 200 B
Force, kN
200
M pl.Rd h = 1 000
1 000
20 15
N Rd
F t . Rd = Aeff f Column j − ∑ resistance
0 1 600 420 590
200
M Rd 100
= ∑ F t . Rd r b + Aeff f j r c .
420
0
80
Base plate 0,5
200 E k c Force, kN
1 600
0
N Rd 40 = Aeff f j 20 Rd
M
0,5 Concrete , mm
Deformation,
Experiment W7-4.20-prop
60
100
Moment, kNm
Sensitivity study, baseplate thickness, resistance
Anchor bolt 0,5 Force, kN
100 E k p 590
0
Moment, kNm
E k b
100
Npl.Rd 30 25
Assembly
−Prediction ∑ F t . Rd
N HE 160 B t = 20 h = 500
= ∑ F t . Rd r b + Aeff f j r c .
0 0
Comparison to experiment
10
Rotation, mrad
M
Pre-design, stiffness
Scope of the Lecture
2
S j .ini .app =
E z t
20
M
M
Sd
N Rd
= Aeff f j − ∑ F t . Rd
M Rd
= ∑ F t . Rd r b + Aeff f j r c .
– Base plate in bending and bolt in tension – Base plate and concrete in compression – Anchor bolt in shear
Sd
z
Basis of design Components
Assembly – Resistance – Stiffness – Pre-design
z
Lever arm
Classification
Classification Worked examples Summary
Non-Sway by Resistance
According to stiffness
t = 12 mm a 1 = b1 = 280 mm a = b = 500 mm h = 1000 mm M 24 -420 S j,ini,pin = 7 100 kNm / rad
F cr.pin
β =
F cr,res
1
Accuracy
0,9
5% in resistance and 10% in serviceability
S j,ini,pin
t = 40 mm a 1 = b1 = 420 mm a = b = 500 mm h = 1000 mm M 24 -420 S j,ini,stif = 74 800 kNm / r
0,8
S j,ini,stif 0,7
Simillar to beam-to-column joints
0,6
_
0,0001
0,01
1,00
100,0
log S
2
o
pro
o
pro 0,5 < pro
o
0,5 o
S j,ini < 3,93
3,93
Sway Frames for Serviceability
0
S j,ini 7 (2
o
- 1) E I c / L c
S j,ini 48 E I c / L c
115 kN
y HE 200 B
1,0
1 , 36
0,6
S j,ini 12 E I c / L c.
S j,ini,pin
0,4
5m
S j,ini,stif
0,2
Asked stiffness for relative slenderness
0 0,0001
4m
HE 200 B
0,8
o
115 kN
5 kN
yS / yP
0,01
1
100
log S
Scope of the Lecture
Relative moment 1,0 Rigid connection 0,8 S j.ini.c.n 0,6
= 30 E Ic / L c
S j.ini.c.s
0,4 0,2 0
= 12 E Ic / Lc Semi-rigid connection
o
– Base plate in bending and bolt in tension – Base plate and concrete in compression – Anchor bolt in shear
= 1,36
Hinge
0
0,1
0,2
0,3
Basis of design Components
Relative rotation,
Assembly – Resistance – Stiffness – Pre-design
In relative values
Classification Worked examples Summary
c b c =200
Worked Example – Base plate
c
c tw=9 c a1 = 1600
M Sd
FSd
a = 420
a r = 590
HE 200 B M 24
t = 30 30
c c
t f =15 e a= 50
b r = 590
h c =200
e b = 90 b = 420
p = 240 h = 1000
b1 = 1600
b eff
t f =15 c c
r b = 160
e c = 60
r b r c
Contact area
Worked Example – Frame (sway) M j.Rd / M Ny.pl.Rd
1,0
F
Sd
0,8 S
0,6
j.ini.c.n
0,4
S
(for
= 12 E I c / L c
o
Sd
F
F
Sd
Sd
F
Sd
F
Sd
F
Sd
IPE 550
F
Sd
2
1,2 m
1 , 36 )
HE 340 B
0,2 0
Sd
2
= 30 E I c / L c
j.ini.c.s
F
F
HE 340 B 9 m
0
0,1
0,2
0,3
E I c / L c
Worked diagram 24 m
F y
F y
F y
F y 2
F y
F x
F y F x
F x F x F x 2 F x = 0,38 kN
F y F x
F y F x
F y = 23,00 kN
w
1
F y 2
F y
F y 2
F y
F y
F y
F y
Frame imperfections – by equivalent forces
Element imperfections – by stability check
F y 2
F x 2
N
N H φ
F y = 26,79 kN
w
2
w = 2,64 kN/m
F y
F y
1
w = 1,65 kN/m 2
First load combination
Second load combination
φ
Load combination
H φ N
N
Comparison
Maximal moment in base plate kNm
Elastic design – connection stiffness, pre-design
z
S j .ini . b c
z
S j .ini . b b
E z 2 t
210 000 * 700 2 * 20
k f
8 , 5
E z 2 t
210 000 * 700 2 * 20
k f
6
242 100 kNm / rad
343 000 kNm / rad
Maximal moment in corner kNm
Maximal moment in rafter kNm
Vertical deformation of rafter mm
Horizontal sway of corner mm
0
337,85
318,10
113,68
73,70
108,20
290,13
307,62
109,80
27,43
214,09
305,90
274,73
95,54
19,42
3 2,5 2
S j .ini . cb
E z 2 t
210 000 * 400 2 * 30
k f
20
1,5
50 400 kNm / rad
1 0,5 0
z
Scope of the Lecture
Basis of design Components – Base plate in bending and bolt in tension – Base plate and concrete in compression – Anchor bolt in shear
Assembly – Resistance – Stiffness – Pre-design
Classification Worked examples Summary
Summary
Component method Good accuracy
Worked examples –Savings by taking into account of stiffness (for serviceability only) –Hand calculation unusual
List of Lessons at Seminar 1. 2. 3. 4. 5. 6. 7. 8. 9.
Fire Design of Connections Lessons Connection Design according to EN 1993-1-8 Prof. František Wald
Introduction Bases of design according to EN 1993-1-8 Welded connections Bolted connections Basics of structural joints Design of simple connections Column bases Fire design of connections, EN 1993-1-2 Seismic design, EN 1998-1-1
1
2
Scope of the Lecture
Structural fire design
Temperature of connections
Connectors at elevated temperature
Component method
Structural integrity
Summary
Structural Fire Design – Procedure of Design
Thermal analyses of fire compartment or local fire (EN 1991-1-1)
Transfer of heat into the structure (EN 199x-1-2)
Mechanical loading at fire situation (EN 1990, EN 1991-1-x)
Mechanical modelling of structure at elevated temperature (EN 199x-1-2)
3
Connections under Fire
EN 1993-1-2 Approaches
Steel looses with temperature strength and stiffness
Steel structures expand when heated and contract on cooling
4
Temperature within the connections is lower compare to connecting steel members
Fire protection is applied to the member and its connections
Component approach in EN 1993-1-8 together with a method for calculation the behaviour of welds and bolts at elevated temperature
5
Rules based to protect as members
Connection moment, shear and axial capacity can be evaluated at elevated temperature 6
Scope of the Lecture
Analytical Models of Heat Transfer 1. Section factor ( Am /V) method simmilar as for members Am /V surface/volume ratio
Structural fire design
Temperature of connections
Connectors at elevated temperature
Component method
Structural integrity
Summary
2. Based on the temperature of the beam lower flange Concrete slab
h h h
h ≤ 400 mm 0,62 θ 0
h > 400 mm
0,75 θ 0
0,88 θ 0
0,88 θ 0
0,88 θ 0
0,70 θ 0
7
Accuracy Demonstration on 7th Large Scale Fire Experiments on Steel Frame A
B
9000
C
9000
E
D
9000
9000
Temperatures in elements and connections
9000
Internal forces in the connections
Behaviour of the composite slab
2
6000 1
January 16. 2003
Motivation
3
Fire Test
F
9000
4
6000
8
Fire Compartment for Structural Integrity Fire Test, January 16, 2003
9
10
Fire Compartment Instrumentation
Interier
Exterier, Fire load 11
148 thermocouples 57 low temperature strain gauges 10 high temperature strain gauges 37 deformations 10 video cameras 2 thermo-imaging cameras
12
Moderate Fire
No Collapse Reached
Maximal temperature 1108 °C in 55 min
Deflections over 1000 mm; residual deflections 925 mm
13
14
Fin Plate Connection before the Experiment
Instrumentation
West view
D
E
C442 C443
Walls C454 - 462
2
C486 - 488
G521
C463 - 471 G525
G522
G526 C441 - 449
C447 C444 C448 C445
C441
C472 - 475
C449
C446
C475 - 479 G529
G533
120 D1/2-E1/2
G534
North view
G530 C450 - 453
C483 - 485
C483 C484
G523
G527
G531
FIRE COMPARTMENT
C485
G535 N G536
D2
E2
1
G524
G528
C480 - 482
G532
Window
Fin plate connection
Thermocouples at elements and connections, numbered Cijk Thermocouples in compartment 300 mm below ceiling, numbered Gijk
Fire compartment
DE1/2
West view C450 4th bolt row C451 3rd bolt row C4522nd bolt row C453 1st bolt row
N D1
E1
120 E1/2-D1/2
15
t = 26 min.
t = t0t +t==028’ 2 6hm28’ in
θcon,ø = 275 °C
980, 0°C
16
T= 330 °C = 330 275=°C °C θθ con,ø con,ø con,ø
980,0°C
In 26 min of fire is temperature of the structure under 400°C 800
600
600
Gas temperature
Gas temperature Heating θ ,°C
400
1000
400, 0°C
600 0 0
800
Time 30
60
90
1000
0 0
t, min
17
Heating
θ ,°C
400 400,0°C
600
Time 30
60
90
t,min
18
t = t0 +t =042 h min 42’
Tcon,ø 645 °C = 645=°C θcon,ø
t = t0 +t =044 h min 44’
Tcon,ø 660 °C = 660=°C θcon,ø
980,0°C
980,0°C
Buckling of beam lower flange
1000
Buckling of beam lower flange
θ ,°C
800
800
600
600
400 400,0°C
600 0 0
30
60
90
1000
θ ,°C
400 400,0°C
600 0 0
t,min
30
60
90
t,min
25
t = t0 +t =046 h min 46’
26
Tcon,ø 685 °C = 685=°C θcon,ø
t = t0 +t =048 h min 48’
Tcon,ø 710 °C = 710=°C θcon,ø
980,0°C
1000
θ ,°C
980,0°C
800
800
600
600
400 400,0°C
600 0 0
30
60
90
1000
θ ,°C
400 400,0°C
600 0 0
t,min
30
60
90
t,min
27
t = t0 +t =050 h min 50’
28
Tcon,ø 730 °C = 730=°C θcon,ø
t = t0 +t =052 h min 52’
980,0°C
1000
θ ,°C
0 0
980,0°C
800
800
600
600
400 400,0°C
600
30
60
90
1000
29
θ ,°C
400 400,0°C
600 0 0
t,min
Tcon,ø 775 °C = 775=°C θcon,ø
30
60
90
t,min
30
t = t0 +t =054 h min 54’
Tcon,ø 810 °C = 810=°C θcon,ø
t = t0 +t =056 h min 56’
The maximal temperature of 1088 °C of secondary beam was reached by its lower flange in 57 min
980,0°C
Gastemperature θ ,°C Cooling
1000
30
60
90
800
600
600
400,0°C
Time
0 0
Gas temperature θ ,°C Cooling
400
1000
400,0°C
600
Time
0 0
t,min
30
60
90
t, min
31
t = t0 +t =058 h min 58’
32
Tcon,ø 855 °C = 855=°C θcon,ø
t = t0 +t =160 h min 00’
Tcon,ø 880 °C = 880=°C θcon,ø
980,0°C
Gas temperature Cooling θ ,°C
980,0°C
800
800
600
600
400
1000
400,0°C
600
30
60
0 0
34
800
800
600
600
1000
35
θ ,°C
400 400,0°C
600 0 0
t,min
Tcon,ø 885 °C = 885=°C θcon,ø
980,0°C
400
90
t,min
980,0°C
400,0°C 60
90
t = t0 +t =164 h min 04’
θ ,°C
30
60
Tcon,ø 900 °C = 900=°C θcon,ø
Maximal temperature of fin plate connection 908,3°C was reached in 63 min
600
Time 30
33
t = t0 +t =162 h min 02’
1000
400 400,0°C
0 0
t,min
90
Gastemperature Cooling θ ,°C
1000 600
Time
0 0
980,0°C
800
400
600
Tcon,ø 835 °C = 835=°C θcon,ø
30
60
90
t,min
36
t = t0 +t =178 h min 18’
Tcon,ø 755 °C = 775=°C θcon,ø
t = t0 +t =180 h min 20’
Tcon,ø 745 °C = 745=°C θcon,ø
980,0°C
1000
θ ,°C
980,0°C
800
800
600
600
400 400,0°C
600 0 0
30
60
90
1000
θ ,°C
400 400,0°C
600 0 0
t,min
30
60
90
t,min
43
t = t0 +t =182 h min 22’
44
Tcon,ø 740 °C = 740=°C θcon,ø
t = t0 +t =184 h min 24’
Tcon,ø 730 °C = 730=°C θcon,ø
980,0°C
1000
980,0°C
800
800
600
600
400
θ ,°C
400,0°C
600 0 0
30
60
90
1000
θ ,°C
400 400,0°C
600 0 0
t,min
30
60
90
t,min
45
t = t0 +t =176 h min 26’
46
Tcon,ø 720 °C = 720=°C θcon,ø
t = t0 +t =178 h 28’ min
980,0°C
1000
θ ,°C
0 0
980,0°C
800
800
600
600
400 400,0°C
600
30
60
90
1000
47
θ ,°C
400 400,0°C
600 0 0
t,min
Tcon,ø 710 °C = 710=°C θcon,ø
30
60
90
t,min
48
Fin plate connection after the fire test
Temperature Differences Measured by Thermocouples
Measured temperature, °C D2
E2
D1
E1
Difference shown 1000 by the thermo imaging 800 camera 600 400
Fin plate, by 4th bolt
200
Beam, bottom flange
0 0
15
30
45
60
75
90
105
120
135
Time, min
Maximal temperature of fin plate by 4th bolt 908 °C in 63 min 67
Analytical Prediction Compared to Test Connection temperature, °C
68
Scope of the Lecture
Predicted from gas measured temp. based on "section factor"
1000 800
D2
E2
600 Predicted from beam bottom flange based on measured temp.
400
D1
E1
200 Measured
Structural fire design
Temperature of connections
Connectors at elevated temperature
Component method
Structural integrity
Summary
0 0
15
30
45
60
75
90
105
120
135
Time, min
Measured 908 °C in 63 min.; predicted 878 °C in 53 min 69
Bolts and Welds Properties at Elevated Temperature
70
Bolt Resistance at Elevated Temperature
Factors k b,θ; k w,θ are used to describe the strength reduction
Marked loss of strength between 300 and 700ºC
1
Shear resistance of bolts in fire
Bolt
0,9
F v ,t ,Rd = F v ,Rd k b ,θ
k b,θ
0,8
0,7 Carbon steel
0,6
F b ,t ,Rd = F b ,Rd k b ,θ
k y,θ
0,5
0,4 0,3
Bearing resistance of bolts in fire Tension resistance of a bolts in fire F ten ,t ,Rd = F t ,Rd k b ,θ
Weld k w,θ
0,2 0,1
γ Μ partial safety factor for the resistance
0 0
200
400
600
800
1000
θ a ,°C 71
γ Μ ,fi partial safety factor for fire
72
γ m γ m ,fi γ m γ m ,fi γ m γ m ,fi
Filled Weld Resistance at Elevated Temperature
Design strength per unit length of a fillet weld in a fire F w ,t ,Rd = F w ,Rd k w ,θ
Butt Weld Resistance at Elevated Temperature
For full penetration butt weld up to 700ºC as equal to the strength of the weaker part of the joint using the appropriate reduction factors for steel
For temperatures higher than 700ºC the reduction factors for fillet welds to butt welds
γ m γ m ,fi
γ Μ partial safety factor for the resistance γ Μ ,fi partial safety factor for fire
73
Scope of the Lecture
74
Component Method
Structural fire design
Temperature of connections
Connectors at elevated temperature
Component method
Structural integrity
Summary
Decomposition of joint Componnet description Joint assembly
M
z
75
Component Method
Component Method
Decomposition of joint Componet description Joint assembly
Component
Deformation F i ;θ
K i ;θ
=
k y ;θ k E ;θ
Stiffness K i ;θ = k E ,θ K i ; 20 º C ;
Decomposition of joint Componnet description Joint assembly
M i ;θ = k y ;θ M i ; 20 º C ;
Rotation
δ i ; 20 º C
φ i ;θ =
Stiffness
S i ;θ =
M i ;θ S i ;θ
=
k y ;θ k E ;θ
M
z
Moment
F i ;θ = k y ,θ F i ; 20 º C ; δ i ;θ =
Joint
Force
76
M, kNm
Moment
20 ºC
φ i ; 20 º C ;
100ºC 500ºC
50
600ºC
2
E θ z = k E ;θ S i ; 20 º C ; 1 ∑ k 77 i i ; θ
0
0
20
40
800ºC 60
700ºC 80
Rotation , mrad 100 78
P 28 500 kN
500 kN
150
Worked Example
Fire Resistance
Fire resistance of an end plate connection of the truss lower flange
Required R30
125
40
45
4 x M24
Unprotected Am / V = 54 ,0 / 1 ,24 = 43 ,18 m - 1 Section factor Fire resistance t = 44 min (exposed to nominal standard fire curve)
d p = 15 mm Protected Intumescent paint Am λ p 0 ,1 = 43 ,18 = 288 Wm - 3 K - 1 Fire resistance V d p 0 ,015 (exposed to nominal standard fire curve) t = 112 min 80
P 28 500 kN
85
500 kN
150
85
125
4 x M24
40 45
79
Scope of the Lecture
Structural Integrity
Structural fire design
Temperature of connections
Connectors at elevated temperature
Component method
Structural integrity
Summary
If used catenary actions of beams and slabs
In case of advanced design models
Resistance of connections to horizontal forces at ultimate limit state (for f u)
81
82
FE Simulation of Cardington Test
Experiment in Cardington
Normal force, kN 300 I. Beam only II. One section III. Full floor
200 100 0
40
20
60
-100
80
100 Time, min
-200 Model of structure
- 300 720°C Heating
Cooling 6 x 3,75 m
Observed joint I.
II. III.
4 x 6,0 m
83
84
Low Temperature Strain Gauges D1
PLAN
5th floor
Internal wall of the fire compartment 11,0 m 7,0 m
99
97
103
101
Window 1,27 x 8,70 m D1 UC 305 x 305 x 198
111
109
91
107, 111 89
85
87 E1 UC 305 x 305 x 137
83,87
95
115
20
113
119 15,2 127
309,2 (314,5) 320,5 y 13,8 (339,9) (19,1)
(31,4) 21,7
z
20
105, 109
89, 93
4th floor
500
117 115, 119
93 91, 95
81, 85 500
UC 305 x 305 x 137 (UC 305 x 305 x 198) 20
105
107
500
99, 103 97, 101 81
83
N
Protected Columns E1
113,117
At external columns
125
123
121 127, 123
121, 125 500
20
3rd floor
Internal
85
Measured Stresses at External Columns
External (with 1 m of beam)
86
Measured Bending Moments in Columns
Stress, MPa Column E1 91 89
Column D1 83 81
150
Bending moments, kNm 600
93 100
87
95 87
50
85
95
93
15
30
45
60
75
90
105
120
135
150
165
180
195
-100 -150
3rd floor
200
a-D1
2nd floor Time, min.
0 D1, E1
c-D1; c-E1 b-D1
c-E1
210
-50
81 83 89 91
d-D1; d-E1 4th floor
c-D1
400
Time, min.
0
5th floor
b-D1
0
60
D2
D1
120 d-E1
4th floor
500 mm
d-D1
-200 a-D1
-200
Section 500 mm above the floor at 4th floor 87
Measured Forces in External Columns Force, kN c-E1 3rd floor (5th foor)
100
60
-100 -200
4th floor
-300 -400 -500
d-D1 120
F t,5
F t,4 4th floor F t,4
d-E1
3rd floor
Time, min. d-D1 d-E1
c-D1; c-E1 b-D1
BS 5950: Structural use of steelwork in buildings
EN 1991-1-7 Actions – Exceptional loading
a-D1 Column ties
F t,3
F t,3 0
Required Tie Forces - References d-D1; d-E1
c-D1
200
0
F t,5 5th floor
Everage
300
88
2nd floor D2
D1 Tie anchoring re-entrant corner
Everage c-D1
c-E1 A
Beam model
Tie anchoring free column A Edge ties
Beams not used as ties
Forces at 3rd, 4th and 5th floor calculated from strainganges at level c,d 89
90
Required Tie Forces
Scope of the Lecture
Column ties
Tie anchoring re-entrant corner
A Tie anchoring free column A Edge ties
Beams not used as ties
F t = min [0,5 ( 1,4 g k + 1,6 qk ) st L; 75]
Structural fire design
Temperature of connections
Connectors at elevated temperature
Component method
Structural integrity
Summary
gk the characteristic value of permanent action, qk the characteristic value of variable action, L the beam span st
the mean transverse spacing of the ties adjacent to that being checked
91
Summary
List of Lessons at Seminar
Well designed connections at ambient temperature do not need to be recalculated at elevated temperature, if are not directly exposed to fire
The structural fire design according to EN 1993-1-2 is ready for design of connections exposed to fire
Thermal analyses of fire compartment or local fire EN 1991-1-2
92
Transfer of heat into structure
Mechanical behaviour at elevated temperature
1. 2. 3. 4. 5. 6. 7. 8. 9.
Introduction Bases of design according to EN 1993-1-8 Welded connections Bolted connections Basics of structural joints Design of simple connections Column bases Fire design of connections, EN 1993-1-2 Seismic design, EN 1998-1-1
EN 199x-1-2 93
Thank you for your attention
95
94
List of Lessons at Seminar 1. 2. 3. 4. 5. 6. 7. 8. 9.
Seismic Designof Connections Lessons Connection Design according to EN 1993-1-8 Prof. František Wald
Introduction Bases of design according to EN 1993-1-8 Welded connections Bolted connections Basicsof structural joints Design of simple connections Column bases Fire design of connections, EN 1993-1-2 Seismic design, EN 1998-1-1
1
Scope of the Lecture
Principles
Design criteria
Beam-to-column typologies
Design and fabrication recommendations
Welding technology
Strain-rate loading
M - φ modelling
Column web panel
Summary
2
Principles
Basic conditions
Northridge and Kobe earthquake
Over-strength demand Ductility demand (rotation capacity) Robustness demand (reliable detailing together with material behaviour)
Unexpected damages to connections
Detailing practices
Welding
3
Scope of the Lecture
4
Design Criteria for Seismic Resistant Frames
Principles
Strong Column/Weak Beam design principle
Design criteria
Panel zone strength
Connection strength and degradation characteristics
P-δ effects
Member local buckling
Beam-to-column typologies
Design and fabrication recommendations
Welding technology
Strain-rate loading
M - φ modelling
Column web panel
Summary
5
6
Requirements for Connection Successful Performance
Design Criteria in USA
Guidelines designs for frames with different anticipated seismic demands
1997 NEHRP Provisions
AISC Seismic Provisions
Ordinary Moment Resisting Frames (OMRF)
Intermediate Moment Resisting Frames (IMRF)
Plastic rotation capacities of 0,01rad Plastic rotation capacities of 0,02rad
Special Moment Resisting Frames (SMRF)
Plastic rotation capacities of 0,03rad
7
Design Criteria in Europe
General rules for steel connections in dissipative structures
Rotational stiffness of a jointS j
axial force NSd in the connected member not exceed 10%
Rotation capacity
Beam-to-ColumnTypologies
Base Material Notch-Toughness
Weld Wire Notch-Toughness
Weld backing and Run out Tabs
Reinforcing Fillet Welds
Cope Hole Size, Shape, Workmanship
Bolted Joints
Bolt Sizing, Hole Type, Tightening
Net Section Strength
8
Design criteria
Beam-to-column typologies
Design and fabrication recommendations
Welding technology
Strain-rate loading
M - φ modelling
Column webpanel
Summary
10
Connection Types
FEMA/SAC test programmes
Principles
9
Through-Thickness Strength
Requirements for MRF (Moment Resistant Frame) beam-to-column connections
EN 1993-1-8
Scope of the Lecture
EN 1998-1-1 basic provisions concerning steel joints
Welded Joints
Prescriptive Moment Frame Connection
Connection type classified for certain ranges of
Member size
Plastic rotation angle
Connection types
Welded Unreinforced Flange (WURF)
Welded Cover Plated Flange (WCPF)
Welded Flange Plates (WFP)
Welded Vertical Ribbed Flange (WVRF)
Welded Column Tree with Bolted Beam (WCT/BB)
Welded Single Haunch (WSH)
Welded Double Haunch (WDH)
11
12
Welded Flange Plate Connection
Welded Column Tree with Bolted Beam
13
Field Bolted Types of Connections
Field Bolted Types of Connections
Guidelines as pre-qualified for certain conditions of use
Bolted end plate (BEP)
Welded flange plates with bolted beam(WFPBB)
Bolted single haunch(BSH)
Bolted double haunch(BDH)
14
Bolted end plate (BEP)
15
Field Bolted Types of Connections
16
Field Bolted Types of Connections
Welded flange plates with bolted beam(WFPBB)
17
Bolted double haunch (BDH)
18
Beam-to-ColumnTypologies
Beam-to-ColumnTypologies
Specific joints in Japan
Specific joints in Europe
Stiffener
Extended endplate joint
A
Stiffener
A
. . . 10M20 - 10.9 A-A
19
Beam-to-ColumnTypologies
Beam-to-ColumnTypologies
Specific joints in Europe
Welded joint
20
B
B
Specific joints in Europe
Welded flange plate joint
C
C
.
. .
.
.
.
3M20 - 6.6 C-C
B-B
21
General Rules for Steel Connections in Dissipative Structures
Scope of the Lecture
Principles
Design criteria
Beam-to-column typologies
Design and fabrication recommendations
Welding technology
Strain-rate loading
M - φ modelling
Column web panel
Summary
22
Localisation of plastic strains, high residual stresses, and fabrication defects
Non dissipative connections of dissipative members
Full penetration butt welds
By experimental evidence
Deemed to satisfy the overstrengthcriterion
For fillet weld or bolted non dissipative connections Rd ≥ 1 ,35 R fy
23
24
General Rules for Steel Connections in Dissipative Structures
Bolted joints
Shear joints with fitted bolts are also allowed.
Theshear resistance of the bolts should be higher than 1,2 times the bearing resistance
26
Design and Fabrication Recommendations
Plastic rotation capacity φ Cd in the plastic hinge Not less than 35mradfor structures of ductility class H and 25mrad for structures of ductility class M withq>2. Under cyclic loading without degradation of strength and stiffness greater than 20% Supported by experimental evidence
Partial strength connections
Connections have a rotation capacity consistent with global deformations Members framing into the connections are demonstrated to be stable at the ultimate limit state (ULS) Effect of connections deformation on global drift is taken into account
25
Connection design
Requirements for Moment Resistant Frame Beam-to-ColumnConnections
Connections between the beams and the columns should be designed for the required degree of overstrength Moment resistanceMpl.Rd and the shear force (VG, E d + V M,Ed) evaluated in 6.6.2 of standard EN 1998-1
Dissipative semi-rigid and/or partial strength connections are permitted provided all of the following conditions
Should be supported by experimental evidence For all types of connections in dissipative zones Available plastic rotation φ = δ /( 0 ,5 L ) p
The strength and ductility of members and their connections under cyclic loading
Structure dissipate energy in the beams
Boltedshear connection
In shear categories B and C (slip resistant) only Un tension category E With controlled tightening of the bolts
Requirements for Moment Resistant Frame beam-to-column connections
Material properties Yield-to-Ultimate Stress Ratio (YUSR)
YUSR (f y/f u) = 0,65 or 0,80
YUSR = 0,95
Column capacity design from the plastic capacity of connections
For a plastic rotation capacity up to 0,030 rad. Reduced plastic hinge length at a plastic rotation capacity of 0,030 rad
The plastified length of the beam with YUSR= 0,95
Half the corresponding length in YUSR = 0,80
27
Scope of the Lecture
Principles
Design criteria
Beam-to-column typologies
Design and fabrication recommendations
Welding technology
Strain-rate loading
M - φ modelling
Column web panel
Summary
28
Design and Fabrication Recommendations
29
Access Hole Size and Geometry
30
Design and Fabrication Recommendations
Scope of the Lecture
Access Hole Size and Geometry Increasing the size of the web cope
Easier welding on the beambottom flange Better weld quality
Principles
Design criteria
25 25
10 10
20
38
25
20
25
50
Standard Modified Configurations of weld access hole
Design and fabrication recommendations
Welding technology
Strain-rate loading
M - φ modelling
Column webpanel
Summary
32
Strain-Rate of Carbon Steel
The strain-rate loading has an important influence on the behaviour of joints A strain rate typical for steel members yielding under seismic action in the range of 0,03-0,06 s-1
Beam-to-column typologies
31
Strain-Rate Loading
Stress
Increasesthe yield strength Lower ultimate strength of welded connections Ductility is reduced by up to 27% Decrease of ductility due to high strain rates is not straightforward for cyclic loading
Conventional speed E
Very high speed
Strain
33
Strain-Rate of Carbon Steel
34
Strain-Rate of Austenitic Steel
α DIF , fy = f y ,dyn / f y
800
α DIF , fu = f u .dyn / f u
600
Stress, MPa
α DIF . fy
>1s 100 ms 10 ms 1 ms
1,0 1,1 1,6 1,9
α DIF . fu
-1 -2 -1
10 s
-4 -1
10 s
140 s -1
400
Time to yield stress
502 s
50 s -1 200
1,00 1,05 1,05 1,05
Strain, %
0 15
35
30
45
60
EN 10088-2 1.4307 (304L) increaseof f 02 o cca 7% - 28%
75
36
Scope of the Lecture
M - φ Modelling
Principles
Stable behaviour
Design criteria
Unstable curve
Slip in connection
Beam-to-column typologies
Design and fabrication recommendations
Welding technology
Strain-rate loading
M - φ modelling
Column web panel
Summary
Stable behaviour
Unstable curve
M
φ
φ
φ
37
38
Parametres
M - φ Modelling
M
M
Slip in connection
Rotational capacity
Energy
39
β Δ .i =
β e =
Rotational capacity and energy
E i
β E .i =
β M .i =
Resistance
E i φ i
φ el M j .el (φ ix − φ el ) S j .i S j .ini M j .i M j .ini
M
Models
Exponential Curve
Curve fitting
Initial stiffness
S j,ini
Initial stiffness
Moment resistance
M0
Moment resistance
Unloading
S j,s
M a
Assembling
S j.ini
S j.s S j.ini
φ a
φ
S j.s - M 0
Component Component cycling description
40
M 0
Unloading
φ j .el
M j .el (φ i − φ el )
β S .i =
Stiffness
φ j .i
M j = S j .i φ i = M i −1 −
41
) − S j .s (φ a − φ ) 1 / n n ⎤ (S j .ini − S j .s )(φ a − φ ) S j .ini − S j .s (φ a − φ )
⎡ ⎢1 + ⎢⎣
2 M 0
⎥ ⎥⎦
42