CGNA18563ENS_001
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CGNA18563ENS_001...
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COMMISSION SCIENCE RESEARCH DEVELOPMENT
technical steel research
Properties and in-service performance
Frame design including joint behaviour
Report EUR 18563 EN
h STEEL RESEARCH
EUROPEAN COMMISSION Edith CRESSON, Member of the Commission responsible for research, innovation, education, training and youth DG XII/C.2 — RTD — Actions: Industrial and materials technologies Materials and steel fl
Contact: Mr H. J.-L. Martin Address: European Commission, rue de la Loi 200 (MO 75 1/10), B-1049 Bruxelles — Tel. (32-2) 29-53453; fax (32-2) 29-65987
European Commission
technical steel research Properties and in-service performance
Frame design including joint behaviour Prof. R. Maquoi Université de Liège Département M.S.M. Quai Banning 6 B-4000 Liège
Β. Chabrolin Centre Technique Industriel de la Construction Métallique Domaine de Saint-Paul BP64 F-78470 Saint-Remy-les Chevreuses
Contract No 7210-SA/212/320 1 July 1993 to 30 June 1996
Final report
Directorate-General Science, Research and Development
1998
EUR 18563 EN
LEGAL NOTICE Neither the European Commission nor any person acting on behalf of the Commission is responsible for the use which might be made of the following information.
A great deal of additional information on the European Union is available on the Internet. It can be accessed through the Europa server (http://europa.eu.int). Cataloguing data can be found at the end of this publication. Luxembourg: Office for Official Publications of the European Communities, 1998 ISBN 92-828-4904-X © European Communities, 1998 Reproduction is authorised provided the source is acknowledged. Printed in Luxembourg PRINTED ON WHITE CHLORINE-FREE PAPER
FOREWORD This book, or manual, is the result of the work of eight individuals from four research centres and university departments. This work has been three years long, all the way enjoyable if difficult. The design of steel frames has long been considered as being composed of two different stages, the design of members being quite a separate task from the design of joints. The original idea of this manual occurred soon after the moment when the developments of knowledge resulted into the introduction in the European design code (Eurocode 3) of the so-called concept of semi-rigid design or the semicontinuous design. But the book is more general and refers to any kind of joints in building frames. As is often the case with progress, those semi-rigid developments, while recognising the true behaviour of joints in steel frames, were at first sight seen as a nest of complications for any designer. When using the wording « progress », it is of course not only for the sake of science, far from that ! One main motivation for this work was to show how the semi-continuous concept may help the designer to achieve a better global economy in the project, through proper and « custom-made » balancing between the material costs (members weight) and the fabrication costs (joints). These ways for better economy have been suggested in several publications already. It is expected that this manual will provide the reader with the tools for mastering the ways towards cheaper structures which means a larger marketshare for steel construction. That definitely meant encompassing the complete progress of designing, including global analysis and design checks. But this is not the end. As was amply demonstrated through the discussions within the drafting panel (and believe me it is quite difficult to get eight people to agree on any practical issue), there seems to exist quite a world between the frame designers and the joint designers. No doubt that this state of facts is due to the traditional habit of considering joints as pinned or rigid - thus simplifying the assumptions for frame
design -, but also to the fact that different people (either within the same company, or in different companies for several European countries) deal with the design of members and joints respectively. Hence this book boldly tries at considering the design of members and joints as a whole, whenever the design organisation allows for it, and please take that statement in a broad sense ! The authors have made their best efforts to include those different design situations in this work, and I truly believe that this is rather unusual in that kind of manual. So praise to them if they have succeeded ! The reader will find in this manual some theoretical background, application rules (compatible with Eurocode 3) and worked examples . Also a software has been developed, and this fits with the present economical way to deal with calculations within design offices. Regarding joints, it is to be noted that, instead of the original Annex J to Eurocode 3, the revised Annex J was considered. This revised Annex was adopted in 1994 and its publication as an ENV is expected in 1997. Within our drafting panel, I was personally the lowest ranking expert (you may understand not a real expert!) either in frame design or in joints behaviour knowledge, the reason, why, supposedly, I was kindly asked by Professor René Maquoi, Project Manager, to produce this foreword, thus acting in the process as a kind of Candid. I am glad, and not the least ashamed, to say that, despite the occasional fences and difficulties in the work, I took profit of it by learning quite a lot, and I feel sure that my fellow writers learned some things also during the process. So what is only left to be expected is that you, our reader, will also gather a lot and take a very good profit from this book. So be it, and long live our weil designed steel structures! But a work is never quite finished. Eurocode 3 will come, slowly or quickly, into common use. Practical experience will for sure suggest a lot of improvements or afterthoughts. Our interest and please will be to know of your comments and criticisms.
Bruno Chabrolin, CTICM, Head of R&D Department
TABLE OF CONTENTS
VOLUME 1 USER'S MANUAL Symbols
15
Abbreviations
19
Chapter 1 : Introduction
21
1.1
Aims of this manual 1.1.1 The present common way in which joints are modelled for the design of a frame 1.1.2 The semi-rigid approach 1.1.3 The merits of the semi-rigid approach 1.1.4 A parallel between member sections and joints in the semi-rigid approach 1.2 Brief description of the contents of the manual 1.3 Division of the manual and directions to use it 1.4 Types of joints covered 1.5 Domain of validity
21
PART 1 : TECHNICAL BACKGROUND
33
Chapter 2 : Design methodology
35
2.1 2.2 2.3 2.4
35 37 41 42
Introduction Traditional design approach Consistent design approach Intermediate design approaches
29 30 30 31
Chapter 3 : Global frame analysis
45
3.1
45
Introduction 3.1.1 Scope 3.1.2 Load-displacement relationship of frames
3.2
Methods of global analysis 3.2.1 General 3.2.2 Second-order effects 3.3 Elastic global analysis 3.3.1 First-order theory 3.3.1.1 Assumptions, limitations, section/joint requirements 3.3.1.2 Frame analysis 3.3.1.3 Frame design 3.3.2 Second-order theory 3.3.2.1 Assumptions, limitations, section/joint requirements 3.3.2.2 Frame analysis 3.3.2.3 Frame design 3.4 Plastic global analysis 3.4.1 Elastic-perfectly plastic analysis (Second-order theory) 3.4.1.1 Assumptions, limitations, section/joint requirements 3.4.1.2 Frame analysis and design 3.4.2 Elastoplastic analysis (Second-order theory) 3.4.2.1 Assumptions, limitations, section/joint requirements 3.4.2.2 Frame analysis and design 3.4.3 Rigid-plastic analysis (First-order theory) 3.4.3.1 Assumptions, limitations, section/joint requirements 3.4.3.2 Frame analysis 3.4.3.3 Frame design
46 48
Chapter 4 : Joint properties and modelling
61
4.1 4.2
61 63
4.3
4.4
Introduction and definitions Sources of joint deformability 4.2.1 Beam-to-column joints 4.2.1.1 Major axis joints 4.2.1.2 Minor axis joints 4.2.1.3 Joints with beams on both major and minor column axes 4.2.2 Beam splices and column splices 4.2.3 Beam-to-beam joints 4.2.4 Column bases Joint modelling 4.3.1 General 4.3.2 Modelling and sources of joint deformability 4.3.3 Simplified modelling according to Eurocode 3 4.3.4 Concentration of the joint deformability 4.3.4.1 Major axis beam-to-column joint configurations 4.3.4.2 Minor axis beam-to-column joint configurations and beam-to-beam configurations Joint idealisation
70
75
4.5
Joint characterisation 4.5.1 General 4.5.2 Introduction to the component method 4.6 Joint classification 4.6.1 General 4.6.2 Classification based on mechanical joint properties 4.7 Ductility classes 4.7.1 General concept 4.7.2 Requirements for classes of joints
78
Chapter 5 : Frame and element design
89
5.1
89
Frames and their components 5.1.1 Introduction 5.1.2 Frame components 5.1.2.1 Beams 5.1.2.2 Columns 5.1.2.3 Beam-columns 5.1.2.4 Joints 5.2 Classification of frames and their components 5.2.1 Classification of frames 5.2.1.1 Braced and unbraced frames 5.2.1.2 Sway and non-sway frames 5.2.2 Classification of frame components 5.2.2.1 Classification of member cross-sections 5.2.2.2 Classification of joints according to ductility 5.3 Checking frame components 5.3.1 Resistance check of member cross-sections 5.3.1.1 Elastic global analysis 5.3.1.2 Plastic global analysis 5.3.2 Check of member instability 5.3.2.1 Beam in bending and column in compression 5.3.2.2 Beam-column 5.3.3 Additional resistance checks 5.3.4 Resistance checks for members and joints 5.3.4.1 Elastic global analysis 5.3.4.2 Plastic global analysis 5.4 Modelling of joints 5.4.1 Design assumptions 5.4.2 Simple joints 5.4.3 Continuous joints 5.4.4 Semi-continuous joints 5.5 Frame design procedure tasks 5.5.1 Elastic global analysis and relevant design checks 5.5.1.1 First-order analysis 5.5.1.2 Second-order analysis 5.5.2 Plastic global analysis and relevant design checks 5.5.2.1 First-order analysis 5.5.2.2 Second-order analysis
83 84
91
95
^Q2
103
PART 2 : APPLICATION RULES
113
Chapter 6 : Guidelines for design methodology
115
6.1
116
6.2 6.3
Use of a good guess for joint stiffness 6.1.1 Simple prediction of the joint stiffness 6.1.2 Required joint stiffness Use of the fixity factor concept (traditional design approach) Design of non-sway frames with rigid-plastic global frame analysis
Chapter 7 : Guidelines for frame and element design Sheet 7-1 Sheet 7-2 Sheet 7-3 Sheet 7-4 Sheet 7-5 Annex 7-A Annex 7-B Annex 7-C
122 123 129
General procedure Elastic global analysis Plastic global analysis Checks following an elastic global analysis Checks following a plastic global analysis Assessment of imperfections Determination of the structural system Effective buckling lengths for columns with end restraints
Chapter 8 : Guidelines for joint properties and modelling
145
Sheet 8-1 Joint characterisation Sheet 8-1 A: Evaluation of the stiffness and resistance properties: Eurocode 3-(revised) Annex J Sheet 8-1 B: Evaluation of the stiffness and resistance properties: Design sheets Sheet 8-1 C: Evaluation of the stiffness and resistance properties: Design tables Sheet 8-1 D: Evaluation of the stiffness and resistance properties: PC software DESIMAN Sheet 8-1 .E: Evaluation of the rotation capacity Sheet 8-2 Joint classification Sheet 8-3 Joint modelling Sheet 8-4 Joint idealisation Annex 8-A Evaluation of the stiffness and resistance properties of the joints according to Eurocode 3-(revised) Annex J Annex 8-B Stiffness and resistance properties of joints with haunched beams Chapter 9 : Guidelines for global analysis Sheet Sheet Sheet Sheet Sheet
9-1 9-2 9-3 9-4 9-5
Joints Elastic critical buckling load in the sway mode First-order elastic analysis at the ultimate limit state Second-order elastic analysis at the ultimate limit state First-order plastic analysis at the ultimate limit state
181
Sheet 9-6
Second-order elastic-perfectly plastic analysis at the ultimate limit state Annex 9-A Assessment of the elastic critical buckling load in the sway mode Annex 9-B Methods for elastic global analysis PART 3 : WORKED EXAMPLES Chapter 10 : Worked example 1 Design of a braced frame 10.1 Frame geometry and loading 10.2 Objectives and design steps 10.3 Frame with pinned joints 10.3.1 Introduction 10.3.2 Preliminary design of beams and columns 10.3.3 Frame analysis 10.3.3.1 Serviceability limit state 10.3.3.2 Ultimate limit state 10.3.4 Design checks 10.3.4.1 Serviceability limit state 10.3.4.2 Ultimate limit state 10.3.5 Design of joints 10.4 Frame with semi-rigid joints 10.4.1 Introduction 10.4.2 Preliminary design of beams, columns and joints 10.4.3 Frame analysis 10.4.3.1 Serviceability limit state 10.4.3.2 Ultimate limit state 10.4.4 Design checks 10.4.4.1 Serviceability limit state 10.4.4.2 Ultimate limit state 10.4.5 Design of joints 10.5 Frame with partial-strength joints 10.5.1 Introduction 10.5.2 Preliminary design of beams and columns 10.5.3 Design of the joints 10.5.4 Frame analysis 10.5.4.1 Serviceability limit state 10.5.4.2 Ultimate limit state 10.5.5 Design checks 10.5.5.1 Serviceability limit state 10.5.5.2 Ultimate limit state 10.6 Conclusion Chapter 11 : Worked example 2 Design of a 3-storey unbraced frame 11.1 Frame geometry and loading 11.1.1 Frame geometry
203
205 205 206 207
211
219
225 227 227
11.2 11.3
11.4
11.5
11.1.2 Loading 11.1.2.1 Basic loading 11.1.2.2 Frame imperfections 11.1.2.3 Load combination cases 11.1.3 Partial safety factors on resistance Objectives Frame with rigid joints 11.3.1 Assumptions and global analysis 11.3.2 Member sizes 11.3.3 Serviceability limit state requirements 11.3.4 Joint design Frame with semi-rigid joints 11.4.1 Design strategy 11.4.2 Preliminary design 11.4.3 Characteristics and classification of the joints 11.4.4 Structural analysis 11.4.5 Design checks of the frame with semi-rigid joints 11.4.5.1 Serviceability limit state 11.4.5.2 Ultimate limit state Conclusion
Chapter 12 : Worked example 3 Design of an industrial type building 12.1 Frame geometry 12.2 Objectives and design strategy 12.3 Design assumptions and requirements 12.3.1 Structural bracing 12.3.2 Structural analysis and design of the members and joints 12.3.3 Materials 12.3.4 Partial safety factors on resistance 12.3.5 Loading 12.3.5.1 Basic loading 12.3.5.2 Basic load cases 12.3.5.3 Load combination cases 12.3.5.4 Frame imperfections 12.4 Preliminary design 12.4.1 Member selection 12.4.2 Joint selection 12.5 Classification of the frame as non-sway 12.6 Design checks of members 12.7 Joint design and joint classification 12.7.1 Joint at mid-span of the beam 12.7.2 Haunch joint at the beam-to-column connection 12.8 Conclusion
232 233
234
250 251 251 251 252
257 258 262 263 267
Additional reading
269
Glossary
277
io
VOLUME 2 STEEL MOMENT CONNECTIONS ACCORDING TO EUROCODE 3 SIMPLE DESIGN AIDS FOR RIGID AND SEMIRIGID JOINTS
Chapter 1 : Guidelines for use
285
1.1 1.2
285 286
Introduction Stresses in the column web panel and flange 1.2.1 Factor β 1.2.2 Factor kwc 1.2.3 Factor kfc 1.3 Additional design considerations and options taken for the design tables 1.3.1 Weld sizes 1.3.2 Bolt diameters 1.3.3 Cleated joints 1.3.4 Choices for the design tables 1.4 Shear resistance 1.5 Reference length for stiffness classification purposes Annex 1A Joint stiffness classification « Reference length » concept
290
297 297
Chapter 2 ¡Stiffness and resistance calculation for beamto column joints with extended endplate connections
305
2.1 2.2 2.3
307 313 343
Calculation procedure Designed tables Worked example
Chapter 3 : Stiffness and resistance calculation for beamto column joints with flush endplate connections a) Endplate height smaller than beam depth 3.1.a Calculation procedure 3.2.a Design tables 3.3.a Worked example
349 351 357 387
b) Endplate height larger than beam depth 3.1.b Calculation procedure 3.2.b Design tables 3.3.b Worked example
393 395 401 43I
Chapter 4 ¡Stiffness and resistance calculation for beam splices
with flush end-plates a) End-plate height smaller than beam depth 4.1.a Calculation procedure 4.2.a Design tables 4.3.a Worked example
437 439 445 451
b) End-plate height larger than beam depth 4.1.b Calculation procedure 4.2.b Design tables 4.3.b Worked example
455 457 463 469
Chapter 5 ¡Stiffness and resistance calculation for beam-tocolumn joints with flange cleated connections
473
5.1 5.2 5.3
475 481 511
Calculation procedure Design tables Worked example
VOLUME 3 COMPUTER PROGRAM FOR THE DESIGN OF RIGID AND SEMI-RIGID JOINTS
Chapter 1 : The DESIMAN program
521
Chapter 2 : Installation of DESIMAN
528
I2
VOLUME 1 USER'S MANUAL
SYMBOLS
bett
effective width
dn
nominal diameter of the bolt shank
e0
magnitude of initial outofstraightness
f
fixity factor
fu
material ultimate tensile strength
fy
material yield strength
hb
depth of beam crosssection
hc
depth of column crosssection
ht
distance between the centroïds of the beam flanges
lett
effective length
rc
fillet radius of the structural shape used as column
tf,c
thickness of the column flange
tf,b
thickness of the beam flange
tp
thickness of the endplate
tWtC
thickness of the column web
ζ
lever arm of the resultant tensile and compressive forces in the connection
xx
longitudinal axis of a member
yy
major axis of a crosssection
zz
minor axis of a cross-section
A0
original cross-sectional area
As
shear area of the bolt shank
AViC
shear area of the column web
E
Young modulus for steel material
Fb
tensile and compressive forces in the equivalent to the beam end moment
Fc.sd
design compressive force
Fttsd
design tensile force
Fv.sd
design shear force (bolts)
Fb.sd
design bearing force (bolt hole)
H
horizontal load
/
second moment of area
lb
second moment of area of the beam section (major axis bending)
la
second moment of area in the column section (major axis bending)
L
member length
Lb
beam span (system length)
Lc
column height (system length measured between two consecutive storeys)
M
bending moment
Mb
bending moment at the beam end (at the location of the joint)
Mc
bending moment in the column (at the location of the joint)
Mj
bending moment experienced by the joint (usually M¡= Mb )
Mj.u
ultimate bending moment resistance of the joint
Mj,Rd
design bending moment resistance of the joint
Mj,sd
design bending moment experienced by the joint
connection,
statically
Mpb
plastic bending resistance of the beam cross-section
Mpc
plastic bending resistance of the column cross-section
MpiiRd
design plastic bending resistance of a cross-section
Mu
ultimate bending moment
Msd
design bending moment
N
axial force
Nb
axial force in the beam (at the location of the joint)
Nc
axial force in the column (at the location of the joint)
Ρ
axial compressive load
S
rotational joint stiffness
Sj
nominal rotational joint stiffness
Sj,app
approximate rotational joint stiffness (estimate of the initial one)
Sjjni
initial rotational joint stiffness
Sj, post-iimit
post-limit rotational joint stiffness
V
shear force or gravity load
Vb
shear force at the beam end
Vc
shear force in the column
Vcr
critical value of the resultant gravity load
Vn
shear force experienced by the column web panel
Vsd
design shear force in the connection
Vwp
shear force in the column web panel (sheared panel)
W
gravity load
β
transformation parameter
ε
= (Un) JN/El
Sy
material yield strain
17
£u
material ultimate strain
δ
magnitude of the member deflection or local second-order effect
φ
relative rotation between the axes of the connected members or sum of the rotations at the beam ends
§b
rotation of the beam end
φί
rotation of the (beam + joint) end
γ
shear deformation
jf
partial safety factor for the loads (actions)
yM
partial safety factor for the resistance (strength function)
A
s w a y displacement or global second-order effect
η
stiffness reduction factor (Sj/ Sj,¡ni)
λ
slenderness
ÅL
load parameter
Xcr
elastic critical load parameter (gravity loads)
λρ
plastic load parameter
λ
reduced slenderness
9b
absolute rotation of the b e a m e n d
9C
absolute rotation of the column axis
συ
average ultimate stress
ψ
load combination factor
Φ
reference rotation of a plastic hinge in a plastic m e c h a n i s m
is
ABBREVIATIONS
EC1
Eurocode 1 : Basis for design
EC3
Eurocode 3: Design of steel structures.
EN 10025
Euronorm 10025: Hot rolled products of non-alloy structural steels Technical delivery conditions.
EN 10113
Euronorm 10113: Hot rolled products in weldable fine grain structural steels.
SLS
Service limit state(s).
ULS
Ultimate limit state(s).
19
CHAPTER 1
INTRODUCTION
1.1 Aims of this manual The aim of this manual is threefold: • To present, in simple terms, the behaviour of steel structural frames and the techniques to model this behaviour; • To provide the designer with practical guidance and tools for the design of the structure, incorporating a treatment of the joints at all design stages; • To illustrate the possibilities of producing more economical structures using the new approaches offered in Eurocode 3. The organisation of the manual reflects the belief that, in addition to the sizing of the members (beams and columns), consideration should also be given to the joint characteristics throughout the design process. This approach, despite the novelty it may present to many designers, is shown to be relatively easy to integrate into everyday practice using present day design tools. Hence the present manual addresses design methodology, structural analysis, joint behaviour and design checks, at three different levels: • Presentation and discussion of concepts; • Practical guidance and design tools; • Worked examples. 1.1.1
T h e p r e s e n t c o m m o n way in w h i c h m o d e l l e d for the d e s i g n of a f r a m e
joints
are
Generally speaking, the process of designing building structures has been up to now made up of the following successive steps: • Frame modelling (including the choice of rigid or pinned joints); • Initial sizing of beams and columns; • Evaluation of internal forces and moments (load effects) for each ultimate limit state (ULS) and serviceability limit state (SLS) load combination; • Design checks of ULS and SLS criteria; • Iteration on member sizes until all design checks are satisfactory; • Design of joints to resist the relevant members end forces (either those calculated or the maximum ones able to be transmitted by the actual
2I
members); the design is carried out in accordance with the prior assumptions (frame modelling) on joint stiffness. This approach was possible since designers were accustomed to considering the joints to be either pinned or rigid only. In this way, the design of the joints became a separate task from the design of the members. Indeed, joint design was often performed at a later stage, either by other personnel or by another company. Recognising that most joints have a real behaviour which is intermediate between that of pinned and rigid joints, Eurocode 3 offers the possibility to account for this behaviour by opening up the way to what is presently known as the semi-rigid approach. This approach to design offers the potential for achieving better and more economical structures. 1.1.2 The s e m i - r i g i d a p p r o a c h The rotational behaviour of actual joints is well recognised as being often intermediate between the two extreme situations, i.e. rigid or pinned. In chapter 4, the difference between joints and connections will be introduced. For the time being, we will use examples of joints between one beam and one column only. Let us now consider the bending moments and the related rotations at a joint (Figure 1.1):
//
Φ
(a) Rigid joint
(b) Pinned joint
(c) Semi-rigid joint
Figure 1.1 Classification of joints according to stiffness When all the different parts in the joint are sufficiently stiff (i.e. ideally infinitely stiff), the joint is rigid, and there is no difference between the respective rotations at the ends of the members connected at this joint (Figure 1.1 .a). The joint experiences a single global rigid-body rotation which is the nodal rotation in the commonly used analysis methods for framed structures.
TT
Should the joint be without any stiffness, then the beam will behave just as a simply supported beam, whatever the behaviour of the other connected member(s) (Figure 1.1 .b). This is a pinned joint. For intermediate cases (non zero and non infinite stiffness), the transmitted moment will result in there being a difference φ between the absolute rotations of the two connected members (Figure 1.1.c). The joint is semi-rigid in these cases. The simplest means for representing the concept is a rotational (spiral) spring between the ends of the two connected members. The rotational stiffness S of this spring is the parameter that links the transmitted moment M¡ to the relative rotation φ, which is the difference between the absolute rotations of the two connected members. When this rotational stiffness S is zero, or when it is relatively small, the joint falls back into the pinned joint class. In contrast, when the rotational stiffness S is infinite, or when it is relatively high, the joint falls into the rigid joint class. In all the intermediate cases, the joint belongs to the semirigid joint class. M,
M,
M,
I
9-
(a) Rigid joint (φ = 0)
(b) Pinned joint
(c) Semirigid joint
(Mj=0)
(Mj and φ Φ 0)
Figure 1.2 Modelling of joints (case of elastic global analysis) For semirigid joints the loads will result in both a bending moment M¡ and a relative rotation φ between the connected members. The moment and the relative rotation are related through a constitutive law depending on the joint properties. This is illustrated in Figure 1.2, where, for the sake of simplicity, the global analysis is assumed to be performed with linear elastic assumptions
2λ
(how to deal with non-linear behaviour situations will be addressed later on, especially in chapters 3, 5, 7, 9). It shall be understood that the effect, at the global analysis stage, of having semi-rigid joints instead of rigid or pinned joints is to modify not only the displacements, but also the distribution and magnitude of the internal forces throughout the structure. As an example, the bending moment diagrams in a fixed-base simple portal frame subjected to a uniformly distributed load are given in Figure 1.3 for two situations, where the beam-to-column joints are respectively either pinned or semi-rigid. The same kind of consideration holds for deflections.
(a) Pinned joints
(b) Semi-rigid joints
Figure 1.3 Elastic distribution of bending moments in a simple portal frame
1.1.3 T h e m e r i t s of the s e m i - r i g i d a p p r o a c h Both the Eurocode 3 requirements and the desire to model the behaviour of the structure in a more realistic way leads to the consideration of the semi-rigid behaviour when necessary. Many designers would stop at that basic interpretation of Eurocode 3 and hence would be reluctant to confront the implied additional computational effort involved. Obviously a crude way to deal with this new burden will be for them to design joints that will actually continue to be classified as being either pinned or fully rigid. However such properties will have to be proven at the end of the design process; in addition, such joints will certainly be found to be uneconomical in a number of situations.
24
It shall be noted that the concept of rigid and pinned joints still exists in Eurocode 3. It is accepted that a joint which is almost rigid or, on the contrary, almost pinned ) may still be considered as being truly rigid or truly pinned in the design process. How to judge whether a joint can be considered as rigid, semi rigid or pinned depends on the comparison between the joint stiffness and the beam stiffness, which latter depends on the second moment of area and length of the beam. The designer is strongly encouraged to go beyond this "all or nothing" attitude. Actually it is possible, and therefore of interest, to consider the benefits to be gained from the semi-rigid behaviour of joints. Those benefits can be brought in two ways : 1. The designer decides to continue with the practice of assuming -sometimes erroneously- that joints are either pinned or fully rigid. However, Eurocode 3 requires that proper consideration be given to the influence that the actual behaviour of the joints has on the global behaviour of the structure, i.e. on the precision with which the distribution of forces and moments and the displacements have been determined. This may not prove to be easy when the joints are designed at a late stage in the design process since some iterations between global analysis and design checking may be required. Nevertheless, the following situations can be foreseen: •
So that a joint can be assumed to be rigid, it is common practice to introduce web stiffeners in the column. Eurocode 3 now provides the means to check whether such stiffeners are really necessary for the joint to be both rigid and have sufficient resistance. There are practical cases where they are not needed, thus permitting the adoption of a more economical joint design.
•
When joints assumed to be pinned are later found to have fairly significant stiffness (i.e. to be semi-rigid), the designer may be in a position to reduce beam sizes. This is simply because the moments carried by the joints reduce the span moments in the beams.
2. The designer decides to give consideration, at the preliminary design stage, not only to the properties of the members but also to those of the joints. It will be shown that this new approach is not at all incompatible with the sometimes customary separation of the design tasks between those who have the responsibility for conceiving the structure and carrying out the global analysis and those who have the responsibility for designing the joints. Indeed, both tasks are very often performed by different people, indeed, or by different companies, depending on national or local industrial habits. Adopting this novel manner towards design requires a good understanding of the balance between, on the one hand, the costs and the complexity of joints and, on the other hand, the optimisation of the structural behaviour and
performance through the more accurate consideration of joint behaviour for the design as a whole. Two examples are given to illustrate this: •
It was mentioned previously that it is possible in some situations to eliminate column web stiffeners, therefore reduce costs. Despite the reduction in its stiffness and, possibly, in its strength, the joint can still be considered to be rigid and be found to have sufficient strength. This is shown to be possible for industrial portal frames with raftertocolumn haunch joints, in particular, but other cases can be envisaged.
•
In a more general way, it is worthwhile to consider the effect of adjusting the joint stiffness so as to strike the best balance between the cost of the joints and the costs of the beams and the columns. For instance, for braced frames, the use of semirigid joints, which are probably more costly than the pinned joints, leads to reducing the beam sizes. For unbraced frames, the use of less costly semirigid joints, instead of the rigid joints, leads to increased beam sizes and possibly column sizes.
Of course the task may seem a difficult one, and this is why this manual is aimed at providing the designer with a set of useful design tools. The whole philosophy could be termed as "As you must do it, so better make the best of it". Thus Eurocode 3 now presents the designer with a choice between a traditionalist attitude, where however something may often be gained, and an innovative attitude, where the best economical result may best be sought. It is important to stress the high level of similarity that exists between the member classification and the joint classification. This topic is addressed in the Section 1.1.4. 1.1.4 A parallel b e t w e e n m e m b e r s e c t i o n s and j o i n t s in t h e s e m i r i g i d approach Member crosssection behaviour may be considered through an Μ-φ curve for a simply supported beam loaded at mid span (M : bendingmoment at midspan ; φ : sum of rotations at the span ends). Joint behaviour will be considered through a similar relationship, but with M = M¡ being the bending moment transmitted by the joint and φ being the relative rotation between the connected member and the rest of the joint. Those relationships have a similar shape as illustrated in Figure 1.4. According to Eurocode 3 member crosssections are divided into four classes according to their varying ability to resist local instability, when partially or totally subject to compression, and the consequences this may have on the possibility for plastic redistribution. Therefore their resistance ranges from the full plastic
26
resistance (class 1 and 2) to the elastic resistance (class 3) or the sub-elastic resistance (class 4).
M
M,
Figure 1.4 Μ-φ characteristics for member cross-section and joint The belonging of a cross-section to a specific class governs the assumptions on: • The behaviour to be idealised for global analysis (i.e. class 1 will allow the formation of a plastic hinge and permit the redistribution of internal forces in the frame as loads are increased up to or beyond the design loads); • The behaviour to be taken into account for local design checks (i.e. class 4 will imply that the resistance of the cross-section is based on the properties of a relevant effective cross-section rather than of the gross cross-section). In Eurocode 3, the classification of a cross-section is based on the width-tothickness ratio of the component walls of the section. Ductility is directly related to the amount of rotation during which the design bending resistance will be sustained. The also used rotation capacity concept is equivalent to the ductility concept. In a manner similar to that for member cross-sections, joints are classified in terms of ductility or rotation capacity, joints are classified. This classification is a measure of their ability to resist premature local instability and, even more likely, premature brittle failure (especially due to bolt failure) with due consequences on the type of global analysis allowed. The practical interest of such a classification for joints is to check whether an elastoplastic global analysis may be conducted up to the formation of a plastic collapse mechanism in the structure, which implies such hinges in at least some of the joints.
Figure 1.5 Ductility or rotation capacity in joints As will be shown, this classification of joints by ductility, while not explicitly stated in Eurocode 3, may be defined from the geometric and mechanical properties of the joint components (bolts, welds, plate thickness, etc.). Joints may therefore be classified according to both their stiffness and their ductility. Moreover, joints may be classified according to their strength. In terms of their strength, joints are classified as full-strength or partial-strength according to their resistance compared to the resistance of the connected members. For elastic design, the use of partial-strength joints is well understood. When plastic design is used, the main use of this classification is to foresee the possible need to allow a plastic hinge to form in the joint during the global analysis. In order to permit the increase of loads, a partial-strength joint may be required to act as a hinge from the moment when its plastic bending resistance is reached, in that case, the joint must also have sufficient ductility. The final parallel to be stressed between joints and members is that the same kind of link exists between the global analysis stage and the ultimate limit states design checking stage. The latter has to extend to all aspects that were not implicitly or explicitly taken into account at the global analysis stage. Generally speaking, one can state that the more sophisticated the global analysis is, the simpler are the ultimate limit states design checks required. The choice of global analysis will thus depend not only of what is required by Eurocode 3 but also on personal choices, depending on specific situations, available software's, etc. A particular choice means striking a balance between the amount of effort devoted to global analysis and the amount of effort required for the check of remaining ULS (Figure 1.6).
28
Sophistication of global analysis 100
< l ·
Τ
Global analysis Relative amount of design effort (in %)
/S
ULS checks Ni'
Simplification of global analysis
[>
Figure 1.6 Schematic of the proportion of effort for global analysis and for ULS checks
1.2 Brief description of the contents of the manual This manual is divided into three main parts: • Part 1 deals with technical background, and it is primarily an explanation of the new concepts as well as a simple presentation of the contents and consequences of the novel approach to design offered by Eurocode 3. • Part 2 presents application rules and it is aimed at daily use by the designer. It is the translation of Part 1 in terms of formulae, by-hand methods and software presentation. Guidelines, data and hints are given for those who wish to develop their own software aids on common PC hardware. For example, in addition to the design tables that are given for a variety of joints, the design sheets are also provided. These sheets should allow users having a basic programming knowledge to develop their own programme. • Part 3 consists in a set of worked examples. In Part 1, three chapters address in succession the design, the characterisation of joints, the available methods of global analysis and, finally, the decision on the type of global analysis and the related checks of limit states. For Part 2, the order is different than in Part 1, with Chapters 8 and 9 describing design tools the general use of which is outlined in Chapter 7. Part 3 is truly the place where the designer will find clues to decide which overall strategy is the best for his purposes. The contents of the present manual is in accordance with Eurocode 3-Part 1 and, as such, makes the many references to design values. These design values are related to structural safety as defined in Eurocode 1 and Eurocode 3 and they include relevant partial safety factors for resistance (y ), as opposed to either nominal or characteristic values. They are generally indicated by the
subscript d ; for instance Mpl\pd ' s member cross-section.
tne
design plastic bending resistance of a
Concerning the loads, only one load case is generally considered in the manual, it being understood that the described operations shall be performed for each load combination case.
1.3 Division of the manual and directions to use it For a first reading of this manual, it is strongly advised to give a thorough consideration to the present introduction and to Part 1, in order to grasp the basic concepts once and for all. For practical daily use, Part 2 (design rules) is of the main interest, it being supplemented by the worked examples presented in Part 3. Part 1 may always be reconsulted for clarification of problems related to general fundamentals. It should be noted that this manual has been written according to the most recent version of Eurocode 3, and especially to the revised Annex J to Eurocode 3, dealing with the design of joints. However, some evolution in Eurocode 3 is to be expected in the near future, either at the European level or at each national level (on this latter respect, the values of partial safety factors are a particular case of point). This manual will, as far as possible, be maintained up-to-date. However the reader is strongly advised to check on the current state of the Eurocode 3-Part 1 Standard and to proceed with the possible modifications that may be required. Similarly, the software tools that may be developed by third parties, based on the contents of this manual, should be checked to be in accordance with the latest version of the design rules. The same remark obviously holds for any software developed by the reader using the information given in this manual. To that effect, the date of issue is clearly indicated on the front page of the manual. Any possible revised version of the latter will be supplied with a revision index.
1.4 Types of joints covered Strictly speaking, the joints covered are those directly covered by Eurocode 3(revised) Annex J, as listed hereafter; however, the same principles are also valid for many other types of joints and cross-sections. The manual addresses: • Members cross sections : H or I rolled or welded sections. • Beam-to-column joints : Welded joints (with or without haunch). Bolted end-plate connections (with or without haunch).
30
• Beam splices :
Bolted top and seat angle connections (with or without web angles). Bolted endplate connections.
When relevant, both major axis (moment acting in the plane of greatest inertia of the column crosssection) and minor axis (moment acting in the plane of lowest inertia of the column crosssection) joints are covered, as regard principles. Application rules deal only with major axis joints.
1.5 Domain of validity The use of information given in this manual when designing structures and joints shall be restricted to the following:
•Static loading only. •Steel grades for members and joints: S235 to S355 according to EN 10025; S355ÌO S460 according to EN 10113. • For welded sections and for some rules: depthtothickness ratio of the web d/tw < 69ε.
PART 1: TECHNICAL BACKGROUND
CHAPTER 2
DESIGN METHODOLOGY
2.1 Introduction This chapter describes the various approaches which can be used to design steel frames with due attention being paid to the behaviour of the joints. In practice, this design activity is normally performed by one or two parties, according to one of the following ways: • An engineering office (in short engineeή and a steel fabricator (in short fabrica^, referred as Case A; • An engineering office (engineer) alone, referred as Case B1; • A steel fabricator (fabricator) alone, referred as Case B2. At the end of this design phase, fabrication by the steel fabricator takes place. The share of responsibilities for design and fabrication respectively is given in Table 2.1 for these three cases. Role
Case A
Case B1
Case B2
Design of members
Engineer
Engineer
Fabricator
Design of joints
Fabricator
Engineer
Fabricator
Fabrication
Fabricator
Fabricator
Fabricator
Table 2.1 Parties and their roles in the design/fabrication process of a steel structure The design process is ideally aimed at ascertaining that a given structure fulfils architectural requirements, on the one hand, and is safe, serviceable and durable for a minimum of global cost, on the other hand. The parties involved in the design activities also care about the cost of these latter, with a view to optimising their respective profits. In Case A, the engineer designs the members while the steel fabricator designs the joints. It is up to the engineer to specify the mechanical requirements to be fulfilled by the joints. The fabricator has then to design the joints accordingly, keeping in mind the manufacturing aspects also. Due to the disparity in the
35
respective involvements of both parties, the constructional solution adopted by the fabricator for the joints may reveal to be sub-optimal; indeed it is dependent on the beam and column sizing that is made previously by the engineer. The latter may for instance aim at minimum shape sizes, with the consequence that the joints then need stiffeners in order to achieve safety and serviceability requirements. If he chooses larger shapes, then joints may prove to be less elaborated and result in a better economy of the structure as a whole (Figure 2.1). In Case B1, the engineer designs both the members and the joints. He is thus able to account for mechanical joint properties when designing members. He can search for global cost optimisation too. It may happen however that the engineer has only a limited knowledge of the manufacturing requisites (machinery used, available materials, bolt grades and spacing, accessibility for welding, ...); then this approach may contribute some increase in the fabrication cost.
IPE180
IPE140
HE220A
HE220A
a. Bolted end-plate with haunch
b. Bolted flush end-plate
Figure 2.1 Two solutions: different economy Case B2 is ideal with regard to global economy. Indeed the design of both members and joints are in the hands of the fabricator who is presumably well aware of all the manufacturing aspects. Before commenting on these various approaches, it is necessary to introduce some wording regarding joints. A joint is termed simple, semi-continuous or continuous. This wording is general; it is concerned with resistance, with stiffness or with both. Being a novelty for most readers, some detailed explanations are given in Chapter 4 on joints. In two circumstances only - that are related to the methods of global frame analysis (see Chapter 5) -, this wording leads to more commonly used terms:
3ft
1. In an elastic global frame analysis, only stiffness of joints is involved. Then, a simple joint is a pinned joint, a continuous joint is a rigid joint while a semicontinuous is a semi-rigid joint; 2. In a rigid-plastic analysis, only resistance of joints is involved. Then, a simple joint is a pinned joint, a continuous joint is a full-strength joint while a semicontinuous joint is a partial-strength joint. The various cases described above are commented on in the present chapter. For the sake of simplicity, it is assumed that global frame analysis is conducted based on an elastic method of analysis. This assumption is however not at ali a restriction; should another kind of analysis be performed, similar conclusions would indeed be drawn. For the design of steel frames, the designer can follow one of the following design approaches: • Traditional design approach : The joints are presumably either simple or continuous. The members are designed first; then the joints are. Such an approach may be used in any Case A, B1 or B2; it is of common practice in almost all the European countries. • Consistent design approach : Both member and joint properties are accounted for when starting the global frame analysis. This approach is normally used in Cases B1 and B2, and possibly in Case A. • Intermediate design approach : Members and joints are preferably designed by a single party (Case B1 or B2). These approaches are described more in detail in the following paragraphs. They are illustrated by some case studies in Chapter 6.
2.2 Traditional design approach In the traditional design approach, any joint is assumed to be either simple or continuous. A simple joint is capable of transmitting the internal forces got from the global frame analysis but does not develop a significant moment resistance which might affect adversely the beam and/or column structural behaviour. A continuous joint exhibits only a limited relative rotation between the members connected as long as the applied bending moment does not exceed the bending resistance of the joint. The assumption of simple and/or continuous joints results in the share of design activities into two more or less independent tasks, with limited data flow in between. The traditional design approach of any steel frame consists of eight steps (Figure 2.2).
37
STRUCTURAL IDEALISATION Frame
Step1\
Joints
(Geometry, Member types, etc.)
(Simple,
ï
ESTIMATION OF LOADS
Continuous)
Step 2
I
PRELIMINARY DESIGN
Step 3
Choice and classification of members Task 1 Step 4 GLOBAL ANALYSIS
STRUCTURAL RESPONSE Limit States Design criteria (ULS, SLS)
Step 5
(Sway/Non sway, Elastic/Plastic)
DESIGN OF JOINTS Type of joint
no
(Rigidity Rotation capacity & Strength)
Step 6
Tables.
Softwares
Step 7
JÍ
no other members
other type of joint
^>KJ/Step 8 STOP
Task 2
Figure 2.2 Traditional design approach (simple/continuous joints) Srep 1 :
The structural idealisation is a conversion of the real properties of the frame into the properties required for frame analysis. Beams and columns are normally modelled as bars. Dependent on the type of frame analysis which will be applied, properties need to be assigned to these bars. For example, if an elastic analysis is used, only the stiffness properties of the members are relevant; the joints are pinned or rigid and are modelled accordingly (Figure 2.3).
38
ν Rigid joint
Pinned joint
>
Modelling
Modelling
Figure 2.3 Modelling of pinned and rigid joints (elastic global analysis) Step 2 :
Loads are determined based on national or European standards.
Step 3 :
The designer normally performs the preliminary design - termed pre design in short - of beams and columns by taking advantage of his own design experience from previous projects. Should he have a limited experience only, then simple design rules can help for a rough sizing of the members. In the pre-design, an assumption shall be made concerning the stress distribution within the sections (elastic, plastic), on the one hand, and, possibly, on the allowance for plastic redistribution between sections, on the other hand. Therefore classes need to be assumed for the structural shapes composing the frame (see Chapter 3); the validity of this assumption shall be verified later in Step 5.
Step 4 :
The input for global frame analysis is dependent on the type of analysis. In an elastic analysis, the input is the geometry of the frame, the loads and the flexural stiffness of the members. In a rigidplastic analysis, the input is the geometry of the frame, the loads and the resistance of the members. An elastic-plastic analysis requires both resistance and flexural stiffness of the members. Whatever the type of global frame analysis, the distribution and the magnitude of the internal forces and displacements are the output (however rigidplastic analysis does not allow for any information regarding displacements).
y>
Step 5 :
Limit state verifications consist normally in checking the displacements of the frame and of the members under service loading conditions (Serviceability Limit States, in short SLS), the resistance of the member sections (Ultimate Limit States, in short ULS), as well as the frame and member stability (ULS). The assumptions made regarding the section classes (see Step 3) are checked also.
Step 6 :
The adjustment of member sizing is to be carried out when the limit state verifications fail, or when undue under-loading occurs in a part of the structure. Member sizing is adjusted by choosing larger shapes in the first case, smaller ones in the second case. Normally the designer's experience and know-how form the basis for the decisions made in this respect.
Steps 7/S.The member sizes and the magnitude of the internal forces that are experienced by the joints are the starting point for the design of joints. The purpose of any joint design task is to find a conception which allows for a safe and sound transmission of the internal forces from the beam into the column. Additionally, when a simple joint is adopted, the fabricator shall verify that no significant bending moment develops in the joint. For a continuous joint, the fabricator shall check whether the joint satisfies the assumptions made in Step 1 (for instance, whether the joint stiffness is sufficiently large when an elastic global frame analysis is performed). In addition, the rotation capacity shall be appropriate when necessary. The determination of the mechanical properties of a joint is called joint characterisation (see Section 4.5). To check whether a joint may be considered as simple or continuous, reference will be made to joint classification (see Section 4.6). Guidance provided in this manual is implemented by design tables for joints. These tables are in compliance with Eurocode 3. They can be very helpful during the design process because they enlighten drastically the design tasks. The designer selects the joints out of these tables which provide the strength and stiffness properties of the relevant joints, as well as, when necessary, the rotation capacity. A dedicated software, called DESIMAN, developed as a supplement to these tables, may be an alternative to the latter; it requires the whole layout of the joint as input and provides strength, stiffness and rotational capacity as output. Computer based design proceeds interactively by trial and error; for instance, the designer first tries a simple solution and improves it by adjusting the joint layout until the strength and stiffness criteria are fulfilled. Such a convivial software was developed in the frame of the preparation of present manual.
40
The mechanical properties of a joint shall be consistent with those required by the modelling of this joint in view of global frame analysis. Either the design of the joint and/or that of the members may need to be adjusted. In any case, some steps of the design approach need to be repeated.
2.3 Consistent design approach In the consistent design approach, the global analysis is carried out in full consistency with the presumed real joint response (Figure 2.4). It is therefore different from the traditional design approach described in Section 2.2 in several respects: • Structural conception : In the structural conception phase, the real mechanical behaviour of the joints is modelled; • Preliminary design : In the pre-design phase, joints are selected by the practitioner based on his experience. Proportions for the joint components are determined : end-plate or cleat dimensions, location of bolts, number and diameter of bolts, sizes of column and beam flanges, thickness and depth of column web, etc.; • Determination of the mechanical properties : In Step 4, the structural response of both the selected members and joints is determined. First the joints are characterised (see Section 4.5) with the possible consequence of having a non-linear behaviour. This characterisation is followed by an idealisation, for instance according to a linear or bi-linear joint response curve (see Section 4.4), which becomes a part of the input for global frame analysis; • Global frame analysis : For the purpose of global frame analysis, any joint structural response is assigned to a relevant spring in the frame model. This activity is called modelling (see Section 4.3). Of course the consistent design approach is only possible when both members and joints are designed by a single party, because the mechanical properties of the joints must be accounted for when starting the global frame analysis. In other words, this approach suits both Case B1 and Case B2. In Chapter 6, information is given on intermediate forms. As it accounts for any kind of behaviour, the consistent design especially applicable to frames with so-called semi-continuous modelling of semi-continuous joints is presented in Section 4.3 in the global frame analysis. It may also be applied when designing simple or continuous joints.
4I
approach is joints. The relation with frames with
STRUCTURAL IDEALISATION Frame Joints (Geometry, Member types etc.) (Simple, Semi-continuous, Continuous) Stepl ESTIMATION OF LOADS
Step 2
PRELIMINARY DESIGN Choice and classification of members
Step 3
Choice of joints
ï
Taskl
DETERMINATION OF MECHANICAL PROPERTIES ! : (Stiffness, Rotation capacity & Strength) I Step 4 Tables, Softwares
GLOBAL ANALYSIS
Step5
I
STRUCTURAL RESPONSE Limit States Design criteria (ULS, SLS)
(Sway/Non sway, Elastic/Plastic)
Step 6
Figure 2.4 Consistent design approach
2.4 Intermediate design approaches The two design approaches described in Section 2.2 (for frames with simple or continuous joints) and in Section 2.3 (for frames with semi-continuous joints) correspond to extreme situations. Intermediate approaches can be used. For example, the procedure given in Figure 2.1 can also be applied for semi-
42
continuous joints. In that case, during the first pass through the design process, the joints are assumed to behave as simple or continuous joints. Joints are then chosen, the real properties of which are then accounted for in a second pass of the global analysis (i.e. after Step 8). The design process is then pursued similarly to the one described in Figure 2.4. Some applications of intermediate design approaches are commented on in Chapter 6.
43
CHAPTER 3
GLOBAL FRAME ANALYSIS
3.1 Introduction 3.1.1
Scope
Global analysis aims at determining the distribution of the internal forces and moments and the corresponding displacements in a structure subjected to a specified loading. Achieving this purpose requires the adoption of adequate models which incorporate assumptions about the behaviour of the structure and in particular of its component members and joints. Only the essential aspects are reviewed here. For example, as the basic concepts of structural analysis are considered to be largely known and furthermore are covered by many textbooks, they will not be elaborated on here. 3.1.2 L o a d - d i s p l a c e m e n t r e l a t i o n s h i p of f r a m e s The relationship between the load parameter and a significant displacement parameter characterises the frame behaviour (Figure 3.1). The load parameter λ is most often a multiplier applied to all the load components so as to produce monotonous and proportional increase in the loading, while the displacement parameter may be taken as the lateral displacement at the top level. The slope of the curve is a measure of the stiffness of the structure. One observes that the response of the structure is quasi-linear up to a certain point (the linear limit). Once the linear limit is reached, the positive slope of the rising part of the curve gradually reduces due to a combination of three kinds of non-linearities: geometrical non-linearity, joint non-linearity and material nonlinearity. Joint non-linearity usually manifests itself at relatively low levels of load. Geometrical non-linearity expresses the influence of the actual deformed shape of the structure on the distribution of the internal forces and moments. Typically it becomes evident well before the onset of material yielding. Beyond the latter, the response becomes progressively non-linear as the load increases up to a maximum. Once the maximum load is reached, equilibrium would require a decrease in the magnitude of the loads.
43
Load parameter
Linear elastic response Peak load
Load =
Frame Linear limit where connection and/or geometric and/or material non-linearities become apparent
*
Displacement parameter
Figure 3.1 Load-displacement response of a framed structure The slope of the curve (i.e. the frame sway stiffness) is zero at the peak load; and then it becomes negative indicating that the structure is henceforward unstable. The peak load, often termed the ultimate load, is the point of imminent structural collapse in the absence of the possibility of load shedding.
3.2 Methods of global analysis 3.2.1 General The determination of the actual load-displacement response generally requires the use of a sophisticated analysis method. For practical purposes, assumptions for the frame and its component members and joints models are made that permit obtaining a safe bound for the ultimate load. Hence models for global analysis range from the simple elastic analysis to the most complex elastoplastic analysis (in short plastic analysis) which can provide the real inelastic behaviour of the structure. The first important distinction that can be made between the methods of analysis is the one that separates elastic and plastic methods. Whilst elastic analysis can be used in all cases, plastic analysis is subjected to some restrictions (see Section 3.4). Another important distinction is between the methods which make allowance for and those which neglect the effects of the actual displaced configuration of the structure. They are referred to respectively as second-order theory and first-order theory based methods (see Section 3.2.2). The second-order theory can be adopted in all cases, while first-order theory may be used only when the displacement effects on the structural behaviour are negligible. In the following discussion of the methods of analysis, for clarity, reference will be restricted to two dimensional frames subject to in-plane loading and displacements.
46
Although only one load combination case is considered, it is understood that a number of load combination cases must be analysed. 3.2.2 S e c o n d - o r d e r effects As the displacements due to the external loads may modify the structural response and therefore the distribution of the internal forces and moments, it is necessary to evaluate the degree to which they are significant enough to merit allowance in the design. For frames, the external loads that cause the largest modifications to the linear response are the axial loads. Shown in Figure 3.2 is a fixed-base cantilever column subject to combined axial and horizontal loads applied at the top. The horizontal displacement at the top of the column as well as the column curvature lead to secondary moments.
χ
7777 M(x) = Hx
Μ(χ) = Ηχ+Ρδ + ΡΔ x / L
M(L) = HL
M(h) = H L + P A
1st-order bending moment
2d-order bending moment
Figure 3.2 First-order and second-order theory These moment modifications are made up of a local or member second-order effect, referred to as the Ρ-δ effect, and a global second-order effect, referred to as the Ρ-Δ effect. Local second-order effects arise in each element subject to axial force due to the member deflections relative to the chord line connecting the member ends. Global second-order effects arise throughout the frame due to relative horizontal displacements between the floors. In general, the Ρ-Δ effects, which only occur when sway is permitted, are greater than the Ρ-δ effects, which are significant for slender columns only. When the Ρ-Δ and the Ρ-δ effects are ignored, each structural element can be characterised by a linear stiffness matrix.
47
Account for the Ρ-δ effects is achieved by modifying the terms of the linear stiffness matrix so that they become functions of the factor ε = L^jp/El, where Ρ is the axial load in the member of length L and second moment of area /. The Ρ-Δ effects result in modifications of the end shear forces and moments; this fact is reflected by additions, corresponding to each of these components, to the member stiffness matrix.
3.3 Elastic global analysis 3.3.1 First-order theory 3.3.1.1
Assumptions, limitations, section/joint requirements
Elastic analysis implies an indefinite linear response of sections and joints (Figure 3.3). In a first-order analysis, equilibrium is expressed with reference to the non-deformed configuration of the structure.
M
Elastic
Member
Joint
Figure 3.3 Moment-rotation characteristics of member and joint Sections and joints are not subordinated to any requirement related to their ability to exhibit ductile behaviour (class of member, ductility class of joint). 3.3.1.2 Frame analysis First-order elastic global analysis with linear member and joint behaviour results in a linear load-displacement curve (Figure 3.4). Designers are quite familiar with first-order elastic analysis which is the simplest of all possible types of analysis. Over the years a variety of methods have been developed, which are suited to hand calculations (such as the slope-deflection method and the moment-distribution method). They can be generalised so as to
4X
include the joint behaviour. The same applies to procedures based on matrix formulation, which have now almost entirely supplanted the hand calculation methods, ever since computers became commonplace in design offices. A significant advantage of the first-order elastic analysis is that it permits one to apply the principle of superposition of loading and load effects (i.e. internal forces and moments and displacements).
Load parameter 1st order elastic analysis Linear member- and joint behaviour
Displacement parameter Figure 3.4 Load-displacement response: first-order elastic analysis 3.3.1.3 Frame design Once the design forces (axial force, bending moment and shear force) have been determined throughout the structure, the resistance (ultimate limit state) check of the cross-section members consists in verifying that the stress (force) in the critical section does not exceed the design stress (resistance). Since elastic analysis has been used, it would seem logical to consider the yield stress in the extreme fibres as the design stress for a member (Figure 3.5). It is however generally accepted that first-order elastic analysis can be used to determine the value Xu of the load multiplier corresponding to when the first plastic event takes place (onset of the first plastic hinge). Therefore, provided the sections meet the requirements for ductile behaviour (class 1 or 2), the section resistance may be checked using the plastic interaction formula. In the same way, the resistance (ultimate limit state) check of the joints consists in verifying that the design forces (bending moment and shear force) in the joint do not exceed the design resistance (moment resistance and shear resistance) of the joint. However, this assumes that the structure and its members remain stable. Therefore it is of major importance to investigate additionally the instability phenomena (in-plane and/or out-of-plane frame and/or member instability). Instability may indeed reduce the value of XL1. For the design to be adequate,
4lJ
the value of Xu must be at least unity (i.e. the structure can withstand at least the applied design loads). First-order elastic analysis provides a safe basis for design as long as the predicted response of the structure deviates only slightly from the actual response over a considerable range of loading (i.e. structures in which axial loads are low). For structures with heavier axial loads, Xu is not a lower bound of the maximum load because the second-order effects have been neglected. Load parameter / U /
λ|_ΐ
1st order elastic analysis Linear member and joint behaviour
Elastic limit beyond which the adopted assumptions are no longer strictly valid
Displacement parameter
Figure 3.5 Range of validity of first-order elastic analysis Resistance to concentrated loads may have to be checked for some members. As regards the serviceability limit state (permissible displacements and/or deflections), a first-order elastic analysis generally provides a good tool for predicting the response of the structure and of its elements. 3.3.2 S e c o n d - o r d e r theory 3.3.2.1 Assumptions, limitations, section/joint requirements In this type of elastic analysis, the indefinitely linear elastic response of sections and joints is still implied (Figure 3.3). The distribution of the internal forces and moments is now computed on the basis of a second-order theory of the kind outlined in 3.2.2. Equilibrium equations are formulated with reference to the deformed structure (Ρ-Δ effects) and the decrease in member stiffness due to axial force (Ρ-δ effects) may be included when necessary. As is the case of the first-order elastic analysis, sections and joints are not subordinated to any requirement related to their ability to exhibit ductile behaviour (class member, ductility class of joint). However one can no longer superimpose the results from the analysis of individual loading cases, as was possible for the first-order elastic analysis.
50
3.3.2.2 Frame analysis Figure 3.6 shows the load-displacement response that results from a secondorder elastic analysis in which all the loads are increased monotonously by the same load multiplier (proportional loading). The load-displacement curve, which now includes geometric non-linearity, approaches asymptotically a horizontal corresponding to a peak value of Xcr (critical multiplier). This value of Xcr corresponds to the elastic critical buckling load of the frame, relevant to the specified load case combination. If the Ρ-δ effects are neglected, then the computed peak load may be higher than the actual one. The more slender are the compression members the more significant the Ρ-δ effects become. The elastic critical buckling load is an important reference, as it is the highest theoretical load that the frame can experience in the absence of any material yielding. Yielding will reduce the actual maximum load that can be attained to a value often appreciably lower than the elastic critical buckling load.
Load parameter
2nd order elastic analysis
Displacement parameter
Figure 3.6 Load-displacement response: second-order elastic analysis 3.3.2.3 Frame design In contrast to first-order elastic analysis, second-order analysis provides internal forces and moments at the ends of the members that include the second-order effects. The elastic critical buckling load of the frame may also be provided by a second-order elastic analysis but only if the load multiplier is increased
51
sufficiently. In practice the elastic critical buckling load is evaluated using an approximate procedure referred to in Section 7.1. With due attention being paid to these differences, the frame design may proceed in the same manner as for the firstorder elastic analysis. The critically loaded section or joint permits one to obtain the upper limit value of the load multiplier value X¡_2 (Figure 3.7) for which the elastic analysis is valid. When secondorder elastic analysis is used in calculating frames, the inplane frame stability in terms of sway buckling is covered by the structural analysis. In most practical cases, the local member imperfections are not introduced and only planar behaviour is considered. Therefore the check against instability of members (inplane and/or outofplane) and of the frame (outofplane) may indeed reduce the value of Χι2· For the design to be adequate, the value of XL2 must be at least unity. Resistance to concentrated loads may have to be checked for some members. As regards the serviceability limit state (permissible displacements and/or deflections), a firstorder elastic analysis generally provides a good tool for predicting the response of the structure and of its elements.
Load parameter 1st order elastic analysis
2nd order elastic analysis
/
λί2
/ /
// / Limit load beyond which the elastic assumptions are no longer strictly valid
Displacement parameter
Figure 3.7 Range of validity second-order elastic analysis
3.4 Plastic global analysis The plastic methods are applicable within the following main restrictions
52
1. The steel complies with the following specified requirements : • The ratio of the specified minimum tensile strength fu to the specified minimum yield strength fy satisfies : fu/fy*1.2 • The elongation at failure on a gauge length of 5.65^Α~0 (where A0 is the original cross-section area) is not less than 15%; • In a stress-strain diagram, the ultimate strain ευ corresponding to the ultimate strength fu is at least 20 times the yield strain ey corresponding to the yield strength fy. 2. Lateral restraint shall be provided at all plastic hinge locations at which plastic hinge rotation may occur under any load case. The restraint should be provided within a distance along the member from the theoretical plastic hinge location not exceeding half the depth of the member. 3. Sections and/or joints where plastic hinges are likely to occur have sufficient rotation capacity and are therefore of class 1 (see Section 5.2.2 of Chapter 5). 3.4.1 E l a s t i c - p e r f e c t l y plastic a n a l y s i s ( S e c o n d - o r d e r t h e o r y ) 3.4.1.1
Assumptions, limitations, section/joint requirements Elastic perfectly plastic ._
Elastic perfectly plastic
\ M¡ A M A
Φρ M,pl.Rd Mpl.Rd
Mpi.Rd M;
► Plastic hinge
Rd
Plastic hinge
>Φ Section
Joint
Figure 3.8 Moment-rotation characteristic of section and joint
SI
In the elastic-perfectly plastic analysis, it is assumed that any section and/or joint remains elastic till the plastic moment resistance is reached at which point it becomes ideally plastic. Plastic deformations are assumed to be concentrated at the plastic hinge locations which are assumed to have an infinite rotational capacity. That the actual rotation capacity is sufficient to meet what is required is checked at a later stage. Figure 3.8 shows the elastic-perfectly plastic behaviour of a section and a joint. The influence of the axial force and/or the shear force on the plastic moment resistance of the sections may either be accounted for directly or be checked later at the design verification stage. The use of elastic-perfectly plastic analysis implies that some requirements concerning the structure and its component members and joints are met. These are needed in order to guarantee that sections and joints, at least at the locations at which the plastic hinges may form, have sufficient rotation capacity to permit all the plastic hinges to develop throughout the structure. The load-displacement curve of the frame can be determined. Computation of the plastic rotations of the plastic hinges may also be carried out so as to permit the check that the required rotation capacity is available. 3.4.1.2 Frame analysis and design The load is usually applied by increments. The following is a typical description of how the various steps of the analysis is performed. It assumes that a second-order analysis has been used. For clarity, it is also assumed that the plastic hinges form successively (one by one) without any reversal of the rotation in them, although it is recognised that two (or more) hinges can develop at the same time and that reversal does sometimes occur. An elastic second-order analysis is first performed and from it, the load at which the first plastic hinge forms in a section and/or in a joint is determined. The next analysis is made for further incremental loads for which the frame behaves differently due to the introduction of a hinge at the first plastic hinge (modified frame). It is recalled that a plastic hinge continues to permit rotation without any increase or reduction in its moment and, furthermore, it is assumed to have sufficient ductility to undergo the necessary rotation. The modified frame is said to be the deteriorated frame. The next plastic hinge is formed after further increase of the load level and the process is repeated until the failure mechanism is developed. A typical second-order elastic-perfectly plastic analysis is shown by the solid curve in Figure 3.9. Branch 1 corresponds to a fully elastic frame behaviour. This curve becomes asymptotic to the elastic buckling load of the frame only if infinite elastic behaviour is assumed. A first hinge is formed, and the frame now behaves under further load increments as if one hinge exists in it (branch 2) until the next hinge is developed. If unlimited elastic behaviour is assumed after the first hinge has formed, then branch 2 continues and becomes asymptotic to
54
the buckling load of the deteriorated frame, which is the frame with one hinge. The process is continued with the load being increased and the structure being progressively « deteriorated » up to the moment when it becomes unstable (formation of plastic mechanism or frame instability). The maximum load of the second-order elastic plastic analysis corresponds to this load level which is shown as the load multiplier XL=XL3 in Figure 3.9. Load parameter
Elastic buckling load of frame
Buckling load of deteriorated'frame
Displacement parameter
Figure 3.9 Load-displacement response: second-order elastic-perfectly plastic analysis No additional design checks for the sections and the joints are required when the influence of the axial force and/or the shear force is accounted for in their behavioural model. As the rotations at the plastic hinges have been calculated, this permits one to check that the required rotation capacity is available there. When second-order theory is used in calculating frames, the in-plane frame stability is covered by the structural analysis. However, the out-of-plane stability of the frame and the members will have to be verified. Except when local member imperfections are taken into account, in-plane stability of the members will also have to be verified These checks may indeed reduce the value of XL3. For the design to be adequate, the value of λ ί 3 must be at least unity when applied to the factored loads. Resistance to concentrated loads may have to be checked for some members.
The serviceability limit state checks (permissible displacements deflections) shall be carried out. too.
and/or
3.4.2 E l a s t o p l a s t i c a n a l y s i s ( S e c o n d - o r d e r t h e o r y ) 3.4.2.1
Assumptions, limitations, section/joint requirements
A better estimation of the maximum load than that provided by the elasticperfectly plastic analysis can be obtained by carrying out a second-order elastoplastic analysis. Yielding of members and joints is a progressive process and so the transition from elastic behaviour to plastic one is a gradual phenomenon. As the moment in the member cross-section continues to increase, the plastic zone extends partially along the member. This behaviour is considered by the plastic zone theory. Figure 3.10 shows the moment-rotation characteristics of section and joint which are adopted in this type of analysis. The ductility requirements for the sections and joints and the procedure for analysis and check of the frame are the same as those outlined in Section 3.4.1. Elasto-plastic
Elasto-plastic
Λ
M
>4
M;'j.Rd
Mjel.Rd
Joint
Section
Figure 3.10 Moment-rotation characteristics of section and joint 3.4.2.2 Frame analysis and design The second-order elastoplastic analysis gives the values of the maximum load that the frame can carry, as well as the magnitude of the displacements corresponding to any load level.
56
Usually only the in-plane behaviour of the frame is considered. Therefore separate checks on out-of-plane stability shall be carried out. The elastoplastic method of analysis restricted to computer applications and because of its complexity, it is unlikely to be used for practical design purposes, but more as a tool for research. 3.4.3 R i g i d - p l a s t i c a n a l y s i s ( F i r s t - o r d e r t h e o r y ) 3.4.3.1
Assumptions, limitations, section/joint requirements
In this type of plastic analysis, the elastic strains in members, joints and foundations are disregarded, as they are small compared to plastic strains. Material strain-hardening is also ignored. In addition, plastic deformations are arbitrarily concentrated in sections and joints where plastic hinges are likely to occur. These sections and joints are assumed to have an infinite rotational capacity. Figure 3.11 shows the idealised rigid-plastic response of the sections and the joints which are adopted for the analysis. As a result, the values of the design moment resistance for sections and joints as well as the structural configuration and the loading are the only parameters that affect rigid-plastic analysis. Rigid-plastic
Rigid-plastic
M
M
pl.Rd
J>P
M.
M
Plastic hinge
Section
j.Rd
f M j,Rd
Plastic hinge
Joint
-> φ
Figure 3.11 Moment-rotation characteristics of section and joint The ductility requirements for the sections and the joints are the same as those outlined for elastic-perfectly plastic analysis.
57
3.4.3.2 Frame analysis On the basis that the maximum loading a given structure can sustain corresponds to that for which collapse occurs (because a realistic plastic mechanism has been created), the analysis consists in identifying the governing plastic mechanism. The basic principle behind this method is that when the collapse load, i.e. the maximum load that the structure can sustain, is attained, the following three conditions are satisfied simultaneously: • Mechanism: there are a sufficient number of plastic hinges or real hinges (pinned joints) for the structure to form a kinematically admissible mechanism; • Equilibrium: the bending moment distribution throughout the structure is in equilibrium with the external loads and reactions; • Plasticity, the plastic moment resistances of the sections and joints are nowhere exceeded. The collapse load can be obtained by the direct application of the fundamental theorems of simple plastic design. These fundamental theorems are the lower bound and the upper bound theorems, also known as the static theorem and the kinematic theorem respectively. An approach suitable for the manual application of the upper bound theorem is summarised here. According to this theorem, for a given structure and loading, any assumed plastic collapse mechanism occurs at a value of the load multiplier configuration that is greater than or equal to the value of the collapse load multiplier. By examining the various possible mechanisms, one identifies the collapse mechanism for which the value of the load multiplier is least and which is both statically and plastically admissible. Figure 3.12 shows the elementary mechanisms 1 and 2 as well as the combined mechanism 3 for a simple portal frame. Any load-displacement response is represented by a horizontal line, the ordinate of which is the associated collapse load. In accordance with the upper bound theorem, the lowest load parameter, which is that for mechanism 3, shall be retained. The collapse load given by the rigid-plastic analysis for this structure and loading corresponds to the load level shown as the reference load multiplier XL4 in the figure. For most cases of simple rectangular frames, the by hand application of the rigid plastic concept is simple and straightforward. Pitched roof portal frames
58
can also be analysed using this approach. For multi-storey and/or multi-bay frames, the use of computers is usually required. Load parameter
-KD l
L4
Collapse load Plastic mechanism
-KÎ)
Displacement parameter W H—►
rn
rn Beam mechanism
Combined mechanism
Figure 3.12 Load-displacement response: rigid-plastic analysis 3.4.3.3 Frame design Additional design checks for sections and joints is required if the influence of the axial force and/or the shear force on the design moment resistance may not be negligible. As the rotations at the plastic hinges have been supposed infinite, these requirements must also be checked. The in-plane frame instability load should be assessed, with provision for interaction with plasticity (e.g. Merchant-Rankine estimate) when necessary. The out-of-plane frame stability will have to be verified as well as the in-plane and/or the out-of-plane member stability. These checks may indeed reduce the value of XL4. For the design to be adequate, the value of XL4 must be at least unity when applied to the factored loads.
5lJ
Resistance to concentrated loads may have to be checked for some members. The rigid-plastic analysis provides direct information in terms of the design frame resistance, but it does not provide any information on the displacements and rotations that have occurred. Therefore, it has usually to be complemented by an elastic analysis of the structure for the serviceability loading conditions.
60
CHAPTER 4
JOINT PROPERTIES AND MODELLING
4.1 Introduction and definitions Building frames consist of beams and columns, usually made of H or I shapes, that are assembled together by means of connections. These connections are between two beams, two columns, a beam and a column or a column and the foundation (Figure 4.1).
A
IB Όζ D
1
)(
— D
VJ
L
D
A
Beam-to-column joint
Β
Beam splice
C
Column splice
D
Column base
Figure 4.1 Different types of connections in a building frame A connection is defined as the set of the physical components which mechanically fasten the connected elements. One considers the connection to be concentrated at the location where the fastening action occurs, for instance at the beam end/column interface in a major axis beam-to-column joint. When the connection as well as the corresponding zone of interaction between the connected members are considered together, the wording joint is then used (Figure 4.2.a). Depending on the number of in-plane elements connected together, singlesided and double-sided joint configurations are defined (Figure 4.3). In a double-sided configuration (Figure 4.3.b), two joints - left and right - have to be considered (Figure 4.2.b.).
The definitions illustrated in Figure 4.2 are valid for other joint configurations and connection types.
Right joint
Left connection
Connection Right connection
Left joint (a) Single sided joint configuration
(b) Double sided joint configuration
Figure 4.2 Joints and connections As explained previously, the joints which are traditionally considered as rigid or pinned and are designed accordingly, possess, in reality, their own degree of flexibility resulting from the deformability of all the constitutive components. Section 4.2 is aimed at describing the main joint deformability sources. Section 4.3 provides information on how to model the joints in view of the frame analysis; this modelling depends on the level of joint flexibility. In Section 4.4, the way in which the shape of the non-linear joint deformability curves may be idealised is given. Section 4.5 refers to the component method as a general tool for the prediction of the main joint mechanical properties in bending. The concept of joint classification is introduced in Section 4.6. Finally, it is commented on the ductility classes of joints in Section 4.7.
S
(a) Single-sided
(b) Double-sided
Figure 4.3 In-plane joint configurations
62
4.2 Sources of joint deformability As said in Chapter 1, the rotational behaviour of the joints may affect the local and/or global structural response of the frames. In this section, the sources of rotational deformability are identified for beamtocolumn joints, splices and column bases. It is worthwhile mentioning that the rotational stiffness, the joint resistance and the rotation capacity are likely to be affected by the shear force and/or the axial force acting in the joint. These shear and axial forces may obviously have contributions to the shear and axial deformability within the connections. However it is known that these contributions do not affect significantly the frame response; therefore, the shear and axial responses of the connection, in terms of rotational deformability, are neglected. 4.2.1 B e a m t o c o l u m n joints 4.2.1.1 Major axis joints In a major axis beamtocolumn joint, different sources of deformability can be identified. For the particular case of a singlesided joint (Figure 4.4.a and Figure 4.5.a), these are: • The deformation of the connection. It includes the deformation of the connection elements : column flange, bolts, endplate or angles,... and the loadintroduction deformation of the column web resulting from the transverse shortening and elongation of the column web under the compressive and tensile forces F¿> acting on the column web. The couple of Fb forces are statically equivalent to the moment Mb at the beam end. These deformations result in a relative rotation φ0 between the beam and column axes; this rotation, which is equal to Qb - Qc (see Figure 4.4.a) is concentrated mainly along edge BC and provides a flexural deformability curve Mb - φο· • The shear deformation of the column web panel associated to the shear force Vwp acting in this panel. It leads to a relative rotation γ between the beam and column axes; this rotation makes it possible to establish a shear deformability curve Vwp-γ. The deformability curve of a connection may obviously be influenced by the axial and shear forces possibly acting in the connected beam. Similar definitions apply to doublesided joint configurations (Figure 4.4.b and Figure 4.5.b). For such configurations, two connections and a sheared web panel, forming two joints, must be considered. In short, the main sources of deformability which must be contemplated in a beamtocolumn major axis joint are :
63
Single-sided joint configuration : - the connection deformability Μύ-φ0 characteristic; - the column web panel shear deformability l/^/characteristic. Double-sided joint configuration : - the left hand side connection deformability Μ^-φαι characteristic; - the right hand side connection deformability Μο2-φο2characteristic; - the column web panel shear deformability VVp-/characteristic.
F b = Mb/z
F h ?= Mh?/z
(a) Single-sided joint configuration
F b i = Mhi/z
(b) Double-sided joint configuration
Figure 4.4 Sources of joint deformability The deformability of the connection (connection elements + load-introduction) is only due to the couple of forces transferred by the flanges of the beam (equivalent to the beam end moment Mb). The shear deformability of the column web panel results from the combined action of these equal but opposite forces and of the shear forces in the column at the level of the beam flanges. Equilibrium equations of the web panel provide the shear force Vwp (see Figure 4.5 for the sign convention) : V
=
&L
■M
fc>2
vci-vc2
wp
(4.1)
Another formula to which it is sometimes referred, i.e. Mbi - Mb2 V WD
~
64
(4.2)
is only a rough and conservative approximation of (4.1). In both formulae, ζ is the lever arm of the resultant tensile and compressive forces in the connection(s). How to derive the value of ζ is explained in Chapter 8. Mn
Mc2
► vc
►
Vc2
νb1
Vb2
'b1
Νb2
^4—
.t
< . Mb2
~H\*v; À . 'i
i.
Nh
> Mb1
►
Yvcl
M Nd
Md
Joint configurations V wp
V.wp
ν wp
v,,
Web panels
V
Vb1
> >
Uih
Nbi
Nb2
^i
Mb2
MH
b2
N b1 Ìl+Λ
M b1
Connections
(a) Singlesided joint
(b) Doublesided joint
Figure 4.5 Loading of the web panel and the connections 4.2.1.2 Minor axis joints A similar distinction between web panel and connection shall also be made for a minor axis joint (Figure 4.6). The column web exhibits a socalled outofplane deformability while the connection deforms in bending as it does in a major axis joint. However no loadintroduction deformability is involved.
65
In the double-sided joint configuration, the out-of-plane deformation of the column web depends on the bending moments experienced by the right and left connections (see F igure 4.7) : àMb
=
(4.3.)
Mbi-Mb2
For a single-sided joint configuration (F igure 4.6), the value of ΔΜύ equals that of Mb.
Fb-Mb/Z Figure 4.6 Deformability of a minor axis joint
Mh
Mb
Figure 4.7 Loading of a double-sided minor axis joint 4 . 2 . 1 . 3 J o i n t s w i t h b e a m s on b o t h m a j o r a n d m i n o r c o l u m n axes A 3-D joint is (Figure 4.8) characterised by the presence of beams connected to both the column flange(s) and web. In such joints, a shear deformation (see 4.2.1.1) and an out-of-plane deformation (see 4.2.1.2) of the column web develop coincidently.
66
The loading of the web panel appears therefore as the superimposition of the shear loading given by formulae (4.1) or (4.2) and the out-of-plane loading given by formula (4.3). The joint configuration of Figure 4.8 involves two beams only; configurations with three or four beams can also be met.
Figure 4.8 Example of a 3-D joint 4.2.2 Beam s p l i c e s and c o l u m n s p l i c e s The sources of deformability in a beam splice (Figure 4.9) or in a column splice (Figure 4.10) are less than in a beam-to-column joint; indeed they are concerned with connections only. The deformability is depicted by the sole Μύ-φ curve.
Left connection
Right connection
Left connection
Right connection
Figure 4.9 Deformation of a beam splice The single Μ0-φ curve corresponds to the deformability of the whole joint, i.e. the two constituent connections (left connection and right one in a beam splice, upper connection and lower one in a column splice).
67
Mc
Mc
V
K.
\r~\r Upper connection
Upper connection o o
£Η-ΗΊ-ΗΙ£
o o
o o
Lower connection
Lower connection
LL-J> A
Nc
Nc Mc
M,
Figure 4.10 Deformation of a column splice In a column splice where the compressive force is predominant, the axial force affects in a significative way the mechanical properties of the joint, i.e. its rotational stiffness, its strength and its rotation capacity. The influence, on the global frame response, of the axial deformability of splices is however limited; therefore it is neglected. 4 . 2 . 3 B e a m - t o - b e a m joints The deformability of a beam-to-beam joint (Figure 4.11) is quite similar to the one of a minor axis beam-to-column joint; the loadings and the sources of deformability are similar to those expressed in 4.2.1.2 and can therefore be identified.
Figure 4.11 Deformation of a beam-to-beam joint
68
4.2.4 C o l u m n bases In a column base, two connection deformabilities need to be distinguished (Figure 4.12) : • the deformability of the connection between the column and the concrete foundation (column-to-concrete connection); • the deformability of the connection between the concrete foundation and the soil (concrete-to-soil connection). For the column-to-concrete connection, the bending behaviour is represented by a Mc - φ curve, the shape of which is influenced by the ratio of the bending moment to the axial load at the bottom of the column. For the connection between the concrete foundation and the soil, two basic deformability curves are identified: • a Nc-u curve which corresponds to the soil settlement due to the axial compressive force in the column; in contrast with the other types of joint, this deformability curve may have a significant effect on the frame behaviour; • a Mc - φ curve characterising the rotation of the concrete block in the soil. As for all the other joints described above, the deformability of the column base due to the shear force in the column may be neglected. The column-to-concrete connection and concrete-to-soil connection Μ0-φ characteristics are combined in order to derive the rotational stiffness at the bottom of the column and conduct the frame analysis and design accordingly. Similar deformability sources exist in column bases subjected to biaxial bending and axial force. The connection Μ0-φ characteristics are then defined respectively for both the major and the minor axes.
Col u m n-to-concrete "connection"
Concrete-to-soil "connection"
Figure 4.12 The connections in a column base
69
4.3 Joint modelling 4.3.1 General Joint behaviour affects the structural frame response and shall therefore be modelled, just like beams and columns are, for the frame analysis and design. Traditionally, the following types of joint modelling are considered : For rotational stiffness : • rigid • pinned
For resistance : · full-strength · partial-strength • pinned
When the joint rotational stiffness is of concern, the wording rigid means that no relative rotation occurs between the connected members whatever be the applied moment. The wording pinned postulates the existence of a perfect (i.e. frictionless) hinge between the members. In fact these definitions may be relaxed, as explained in Section 4.6 devoted to the joint classification. Indeed rather flexible but not fully pinned joints and rather stiff but not fully rigid joints may be considered as fairly pinned and fairly rigid respectively. The stiffness boundaries allowing one to classify joints as rigid or pinned are examined in Section 4.6. For what regards the joint resistance, a full-strength joint is stronger than the weaker of the connected members, what is in contrast with a partial-strength joint. In the daily practice, partial-strength joints are used whenever the joints are designed to transfer the internal forces and not to resist the full capacity of the connected members. A pinned joint transfers no moment. Related classification criteria are conceptually discussed in Section 4.6. Consideration of rotational stiffness and resistance joint properties leads to three significant joint modellings: • rigid/full-strength; • rigid/partial-strength; • pinned. However, as far as the joint rotational stiffness is considered, joints designed for economy may be neither rigid nor pinned but semi-rigid. There are thus new possibilities for joint modelling : • semi-rigid/full-strength; • semi-rigid/partial-strength. With a view to simplification, Eurocode 3 - Chapter 6 and Annex J account for these possibilities by introducing three joint models (Table 4.1) :
70
• continuous : • semi-continuous • simple :
covering the rigid/full-strength case only; covering the rigid/partial-strength, the semi-rigid/fullstrength and the semi-rigid/partial-strength cases; covering the pinned case only. RESISTANCE
STIFFNESS Full-strength Continuous
Rigid
Semicontinuous
Semi-rigid
Partial-strength Semicontinuous Semicontinuous
*
Pinned
*
Pinned * *
Simple
* : Without meaning
Table 4.1 Types of joint modelling The following meanings are given to these terms continuous: semi-continuous: simple:
the joint ensures a full rotational continuity between the connected members; the joint ensures only a partial rotational continuity between the connected members; the joint prevents from any rotational continuity between the connected members.
The interpretation to be given to these wordings depends on the type of frame analysis to be performed. In the case of an elastic global frame analysis, only the stiffness properties of the joint are relevant for the joint modelling. In the case of a rigid-plastic analysis, the main joint feature is the resistance. In all the other cases, both the stiffness and resistance properties govern the manner the joints shall be modelled. These possibilities are illustrated in Table 4.2.
TYPE OF FRAME ANALYSIS
Continuous Semicontinuous
Rigid Semi-rigid
Rigid-plastic analysis Full-strength Partial-strength
Simple
Pinned
Pinned
MODELLING
Elastic analysis
Elastic-perfectly plastic and elastoplastic analysis Rigid/full-strength Rigid/partial-strength Semi-rigid/full-strength Semi-rigid/partial-strength Pinned
Table 4.2 Joint modelling and frame analysis
71
4.3.2 M o d e l l i n g and sources of joint d e f o r m a b i l i t y The difference between the loading of the connection and that of the column web in a beamtocolumn joint (see Section 4.2) requires, from a theoretical point of view, that account be taken separately of both deformability sources when designing a building frame. However doing so is only feasible when the frame is analysed by means of a sophisticated computer program which enables a separate modelling of both deformability sources. For most available softwares, the modelling of the joints has to be simplified by concentrating the sources of deformability into a single rotational spring located at the intersection of the axes of the connected members. 4 . 3 . 3 S i m p l i f i e d modelling a c c o r d i n g to Eurocode
3
For most applications, the separate modelling of the connection and of the web panel behaviour is neither useful nor feasible; therefore only the simplified modelling of the joint behaviour (see Section 4.3.2) will be considered in the present document. This idea is the one followed in the ENV 1993-1-1 experimental standard (Chapter 6 and Annex J). Table 4.3, excerpted from the revised Annex J, shows how to relate the simplified modelling of typical joints to the basic wordings used for the joint modelling: simple, semicontinuous and continuous.
JOINT MODELLING
BEAMTOCOLUMN JOINTS MAJOR AXIS BENDING
BEAM SPLICES
COLUMN BASES
™
SIMPLE
> ■
i—1° °^
SEMI CONTINUOUS
8 :
CONTINUOUS
Hi
Table 4.3 Simplified modelling for joints according to EC3
72
--Ã~
4.3.4 C o n c e n t r a t i o n of the joint d e f o r m a b i l i t y For the daily practice a separate account of both the flexural behaviour of the connection and the shear (major axis beam-to-column joint) or out-of-plane behaviour of the column web panel (minor axis beam-to-column joint configurations or beam-to-beam configurations) is not feasible. This section is aimed at explaining how to concentrate the two deformabilities into a single flexural spring located at the intersection of the axes of the connected members. 4.3.4.1 Major axis beam-to-column joint configurations In a single-sided configuration, only one joint is concerned. The characteristic shear-rotation deformability curve of the column web panel (see Figure 4.4 and Figure 4.13.b) is first transformed into a Mb-y curve through the use of the transformation parameter β. This parameter, defined in Figure 4.14.a, relates the web panel shear force to the (load-introduction) compressive and tensile forces connection (see also formulae 4.1 and 4.2). The Mb-φ spring characteristic which represents the joint behaviour is shown in Figure 4.13.c; it is obtained by summing the contributions of rotation, from the connection (φ0) and from the shear panel (γ). The Mj-φ characteristic of the joint rotational spring located at the beam-to-column interaction is assumed to identify itself to the Mb-φ characteristic obtained as indicated in Figure 4.13.C. Mb, M,
Mfc
M,
(a) Connection
(b) Shear panel
(c) Spring
Figure 4.13 Flexural characteristic of the spring
73
Vwp = β Fb where Fb = M^z (a) Single-sided joint configuration
VWp — βι Fbi = β2 Fb2 where Fb1 = Mb1/z Fb2 = Mb2/z (b) Double-sided joint configuration
Figure 4.14 Definition of the transformation parameter β In a doubie-sided configuration, two joints - the left one and the right one - are concerned. The derivation of their corresponding deformability curves is conducted similarly as in a single-sided configuration by using transformation parameters βι and β2 (Figure 4.14.b). Because the values of the β parameters can only be determined once the internal forces are known, their accurate determination requires an iterative process in the global analysis. For practical applications, such an iterative process is hardly acceptable provided safe β values be available. These values may be used a priori to model the joints and, on the basis of such joint modelling, the frame analysis may be performed safely in a non-iterative way. The recommended but approximate values of β, where β-ι is taken as equal to β2 for double-sided configurations, are given in Chapter 8. They vary from β = 0 (double-sided joint configuration with balanced moments in the beams) to β = 2 (double-sided joint configuration with equal but unbalanced moments in the beams). These two extreme cases are illustrated in Figure 4.15.
(a) Balanced beam moments
(b) Equal but unbalanced beam moments
Figure 4.15 Extreme cases for β values
74
Mbi AMb = ß, M bl = ß2 Mb2
AMb = β Mb = Mb =»β = 1
(b) Doublesided joint configuration
(a) Singlesided joint configuration
Figure 4.16 Definition of the transformation parameter β
4.3.4.2 Minor axis beamtocolumn joint configurations and beamtobeam configurations Similar concepts as those developed in Section 4.3.4.1 are referred to for minor axis beamtocolumn joint configurations and beamtobeam configurations. The definition of the transformation parameter is somewhat different (see Figure 4.16). Approximate values of β (assuming β1 = β2) for these joint configurations are also given in Chapter 8.
4.4 Joint idealisation The nonlinear behaviour of the isolated flexural spring which characterises the actual joint response does not lend itself towards everyday design practice. However the momentrotation characteristic curve may be idealised without significant loss of accuracy. One of the most simple idealisations possible is the elasticperfectly plastic one (Figure 4.17.a). This modelling has the advantage of being quite similar to that used traditionally for the modelling of member crosssections subject to bending (Figure 4.17.b). The moment M¡,Rd that corresponds to the yield plateau is termed design moment resistance in Eurocode 3. It may be understood as the pseudo-plastic moment resistance of the joint. Strainhardening effects and possible membrane effects are henceforth neglected; that explains the difference in Figure 4.17 between the actual Μ-φ characteristic and the yield plateau of the idealised one.
75
Mb , Mc Mj, Rd
Mpl.Rd
Si.ini/η
+ Φ (b) Member
(a) Joint
Actual Μ-φ characteristic Idealised Μ-φ characteristic
Figure 4.17 Bi-linearisation of moment-rotation curves The value of the constant stiffness is discussed below. In fact there are different possible ways to idealise a joint Μ-φ characteristic. The choice of one of them is subordinated to the type of frame analysis which is contemplated: Elastic idealisation for an elastic analysis (Figure 4.18) : The main joint characteristic is the constant rotational stiffness. Mi
Mj,Rd
Mj.Rd
2/3 Mj,Rd
Si.ini/η
j.ini
►Φ Actual Μ-φ curve Idealised representation (a) For elastic verification
(b) For plastic verification
Figure 4.18 Linear representation of a Μ-φ curve
76
Two possibilities* are offered in Eurocode 3-(revised) Annex J: • Elastic verification of the joint resistance (Figure 4.18.a) : the constant stiffness is taken equal to the initial stiffness S/./n,·; at the end of the frame analysis, it shall be checked that the design moment MSd experienced by the joint is less than the maximum elastic joint moment resistance defined as 2/3 M¡,RC¡; • Plastic verification of the joint resistance (Figure 4.18.b) : the constant stiffness is taken equal to a fictitious stiffness, the value of which is intermediate between the initial stiffness and the secant stiffness relative to M¡,Rd; it is defined as Sj.in/η (values of η are given in Chapter 8). This idealisation is valid for MSd values less than or equal to Mj,Rd. Rigid-plastic idealisation fora rigid-plastic analysis (Figure 4.19). Only the design resistance M¡,Rd is needed. In order to allow the possible plastic hinges to form and rotate in the joint locations, it shall be checked that the joint has a sufficient rotation capacity. Mi
Mj,Rd
Figure 4.19 Rigidplastic representation of a Μ-φ curve Non-linear idealisation for an elastic-plastic analysis (Figure 4.20). The stiffness and resistance properties are of equal importance in this case. The possible idealisations range from bilinear, trilinear representations, ... to the fully nonlinear curve. Again rotation capacity is required in joints where plastic hinges are likely to form and rotate.
A third possibility is expressed in Annex J. It leads to an iterative analysis procedure and is not of practical interest. It is therefore not presented here.
77
M, Mj,Rd
M|,Rd
(a) Bi-linear
(b)Tri-linear
(c) Non linear
Figure 4.20 Non-linear representations of a Μ-φ curve
4.5 Joint characterisation 4.5.1 General An important step when designing a frame consists in the characterisation of the rotational response of the joints. Three main approaches may be followed : • experimental; • numerical; • analytical. The only practical one for the designer is the analytical approach. Analytical procedures enable a prediction of the joint response based on the knowledge of the mechanical and geometrical properties of the joint components.
78
In this section a general analytical procedure, termed component method, is introduced. It applies to any type of steel or composite joints, whatever the geometrical configuration, the type of loading (axial force and/or bending moment, ...) and the type of member sections. The method is used in Chapter 8 where the mechanical properties of joints subjected to bending moment and shear force are computed. 4 . 5 . 2 I n t r o d u c t i o n to the c o m p o n e n t m e t h o d A joint is generally considered as a whole and studied accordingly ; the originality of the component method is to consider any joint as a set of individual basic components. For the particular joint shown in Figure 4.4.a (joint with an extended end-plate connection subject to bending), the relevant components are the following : • • • • • • • •
column web in compression; beam flange and web in compression; column web in tension; column flange in bending; bolts in tension; end-plate in bending; beam web in tension; column web panel in shear.
Each of these basic components possesses its own strength and stiffness either in tension or in compression or in shear. The column web is subject to coincident compression, tension and shear. This coexistence of several components within the same joint element can obviously lead to stress interactions that are likely to decrease the resistance of the individual basic components. The application of the component method requires the following steps : a) identification of the active components in the joint being considered; b) evaluation of the stiffness and/or resistance characteristics for each individual basic component (specific characteristics - initial stiffness, design resistance, ... - or whole deformability curve) ; c) assembly of all the constituent components and evaluation of the stiffness and/or resistance characteristics of the whole joint (specific characteristics initial stiffness, design resistance, ... - or whole deformability curve). The assembly procedure consists in deriving the mechanical properties of the whole joint from those of all the individual constituent components. That requires a preliminary distribution of the forces acting on the joint into internal forces acting on the components in a way that satisfies equilibrium and respects the behaviour of the components.
7l)
In Eurocode 3 Annex J, the analytical assembly procedures are described for the evaluation of the initial stiffness and the design moment resistance of the joint; these two properties enable to build design joint moment-rotation characteristic whatever the type of analysis (Figure 4.18 to Figure 4.20). The application of the component method requires a sufficient knowledge of the behaviour of the basic components. Those covered by Eurocode 3 are listed in Table 4.4. The combination of these components allows one to cover a wide range of joint configurations, which should be largely sufficient to satisfy the needs of practitioners as far as beam-to-column joints and beam splices in bending are concerned. Examples of such joints are given in Figure 4.21. Some fields of application can also be contemplated : • Joints subject to bending moment (and shear) and axial force; • Column bases subject to coincident bending moment, shear force and axial force where the components such as : - concrete foundation in compression; - end-plates with specific geometries; - anchorages in tension; - contact between soil and foundation, will be activated. These situations are however not yet covered, or only partially covered, by Eurocode 3. Component
N° 1
Vsd
Column web panel in shear
rr4-
Vsd
2
-VTI
Column web in compression
«—
Fc.Sd
Table 4.4 List of components covered by Eurocode 3 (continued)
so
Beam flange compression
and
web
in
Column flange in bending
Column web in tension
V" End-plate in bending
7
Beam web in tension
8
Flange cleat in bending
Bolts in tension 10
Bolts in shear
11
Bolts in bearing (on beam flange, column flange, end-plate or cleat)
12
Plate in tension or compression
-41
O
Table 4.4 List of components covered by Eurocode 3
si
F..E
(b) Bolted joint with extended end-plate
(a) Welded joint
(c) Two joints with flush end-plates (Double-sided configuration)
(d) Joint with flush end-plate
L (e) End-plate type beam splice
(f) Cover-joint type beam splice
(g) Bolted joint with angle flange cleats
(h) Two beam-to-beam joints (Double-sided configuration)
Figure 4.21 Examples of joints covered by Eurocode 3
s:
4.6 Joint Classification 4.6.1 General In Section 4.3, it is shown that the joints need to be modelled for the global frame analysis and that three different types of joint modelling are introduced : simple, semi-continuous and continuous. It has also been explained that the type of joint modelling to which it shall be referred is dependent both on the type of frame analysis and on the class of the joint in terms of stiffness and/or strength (Table 4.2). Classification criteria are used to define the stiffness class and the strength class to which the joint belongs and also to determine the type of joint modelling which shall be adopted for analysis. They are described in Section 4.6.2.
4.6.2 Classification based on mechanical joint properties 1 The stiffness classification is performed by comparing simply the design joint stiffness to two stiffness boundaries (Figure 4.22). For sake of simplicity, the stiffness boundaries have been derived so as to allow a direct comparison with the initial design joint stiffness, whatever the type of joint idealisation that is used afterwards in the analysis (Figure 4.18 and Figure 4.20). Mi
Boundaries for stiffness Joint initial stiffness
Figure 4.22 Stiffness classification boundaries
This classification is that given in Eurocode 3-(revised) Annex J. As this annex is not fully compatible with the questionable classification diagram proposed in Eurocode 3-Chapter 6.9, no information on the latter is given in the present manual.
K3
The strength classification simply consists in comparing the joint design moment resistance to "fullstrength" and "pinned" boundaries (Figure 4.23). M¡
Fullstrength
Mj,Rd
Partialstrength
Pinned ■
Boundaries for strength Joint strength
Figure 4.23 Strength classification boundaries It is while stressing that a classification based on the experimental joint Μ-φ characteristics is not allowed, as design properties only are of concern. The stiffness and strength boundaries for the joint classification are given in Chapter 8.
4.7 Ductility classes 4.7.1 General concept Experience and proper detailing result in socalled pinned joints which exhibit a sufficient rotation capacity to sustain the rotations imposed on them. For moment resistant joints the concept of ductility classes is introduced to deal with the question of rotation capacity. For most of these structural joints, the shape of the Μ-φ characteristic is rather bilinear (Figure 4.24.a). The initial slope S,,,n, corresponds to the elastic deformation of the joint. It is followed by a progressive yielding of the joint (of one or some of the constituent components) until the design moment resistance Mj,Rd is reached. Then a postlimit behaviour (Sj,p0st-iim) develops which corresponds to the onset of strainhardening and possibly of membrane effects. The latter are especially important in components when rather thin plates are subject to transverse tensile forces as, for instance, in minor axis joints and in joints with columns made of rectangular hollow sections. In many experimental tests (Figure 4.24.a) the collapse of the joints at a peak moment M¡,u has practically never been reached because of high local deformations in the joints involving extremely high relative rotations. In the
S4
others (Figure 4.24.b) the collapse has involved an excessive yielding (rupture of the material) or, more often, the instability of one of the constituent components (ex : column web panel in compression or buckling of the beam flange and web in compression) or the brittle failure in the welds or in the bolts. In some joints, the premature collapse of one of the components prevents the development of a high moment resistance and high rotation. The post-limit range is rather limited and the bi-linear character of the Mj-φ response is less obvious to detect (Figure 4.24.c). As explained in Section 4.4, the actual Mj-φ curves are idealised before performing the global analysis. As for beam and column cross-sections, the usual concept of plastic hinge can be referred to for plastic global analysis.
'l
Mj.u
:
Mj.Rd
-
'
/
Oj, post limit
λ,^ί,ίηί
Φ
►
(a) Infinitely ductile behaviour
(b) Limited ductility M,
Mj,Rd
M,.u
\
(c) Non-ductile behaviour
Figure 4.24 Shape of joint Μ-φ characteristics The development of plastic hinges during the loading of the frame and the corresponding redistribution of internal forces in the frame require, from the joints where hinges are likely to occur, a sufficient rotation capacity. In other words, there must be a sufficiently long yield plateau φρ, (Figure 4.25) to allow the redistribution of internal forces to take place.
S5
M¡
Mi, Rd
Φ
Figure 4.25 Plastic rotation capacity For beam and column sections, deemedtosatisfy criteria allow one to determine the class of the sections and therefore the type of global frame analysis which can be contemplated (see Chapter 3). A strong similarity exists for what regards structural joints; moreover a similar classification may be referred to : • Class 1 joints : M¡,Rd is reached by full plastic redistribution of the internal forces within the joints and a sufficiently good rotation capacity is available to allow, without specific restrictions, a plastic frame analysis and design to be performed if required; • Class 2 joints : M¡,Rd is reached by full plastic redistribution of the internal forces within the joints but the rotation capacity is limited. An elastic frame analysis possibly combined with a plastic verification of the joints has to be performed. A plastic frame analysis is also allowed as long as it does not result in a too high required rotation capacity in the joints where hinges are likely to occur. The available and required rotation capacities have therefore to be compared before validating the analysis; • Class 3 joints : brittle failure (or instability) limits the moment resistance and does not allow a full redistribution of the internal forces in the joints. It is compulsory to perform an elastic verification of the joints unless it is shown than no hinge occurs in the joint locations. As the moment design resistance MjiRd is known whatever the collapse mode and the resistance level, no Class 4 has to be defined as for member sections. 4 . 7 . 2 R e q u i r e m e n t s for c l a s s e s of j o i n t s In Eurocode 3, the procedure given for the evaluation of the design moment resistance of any joint provides the designer with other information such as : • the collapse mode; • the state of stresses inside the joint at collapse.
86
Through this procedure, the designer knows directly whether the full plastic redistribution of the forces within the joint has been reached - the joint is then Class 1 or 2 - or not - the joint is then classified as Class 3. For Class 1 or 2 joints, the knowledge of the collapse mode, and more especially of the component leading to collapse, gives an indication about whether there is adequate rotation capacity for a global plastic analysis to be permitted. The related criteria are expressed in Chapter 8.
87
CHAPTER 5
FRAME AND ELEMENT DESIGN
5.1 Frames and their components 5.1.1 Introduction Global frame analysis is conducted based on assumptions made regarding the section and joint behaviour (elastic/plastic) and the geometric response (firstorder/second-order theory). Once the analysis is achieved, the design checks of all these frame components shall be performed. 5.1.2 F r a m e c o m p o n e n t s A frame is composed of members and joints (Figure 5.1).
Beam
Θ«-
Joint
Beam-column.
Figure 5.1 Frame and their components A member is a structural element which is much longer than it is deep; a joint is an assembly of basic components which enable the sound transfer of internal forces from one member to another one. Member is a general wording; very often a member is designated by an appellation which reflects the kind of its loading : beam if bending predominates, beam-column if significant amounts of both bending and axial force are coincident and column if compressive force is dominant.
89
5.1.2.1
Beams
Most beams are designed to carry gravity loads which produce bending about the major principle axis of the cross-section only; this mono-axial bending is commonly called in-plane bending. Beams are typically the horizontal or slightly sloped members of a framed structure. Because of the unavoidable initial geometrical imperfections in the beam geometry and in the load transfer, some torsion will most often be present in the case of in-plane bending. If the beam is laterally supported in an efficient way, the torsional effects may usually be disregarded and in-plane bending is governing the design. In contrast, for a laterally unsupported beam, the out-ofplane deformations are magnified by an increase of the in-plane loading and the ultimate limit state refers then to lateral-torsional buckling when this occurs. Beams are made of rolled or of welded (built-up) sections. In the latter case, the wall components may be prone to local plate buckling because of their large slenderness. Local plate buckling may possibly interact with lateral-torsional buckling and precipitate the collapse of welded beams. When bending develops simultaneously about both principal axes of the beam cross-section, the beam is said subject to bi-axial bending. As for the in-plane bending case, some torsion is generally present. In addition, the effects of material yielding within the cross-section can accelerate the onset of the ultimate limit state. 5.1.2.2
Columns
Columns are also termed compression members. A short column, post or pedestal reaches its ultimate limit state when the resistance in compression of its cross-section is exhausted. A long or slender column fails by buckling in the elastic or elasto-plastic range. The ultimate buckling load of any column depends basically on the column slenderness. It is less than the squash load of the cross-section and than the elastic critical buckling load because of unavoidable member out-of-straightness, load eccentricities and residual stresses present in the cross-section, on the one hand, and of the elasto-plastic behaviour of the material, on the other hand. 5.1.2.3
Beam-columns
Members which support loads causing both significative bending and axial compression are called beam-columns. Such members are typically the vertical members of a framed structure. (In the current language, the vertical members of a frame are usually termed columns despite the fact they are most often subject to combined axial force and bending). Indeed they transfer gravity loads from the beams to the foundation and are subject to bending moments because of the full or partial continuity of the beam-to-column joints. Strictly speaking
90
most members of a frame are beam-columns; a beam represents the limit case where the axial force can be disregarded and a column the limit case where the bending moments are not significant. 5.1.2.4 Joints Because described extensively in Chapter 4, there is no need to comment anymore on the joints.
5.2 Classification of frames and their components 5.2.1 C l a s s i f i c a t i o n of f r a m e s 5.2.1.1 Braced and unbraced frames For a frame to be classified as a braced frame, it must possess a bracing system which is adequately stiff (Figure 5.3.a). Common bracing systems are trusses or shear walls (Figure 5.2) or even a concrete central core where stairs and lifts take place. Shear wall
Trusses
Figure 5.2 Common bracing systems When it is justified to classify the frame as braced, it is possible to analyse the frame and the bracing system separately as follows: • The frame without its bracing system resists all the vertical loads; • The bracing system resists all the horizontal loads. In the cases where there is either no bracing system or no stiff enough bracing system, the frame is said unbraced (Figure 5.3.b). The frame with possibly its bracing system is then the single structure to be analysed. In chapter 9, specific application rules are provided which enable to classify frames as braced or unbraced.
l
)l
5.2.1.2 Sway and non-sway frames The wording non-sway f rame applies to a frame when its response to in-plane horizontal forces is sufficiently stiff for it to be acceptable to neglect any additional forces or moments arising from horizontal displacements of its storeys; that means that the global second-order effects may be neglected. When the later is not negligible, the frame is said sway. In Chapter 9, criteria are given which enable to classify frames as sway or nonsway.
a. Braced frame (may be sway if bracing is unduly flexible)
b. Unbraced frame (may be non-sway if it is insensitive to horizontal loads)
Figure 5.3 Braced and unbraced frame 5.2.2 C l a s s i f i c a t i o n of frame c o m p o n e n t s 5.2.2.1 Classification of member cross-sections Local buckling can be prevented by limiting appropriately the width-to-thickness ratio of the wall elements. These limits are given in Eurocode 3. The class of a cross-section is determined by the worst class of its wall components. Crosssections are classified as follows according to their behaviour in bending and/or compression. For member cross-sections subject to bending, there are 4 classes (Figure 5.4): • Class 1 : Plastic cross-sections. A plastic cross-section is able to develop the plastic moment resistance of the gross section (plastic hinge) and to exhibit a sufficiently large rotation capacity. • Class 2:
Compact cross-sections. A compact cross-section is able to develop the plastic moment resistance of the gross section but local buckling in the plastic
92
range limits significantly the rotation capacity once the plastic moment resistance is reached. • Class 3:
Semi-compact cross-section. A semi-compact cross-section is only able to develop the elastic moment resistance of the gross section because local buckling in the elasto-plastic range occurs before the plastic moment resistance is reached.
• Class 4:
Slender cross-section. Premature local plate buckling occurs before the elastic moment resistance is reached. The bending resistance of an appropriate effective cross-section shall be considered. M
Compact Class 2
Plastic Class 1
Non compact Class 3 Slender Class 4
Figure 5.4 Classification of the cross-section in bending Above concept of classes applies also to cross-sections subject to combined dominant bending and axial force. For member cross-sections subject to axial compression only, there are only two classes, according to the ability of the cross-section to reach or not its squash load. There is indeed no further need for some available rotation capacity. In general, the classification will depend on both the loading case - i.e. on the distribution of the direct stresses within the cross-section - and the loading plane.
93
5.2.2.2 Classification of joints according to ductility For joints a classification similar to the one used for member cross-sections may be introduced (Figure 5.5). There are three classes of joints: • Classi:
Ductile joints. A ductile joint is able to develop its plastic moment resistance and to exhibit a sufficiently large rotation capacity.
• Class 2 : Joints of intermediate ductility. A joint of intermediate ductility is able to develop its plastic moment resistance but exhibits only a limited rotation capacity once this resistance is reached. • Class 3 : Non ductile joints. Premature failure (due to instability or to brittle failure of one of the joint components) occurs within the joint before the moment resistance based on a full plastic redistribution of the internal forces is reached. M¡
Figure 5.5 Classification of the joint by ductility
94
5.3 Checking frame components 5.3.1 Resistance check of member cross-sections To which extent the check of the resistance of the member cross-sections is concerned depends upon the type of global frame analysis that has been performed. 5.3.1.1 Elastic global analysis A strictly elastic design would limit the carrying capacity of a frame to the onset of the very first yielding in the outer fibre(s) of any cross-section. That leads to an elastic resistance design check of the member cross-sections. However a less severe attitude is acceptable. While an elastic global analysis is performed, the internal forces and moments that are obtained accordingly can be checked against the resistance of the cross-sections by using the relevant plastic interaction formulae for section resistance. Doing so allows only for one plastic hinge (or more than one but occurring simultaneously) to form in the structure. That leads to a plastic resistance design check of the member crosssections. - Elastic resistance check The elastic distribution of the direct stresses σ in an l-section and a T-section subject to mono-axial bending is shown in Figure 5.6.
y
y
Section
Stress
Stress
Figure 5.6 Beams subject to elastic mono-axial bending The design bending moment MSd in any cross-section, in the absence of the shear and axial force, shall be less than or equal to the design elastic moment resistance Mei,Rd of the cross-section. The width-to-thickness ratio limits for class 3 shall be met by all the wail components of these cross-sections. If the width-to-thickness ratio of any wall element is larger than the relevant limit for
95
class 3, then an elastic moment resistance based on the effective crosssection characteristics Mei,eff,Rd shall be used. Similar principles apply when biaxial bending. Interaction with shear and/or axial forces shall be accounted for by referring to the equivalent stress deduced from the von Mises criterion. Plastic resistance check The plastic distribution of the direct stresses in an lsection and a Tsection subject to monoaxial bending is shown in Figure 5.7. Such a distribution is permitted when the section belongs either to class 1 or to class 2. ζ
ι
y
ι
. _ l
_
. y
y
Dy^
^ ζ
Section
Section
Stress
Stress
Figure 5.7 Beams subject to plastic monoaxial bending As far as the interaction between bending moment and shear and/or axial force(s) is sufficiently small for it to be regarded as negligible, the design value of the bending moment Msd in each crosssection shall be less than or equal to the plastic moment resistance Mp¡,Rd of the crosssection. When the interaction between bending and shear and/or axial force(s) can no more be disregarded, a plastic interaction formula shall be used when checking the resistance of the crosssection. It will be done similarly when biaxial bending. 5.3.1.2 Plastic global analysis When an elasticperfectly plastic or a rigidplastic global frame analysis is performed, the behaviour of the crosssections is accounted for in the global analysis with the result of a redistribution of internal forces. For this purpose, the bending response of a crosssection is usually simplified as shown in Figure 5.8. Any crosssection where a plastic hinge is likely to occur shall be either a class 1 or a class 2 section. However when a class 2 section is used, the available rotation capacity must be checked to ensure that
96
it is sufficient to meet what is required by the formation of the relevant plastic mechanism.
M
M
Mpl.Rd
Mpl.Rd Mpl.Rd
Mpl.Rd
M pl.Rd
► Plastic hinge
Elastic-perfectly plastic
Mpl.Rd
Plastic hinge
Φ
Rigid plastic
Φ
Figure 5.8 Moment-rotation characteristics of a cross-section : plastic global
analysis 5.3.2 C h e c k of m e m b e r i n s t a b i l i t y 5.3.2.1 Beam in bending and column in compression Any member which is subject to direct compressive stresses over the whole or a part only of its cross-section may become unstable because of a buckling phenomenon: column buckling for an axially loaded column and lateraltorsional buckling for a beam subject to predominant bending (Figure 5.9). An axially loaded column the cross-section of which is doubly symmetrical may collapse by in-plane buckling either by bending about the major axis of its cross-section or, more commonly, about the minor axis. When the crosssection is not doubly symmetrical, instability may occur by torsional-flexural buckling; this phenomenon is of major importance in thin-walled cold-formed compression members. Lateral-torsional buckling of a beam has much in common with the minor axis column buckling phenomenon due to the buckling of the compression part by bending about the minor axis of the section. This column buckling is however accompanied by torsional effects that are induced by the necessary continuity between both tensile and compressive parts of the cross-section. The greater the slenderness of the member about the minor axis, the smaller the lateraltorsional buckling resistance of the member.
97
i ζ
ζ.
y
*- ν
'
»
χ
'
— ! -»—»
YÍ
'VΛ
-1- H '
Ilt
Ii
V
►
Ρ
\
χ
Ν
Ν
Minor axis buckling
Lateraltorsional buckling
Major axis buckling
b) Beam in bending
a) Columns in compression
Figure 5.9 Buckled position of columns and beam
Normalised load
Elastic critical behaviour >
Actual behaviour
1 / Smal
Intermediate
Large
k
r Normalised slenderness
Figure 5.10 Buckling behaviour curve of columns and beams Column buckling resistance (respect, lateraltorsional buckling resistance) depends on the member slenderness. It can be described schematically by the solid line in Figure 5.10, where use is made of normalized coordinates. The dotted lines correspond to an ideal behaviour : plastic resistance of the cross section in compression (respect, in bending) and elastic critical column buckling load (respect, lateraltorsional buckling load of the beam). The loss in resistance with regard to such an ¡deal behaviour is due to geometrical
9K
imperfections (initial out-of-straightness or initial twist), structural imperfections (residual stresses) and effects of material yielding. It is usual to distinguish three slenderness ranges : • Small slenderness range, where the member slenderness is so small that the detrimental effects of imperfections is more than compensated by the strainhardening effects (the latter are generally not accounted for in the design rules), so that only yielding governs the resistance; • Large slenderness range, where the member slenderness is sufficiently large for the instability to occur in the elastic range with the result that only the imperfections affect the resistance; • Intermediate slenderness range, when the interaction between the detrimental effects of material yielding and member imperfections is the most pronounced, with the result of the largest drop in resistance compared to the ideal behaviour. Guidance on the design for buckling resistance of columns and beams is given in Eurocode 3. 5.3.2.2
Beam-column
The behaviour of a beam-column combines the respective behaviours of both a column and a beam. That results in a complex structural response for what regards instability. One can identify five cases according to the member unbraced length and the type of loading (see Table 5.1). 5.3.3 A d d i t i o n a l resistance c h e c k s In addition to cross-section checks (see Section 5.3.1) and member instability checks (see Section 5.3.2), the following checks shall be considered: • resistance of the web to shear buckling; • resistance of the web to transverse concentrated loads (patch loading). Eurocode 3 provides the information required for those additional checks. 5.3.4 R e s i s t a n c e check of joints The type of resistance checks to be carried out depends on the type of global analysis that has been performed.
99
Case
Type member / Type of loading / Restraints
Failure mode
1
Short member subject to combined axial compressive force and either monoaxial bending or biaxial bending.
Exhaustion of the elastic or plastic resistance of a crosssection.
2
Slender member subject to combined axial compressive force and monoaxial bending about the major axis (yy) and supported laterally so that buckling about the minor axis (zz) is prevented.
Buckling about the major axis (yy).
3
Slender member with no lateral support, subject to combined axial compressive force and monoaxial bending about the minor axis (zz) and where no lateral buckling out of the plane of bending is prevented.
Buckling about the minor axis (zz).
4
Slender member with no lateral support, subject to combined axial compressive force and monoaxial bending about the major axis (yy).
Combination of buckling and lateraltorsional buckling. The member section twists as well as deflects in both major and minor axes.
5
Slender member with no lateral support, subject to combined axial compressive force and biaxial bending.
Similar to Case 4 but accentuated by the minor axis bending.
Table 5.1 Failure modes of beamcolumns 5.3.4.1 Elastic global analysis When an elastic global frame analysis is performed, the behaviour of the joints is assumed to be indefinitely linear. Any joint shall be verified on the basis of its socalled design elastic or plastic resistance. The design elastic bending resistance of the joint is taken nominally equal to 2/3 of the design plastic bending resistance M¡,Rd, when the analysis has been carried out based on the initial stiffness Sy,,n; of the joint. To be able to use the design plastic resistance Mj,Rd, a reduced stiffness Sj,ini /η of the joint shall be adopted in the global analysis (see Figure 5.11). 5.3.4.2 Plastic global analysis When either an elasticperfectly plastic or a rigidplastic global frame analysis is performed, the joint behaviour is idealised as shown in Figure 5.12; a quite
100
similar idealisation is currently adopted for the member crosssections. Any joint where a plastic hinge is likely to occur shall be either a class 1 or a class 2 joint. Shall this joint belong to class 2, then it shall be checked whether the available rotation capacity of the joint is at least equal to the rotation capacity required by the relevant plastic mechanism. Elastic
M, Mj.Rd
Elastic resistance check
ψ
Plastic resistance check
Figure 5.11 Elastic idealisation of the joint behaviour Elastic perfectly plastic
Rigidplastic
^ —
M¡ ▲
M¡ f
Mj.Rd
f 'fp
Mi.
Plastic hinge
Plastic hinge
Sj.ini /η
Figure 5.12 Plastic idealisation of the joint behaviour
ΙΟΙ
M, ""j.Rd
5.4 Modelling of joints 5.4.1 D e s i g n a s s u m p t i o n s Joint modelling requires a particular attention as joints are classified by strength, stiffness and ductility. The following table (Table 5.2) shows the different cases of joint modelling (simple, continuous and semi-continuous) as related to both the type of global analysis and the joint classification. 5.4.2 S i m p l e j o i n t s In a simple joint, the connection between the members may be assumed to be unable to develop any bending moment. The in-plane sway stability of a frame with simple joints only must be provided by the bracing system which shall resist all the horizontal loads. Vertical loads are resisted by both the frame and the bracing system. Such a frame is invariably designed as a non-sway frame, with the result that the distribution of internal forces and moments is not significantly affected by the sway displacements. GLOBAL ANALYSIS
JOINT CLASSIFICATION
Elastic
Nominally pinned
Rigid
Semi-rigid
Rigid-Plastic
Nominally pinned
Full-strength
Partial-strength
Elastic-Plastic
Nominally pinned
Rigid and fullstrength
Semi-rigid and partial-strength Semi-rigid and full-strength Rigid and partial-strength
JOINT MODELLING
Simple
Continuous
Semi-continuous
Table 5.2 Type of joint model 5.4.3 C o n t i n u o u s j o i n t s In a frame with continuous joints, the joints ensure a full continuity between the connected members. The internal forces and moments can be determined either by an elastic or a plastic global analysis, with account being taken for second-order effects when necessary. 5.4.4 S e m i - c o n t i n u o u s joints In a frame with semi-continuous joints, only a partial continuity exists between the connected members. The internal forces and moments can be determined
102
by either an elastic or a plastic global analysis, with account being taken for second-order effects when necessary. As partial-strength and/or semi-rigid joints usually influence significantly the frame behaviour, the analysis of the frame shall account for the joint structural response (strength, stiffness).
5.5 Frame design procedure tasks At the preliminary design stage, the frame must be first defined. In particular, in addition to the structure layout and the member and joint sizing, the braced or unbraced character of the overall frame must be determined. The frame imperfections are taken as an initial out-of-plumb of the vertical members, i.e. by an initial sway of the storeys (Figure 5.13.a); how to assess these imperfections is described in Eurocode 3. For sake of easiness equivalent horizontal loads at the floor levels are generally substituted for the global frame imperfections; then the global analysis may still be conducted on the ideal frame, i.e. without out-of-plumb, but these equivalent loads must of course be superimposed to the other actions. The member imperfections are taken as geometrical imperfections (out-ofstraightness) and residual stresses. Usually residual stresses are not accounted for explicitly but converted into a magnification of the initial out-ofstraightness. Thus the member imperfection is normally represented by an equivalent initial out-of-straightness. These imperfections have sometimes, but rarely, to be taken into account by fitting the members with an appropriate initial camber (Figure 5.13.b) and conducting the global analysis accordingly.
I
v.
-
(a) Frame imperfections
(b) Member imperfections
Figure 5.13 Imperfections
103
At the next stage, an appropriate method of global analysis is chosen. Whereas a second-order analysis is always practicable, there are cases where a less sophisticated analysis provides the designer with a satisfactorily accurate distribution of internal forces : • A first-order analysis may be sufficient, without there being any need to account for second-order effects; • A first-order analysis may be performed, but its results need for some corrections because of significant second-order effects. To make this selection possible, the designer needs a mean to evaluate to which extent the sway displacements can modify the distribution of internal forces. That is measured by the elastic critical load parameter Xcr, i.e. the ratio between the vertical load resultant Vcr producing sway instability and the resultant Vsd of the design vertical loads applied onto the frame. If the value of this ratio is sufficiently large (non-sway frame), first-order analysis is adequate. If it is sufficiently small (sway frame), second-order analysis is required. However many structures are characterised by an intermediate value of the critical load parameter; then it is acceptable to conduct a first-order analysis provided that the first-order internal forces and moments are amplified appropriately to account for the second-order effects that have been fully disregarded by the global analysis. The designer will also have to opt for the use either of an elastic method of analysis or, when appropriate, of a plastic method of analysis. While an elastic global analysis is always permitted, the use of a plastic global analysis is subordinated to some requirements (see Section 5.5.2). When the design internal forces have been determined accordingly (first-order, second-order of first-order with amplification), the resistance and the stability of both the frame and its components have to be checked. The aim of Section 5.5.1 and Section 5.5.2 is to give guidelines for global elastic analysis and plastic analysis respectively. The question of the overall equilibrium of the frame in terms of uplifting, overturning and sliding is not addressed here. It can usually be verified without additional modelling of the structure. The support reactions provided by the global frame analysis shall be compared to the corresponding foundation support resistances. 5.5.1 Elastic global analysis and relevant d e s i g n c h e c k s To enable an elastic global analysis, the frame components (sections and joints) are not subordinated to any requirement related to their ability to exhibit ductile behaviour. Figure 5.14 summarizes the different possibilities of the elastic global analysis and the relevant checks with reference to Eurocode 3.
104
Sway frame
Non-Sway frame
J
V
ν
V
V
V
1st order analysis
Elastic 1st order analysis
Amplfied Sway Moment
Sway Mode Buckling Length
Method
Method
2nd order analysis
global analysis
Account for 2nd order effects
}r
(in specific cases)
(general)
I
t
\t
Amplified sway
Beam end and joint moments
moments
amplified by 1.2
t
f
In plane member stability
In plane member stability
with non sway buckling length
with sway buckling length
Check of components
Cross-section resistances and local stability
and frame Joint resistances Out-of-plane stability of the members
Figure 5.14 Elastic global analysis and relevant design checks (according to Eurocode 3) In Section 5.5.1.1 and Section 5.5.1.2 details are given on how to proceed when an elastic global analysis is used. Once the designer has opted for an elastic global analysis, he shall question about a first-order or a second-order theory for this analysis. 5.5.1.1 First-order analysis First-order elastic analysis with appropriate allowance for frame imperfections may be used to calculate the distribution of internal forces in a non-sway frame. The frame shall be analysed for various load combinations. A maximum error of 10% is expected on the values of both first-order sway and bending moments compared to those got from a second-order analysis. The resistance of the frame components (member sections and joints) and of the in-plane member stability, using the buckling lengths for the non-sway
I 05
mode, are checked. Separate design checks of the local resistance and of the out-of-plane stability of the members shall also be carried out. No further check of the in-plane global frame stability for sway buckling mode is required because of the non-sway character of the frame. A first-order analysis may also be used for sway frames provided some corrections be made to allow for the second-order effects (see Section 5.5.1.2). 5.5.1.2 Second-order analysis Second-order analysis with due allowance made for frame imperfections may be used in all cases. It is required when the frame is classified as sway. Eurocode 3 allows the procedures described hereafter. - General Method Second-order effects due to frame imperfections and sway displacements are explicitly accounted for in the method of global analysis. Second-order effects due to member imperfections and in-plane member deflections can also be taken into account when necessary. The resistance of the frame components (member sections and joints) and of the in-plane stability of each member, using buckling lengths for the non-sway buckling mode, are checked. The latter check is not necessary when member imperfections are considered prior to the global analysis. Separate design checks of the local resistance to concentrated forces and of the out-of-plane stability of the members shall also be carried out. No further check of the in-plane global frame stability for the sway buckling mode is required because it is already implicitly covered by the type of theory used for the global analysis. Alternatively, the approximate method known as the Equivalent Lateral Load procedure can be used. It consists in an iterative procedure, using the results of a standard first-order analysis, to include the sway frame effects. The same considerations as above still hold for the design checks of the frame. What is especially of concern in a sway frame is the determination of internal forces and moments which include second-order effects. It is thus more a problem of an appropriate assessment of these internal forces and moments than, strictly speaking, a question of theory used for the analysis. In this respect, the heading of present section could appear a bit ambiguous to the attentive reader. Therefore tricks have been imagined which enable the designer to make a realistic assessment of the design internal forces and moments without conducting a so-called second-order analysis properly. Of course the range of
106
application of such tricks is, as said previously, subordinated to some conditions. The basic philosophy of these alternative approaches is first to conduct a first-order analysis and second to introduce an estimate of the second-order effects. In this respect, Eurocode 3 allows for two simplified procedures : a) the so-called amplified sway moment method where second-order effects are accounted for by amplifying the loading side in the check expressions to be fulfilled; b) the so-called sway mode buckling length method where second-order effects are introduced both as a magnification of the loading side and as a penalty on the resistance side in the check expressions to be fulfilled. Let us comment a bit more on both procedures. - Amplified Sway Moment Method As an alternative to a second-order elastic analysis, the simplified method known as the Amplified Sway Moment Method may be adopted, provided that the distribution of the second-order bending moments shows approximate affinity to the one of the first-order bending moments; that is acceptably the case in structures exhibiting a low to moderate sway. The sway moments result from the horizontal applied loads and, if the frame and/or the vertical loading are asymmetrical, from the effects of the sway displacements. They can be obtained by proceeding as follows : 1. Perform a first-order elastic analysis of the frame under the whole loading with, in addition to the real supports, the floor levels restrained against horizontal displacement; 2. Determine the horizontal reactions at those horizontal restraints; 3. Perform a first-order elastic analysis of the real frame, i.e. where the horizontal restraints are removed, under the sole horizontal forces equal but opposite to the horizontal reactions found in above Step 1 ; 4. The sway moments are the moments obtained at the end of above Step 3. The moments to be used for further design checks are equal to the sum of : a) the moments obtained at Step 1 ; b) the sway moments obtained at Step 4 but magnified by an appropriate amplification factor. Of course, the amplification process described above for bending moments applies as well to shear and axial forces.
I07
The resistance of the frame components (sections and joints) and the out-ofplane stability of the beams, using the amplified moments, are then checked. The in-plane and the out-of-plane column stability, using the non-amplified moments (i.e. the sum of those obtained respectively at Steps 1 and 3), and the in-plane buckling length for the sway mode are then checked. Separate design checks of the local resistance of the members are carried out. According to Eurocode 3, the fulfilment of these checks is sufficient to guarantee the overall sway stability of the frame. - Sway Mode Buckling Length Method The simplified method known as the Sway Mode Buckling Length Method shall be adopted for structures either which exhibit a large sway or the sway sensitivity of which is unknown and uneasily predictable. The internal forces and moments are computed based on a first-order analysis; then the internal moments at the beam ends and joints are amplified by a nominal factor 1,2. Besides the resistance of the frame components (member sections and joints) and of the in-plane member stability, using the buckling lengths for the sway mode, are then checked. Separate design checks of the local resistance to concentrated loads and of the out-of-plane stability of the members shall also be carried out. According to Eurocode 3, the fulfilment of these checks is sufficient to guarantee the overall sway stability of the frame. 5.5.2 Plastic global analysis a n d relevant d e s i g n c h e c k s The use of a plastic global analysis is subordinated to the fulfilment of some requirements regarding the steel grades and the classes of cross-sections and joints. It is indeed necessary to ensure that the full plastic resistance of sections and joints can be reached and that sufficient rotations can develop at the locations where plastic hinges are likely to form. Figure 5.15 summarizes the different possibilities for performing a plastic global analysis and the relevant checks with reference to Eurocode 3. In Section 5.5.2.1 and Section 5.5.2.2 details are given on how to proceed when plastic global analysis is used. Once the designer is allowed to perform a plastic global analysis and has decided to do accordingly, he shall question about a first-order or a secondorder theory for this analysis.
IOS
Non-sway frame
Sway frame
1st-order (rigid-plastic) analysis Plastic global analysis
1st-order analysis
(rigid-plastic or elasticperfectly plastic)
2nd-order analysis
(elastic-perfectly plastic)
Eurocode 3 Approach (in specific cases only)
Í Amplification of all internal forces and moments
Account for 2nd order effects
Collapse load parameter must be at least equal to unity
Check of components and frame
Collapse load parameter must be at least equal to the value of the amplification factor
In-plane member stability with buckling lengths for the non-sway mode and due allowance for the presence of plastic hinges Cross-section resistance and, when necessary, rotation capacity, local stability Joint resistance and, when necessary, rotation capacity Out-of-plane stability of the members
Figure 5.15 Plastic analysis and relevant design checks (according to Eurocode 3) 5.5.2.1 First-order analysis First-order analysis (rigid-plastic analysis or elastic-perfectly plastic analysis) is especially appropriate for non-sway frames. Rigid-plastic analysis is also permitted for sway frames in specific cases only. The loads are assumed to increase in a proportional and monotonie manner. The plastic load parameter Xp, at which collapse occurs by the onset of a plastic hinge mechanism, must at least amounts unity. Checks of the resistance of the cross-sections and joints are required to account for the influence of axial and/or shear forces. As the first-order plastic method does not make allowance for any buckling in-plane and, out-of-plane phenomena in the members, these checks shall be carried out with due account taken of the presence of plastic hinges and of their effects on buckling lengths. Separate design checks of local resistance to concentrated forces shall also be performed.
109
No further check of the in-plane global frame stability for the sway buckling mode is required because of the non-sway character of the frame. First-order plastic analysis may also be applicable to sway frames under the reservation that some corrections be brought to the results to allow for secondorder effects (see the alternative methods to second-order plastic analysis described in Section 5.5.2.2.). 5.5.2.2 Second-order analysis Second-order analysis, with due allowance being made for frame imperfections is applicable in any circumstance. Second-order theory is especially required when the frame is classified as sway. Second-order effects due to global frame imperfections and sway displacements are necessarily included in the results of the global analysis. Second-order effects due to local member imperfections and in-plane member deflections can also be accounted for provided that the global analysis is conducted on the structure with initially deflected members. The influence of the axial and/or shear forces on the plastic moment resistance of the sections may also be reflected if the software proceeds appropriately. As the loads are assumed to be incremented proportionally, the plastic collapse load parameter Xu, which is the one at which collapse develops in the structure, due either to a plastic mechanism or to frame instability, must at least amount unity. Additional design checks for the cross-sections and joints are required only when the influence of the axial and/or shear forces has not yet been accounted for in the global analysis. As the rotations in the plastic hinges are results of the global analysis, a direct check of the rotation capacity is possible when necessary. The design checks of the members against in-plane buckling phenomena, using the buckling lengths for the non-sway mode and with due allowance for the presence of plastic hinges, shall be carried out except when the member imperfections have yet been introduced in the structure prior to its global analysis. Local resistance to concentrated forces may have to be checked in some members. In most cases where elastic-perfectly plastic global analysis is used, only the in-plane behaviour of members is considered. Therefore separate checks of the out-of-plane member stability shall be needed. No further check of the in-plane frame stability for the sway buckling mode is required, because it has been covered by the structural analysis. Similarly to what was said about second-order elastic global analysis (see Section 5.5.1.2), it is still possible to account for second-order effects by means of corrections to be brought to the results of a first-order plastic analysis. In this respect, two simplified approaches are available :
I IO
a) the Eurocode 3 approach (Simplified a1pproach) ; b) the so-called Merchant-Rankine approach. • Simplified second-order elastic-perfectly plastic analysis - Eurocode 3 Approach1 As an alternative to the general second-order elastic-perfectly plastic analysis, Eurocode 3 offers a simplified second-order method, which may be adopted for sway frames in specific cases (frames with low to moderate sway). In this approach, the collapse load parameter Xp is first computed based on a first-order rigid-plastic analysis. It is then reduced to take account of secondorder effects and must then have a value which is at least equal to unity. The internal forces and moments resulting from the rigid-plastic analysis are amplified to generate a consistent set of internal forces and moments which then include presumably second-order effects. Safety checks of the cross-section and joint resistance are required which account for the influence of axial and/or shear forces. Checks of the in-plane member stability, using the buckling lengths for the non-sway mode are carried out with allowance being made for the presence of plastic hinges. Separate design checks of the local resistance to concentrated loads and the out-ofplane stability member shall also be performed. According to Eurocode 3, these checks, when fulfilled, guarantee the overall sway stability of the frame.
• Merchant-Rankine approach The Merchant-Rankine approach can only be used for sway frames which meet the following requirement : 4 to S ; > for unbraced frames. ¡' L 1~ L·
Table 6.2 Boundaries for variance between actual and approximate initial stiffnesses
6.2 Use of the fixity factor concept (traditional design approach) Another strategy for a preliminary design is the use of the socalled fixity factor f The fixity factor fis defined as the rotation φ0 of the beam end, due to a unit end moment applied at the same end, divided by the corresponding rotation , of the beam plus the joint. iE
M=1 Ç ¿
Figure 6.4 Beam end rotation
The end rotation of the beam for a unit moment is (Figure 6.4): rS
L
>
The rotation of the beam plus the joint for the same moment is:
wherefrom the fixity factor: / > :
φ,
' l+1.5a
where the symbols E, Lb, /¿and S,are defined in Table 6.2 and 2EL
a
Lb S i
For a truly pinned joint, /is equal to 0 while for a truly rigid joint, /amounts 1. To speed up the process of converging to a solution, the designer can decide to adopt a fixity factor between 0 and 1 and start the global frame analysis accordingly. Recommended values are 0.1 < f < 0.6 for braced frames and 0.7 < f < 0.9 for unbraced frames. Let us assume f = 0.5 for braced frames; then a joint stiffness of 3 EltJLb should be adopted in the global frame analysis. If f = 0.8 is used for unbraced frames, the corresponding value of the joint stiffness is 12 Elt/Lb. These respective values can be considered as a good guess in the design procedure of Figure 6.1. It shall be verified that this good guess is in reasonable agreement with the actual initial stiffness of the joints. For this verification, Table 6.2 can be used, but it merges to Table 6.3 if a fixity factor f = 0.5 for braced frames or f = 0.8 for unbraced frames is adopted.
6.3 Design of nonsway frames with rigidplastic global frame analysis The strategy described above focuses on the joint stiffness only and therefore suits especially for elastic global frame analysis. When plastic design is used the latter is especially appropriate to braced nonsway frames, the resistance of the joints is governing the global frame analysis too.
I 23
Lower boundary
Frame
Upper boundary
Braced (f =0.5) ^
9
¡¿PP
E
l
h
ι -b
s > 24B » ""
L
s
(b) Distribution of the internal forces at the beginning of the loading
Figure 8A.10 Joint with a thin endplate In Eurocode 3-(revised) Annex J, it is assumed that the upper boltrow will reach its design resistance first. This assumption is quite justified in the particular case being considered but is probably less justified for other connection types such as for endplate connections with an extended part in the tension zone where it is usual that the second boltrow that just below the flange in tension reaches its design resistance first. The design resistance of the upper boltrow may be associated to one of the following components : the bolts only, the endplate only, the boltsplate assembly or the beam web in tension. If its failure mode is ductile, a redistribution between the boltrows can take place : as soon as the upper bolt row reaches its design resistance, the supplementary bending moments applied
to the joint are carried by the lower boltrows (the second, then the third, etc.) which, each one in their turn, may reach their own design resistance. The failure may occur in three different ways : i. The plastic redistribution of the internal forces extends to all boltrows when they have sufficient deformation capacity. The redistribution is said to be "complete" and the resulting distribution of internal forces is called "plastic". The design moment resistance MRd is expressed as (Figure 8A.11) M Rd
Σ Γ ™Α
(8A.11)
The plastic forces FRdj vary from one boltrow to another according to the failure modes (bolts, plate, boltplate assembly, beam web, ...). Eurocode 3 considers that a boltrow possesses a sufficient deformation capacity to allow a plastic redistribution of internal force to take place when : • Frdj is associated to the failure of the beam web in tension or; • FRdj is associated to the failure of the boltplate assembly (including failure of the bolts alone or of the plate alone) and : FRäjZ\9BtM FR
hi
, >·
^ ► ►
r Fari ;
. I
Figure 8-A.11 Plastic distribution of forces The plastic redistribution of forces is interrupted because of the lack of deformation capacity in the last bolt-row which has reached its design resistance (FRdk > 1,9 BtRd and linked to the failure of the bolts or of the boltplate assembly). In the bolt-rows located lower than bolt-row k, the forces are then linearly distributed according to their distance to the point of compression (Figure 8A.12). The design moment resistance equals :
I 72
M Rd
2^i Í=U
'Rd,i
+
Rd,k 'it
(8A. 12)
Σ»?
i=k+\,n
where
n is the total number of boltrows;
which is
k is the number of the boltrow, the deformation capacity of not sufficient.
In this case, the distribution is said "elastoplastic". FRd,i
hi
I
, ;
k
hk
,
>
A
· · ' i~Rd,k ■ *■'
' ·<
.1
Figure 8A.12 Elastoplastic distribution of internal forces iii. The plastic or elastoplastic distribution of internal forces is interrupted because the compression force Fc attains the design resistance of the beam flange and web in compression. The moment resistance MRd is evaluated with similar formulae to (8A.11) and (8A. 12) in which, obviously, only a limited number of boltrows are taken into consideration. These bolts rows are such that :
Σ^=^
c.Rd
i=\,n
where :
m is the number of the last boltrow transferring a tensile force; F, is the tensile force in boltrow number l ; Fc.Rd is the design resistance of the beam flange and web in compression
The application of the abovedescribed principles to beamtocolumn joints is quite similar. The design moment resistance MRd is, as for the beam splices, likely to be limited by the resistance of : • the endplate in bending, • the bolts in tension, • the beam web in tension, • the beam flange and web in compression,
I 73
but also by that of : • the column web in tension, • the column flange in bending. • the column web in compression; • the column web panel in shear. In Eurocode 3-(revised) Annex J, evaluation formulae are provided for each of these components. Annex J also presents a full example showing how to distribute the internal forces in a beam-to-column joint with a "multi-bolt-rows" end-plate connection. This example also highlights the concept of individual and group yield mechanisms. When adjacent bolt-rows are subjected to tension forces, various yieid mechanisms are likely to form in the connected plates (end-plate or column flange). • individual mechanisms (see Figure 3-A.13.a) which develop when the distance between the bolt-rows are sufficiently large; • group mechanisms (see Figure 3-A.13.b) including more than one adjacent bolt rows. To each of these mechanisms are associated specific design resistances. When distributing the internal forces, Eurocode 3 recommends never to transfer in a given bolt-row : • a higher load than that which can be carried when it is assumed that the considered bolt-row is the only one able to transfer tensile forces (individual resistance); • a load such that the resistance of the whole group to which the bolt-row belongs is exceeded.
174
\ \ \
\
S?i
72
(a) Individual
U5,
(b) Group mechanism
Figure 8-A.13 Plastic mechanisms
175
ANNEX 8-B
Stiffness and resistance properties of joints with haunched beams
Available tools The four design tools for characterisation described in Sheet 8-1 are available for joints with haunched beams. The three first ones require slight modifications which are expressed in the following paragraphs. Cases covered by the present annex are those where the haunch is not only constituted by a single triangular plate (Figure 8-B.1.a) but possesses a web and a flange (Figure 8-B.1.b). Usually the haunch, as a whole, is extracted from a profile similar to that used for the beam itself.
(a) Without a flange
(b) With a flange
Figure 8-B.1 Different haunches
Characterisation using Eurocode 3-(revised) Annex J The use of haunch beams leads to considering new joint components. These are (Figure 8-B.2.a and Figure 8-B.2.b): •
the haunch flange in compression;
•
the beam web in compression;
176
(a) Haunch flange in compression
(b) Beam web in compression
Figure 8-B.2 Specific active components for joints with haunched beams The « flange and web in compression » (component 3 in the design sheets) has, on the other side, no more to be considered in the list of active components. The evaluation of the stiffness and resistance of the two new components proceeds as follows: Haunch flange in compression (Figure 8-B.3) Stiffness coefficient:
khf = oo
Resistance:
FMRd = bhthffyhl cos$/ yM0
where : W is the thickness of the haunch flange fyhf is the yield strength of the haunch flange bh = min (bhf; bhi) bhf is the width of the haunch flange bhi = 42 thfj235/fyhf
with fyhf in N/mm2
177
"hf.Rd
Figure 8B.3 Haunch flange in compression Beam web in compression (Figure 8B.4) Stiffness coefficient : k
h
— °°
wb
Resistance ρ
_ wb.Rd
'ywb*wbDeff^wb
tg$i
'ywb*wbDeffKwb
¡ΦΊ
if Xwb < 0,673
MO
MO
ï f
λ wb
0,22' if Xwb > 0,673 λ^ο )
These formulae are quite similar to those used to evaluate the resistance of a "column web in compression". "wb.Rd
Fwb.Rdtgß "wb.Rd
Figure 8B.4 Beam web in compression The assembly of the components for the evaluation of the joint stiffness and resistance properties is achieved according to the procedure described in Annex 8A, the component « beam flange and web in compression » being simply replaced by the component « haunch flange in compression ». Further to the evaluation of the joint properties, the resistance of the « beam web in compression » is checked under the bending moment acting in the beam cross section at the root of the haunch.
178
In practical applications, it is recommended not to associate the failure of the whole joint to that of the haunch flange in compression or beam web in compression.
Characterisation using design sheets The simplified design sheets (see Sheet 8-1.B) for end-plated joints presented in Volume 2 may be extended to similar joints with haunched beams. The modifications to be brought are commented here below. Stiffness calculation • Replace the component « beam web in compression » by the « haunch flange in compression » one. • Replace the lever arm h by h* (Figure 8-B.5). • Follow the procedure indicated in the sheets. Resistance calculation • Replace the component « beam flange and web in compression » by the « haunch flange in compression » one. • Replace the lever arm h by h* (Figure 8-B.5). • Follow the procedure indicated in the sheets. • Check the resistance of the component indicated here above.
« beam web in compression » as
h*
Figure 8-B.5 Lever arm of internal forces
Characterisation using design tables The simplified design sheets (see Sheet 8-1.C) for end-plated joints presented in Volume 2 may be extended to similar joints with haunched beams. The modifications to be brought are commented here below.
I71J
Stiffness calculation
s
^=w ψ - SjJni
+
0,385/Vc
(h
-h)
(8 Β 1)
-·
Resistance calculation •
MRd = MRd^
(8-B.2)
This approach is correct as far as the failure mode indicated in the design tables is not « beam flange and web in compression » (BFC in the design tables). If it occurs - the number of such cases is rather limited - MRd represents a conservative assessment of the actual design resistance. If a less conservative value is required, the use of one of the three other available characterisation tools is then recommended. The shear resistance and the reference lengths given in the design tables have to be evaluated according to the guidelines provided in Volume 2, Chapter 1. Finally the resistance of the « beam web in compression » has to be checked as explained in the Section of the present annex devoted to Eurocode 3(revised) Annex J.
ISO
CHAPTER 9
GUIDELINES FOR GLOBAL FRAME ANALYSIS
Sheet 9-1
Joints
Sheet 9-2
Elastic critical load in the sway mode
Sheet 9-3
First-order elastic analysis at the ultimate limit state
Sheet 9-4
Second-order elastic analysis at the ultimate limit state
Sheet 9-5
First-order plastic analysis at the ultimate limit state
Sheet 9-6
Second-order elastic-perfectly plastic analysis at the ultimate limit state
Annex 9-A
Assessment of the elastic critical buckling load in the sway mode
Annex 9-B
Methods for elastic global analysis
Subject : Joints Sheet n° : 9-1
Design Code : Eurocode 3 Manual ref.
Output
Purpose
II II Chapter 8
!^ll|„ liF
lip I o
Joint modelling
1
o
Simple • Simple
l¡
\Γ
=
==
V,|ir
=
Semicontinuous • Semicontinuous
ll_II 11 ;nl IF -\h
Chapter 4
Analysis Routine
= Hr4lr= =
Device
Joint idealisation: • Idealize Μφ curve in accordance with the chosen method of analysis.
Chapter 8
=
Continuous
• Continuous
Manual ref.
JMIL ,||„||!
SPRING
ELEMENT
Joint characterisation: • Stiffness and/or strength.
Chapter 4
Joint idealisation: • Idealize Μφ curve in accordance with the chosen method of analysis.
Chapter 8
EQUIVALENT
BEAM
Joint characterisation: • Length, second moment of area and/or strength.
I S3
ELEMENT
Subject : Joints Sheet n° : 9-1
Design Code : Eurocode 3 Manual ref.
Purpose Before frame analysis, four separate actions have to be carried out :
Chapter 8
• Joint characterization Evaluation of the properties of the joint : stiffness, resistance and/or rotation capacity
Chapter 8
• Joint classification Definition of the class in terms of stiffness, resistance and/or ductility
Chapter 8
• Joint modelling How to include joint response in global frame analysis
Chapter 8
• Joint idealisation Idealisation of the Μ-φ joint response according to the method of analysis (elastic, rigid-plastic, elastic-plastic or elastoplastic)
1S4
Output
Subject : Elastic critical load in the sway mode Sheet n° : 9-2
Design Code : Eurocode 3 Code ref.
5.2.3.1.1
5.2.5.2
Output
Purpose Assess the sensitivity of structure to the (Ρ-Δ) effects.
the
Assessed by the ratio between the vertical load resultant producing sway instability (Vcr) and the actual design vertical load resultant (VSd).
Sway frame or Non sway frame
Values of this ratio shall obtained for each load case. Manual ref.
be
Analysis Routine for Calculation ofVcr
for a given load case
Tools
Specialized softwares: • Bifurcation analysis. • Second order step by step elastic analysis.
COMPUTER PROGRAM
Joints shall normally be characterised by their initial design stiffness (S7./n/).
Annex 9-A
An approximate procedure is given in Eurocode 3.
Annex 9-A
An approximate available.
procedure
EUROCODE 3 PROCEDURE
is
APPROXIMATE PROCEDURE
Charts are available for specific frame configurations ( see for instance Petersen).
CHARTS OR FORMULAE
1S5
Subject : First-order elastic analysis at the ultimate limit state Design Code : Eurocode 3
Sheet n° : 9-3 Output
Code ref.
Purpose
5.2.1.3
May be used to calculate the distribution of design internal forces and moments in non sway frames.
5.2.1.2.1 5.2.1.2.2 5.2.6.2 5.2.4.1.3 5.2.4.3.1 Manual ref.
Bending moments May also be used for sway frames provided allowance be made for the second-order effects (amplified moment method and/or sway buckling length method).
Normal forces
Global frame imperfections shall be considered in the analysis of each load case or load combination case. Analysis Computer available:
Routine
programs
are
Tools widely
• Computer programs shall include joint behaviour; otherwise proceed with the equivalent beam procedure (see also Sheet 9-1).
COMPUTER PROGRAM
Joints shall be characterised by their initial or nominal design stiffnesses, as appropriate. • Slope deflection method. Annex 9-B
• Moment distribution method. Both methods can be generalised so as to include the joint behaviour. Joints shall be characterised by their initial or nominal design stiffnesses, as appropriate.
186
HAND CALCULATION
Subject : Second-order elastic analysis at the ultimate limit state Sheet n° : 9-4
Design Code : Eurocode 3 Code ref. 5.2.1.3 5.2.1.2.3 5.2.4.1.3 5.2.4.2.4 5.2.4.3.1
Manual ref.
Output
Purpose May be used in all cases. Required when the frame is classified as sway (see also Sheet n°:9-3). Global frame imperfections shall be considered in the analysis of each load combination case. Local member imperfections shall be considered for very slender compression members/ may always be considered in order to avoid any further inplane buckling check.
Analysis
Routine
Bending moment
Normal forces
Shear forces Include P-Α effects and, when considered, Ρ-δ effects. Tools
Computer programs are widely available. Joints shall be characterised by their initial or nominal design stiffnesses, as appropriate. Iterative procedure. Annex 9-B
Joints shall be characterised by their initial or nominal design stiffnesses, as appropriate. Non iterative procedure.
Annex 9-B
Joints shall be characterised by their initial or nominal design stiffnesses, as appropriate.
1S7
COMPUTER PROGRAM
EQUIVALENT LATERAL LOAD
SLOPE DEFLECTION METHOD
Subject : First-order plastic analysis at the ultimate limit state Sheet n° : 9-5
Design Code : Eurocode 3
Output
Code ref.
Purpose
5.2.1.1.4
Especially appropriate for non sway frames
5.2.7 5.3.3 3.2.2.2 5.2.1.2.1
May also be used for sway frames provided allowance be made for the second order effects (Eurocode 3 method and Merchant-Rankine method).
Collapse load multiplier.
5.2.1.2.2 5.2.1.4.1 5.2.1.4.3 5.2.1.4.4 5.2.1.4.5 5.2.4.1.3
Requirements are imposed on the steel grades and on the cross-section and joint classes. Global frame imperfections shall be considered in the analysis of each load combination case.
Bending moment (ULS) J—
,-l
Normal forces (ULS)
5.2.4.2.4 5.2.4.3.1
77
Shear forces (ULS) Manual ref.
Analysis Routine
Tools
Computer programs available. Joints shall be characterised by their design moment resistances and, when the elastic behaviour is included, by their nominal stiffnesses.
COMPUTER PROGRAM
• Virtual work method for rigidplastic mechanisms. • Graphical method. Joints shall be characterised by their design moment resistances.
ISS
HAND CALCULATION
Subject : Second-order elastic perfectly-plastic limit statel
Sheet n° : 9-6
Design Code : Eurocode 3 Code ref.
5.2.1.1.4 5.2.7
analysis at the ultimate
Output
Purpose May be used in all cases.
It is required when the frame is classified as sway.
Collapse load multiplier.
5.3.3 3.2.2.2
Requirements are imposed on the steel grades, cross-section and joint classes. Bending moment (ULS)
5.2.1.2.3 5.2.4.1.3
j
.
; -i
Global frame imperfections must be considered in the analysis of each load case. Normal forces (ULS)
5.2.4.2.4 5.2.4.3.1
Local member imperfections shall be considered for very slender compression members, and may be considered in order to avoid a future in-plane buckling check.
T7
Shear forces (ULS) Include the non linear behaviour of joints and sections, Ρ-Δ effects and, when considered, Ρ-δ effects.
Manual ref.
Analysis
Routine
Computer programs are widely available. Joints shall be characterised by their nominal design stiffnesses and design moment resistances.
ISM
Tools
COMPUTER PROGRAM
Annex 9-A
: ASSESSMENT OF THE ELASTIC BUCKLING CRITICAL LOAD IN THE SWAY MODE
9-A.1 Eurocode 3 procedure For plane frames in used in building structures, with beams connecting the columns at each storey level, the elastic critical buckling load for the sway buckling mode may be calculated according to the following procedure : A first order elastic analysis is conducted for the given load combination case. The horizontal displacements due to the design loads (both horizontal and vertical ones) is determined at each storey. The elastic critical load of the frame for the sway buckling mode may be estimated by : ^
= Max
hH
where i
designation of the ith storey;
VSd
design value of the resultant of the vertical loads;
Vcr
elastic critical load for the sway buckling mode;
δ
horizontal displacement at the top of the storey, relative to the bottom of the same storey;
h
storey height;
H
total horizontal reaction at the bottom of the storey;
ν
total vertical reaction at the bottom of storey.
9-A.2 Approximate procedure A multi-storey multi-bay frame with semi-rigid joints can be replaced by an equivalent substitute single bay frame having rigid joints and columns and beams fitted with appropriate equivalent stiffnesses (Figure 9-A.1 (a)-(b). It is assumed that the columns behave elastically and are continuous over their whole height. Accordingly the stiffness of the column at each storey is obtained as follows :
-
i
190
where Kc ■ is the stiffness coefficient of the column j, i.e.
Icj/Lcj.
The equivalent stiffness coefficient of the beam with linear end restraints at each storey is obtained as follows :
κ„ = Σκb.equi, i where : b,equi j
b,equi,i I bj
in which : h.equ.i = hi / ( I +
3
«/)
a n d
« , = 2Ehj
I Si.ini J b i
Elbi ¡lbi
flexural stiffness of the beam /';
S,I,Ml,I
initial joint stiffness at the end of the beam /in the actual structure. For a beam in which the joint stiffnesses are not the same at both ends, either the lowest joint stiffness is used (conservative) or an assessment has to be made in order to get an appropriate single value for the individual equivalent beam stiffness.
Since the socalled substitute frame has rigid joints, the associated Grinter frame can then be derived (Figure 9A.1(b)(c)). The stiffness of the members in the Grinter frame are : K'b=3^Kb,eqUii
ι
K b ,1
K
β» v
'c,1 8
b,2
K'C =
K D =£ K bequi,i
«
c,2
and
'c,3
Kc=yIKci
^KCJ
K
b=3lKbequ¡¡
K*c = Z K c J
8&
«8
A. S
A. foundation beam
(a)
(b)
(c)
Figure 9A.1(a) Actual frame (semirigid joints), (b) Substitute frame (rigid joints),(c) Grinter frame The elastic critical load of the actual frame with semirigid joints can be computed by referring to the associated Grinter frame. The computation steps are as follows :
191
1. The elastic critical load of each column, Vcr ,is computed on the basis of the buckling length for the non sway buckling mode but taking the end restraints into account ( see Eurocode 3- Annex E). Each column of the Grinter frame is thus characterised by a value of Vcr. The lowest of all these values, i.e. V'crmjn , is selected as being a safe lower bound for the elastic critical load of the whole Grinter frame and thus of the whole actual frame.
192
Annex 9-B :
METHODS ANALYSIS
FOR
ELASTIC
GLOBAL
9-B.1 First order theory 9-B. 1.1 Displacement method This method, which has been the subject of many publications, is explained here very concisely. The displacement method states that the forces lo\
applied to the nodes of
the structure consist of those associated with the nodal displacement {D},i.e. [K]{D], and those due to the loads acting on the members fitted with fixed ends, i.e. {Q}. This is expressed by the following matrix equilibrium
equation: {Q}={K){D} + {Q} The structure stiffness matrix [K], which is a square matrix of an order equal to the number of degrees of freedom of the structure, is assembled from the stiffness matrix [/c'] of the individual members. For a first order elastic analysis, this matrix does not include coefficients which would account for relative rotations at the beam ends and for changes in the column flexural stiffness due to axial loads. Above matrix equation is solved for the unknown displacements {D}, which are then used to determine the forces acting on each individual member. Softwares based on the displacement method constitute the mainstay of structural analysis in modern design office practice. Many of these programs are suited for rigid frame analysis only, since they do generally not permit joint flexibility as far as appropriate modifications are not introduced in the terms of the stiffness matrix. In the following section, some straightforward modifications are outlined which would enhance considerably the analytical capabilities of many existing tools for global plane frame analysis. 9-B.1.2 Element stiffness The stiffness of a beam element is obtained as: 1
K^ = E.S,.K;
1 + 4α + 3α'
where :
193
K:, = element stiffness
S n = S 3 3 = ( 1 + a) S22 - S 44 ,22 S12 =
(. 3 ^> 1 +—a
a= 2£/
KR rigid joint \KSR semirigid joint
2B„ is the beam flexural stiffness
Sy is the joint design flexural stiffness ^34
S31 = S41 >
= (1 + a)
^32
s, = sß 9B. 1.3 Fixed end moments The fixed end forces on the member ends due to gravity loads are :
O f = Q2ñ
Q f = Q?
Qf = Of
1 1 + aJ Of" = fixed end forces ( { Ο Γ ^ ω restraint [{Q\
semirigid restraint
1 1+a
9B.1.4 Slope deflection method The basic equations of the slopedeflection method give the end moments in a member as the superimposition of the end moments due to external loads on the member with its ends restrained, on the one hand, and of the moments caused by the actual end displacements and rotations, on the other hand. A set of simultaneous equations is written, that express the equilibrium of the joints, in which the end moments are expressed in terms of the joint displacements and rotations. The solution of these equations gives the unknown joint displacements and rotations. Substituting the latter into the original slopedeflection equations provides the designer with the end moments in the members. The slope deflection method is in fact an application of the more general stiffness method, in which the effects of axial and shear strain energy are neglected compared to the bending strain energy. This simplification is usually justified when analysing frames. Figure 9B.1 shows the symbols adopted as well as the assumptions for the positive sign of moments and shear forces.
194
Figure 9-B.1 Deformation of beam with flexible end joints The basic slope deflection equations for a member with identical joints at both ends may then be written as follows : MAB
= B[R'AB(SAAQA
+SABQB
-SACyAB)-FAAMAB
V -FABMBA]-
ABa
MBA = e[RAB (SBAQA + SBBBB - SBCyAB ) - FBAMAB - FBBMBA ] - V BBa with, in addition to the symbols defined in the Figure 9-B.1 : MAB and MBA moments at the center of nodes A and B; V
AB
and VBA
shear forces at the ends of the simply supported member of length L0;
MAB and MBA
M
AB
-■
L, 1 + 4a + 3a2
fixed end moments due to transverse loads applied between the beam ends; beam flexural stiffness; 2EI with α = — s . where Sj is the joint design flexural stiffness; LQSJ
VAB
195
=
The values of the coefficients SAA, SAB, SBA, SBB, SAC, SBC, FAA, FAB, FBA and FBB are given in Table 9-B.1.
Symbol
$AA
-
$BB
Expression when beam+ rigid stub of length a
2 +3a
2 + 3a + 6(1 + a) — V
$ΑΒ
- SBA
9
'-'AC ~
- 9
'-'BC
'AA
~
'BB
'AB
=
'BA
Expression when zero stub length
L
oJ
1
l + 6(l + a) —
(
a^
V
h) J
/
χ a
3(1 +a)
3(1 +a) 1 + 2 -
1 + 2a
l + 2a + (l + a) —
a
a - ( l + a) — '-0
Table 9-B.1 Semi-rigid joints - Slope-deflection method The expressions given for the MAB and MBA are introduced in the usual node and storey equilibrium equations of the slope-deflection method. The solution of these latter gives the values of the moments at the nodes; the corresponding shear forces can be computed by the following relationships : yAB=jMAB+MM)
+ AB
V ΒΑ =
(ΜΑΒ + ΜΒΑ)
—-
L
+ V, ΒΑ
where : VAB and VBA shear forces at the ends of the simply supported beam of span L. VAB and VBA which are constant in the zone of the joints, represent the values of the shear forces at the joint. The values of the moments at the joints are derived from the equilibrium equations of the rigid beam end stubs of length a:
I 96
MAB - MAB +VAB.a +VBA.a
MBA =MBA
It is usually sufficiently accurate to disregard the joint size compared to the beam length and thus to neglect the stub length a. The basic equations then become: M~AB = z[RAB({2 + 3a)QA+QB-3{l + a)\yAB)-(l MBA =S[R'AB{QA+
+
2a)MAB-aMBA]
(2 + 3α)θ β - 3(1 + α)ψ Λβ ) + αΜ„ Β + (1+ 2α)ΜΒΛ]
The effective stiffness Kb,erf of a member with linear elastic restraints, for which the loading conditions produce a single bending curvature, is obtained by introducing θ„ = - θβ and δ = 0. One obtains : \s
_ b
''AB
'e*~l + a
The effective stiffness KD,efi of a member with linear elastic restraints, for which the loading conditions produce a double bending curvature, is obtained by introducing ΘΑ = ΘΒ and δ = 0 . One obtains: Κ b.eff
RAB 1 + 3a
9-B.1.5 Moment distribution method The moment distribution method is a particular application of the slopedeflection method. The sole difference lies in the way the equations of equilibrium are solved. In the slope-deflection method, use is made of any of available analytical tools for solving sets of equations, while the moment distribution method proceeds by a relaxation procedure .
Figure 9-B.3 Semi-fixed end moment VA = l
VB=0
197
δ=ο
Symbol
semi fixed end moments at the joint centre MSAB
ΓΑΒ carry over factor between the joint centre end rotation stiffness KM
Expression when
Expression when
beam + rigid stub of length a
zero stub length
1+2a+—(1+a) Mm + a+—(1+a)
[ΐ + 2α)ΜΑΒ + α.ΜΒΑ
'-Ό
n + ' VV AB-d
1+4a+3a 2
1 + 6(1 + a ) -
l + 4a + 3a2
MM
1 2 +3a
1+ -o J
1 +a
2 + 3a + 6(1 + a)V
2EKt 2 + 3α + 6(ΐ + α)-
oJ
2EKb(2 + 3a) 1 + 4a + 3a 2
1+·
L• 0 /
l + 4a + 3a~
Ks sidesway stiffness sidesway end moment at node A
l2EKh
Li
MVAB
6EKh
\2EK,
1+a l + 4a + 3a~
Li 6EKh
l + a + 2 — (1 + a)
1+ a l + 4a + 3a_ 1+a l + 4a + 3a"
l + 4a + 3a"
Table 9-B.2 Semi-rigid joints - Moment distribution method
M
BA
M
BA
Figure 9-B.4 Moment carry over and rotation stiffness When the moment distribution method is used, one must determine the carry over factors, the rotation and side-sway stiffness factors and the side-sway end moments. For frames with flexible joints, the moment distribution method
I 98
requires the definition of the semifixedend moments (Figure 9B.3, Figure 9 B.4 and Table 9B.2). The relaxation procedure is identical to that for frames with rigid joints.
9B.2 Second order theory 9B.2.1 Equivalent lateral load procedure The Equivalent lateral load procedure consists in an iterative procedure, using the results of a standard first order analysis, to include the sway displacement effects. The initial step in the modification is to compute the sway forces. The lateral and vertical loads are applied to the system, and the lateral displacements, denoted as Δ, in Figure 9B.5 (a), are computed by first order theory. The storey level is denoted by /'. The additional storey shears due to the vertical loads are computed by :
Κ'=^-(Δ, +1 -Δ,) in which : V'¡
additional shear in storey / due the sway forces;
V P¡
sum of the column axial loads in storey;
h¡
height of storey /;
Δ,.+1, Δ,
displacements of levels /'+1 and /' respectively.
The sway forces due to the vertical loads H\ are then computed as the difference between the additional storey shears at each level, i.e.: H;
= v'1-1 v;
The sway forces //,' are added to the applied lateral loads, and the structure is reanalysed using the first order theory. When the Δ, values at the end of cycle are nearly equal to the previous cycle, the method has sufficiently converged. If it does not converge within five or six trials, it can be concluded that the structure is unstable. Once convergence is established, the resulting forces or moments in every member now include the Ρ-Δ effects. The method is summarised in Figure 9B.5.(b).
199
9-B.2.2 Slope-deflection method Only the equation for the equilibrium of translation at each storey need to be modified in order to account for global second order effects. This equation is transformed by means of the following one:
^Σ(Μ, β +Μβ.)-ψ,]>> = Σ " - Σ η Η **/
where ^V
/
/
i
i
is the sum of the vertical components of all the loads acting on the
frame above the plane (aa) as shown in Figure 9-B.6. Setting up the equation is not any more difficult than for the usual application of the slope deflection equations, and the solving procedure is precisely the same. One obtains the system of equations which is linear in terms of the joint rotations θ and in terms of sway angles ψ . Solving the former system immediately provides the values of the joint rotations θ, the sway angles ψ, and the bending moments, including the global second order effects.
ψ
beam i storey I
beam i-1
Figure 9-B.6
200
namm
1st order analysis Lateral deflection A¡
H'i+2
"Compute Ρ Δ shear V'
s t o r e y Ί+1
^Pi
Vi =——(Δί+1-Δί) hi Compute Ρ Δ force Η' V'i-1-V'i Compute effective force Hi+H'i Τ Hi=Hi+H'i
storey 1 1 1 1 1 1 1 1 I Pi Hi+H'i
£ 1st order analysis s t o r e y i-1
Lateral deflection Δ; i ft?
η
Δ i values are nearly equal to those of the previous cycle
Yes
(a)
No
(b)
Figure 9-B.5 Equivalent lateral force procedure
PART 3 : WORKED EXAMPLES
CHAPTER 10 WORKED EXAMPLE 1 DESIGN OF A BRACED FRAME
10.1 Frame geometry and loading Figure 10.1 shows a non-sway braced frame. The frame consists of two storeys and two bays. The beam span is 7,2 m. The height from column foot to the beam at floor level is 4,5 m, the height from floor to roof is 4,2 m. It is assumed that the column foot is pinned to the foundation.
3
rnrr IPE
Roof
HEA
1
m Floor
IPE HEA
4,2 m
HEA
4,5 m
IPE
IPE
HEA
HEA
HEA
7,2 m
7,2 m
Figure 10.1 Geometry of the braced frame The following load case, corresponding to dead and life load (no horizontal loads) is governing; the design loads include the partial safety factors for actions.
205
Roof
Floor
Serviceability limit state
40 kN/m
59 kN/m
Ultimate limit state
54 kN/m
81 kN/m
Design loads
Table 10.1 Governing load case The steel grade chosen for beams, columns and joints is S235, with fv = 235 N/ mm2. The following partial safety factors for strength have been adopted during the design : >Mo= 1,1; }fvii = 1,1; >fvib = 1,25. The columns are HEA sections. They are fully supported against lateral torsional buckling. The columns are continuous from column foot to roof. They are supported against out-of-plane movement at foot, floor and roof levels. Beams are IPE sections. The beams are supported against lateral torsional buckling; they have no initial camber. All the sections are fulfilling the requirements for Class 1 sections.
10.2 Objectives and design steps In this example, the beams, columns and joints will be designed. For this, three solutions will be studied : •
Frame design with pinned joints;
•
Frame design with semi-rigid joints;
•
Frame design with partial-strength joints.
One starts with the design of a simple frame with pinned joints (Section 10.3). Then, one introduces joints having a certain rotational stiffness and moment resistance; this allows probably lower beam sizes. To see whether this expectation is confirmed, an elastic analysis (Section 10.4) and a plastic analysis (Section 10.5) have been respectively carried out.
206
10.3 Frame design with pinned joints 10.3.1 Introduction Frame design with pinned joints is typical when the members are designed by an engineer and the joints in a subsequent step by the steel fabricator. The steps described in Sections 10.3.2 to 10.3.4.2 are normally performed by the engineer; the step described in Section 10.3.5 is the task of the steel fabricator (refer to Chapters 2 and 6 for more explanation in this respect). 10.3.2 P r e l i m i n a r y design of b e a m s and c o l u m n s The following sizes for beams and columns are chosen : • F loor beams :
IPE 550
• Roof beams :
IPE 450
• Outer columns : HE 200 A • Inner columns : HE 240 A. 10.3.3 Frame analysis 10.3.3.1 Serviceability limit state The maximum deflection amounts : u
384Elb
where : u
deflection;
E
Young modulus equal to 210000 N/mm2;
/b
second moment of area of the beam;
gsd
design uniformly distributed load at serviceability limit state.
m ^ Floor beams :
5x59x7200 4 r
= 14,6 mm
384x210000x67120x10 4 □ *u Roof beams :
5x40x7200 4 = 19,8 mm 384x210000x33740x10
207
4
1 0 . 3 . 3 . 2 U l t i m a t e limit s t a t e In the case of a frame with pinned joints, the frame analysis is based on simple equilibrium equations. The maximum moment in the beam is : Msd = 1/8 qsd lb2 where : Msd
moment in the beam span;
c/sd
design uniformly distributed load at ultimate limit state;
lb
beam span.
Floor beams :
M Sd = 1/8 χ 81 χ 7,2 2 = 525 kNm
Roof beams :
M Sd = 1/8 χ 54 χ 7,2 2 = 350 kNm
The maximum axial force in the column is : /VSd = X 1 / 2 qsd/b where : Λ/sd
axial force in the columns;
Σ
summation sign for all the connected beams at all floor and roof levels.
Outer columns :
A/Sd = 1/2 χ 81 χ 7,2 + Vi χ 54 χ 7,2 = 486 kN
Inner columns :
A/Sd = 2 χ (1/2 χ 81 χ 7,2 + 1/2 χ 54 χ 7,2) = 972 kN
10.3.4 10.3.4.1
Design checks S e r v i c e a b i l i t y limit s t a t e
To reduce the volume of calculations reported here, only the ¿ w limit (see Eurocode 3- Figure 4.1) has been checked : u < ^nax = /b / 250 (floor beam) and u < Satisfactory.
20S
1 0 . 3 . 4 . 2 U l t i m a t e limit s t a t e To reduce the volume of the worked example, the check of the ultimate limit state is limited to the following aspects : •
Column stability;
•
Crosssectional checks of beams and columns.
10.3.4.2.1 Column stability In accordance with Eurocode 3-Clause 5.5.1.1, the criterion to be fulfilled is : A/sd < χ ßk A /y / wn where : Λ/sd
acting compressive force in the column;
χ
reduction factor for the relevant buckling mode, i.e. χζ in this case;
/3A
= 1 for Class 1 crosssections;
)toi
partial safety factor, taken equal to 1,1;
A
crosssectional area of the column.
The value of χ depends on the reduced slenderness of the columns :
λ = λ / λ, (β Ar where :
λ
= II k
λΑ
= 93,9 (steel grade S235);
iz
radius of gyration;
/
column buckling length (taken here equal to the system length).
Outer columns HE 200 A :
λ =11 iz = 4500/ 49,8 = 90,4 λ = λ Ι λ: {ßA )V2 = 90,4 / 93,9 = 0,96 Λ/sd = 486 kN < χ βΑ A fy I ^
hence χ = 0,58 (buckling curve c).
= 0,58 · 5380 · 235 / 1 , 1 = 666 kN.
=> Satisfactory.
209
Inner columns HE 240 A: λ = / / 4 = 4 5 0 0 / 6 0 , 0 = 75 λ = λ / λλ ( ß j 1 / 2 = 75 / 93,9 = 0,80 Λ/sd = 972 kN < χ βΑ A fY I ^
hence χ = 0,66 (buckling curve c).
= 0,66 · 7680 · 235 / 1,1 = 1082 kN
=> Satisfactory. 10.3.4.2.2 Section check of the beams The check of beam crosssections is conducted in accordance with Eurocode 3- Clause 5.4.5.1. Because the beam sections are Class 1, a plastic verification is permitted : MSd < Mc.Rd = IrVpl fy I }^0 where Wp\ is the plastic section modulus. Floor beam : 525.10 6 Nmm < 2780.10 3 · 235 /1,1 = 593.10 6 Nmm. Roof beam : 350.10 6 Nmm < 1702.10 3 · 235 /1,1 = 364.10 6 Nmm,. => Satisfactory. 10.3.4.2.3 Section check of the columns The section check of the columns is covered by the buckling check carried out in Section 10.3.4.2.1.
10.3.5 D e s i g n of joints Joints may be designed as simple joints, e.g. •
Web cleated joints;
•
Fin plate joints;
•
Flexible endplate joints (thin endplates only welded to the web of the beam).
These types of connections need to be designed for shear force only. Detailing should be such that the rules of Eurocode 3-Chapter 6 are satisfied.
210
10.4 Frame design with semirigid joints 10.4.1 Introduction In this chapter, just like in Section 10.3, the members can be designed by the engineer and the joints by the steel fabricator. During member design (Sections 10.4.2 to 10.4.5), the effect of the joints on the frame behaviour is taken into account by assuming that the engineer makes a good assessment of the mechanical properties of the joints. In the subsequent step of the joint design (Section 10.4.6), the steel fabricator needs to ensure that the mechanical properties of the joints are close enough to the assumptions made by the engineer (See also Chapters 2 and 6 for more explanations). 10.4.2 P r e l i m i n a r y design of b e a m s , c o l u m n s and j o i n t s Column sizes will be chosen as found in Section 10.3. However, we will try to save on the beam sizes. Therefore, beams are chosen one section size lower than in the case of the frame with pinned joints : • Floor beams :
IPE 500
• Roof beams :
IPE 400
• Outer columns :
HE 200 A
• Inner column :
HE 240 A.
For the joints, extended endplate connections will be contemplated. A first assessment of the initial stiffness of these joints is made using the following formula : S
Ez¿t
'
i-app
c .
χ
where : Sj.app
approximate initial stiffness of the joint;
kx
coefficient taken from Table 10.2;
ζ
distance between the compression and tension resultants. For extended endplate joints, this distance equals approximately the beam height;
ff.c
column flange thickness;
E
Young modulus (= 210.000 N/mm2).
The values of Sj,app are listed in Table 10.2.
wι
kx
Type of joint Extended end-plate, single sided
Γ I
:
(
Extended end-plate, double sided symmetrically
I
r\
13
J
7,5
1
Table 10.2 /cx-factor for different types of joints
Joint 1
2
3
4
Sj.app (Nmm/rad)
IPE 500 floor
210000 x500 2 x 10 _ 13
HE200A column IPE 500 floor
210000x500 2 x10
HE240A column
9
ΟΛ Hn9
= 84.10 7,5
IPE 400 roof
210000x400 2 x 10
HE200A column
00
_9
= 2b. 10
13
IPE 400 roof
210000x400 2 x12_ C / 1
HE240A column
7,5
—
OT" .
Hn9 1 \J
Table 10.3 Approximate initial joint stiffness 10.4.3 F r a m e a n a l y s i s In this case, a first order linear frame analysis is carried out. In accordance with Eurocode 3-(revised) Annex J, half of the initial stiffness of the joint is introduced in the frame analysis at the ultimate limit state. Since serviceability limit state is not governing the design of the frame, the same value of the joint stiffness has been used for this limit state. In this worked example, it is assumed that the available frame analysis software cannot reflect the stiffness of the joint by means of a spring element. For this reason, the stiffness of the joint is modelled with a short beam element. The second moment of area of this element is (See Figure 10.2) : lj =
Sjl/E
11 τ
where : Sy
half of the initial stiffness (Sj.app/2);
I
short beam element length (about half the column depth, 100 mm);
E
Young modulus taken equal to 210000 N/mm2.
Figure 10.2 Modelling of joint stiffness Sj by an equivalent beam with length /
Joint
Sj.app (Nmm/rad)
IPE 500 floor
1
HE200A column IPE 500 floor
2
HE240A column IPE 400 roof
3
HE200A column IPE 400 roof
4
HE240A column
/j (mm4)
40.10 9
95.10 4
84.10 9
2000.10 4
26.10 9
620.10 4
54.10 9
1280.10 4
Table 10.4 Calculation of the equivalent beam properties 10.4.3.1 Serviceability limit state The results of the frame analysis program are as follows : Floor beam :
u= 12,2 mm.
Roof beam :
u= 15,9 mm.
2I3
10.4.3.2 Ultimate limit state The results of the frame analysis program are as follows (Figure 10.3) Outer columns :
A/Sd = 444 kN
MSd = 23 kNm
Inner column:
/VSd = 1055kN
Msd = O kNm
Floor beam :
MSd = 360 kNm
Roof beam :
MSd = 225 kNm
1 joint IPE 500 floor beam-to-HE200A column :
Msd = 78 kNm
2 joint IPE 500 floor beam-to HE240A column :
MSd = 251 kNm
3 joint IPE 400 floor beam-to HE200A column :
Msd = 60 kNm
4 joint IPE 400 floor beam-to HE240A column :
Msd = 188 kNm
Figure 10.3 Moment distribution (ultimate limit state) 10.4.4 D e s i g n c h e c k s 10.4.4.1 Serviceability limit state Only the t w limit of Eurocode 3-Figure 4.1 has been checked here u Satisfactory. 1 0 . 4 . 4 . 2 U l t i m a t e limit s t a t e In this worked example, the check of the ultimate limit state is again limited to the following aspects : •
Column stability;
•
Crosssectional checks of beams and columns.
10.4.4.2.1 Column stability Inner column HE 240A : Λ/sd Λ/sd = 1055 kN < χ βΑ A fy I ^
Satisfactory. Outer column HE 200 A : It is assumed that lateral torsional buckling is not a possible failure mode. (It has to be noted that Eurocode 3 is rather conservative concerning stability checks of I or Η columns loaded with axial force and uni-axial bending about the strong-axis compared to tests and other national design standards (for example the German and the Dutch Standards). According to Eurocode 3-Ciause 5.5.4, the criterion to be fulfilled is : Ν sä Xmin^'y ' Y/W1
,
k M
v y.sd
^pl.y'y
^
' T/W1
where : jmin
the smaller of the χ values relative respectively to weakaxis and strong axis buckling, here χζ = 0,58;
k,
. 1 - ^ =1 XyAty
μγ
=K(2^My-4)
+ (Wply-Wely)/Wely
butμν Satisfactory. IPE 400 roof beam : 225.10 6 Nmm < 1 3 0 8 . 1 0 3 x 235/1,1 = 307.10 6 Nmm. => Satisfactory. 10.4.4.2.3 Section check of the columns Since weakaxis buckling is the governing failure mode for the inner column, no check of the inner column section needs to carried out. The section check of the outer column can be carried out using Eurocode 3 Clause 5.4.8.1 (3): Μ /Λ, A/sd / A/pi.Rd = P
Msd / Myn, = yp
444.103
„00 , = 0.38 < 1
5380x235/1,1
2310 6
430.10 3 x 235/1,1
= 0,25 < 1
Since Λ/sd / A/pi.Rd < 0.5, there is no need to check the interaction between axial force and bending moment.
216
=> Satisfactory. 1 0 . 4 . 5 D e s i g n of the joints Joints have been designed using the DESIMAN software (Table 10.5). Extended endplates have been contemplated for all the joints. This was unsuccessful because extended endplate joints possess insufficient strength to transfer the bending moments got from the frame analysis. Therefore, haunched connections have been chosen, see Figure 10.4. This type of connection has the advantage that column web stiffeners can be avoided whilst the web remains free for erection of beams out of the plane of the frame. All the endplates have been chosen 20 mm thick. Bolts are M20 8.8. All the connections have four boltrows.
80
O
o
o o
H
Ço
^i 210
o
0
350
520
o
o
tt
60 —«ι—
55.
50
90 55 ■
100i50i
Endplate IPE 500
Endplate IPE 400
Figure 10.4 Geometry of the haunched connections
2I7
Joint 1
MRd (kNm)
Sjjni (Nmm/rad)
160
78.109
246
359.109
128
58.109
140
228.109
IPE 500 floor beam HE200A column
2
IPE 500 floor beam HE240A column
3
IPE 400 roof beam HE200A column
4
IPE 400 roof beam HE240A column
Table 10.5 Joint properties according to DESIMAN calculations Whether the stiffness was accurately enough introduced in the frame analysis has to be checked. This can be done with Table 10.6. Since all the approximate values Sj.app are lower, then the actual stiffness S¡.act computed based on DESIMAN software, it is only required to check the upper limit. Verification of the joints between an IPE 400 roof beam and a HE 240A inner column :
j.act
8 B 6 S,.app/. 10
> S j.app
o o _
; i-app 'b
EL = 54.10E
10 541QT χ 7200 8 210000x23131.10'
Nmm/rad
The results for the other joints in the frame are summarised in Table 10.7. It appears in each case that the actual stiffness is higher than the approximate stiffness. Therefore, only a check on the upper boundary is required. This check is satisfactory. The difference between the actual stiffness and the approximate stiffness will not lead to more than a 5% drop in frame bearing resistance.
218
Braced
Upper boundary
Lower boundary
Frame g
8S
i.appElb
>
iac,
|fS,acr>^>
-10E/ b +S, a p p / b
S
10S,_E/ j.app'-'b < ;ac ' ~ 8 E / „ - S j.app'b
else: where Sj.app j.act
then:
S¡.act ^ °°
assumed stiffness adopted in the frame analysis (this is an approximation of the 'actual' stiffness); 'actual' stiffness of a joint; Young modulus; beam length; second moment of area of the beam.
Table 10.6 Boundaries for variance between actual an approximate stiffnesses
Joint
1
(Nmm/rad)
Upper boundary (Nmm/rad)
(Nmm/rad)
40.109
78.109
78.109
84.109
CO
359.109
26.109
68.109
58.109
54.109
oo
228.109
Sj.epp
IPE 500 floor beam
"3j.act
HE200A column 2
IPE 500 floor beam HE240A column
3
IPE 400 roof beam HE200A column
4
IPE 400 roof beam HE240A column
Table 10.7 Check of joint stiffness
10.5 Frame design with partial-strength joints 10.5.1 Introduction In this application, the theory of plasticity is used. The latter can lead to economical results, as it is shown in the following.
M4
In contrast to the design procedures given in Sections 10.3 and 10.4, both member and joint designs are preferably performed by one single party, e.g. the steel fabricator. The reason for this is as follows : when using plastic design joints, properties need to be determined at an early stage of the design procedure and be included in the frame analysis. This is in contrast with the previous applications, where it was possible first to design beams and columns and then, in a second step, to design the joints. 10.5.2 P r e l i m i n a r y design of b e a m s and c o l u m n s The same beam and column sizes as in Section 10.4 will be used : • Floor beams :
IPE 500
• Roof beams :
IPE 400
• Outer columns :
HE 200 A
• Inner column :
HE 240 A.
10.5.3 D e s i g n of the joints In a first step, flush end-plate joints will be contemplated. All the flush endplates have been chosen 12 mm thick. Bolts are Μ20 grade 8.8. In all the joints, four bolt rows have been used. Figure 10.5 shows the geometry of the flush end- plates. The joint properties were computed by means of the DESIMAN software; they are listed in Table 10.8. The governing failure mode of the joints is related to the bending of the endplate. So a sufficient rotation capacity is available and a plastic design is permitted. Joint
1
IPE 500 floor beam
Mrd (kNm)
Sj.ini (Nmm/rad)
Rotational capacity
70
25.109
sufficient
104
60.109
sufficient
54
16.109
sufficient
80
32.109
sufficient
HE200A column 2
IPE 500 floor beam HE240A column
3
IPE 400 roof beam HE200A column
4
IPE 400 roof beam HE240A column
Table 10.8 Joint properties according to DESIMAN calculations
220
0
1 50
0
0
Iso
0 0
0
0 0
L50 L50
376 476
0
0
0 0 0
0
0 0
IPE 400
fc
fr
feoI 100 l50l
boL 100 J 50J
Flush end-plate/ IPE 500
Flush end-plate/IPE 400
Figure 10.5 Geometry of the flush end plate connections For the design of the joints connecting a beam to the columns, the following rule should be satisfied (see Figure 10.6) : 1/8Q/SÁ2
MpLy+0,5MRd,+0,5MRd,
Satisfactory. Check of the roof beam: 350 307 + 0,5x54 + 0,5x80
0,93 < 1
=> Satisfactory. 10.5.4 F r a m e a n a l y s i s 10.5.4.1 Serviceability limit state For sake of simplicity, the entire stiffness of the joints is neglected when determining the deflections at the serviceability limit state. This yields the following results : m
w
5x59x72004
Floor beam :u=
- = 20,3 mm
384x210000x48200.10
4
Roof beam :
5x40x7200' = 28,8 mm u=384x210000x23130.10'
1 0 . 5 . 4 . 2 U l t i m a t e l i m i t state It is assumed that, at collapse, the outer column is still continuous, but pinned connected to the beams and loaded with 54 kNm (design moment capacity of the joint) at roof level and 70 kNm (design moment capacity joint) at the floor level (see Figure 10.7). Then, the axial force in the outer column is equal to : Λ/c.sd =
Σ (1/2 q/sd k + (MRd.i - MRd.2) / k ) )
1/2 χ 81 χ 7,2 + (70 - 104) / 7,2 + 1/2x54x7,2+ (54-80)/7,2 478 kN The axial force in the inner column is equal to : Λ/c.sd =
X(1/2qsd/b + (MRd.2-M R d .i)// b ))
(1/2 χ 81 χ 7,2 + (70 - 104) / 7,2 + 1/2 χ 54 χ 7,2 + (54 - 80) / 7,2 ) χ 2 989 kN With help of first order elastic analysis, the moment in the outer column just below the floor is : Msd = 23 kNm.
54 kNm
HE 200 A
4,2 m
HE 200 A
4,5 m
70 kNm
Figure 10.7 Moments acting on the outer column
IIT,
10.5.5 D e s i g n c h e c k s 10.5.5.1 Serviceability limit state Floor : 20,3 mm < 72000 mm / 250 = 28,8 mm. Roof : 28,8 mm < 72000 mm/200 = 36 mm. => Satisfactory. (Note : if this verification was not satisfactory, then a first order elastic frame analysis could be carried out, taking the stiffness of the joints into consideration). 1 0 . 5 . 5 . 2 U l t i m a t e limit state 10.5.5.2.1 Column stability With reference to 10.4.4.2.1, the check of column stability will be satisfactory for the inner column. For the outer columns, Eurocode 3-Clause 5.5.4 needs to be checked (see also Section 10.4.4.2.1). Nsd Xmin^'y
kyMySd
|
' Y/W1
**pl.y'y
478.103
'
^ ΊM\
1.23.106 ■+
0,58 x 5380 x 235 /1,1
τ,
430.103 x 235 /1,1
Satisfactory. 10.5.5.2.2 Section checks of the beams
No check is required, since this has been done in Sectionl 0.5.2 10.5.5.2.3 Section checks of the columns
Since weak-axis buckling is the governing failure mode for the inner column, no check of the inner column section needs to be carried out. The section check of the outer columns can be carried out using Euroc ode 3Clause 5.4.8.1 (3): Wsd
478 103 / Wp,,M = -Af * k _ = · , = 0,41 < 1 y/yMo 5380x235/1,1
224
M y.Sd
MSd / My.pl =
Κ,Λ/JMO
23.10e = 0,25 < 1 430.10J x 235/1,1
Since Λ/sd / A/pi.Rd < 0,5, there is no need to check the interaction between axial force and bending moment.
=> Satisfactory.
10.6 Conclusions This worked example showed that semi-rigid / partial-strength concept, as given in Chapter 6.3 can be applied to braced frames in a straightforward manner. Based on the design of a simple frame with pinned joints, the beam and column sizes can be derived. General rules for economic design are : • The columns in the frame with semi-rigid / partial-strength joints are identical to those used in the frame with simple (pinned) joints; • The beam sizes are one section lower. Calculations to the frames with semi rigid / partial strength joints showed that a plastic frame analysis with partial strength joints normally leads to simpler joints then elastic frame analysis. The three possibilities are summarised in Table 10.9 :
Possibility
Frame analysis
Joint modelling
Type of joint
Beam sizes
Section 10.3
Elastic
Simple
Angle cleats, fin plate or partial depth end plate
IPE 550/
Haunched end plates
IPE 500/
Section 10.4
Section 10.5
Elastic
Plastic
Semi rigid
Partial strength
IPE 450
IPE 400
Flush end plates
IPE 500/ IPE 400
Table 10.9 Summary of frame alternatives
225
Parties Engineer and Steel Fabricator Engineer and Steel Fabricator Engineer or Steel Fabricator
Chapter 11
WORKED EXAMPLE 2 DESIGN OF A 3-STOREY UNBRACED FRAME
11.1 Frame geometry and loading 11.1.1 Frame geometry The skeletal structure of a three bay three storey building is shown in Figure 11.1 (dimensions in mm). Roof 3500 2nd floor
1r
ik 3500 1st floor
τ
iV
3500 J L
_D_ 6500 ■*--
I M
6500
6500 ►!*
10000
Figure 11.1 Frame geometry
2~Ί
The frame is 19.5 m wide, each span being 6.5 m; its total height is 10.5 m, each storey being 3.5 m high. The spacing of the frames is 10 m. The structure is assumed to be braced out of its plane and to be unbraced in its plane. In the longitudinal direction of the building, i.e. in the direction perpendicular to the frame plane, a bracing does exist so that the top of the columns is held in place. The lateral support for the floor beams are provided by the floor slabs. The bases of the columns (foundation level) are assumed to be nominally pinned. The total height of the building is less than the maximum length allowed for transportation (about 12 m); therefore, it was decided to use continuous columns throughout the total height of the building. For the members, use is made of standard hot rolled sections. Members, end-plates and stiffeners are made of S235 steel, according to EN 10025. Bolts are property class 10.9, according to EN 20898-1 and EN 20898-2. 11.1.2
Loading
11.1.2.1 Basic loading The values for the characteristic permanent and variable actions are : Roof level Variable actions (imposed loads) :
6 kN/m.
Permanent actions :
20 kN/m.
Floor level Variable actions (imposed loads) :
18 kN/m.
Permanent actions :
30 kN/m.
The wind loads were established, according to the French regulations, for a building erected in France, at an altitude of 200 m in wind region II. They are applied as point loads of respectively 10.5 kN at the roof level and 21 kN at the 1st and 2nd floor levels. The basic loading cases, which are shown schematically in Figure 11.2, have been considered in appropriate combinations.
20kWm i
;
;
30kWm
30kWm
Ψ
PERMANENT LOADING
1Θ kN/m
(G)
WIND LOADING
(W)
18 kN/m
18 kN/m
18 kN/m
18 kN/m
18 kN/m
18 kN/m
18 kN/m
m
l o a d i n g ca se 1
(11 )
l o a d i n g case 2 IMPOSED LOADING
(12)
loading c a s e 3 (13)
CASES
Figure 11.2 Loading cases 11.1.2.2 Frame imperfections Frame imperfections are considered by means of equivalent horizontal. The initial sway imperfection is given as follows (Eurocode 3 - 5.2.4.3(1)) :
Φ = MA with : kr=
0.5 + — < 1 n„
*.Í* Φο
+ ¿S1
200
Here, one has nc = 4 (number of full height columns per floor) and ns = 3 (number of storeys in the frame), wherefrom : /c c = J0.5 + =0.866
ks= ^|o.2 + | = 0.73
iii)
1 φ = (Ό.866| (0.73 J. 200
1 315
The equivalent horizontal load H= \/φ at each storey of the frame is derived from the initial sway φ and the total design vertical load V in any storey for a given load case (Eurocode 3 - 5.2.4.3 (7)). The relevant values are listed in Table 11.1 for all the basic loading cases.
Basic loading
V
H
(kN)
(kN)
Roof
390
1.24
2nd floor
585
1.86
1st floor
585
1.86
Roof
117
0.37
2nd floor
351
1.11
1st floor
351
1.11
Roof
39
0.12
2nd floor
234
0.74
1st floor
117
0.37
Roof
78
0.25
2nd floor
117
0.37
1st floor
234
0.74
Storey
case (see Figure 11.2) G
h
l2
la
Table 11.1 Equivalent horizontal forces They must of course be affected by the appropriate partial safety factors on actions. 11.1.2.3 Load combination cases It was decided to use the simplified combinations for the ultimate limit state (Eurocode 3 - 2.3.3.1 (5)) and the serviceability limit state (Eurocode 3 - 2.3.4.(5)).
230
Ultimate limit state Load combination case 1
1.35 G + 1.5 W
Load combination case 2
1.35 G + 1.5 h
Load combination case 3
1.35 G + 1.5 h
Load combination case 4
1.35 G + 1.5 h
Load combination case 5
1.35 G + 1.35 W+ 1.35
Load combination case 6
1.35 G + 1.35 W+ 1.35
Load combination case 7
1.35 G + 1.35 W+ 1.35 ¡3
Table 11.2 Load combination cases at ULS The basic load cases are combined at the ultimate limit state as summarised in Table 11.1. Serviceability limit state Load combination case 1
G+W
Load combination case 2
G +h
Load combination case 3
G + l2
Load combination case 4
G + I3
Load combination case 5
G + 0.9 W + 0.9 U
Load combination case 6
G + 0.9W + 0.9 I2
Load combination case 7
G + 0.9W + 0.9 I3
Table 11.3 Load combination cases at SLS
231
The basic load cases are combined at the serviceability limit state as summarised in Table 11.3. The requirements on the frame displacements at the serviceability limit state are as follows for a multi-storey building (Eurocode 3 - 4.2.2 (1) and (4)) : The allowable horizontal deflection in each storey is : h/300 = 3500/300 = 11.7 mm. The allowable horizontal deflection of the structure as a whole is : ho/500 = 10500/500 = 21 mm. The allowable vertical deflection of the floor beams is : L/250 = 6500/250 = 26 mm. The allowable vertical deflection of the roof beam shall is : L/200 = 6500/200 = 32.5 mm.
11.1.3 Partial safety factors on resistance For this worked example, the values of the partial safety factors on resistance are adopted as follows : yM0 = 1.0
for the resistance of cross-sections;
γΜ1 = 1.10
for the buckling resistance of members;
yMb = 1.25
for the resistance of bolts;
yMw = 1.25
for the resistance of welds.
(The value of yM0 = 1.0 is permitted in France provided that the steel material bears the quality mark NF).
11.2
Objectives
The objective is to aim at joint economy. It is assumed that there is an interaction between the two respective tasks of frame design and joint design. The use of unstiffened joints, which may consequently become semi-rigid, is a priori considered as the principal means of obtaining this economy. To provide a basis for evaluating the effect on costs, the frame with rigid joints shall be compared to the frame with semi-rigid joints. Elastic global analysis is used to compute the internal forces and moments.
2 32
For the frame with rigid joints, it is only reported on the column and beam sizes and on the connection detailing. For the frame with semi-rigid joints, the detailed calculations of the members are given in addition. 11.3 Frame with rigid joints 11.3.1 A s s u m p t i o n s and global analysis All the beam-to-column joints were assumed to be perfectly rigid. A linear elastic analysis was carried out for each load case. 11.3.2 M e m b e r sizes The member sizes were first determined based on a preliminary design; their validity was confirmed a posteriori on base of detailed calculations conducted at the end of the global analysis for the various load combination cases. The member sizes obtained accordingly are (Figure 11.3) : Inner columns :
HEB 260
Outer columns
HEB 220
Floor beams :
IPE 360
Roof beams :
IPE 450 IPE 360
Roof
IPE 450
2nd floor
IPE 450
HEB 220
HEB 260
1st floor
HEB 260
ü
-Ω.
Figure 11.3 Member sizes (rigid joints) 11.3.3 S e r v i c e a b i l i t y limit state r e q u i r e m e n t s The maximum horizontal deflection of the storeys is 10.1 mm. ( < 11.7 mm)
233
HEB 220
The maximum horizontal deflection of the structure as a whole is 13.5 mm. (
Semirigid joint.
As it might be expected, all the unstiffened joints must be classified as semirigid joints.
'.38
11.4.4 S t r u c t u r a l analysis A linear elastic analysis is conducted for both the ultimate and serviceability limit states. For this purpose, the joints are characterised by their nominal stiffness J j, in/2.
For the sake of simplicity, the mechanical properties of all the joints are computed based on a single value /3=1 of the transformation parameter. It is recalled that the transformation parameter accounts for the influence of the flexibility of the column web panel on both the design moment resistance and rotational stiffness of the joints; therefore, the actual value of β at each joint depends on the actual moments and shear forces relative to each load combination case. Assuming /3=1 for all the joints of the frame and for all the load combination cases results in a significant simplification in the global analysis and in a slight underestimation of both the strength and stiffness of these joints. 11.4.5 D e s i g n c h e c k s of the f r a m e with s e m i - r i g i d j o i n t s 11.4.5.1 Serviceability limit state At the serviceability limit state : The maximum horizontal deflection of all the storeys is 11.9 mm. Ξ
11.7 mm (*))
The maximum horizontal deflection of the structure as a whole is 19.9 mm. ( 0.5
(Eurocode
a
2 " 0.25
1 +V- / - r ; 25.66
3-F2.1(1))
248
= 30.21
λ.Γ = ^ H ( ß J 0 5 = 0.325 < 0.4 λ
1
No allowance for lateral torsional buckling is necessary. ^>
Satisfactory.
11.4.5.2.4 Joint Design Inner beam-to-column joints Floor level joint (HEB280 / IPE450) The load combination case 5 is found the most critical for this joint. The maximum amplified bending moment applied to a joint is 217 kNm and the shear force is 240 kN. For this joint : Design moment resistance :
220.5 kNm
>
217 kNm
Shear resistance :
443.3 kN
>
240 kN
Satisfactory Roof level (HEB280 / IPE360) The load combination case 5 is found the most critical for this joint. The maximum amplified bending moment applied to a joint is 82 kNm and the shear force is 119 kN. For this joint :
=>
Design moment resistance :
115.8 kNm
>
82 kNm
Shear resistance :
161.4 kN
>
119kN
Satisfactory
Outer beam-to-column joints Floor level (HEB240 / IPE450) The load combination case 5 is found the most critical for this joint. The maximum amplified bending moment applied to a joint is 145 kNm and the shear force is 221 kN. For this joint : Design moment resistance :
151.3 kNm
249
>
145 kNm
Shear resistance : O
282.4 kN
>
221 kN
Satisfactory.
Roof level (HEB240 / IPE360) The load combination case 5 is found the most critical for this joint. The maximum amplified bending moment applied to a joint is 66 kNm and the shear force is 115 kN. For this joint :
¿>
Design moment resistance :
94.8 kNm
>
66 kNm
Shear resistance :
161.4kN
>
115 kN
Satisfactory.
11.5 Conclusion Clearly the unbraced frame can get a substantial advantage from the semi-rigid concept. Though the semi-rigidity of the joints requires an increase in the member sizes, because drifts and deflections would be larger than in the solution with rigid joints, significant cost savings may be expected from the use of much less expensive (unstiffened) joints. Eurocode 3 permits the use of the semi-rigid design procedure. This implementation, compared to most previous standards, has been hampered up to now by the lack of appropriate methods of global analysis and design tools. The latter are now becoming readily available and their use in the daily practice is therefore a matter of technology transfer and further code recognition.
150
CHAPTER 12
WORKED EXAMPLE 3 DESIGN OF AN INDUSTRIAL TYPE BUILDING
12.1 Frame geometry The skeletal structure of a two bay pinned-base pitched portal frame with haunches for an industrial building is shown in Figure 12.1. I
11.86m
Ridge
1.5m;
Eaves
8m 23.5m
23.5m
Figure 12.1 Frame geometry The outside dimensions of the building, including the cladding, are Width :
48 m
Height :
10m
Length :
60,5 m
The portal frames, which are at 6,0 m intervals, have pinned-base 8 m high columns at centrelines of 23,5 m and have rafters sloped at 7,7° with a centreline ridge height of 9,5 m above ground level. Haunches are used for the joints of the rafters to the columns.
12.2 Objectives and design strategy The principal objective is to aim at global economy, without increasing the design effort in any significant manner. A traditional approach to the design of the structure including the joints is adopted initially.
251
The traditional approach (see Chapter 2) is taken here to describe when the design of the joints is carried out once the global analysis and the design of the members have been accomplished. With such a separation of the task of designing the joints from those of analysing the structure and designing the structural members, it is possible that they are carried out by different people who may either be within the same company or, in some cases, may be part of another company. It has been usual for designers to put web stiffeners in the columns so as to justify the usual assumption that the rafter-to-column joints are rigid. It is recognised that eliminating these stiffeners simplifies the joint detailing and reduces fabrication costs. Although the removal of the stiffeners may have an impact on the member sizes required, in particular those of the columns, this is not always the case. Therefore, the strategy chosen here is to assume that economy can be achieved by the elimination of the web stiffeners in the columns. For the chosen structure, it is shown that the joint detailing can be simplified without any modification in the member sizes being required and without violating the initial assumption about the rigid nature of the joints. To achieve this end, the methods provided in the Eurocode 3 for the design of the moment resistant joints are used.
12.3 Design assumptions and requirements 12.3.1 S t r u c t u r a l bracing The structure is unbraced in its plane. In the longitudinal direction of the building, i.e. normal to the plane of the portals, bracing is provided so that the purlins act as out-of-plane support points to the frame. It is therefore assumed that the top of each column is held in place against out-of-plane displacement and that the lateral support provided for the rafter is adequate to prevent lateral torsional buckling in it. 12.3.2 S t r u c t u r a l analysis and d e s i g n of the m e m b e r s and joints A widely used elastic linear elastic analysis was adopted for the ultimate and serviceability limit states. Elastic analysis is particularly suited since plastic hinge behaviour in the members or the joints is not considered. At the final stage of the design, an allowance was made in the analysis for the increased section properties of the rafter over the length of the haunches. In accordance with the principle that elastic analysis is valid up to the formation of the first plastic hinge in the structure, the plastic design resistances of the
Ί Ί
5
member cross-sections and of the joints can be used for the verification of the ultimate limit states. The traditional assumption that joints are rigid is adopted. This assumption is verified. 12.3.3
Materials
Hot-rolled standard sections are used for the members. For the members, the haunches, the end-plates, the base-plates and any stiffeners, an S275 steel to EN 10025, with a yield strength of 275N/mm2 and an ultimate strength of 430N/mm2, is adopted. The bolts are Class 10.9 with mechanical characteristics according to EN 20898-1 and EN 20898-2. 12.3.4 Partial safety f a c t o r s on r e s i s t a n c e The values of the partial safety factors on resistance are as follows :
12.3.5
YMO =1,1
for the resistance of cross-sections;
YMI
for the buckling resistance of members;
=1,1
YM2 = 1,25
for the resistance of net sections;
YMb = 1,25
for the resistance of bolts;
YMW = 1,25
for the resistance of welds.
Loading
12.3.5.1 Basic loading While the loads given are typical for a building of this type, they should be taken as indicative since the values currently required at the present time in different countries vary. These differences concern wind and snow loading mainly. Rather than apply the relevant parts of ENV 1991-Basis of Design, which either are recently available or are still under discussion, the French loading standards were used to determine the design load intensities and their distribution on the structure. The building is situated in a rather exposed location for wind. For simplicity, the self-weight of the cladding plus that of its supporting purlins is considered to act as a uniformly distributed load on the frame perimeter.
253
Permanent actions
Roofing selfweight
Purlins: kN/m
0,15
Cladding insulation: kN/m2
with 0,2
Wall selfweight
Cladding insulation: kN/m2
with 0,2
Variable action Permanent and variable actions Wind load
Snow load
Wind pressure of 0,965 kN/m2 at 10 metres from the ground level. Roof under 0,44 kN/m2
Table 12.1 Permanent and variable actions 12.3.5.2 Basic load cases The basic load cases are schematised in Table 12.2. 12.3.5.3 Load combination cases 12.3.5.3.1 Ultimate load limit state combinations The simplified load combination cases of Eurocode 3 -Chapter 2 are adopted. Thus, the following ultimate load limit state combination cases have been examined : 1.35 G + 1.5 W
(2 combinations)
1.35 G + 1.5 S
(4 combinations)
1.35 G + 1.35 W+ 1.35 S
(8 possible combinations).
where G is the permanent loading, W is the wind loading and S is the snow loading. 12.3.5.3.2 Serviceability limit state requirements and load combinations According to Eurocode 3-4.2.2(1) and Table 4.1, the limit for the maximum vertical deflection of the roof is: δ
<
max —
L 200
where L is the span of a rafter.
'54
Dead load other than portal self weight
1.60kN/m
1.60kN/m
\
1.60kN/m
:
ττ ι | ι M :
1.60kN 'm
——LLLLM
;
1.20kN/m
1.20kN/m
(G1)* Internal Wind Pressure (W1)
2.22kN/m_T_T__ 'n
JL___
¡
^JL_—JL__
3.47kN.'m
4.44kN/m
3.96kN/m
4.15 kN/m
3.86kN/nf
a
S
3." 2kN/m
1.8kN/m
Internal Wind Suction (W2)
^
0.483kN/m 0.676kN/m
5.7kN/m________ ^
0.483kN/n»
0.965kN/m
-►
-¥}
}.515kN/m
i.28kN/m
Snow
-2.64kN/m
2.54kN;m j
!
:
¡ :
-2.64 kN/m
■ ί . ι ; ¡ :
-Z.64kN/m I :
(S1)
Snow
^2.64kN/m 1.32kN/m .i i ¡ I ί J —ι — — r — " ~ X T 3 _ _ _ ^ i
:
- 2 - « ^ ^ . 1 .32kN,m \ : ' "r-i-—----
.—
(S2)
Snow
-5.40kN/m -1.32kN/m
-----r-'~
V~---r
_
-1.32kN/m
(S3)
Snow
5.40kN/m
-5.40kM;m
5.4C kN/m
(S4)
* Tfte self-weight of the frame structural members(G2) is added to the selfweight from the cladding and purlins (G1) to give the total dead load (G). Table 12.2 Basic load cases
According to Eurocode 3 - 4.2.2(4), the limit for the horizontal displacement of a portal frame without a gantry crane is : δ,horiz. < —
150
where h is the heiqht of the column at the eaves.
The following serviceability limit state combination cases have been examined: • Maximum vertical deflection at the ridge (mid-span of each bay):
1.0 G + 1.0 S1 1.0 G + 1.0 S4 • Maximum horizontal deflection at the eaves: 1.0 G + 1.0 W1 1.0 G + 1.0 W2 12.3.5.4 Frame imperfections The sway imperfections are derived from the following formula (see Eurocode 3- 5.2.4.3(1)):
Φ = ^ΛΦο where :
α5
Η Ψ
1
ks= J0.2 + — 56
ks = VO.2 +1 = 1,095 > 1.0 1 φ = (Ό,913;χ(Ί,0;. 200
therefore take 1,0
1 219
All the columns are assumed to have an inclination of ψ so that the eaves and the ridges are initially displaced laterally, as shown in Figure 12.2, by an horizontal distance of : ά>.h = Ψ
= 36,5mm at the eaves and à.h = 219
= 43,4mm at the ridge. 219
36.5 mm
Eaves displacement for imperfections
0=1/219
Figure 12.2 Global frame imperfections
12.4 Preliminary design 12.4.1 Member selection It was decided to use standard hot-rolled sections. When resistance is the only determining factor, it is usually possible in a two bay portal frame of this kind to have a smaller column section size for the central column than for the eaves columns. However, in this case the use of similar columns throughout was justified since the wind loads are quite high and serviceability requirements on horizontal deflections are an important consideration in the choice of the member sections. Doing this provided a column-rafter combination with adequate overall structural stiffness and strength and furthermore insured that, despite the fact that the columns are unstiffened, the assumption of rigid joints is not violated. Taking these considerations into account, the following member section sizes were chosen: Columns :
IPE 550
Beams (rafters) :
IPE 400
257
12.4.2 Joint s e l e c t i o n A flush end-plate bolted haunch joint is used for the rafter-to-column joints. The haunch is obtained by welding a part of an IPE 400 section to the bottom flange at the ends of each IPE 400 rafter. The height of the section is increased from 403,6mm (flange-to-flange allowing for the beam slope of 7,7°) to 782,6mm. The haunch extends 1,5 m along the length of the rafter. An extended end-plate bolted joint is used at the mid-span of the rafters, i.e. at the ridge joints.
12.5 Classification of the frame as non-sway The global analysis was conducted using a first-order elastic analysis and assuming rigid joints. Only the results for the two more critical load combination cases are given (see Table 12.3).
U.LS.
Load
Eaves
Eaves
Central
Central
Haunch
Beam
Beam
Haunch
effect
column
Column
column
Column
at
at
at
at
(base)
(top)
(base)
(top)
eaves
haunch
mid-
central
span
column
Load combin.
column
case M
0.0
291.8
0.0
6.44
291.8
220.80
+121.7
326.45
105.1
80.87
179.7
168.53
45.96
45.14
35.5
46.3
36.53
36.42
0.83
0.78
75.87
68.85
6.63
78.79
0.0
328.57
0.0
91.99
328.57
237.99
4-111.9
344.58
101.26
77.16
171.42
160.24
47.00
55.12
35.41
56.28
44.49
37.95
11.53
11.47
71.99
65.50
11.75
75.42
(kNm)
1.35 G 4-1.5 S1
N (kN) V (kN) M (kN/m)
1 35 G 4-1.35 S1 4-1.35 W 2
N (kN) V (kN)
Table 12.3 Internal efforts for the most critical load combination cases at ULS According to Eurocode 3 - 5.2.5.2(4), an unbraced frame can be classified as non-sway for a given load if the following criterion is satisfied :
L58
ÒV_ 2,7m : The connection may be considered rigid. If Lb8,6m : The connection may be considered rigid. If Lb : second moment of area and beam span respectively. For identical joint conditions at the beam ends (Figure 1A.1.b), the following holds: M, = -M, = M0
(1A.2.3)
M, = M , = M,
(1 A.2. b)
φ. = φ . = φ1
(1 A.2 ■c)
Sj,i-Sjj-Sj
(1 A.2. d)
F
i,i=-Fj,j=Fj
(1 A.2. e)
M¡J = -Mu=Mj
(1 A.2:.f)
Equation (1A.1) then becomes : Μ,=Μ0+ψ±^
(1A.3)
L
b
The equilibrium equation of the spring, the stiffness of which is S¡ , gives: M j __ SjFj
(1A.4)
Compatibility of the rotations and equilibrium of the moments at the spring to beam interface requires that:
302
Fj =
(1-A.5.a)
F1
M,+S^,=0
(1-A.5.b)
After substitution in Equation (1-A.3) for F1 from (1-A.5.a and 1-A.5.D), the following equation is obtained for the left hand end of a uniformly loaded beam:
Μ
·=-ΙΙ·"4ΕΓ
(1 Α 6)
-·
L
-b
Equation (1-A.5) demonstrates the influence of the joint stiffness on the end moment. For a joint having a very high stiffness compared to that of the beam, the beam behaves as almost fixed ended. When the joint stiffness is very small compared to that of the beam, the beam behaves as almost pin ended. How the beam behaves essentially depends on the relative stiffnesses of the joint and the beam. The stiffness of a given beam section varies only with its length, It can be deduced that, for a given beam section of inertia /, Lb having end joints of stiffness Sj :
•
when Lb is relatively long (very flexible beam), the joint tends to behave like a fully fixed joint (Μλ =$-pL2b / 1 2 ) ,
•
when L b is relatively short (very stiff beam), the joint tends to behave like a pinned joint (M,=> 0).
Keeping these observations in mind, two characteristic lengths, Lb1 and may be defined: 1 ) Lb1 such that : - if Lb > Lbi
the joint may be considered as rigid,
- if Lb < Lb1
the joint shall to be considered as semi-rigid;
2) Lb2 such that : - if Lb > Lb2
the joint shall to be considered as semi rigid,
- if Lb < Lb2
the joint may be considered as pinned,
303
Lb2,
where Lb2 < Lbì
Taking the lengths in increasing order, the length Lb2 represents the boundary between the "pinned" and "semi-rigid" classifications, and the length Lb1 represents the boundary between the "semi-rigid" and "rigid" classifications. Their values depend on the joint stiffness and on the given beam section properties. It is quite important to stress that, in accordance with Eurocode 3(revised)Annex J, the joint stiffness to be considered for stiffness classification is the elastic initial one.
304
CHAPTERS
STIFFNESS AND RESISTANCE
CALCULATION
FOR BEAM-TO-COLUMN JOINTS WITH EXTENDED END-PLATE CONNECTIONS
-rpr-ir --.-
. . _ ?
ï " '
"*"k
1.
Calculation procedure
2.
Design tables Application example
305
1. CALCULATION PROCEDURE
Cli. 2 - Beam-to-column joint with extended end-plate
Mechanical characteristics Yield stresses Beam web Beam flange Column web Column flange End-plate Bolts
Ultimate stresses
i', 'vlb
fur. 'up
yp
tub
If hot-rolled profiles : fywc = fyfc and fywb = fy
Geometrical characteristics Joint
\
\ | M : F. h
Column
wc
y=;
e m
•0,8rc
e m
ar
w
k < f
J
,
0.8\/2a c
1
1
s = rc for a rolled section s = Λ ac
for a welded section
^1 L
h,
Avc = Ac - 2 bc tfc + ( U + 2 rc ) tf, with Ac - column section area Beam Γ
/\vc
w
^ Uc
_ LIC j L ^
End-plate
l=f*fb m. |0.8a f V2 %
C
D
Bolts dw :
see figure or = df if no washer
A, :
resistance area of the bolts
308
Cli. 2 - Beam-to-column joint with extended end-plate
RESISTANCE
STIFFNESS Column web panel in shear
0,385 A
Ρ* ß
with
Rd,\
M
V
Avcfycw
\/3 Ί„.
1 for onesided joint configurations; 0 for double sided joint configurations symetrically loaded; 1 for doublesided configurations nonsymetrically loaded with balanced moments; 2 for doublesided joint configurations nonsymetrically loaded with unbalanced moments.
For other values, see 1.2.2.1 in chapter 1.
Column web in compression
0,7 b „
Fw,= k
t
ρ b„ wc "c
Rd,2
t f
eff,wc,c
/γ„
wc •'ywc
if λ wc
J
**Rd,2~
%c
P c ^eff.wc,c
* Mo
< 0,67 '
(
'wc / y w c l ^ Λ
~T A
wc
if λ *
ιί/ι λ
"> „
= 0,93
λ
wc
> 0,67 WC
'
d f
ejj.wc,c
E
c •'ywc
Κ
k = min [1,0 ; 1,25- 0 , 5 - ^ ] WC
L
p,= 1
'
»
(
>
'
'/ Ρ = ι
= ?c2
'/β =2
V
/
1
ρ ,: 'ci
(*)
J
/β=0
- pcl
where
"'^Sfo
M + 1,3 (b „ v
t
ejj.wc ,c
1
'1 + 5,2 (b „ v
I A
wc
t
ejj.wc ,c
f vc '
Ι Α
wc
γ vc '
normal stresses in the column web at the root of the fillet radius or of the weld b „ effwc.c
= t, + aJÏ. ¡b
+ t
ƒ*
ρ
+ min(w ; a,JÏ + t )+ 5(r + s) v
'
/'
ρ '
v
¡c
'
(*) see 1.2.2.2 in chapter 1.
Beam flange in compression
F
Rd,3 = Mc.Rä M*»
O
M cRd : beam design moment resistance
3(W
Ch.2 - Beam-to-column joint with extended end-plate Bolts in tension
A, -I
A4 = 3,2
L
b
0,9 ƒ . A F
Jub
t Rd
s
'Mb
Column web in tension
L, 5
_
0,7 b „
eff,wc¿
d
,t
wc
Rd,S
~
Ρt
eff.wcj
»t
'ywc
' y Mo
c
with
p(= 1
'ƒ P=0
'= P„ = 9a
'7P = i '/ß =2
1 u i Ii ι v / i
w na rc
fi M.;
—
«/i + 1,3 (b „ v \
Π ,·, M
'
,/l + 5,2 v(ό „ V
Column flange in bending
wc
Ι Α Ϋ vc '
1
—
b „
t
effwc.t
'
ί
ejj.wc,t
wc
/ /ί
):
vc '
= min [ 47lm ; 8rø + 2,5e ; z? + 4/w + l,25e 1
F 6
Rd,6 = min [ F /cJW e ]
,
m
3
ftRd.il
ρ
fc.Rd,tl
.
^
.
'ffft J
_
pift m
+
ηft
/ƒ σ , < 180 N/mm2 J
k, = 1 fc
V
2m« - e (m «) 11,,, m ,, k, + Α Β „, η
η Je
'Rd
cs nol t o n i p h
Sion ihis should not c
e difficulties, and indeed ii
r these criteria to be ignored in [his
W
Wi
+ CT Q
J3 o
Π3 CD CO
Ρ
β= 1
Wj
Ρr
+ ,
+
'
+
J£3 CQ
+
+ e
Pi
.
%
w
M
Code
Failure mode
Code
C o l u m n web panel in shear
CWS
C o l u m n w e b in tension
CWT
C o l u m n web in compression
CWC
Column flange in tension
CFT
Beam flange in compression Bolts in
BFC
End piate in tension
k
=1
y MO
= 1.10
y
=1-25
ΜΗ
EPT
BT
tension
u
'
Failure mode
Resistance S235
Pp HEB140 io y-
HEB160
"1
Moment (kNm)
af
J
J,iiu
Sj,ini'2
MRd
2/3MRd
Shear (kN) VRd
failure mode Code
Reference length(m) L
bb
L
bu
IPE220
M16
15
140
305
35
90
120
60
40
TO
5309
30.6
20.4
163
CWS
4.4-R
S
IPE240
M16
15
140
325
35
90
140
60
40
90
25
10
4
5
12136
6068
33.4
22.3
163
CWS
5.4-R
S
IPE270
M16
15
140
355
35
95
160
65
40
90
25
10
4
6
14740
7370
37.7
25.1
163
CWS
6.6-R
S
IPE220
M16
15
140
305
35
90
120
60
40
90
25
10
3
5
12928
6464
41.2
27.4
163
CWS
3.6-R
S
IPE240
M16
15
140
325
35
90
140
60
40
90
25
10
4
5
14835
7418
45.0
30.0
163
CWS
4.4-R
S
1PE270
M16
15
154
355
35
95
160
65
40
90
32
10
4
6
18351
9175
50.7
33.8
163
CWS
5.3-R
M20
20
154
365
45
95
160
65
40
90
32
10
4
6
20161
10081
50.7
33.8
255
CWS
4.8-R
M16
15
160
385
35
95
190
65
40
90
35
10
4
6
21630
10815
56.5
37.7
163
CWS
6.5-R
M20
20
160
395
45
95
190
65
40
90
35
10
4
6
23591
11796
56.5
37.7
255
cws
6.0-R
M16
15
160
415
35
95
220
65
40
35
10
4
6
24908
12454
62.2
41.5
163
CWS
7.9-R
M20
20
160
425
45
95
220
65
40
TO TO
35
10
4
6
27044
13522
62.2
41.5
255
cws
7.3-R
M16
15
140
305
35
90
120
60
40
90
25
10
3
5
13692
6846
47.4
31.6
163
CWS
3.4-R
IPE240
M16
15
140
325
35
90
140
60
40
'X)
25
10
4
5
15761
7881
51.7
34.5
163
CWS
4.1-R
IPE270
M16
15
154
355
35
95
160
65
40
90
32
10
4
6
19609
9804
58.4
38.9
163
CWS
5.0-R
M20
20
154
365
45
95
160
65
40
32
10
4
6
21718
10859
58.4
38.9
255
CWS
4.5-R
M16
15
170
385
35
95
ITO
65
40
TO TO
40
10
4
6
23353
11677
65.0
43.3
163
CWS
6.0-R
M20
20
170
395
45
95
ITO
65
40
90
40
10
4
6
25586
12793
65.0
43.3
255
cws
5.5-R
M16
15
180
415
35
95
220
65
40
90
45
10
4
6
27122
13561
71.6
47.7
163
CWS
7.3-R
M20
20
180
425
45
95
220
65
40
90
45
10
4
6
29497
14748
71.6
47.7
255
cws
6.7-R
M24
25
180
440
50
115
200
75
50
110
35
10
4
6
28759
14379
71.6
47.7
367
cws
6.9-R
s s s s s s s s s s s s s s s
IPE330 IPE220
IPE3TO IPE330
I The holt spjLiiH' dot
epl
Rotational stiffness (kNm/rad)
25
IPE300
HEB180
Welds (mm)
Connection detail (mm)
End-plate: S235 (mm)
inettionthai «tll pu
10
3
5
10618
ria to he ignored in tiu;
Resistance
Pp IPE360
IPE400
HEB2TO
epl
af
»1
»1
Rotational stiffness (kNm/rad)
^j,uu
J,im'-
Moment kNm) MRd
2/3MRd
Shear (kN) VRd
failure η ι odi Code
Reference length(m) L
bb
M16
15
180
455
35
95
250
75
40
90
45
20
5
7
31322
15661
78.0
52.0
163
CWS
8.7-R
S
M20
20
180
465
45
95
250
75
40
TO
45
20
5
33781
16891
78.0
52.0
255
CWS
8.1-R
S
M 24
25
180
480
50
115
230
85
110
52.0
367
CWS
8.3-R
495
35
95
290
75
yo
5 5
78.0
180
20 20
16468
15
35 45
32937
M16
50 40
7 7 7
36537
18269
86.8
57.9
163
CWS
10.6-R
M20
20
180
505
45
95
290
75
40
90
45
20
5
7
39226
19613
86.8
57.9
255
CWS
9.yR
270
85
50
110
35
20
5
7
38304
19152
86.8
57.9
367
CWS
10.1-R
5 5
15212
7606
48.5
32.4
163
EPT
3.1-R
17568
8784
53.0
35.3
163
EPT
3.7-R
11011
68.3
45.5
163
EPT
4.4-R 3.y-R
s s s s s s s s s s s s s s s s s s s s s s s s s s s s s s s s
M24
25
180
520
50
115
IPE220
M16
15
140
305
35
90
120
60
40
90
25
10
1PE240
M16
15
140
325
35
90
140
60
40
90
25
10
3 4
IPE270
M16
15
154
355
35
95
160
65
40
TO
32
10
4
6
22022
M 20
20
154
365
45
95
160
65
40
90
32
10
4
6
24731
12366
71.6
47.7
255
cws
IPE3TO
M16
15
170
385
35
95
190
65
40
10
4
6
26373
13186
79.7
53.2
163
cws
5.3-R
M20
20
170
395
45
95
190
65
40
yo yo
40 40
10
4
6
29271
14635
79.7
53.2
255
CWS
4.8-R
M16
15
180
415
35
95
220
65
40
90
45
10
4
6
30766
15383
87.8
58.5
163
CWS
6.4-R
220
65
40
90
45
10
4
6
33875
16937
87.8
58.5
255
cws
5.8-R
1PE330
IPE360
IPE400
M 20
20
180
425
45
95
M24
25
180
440
50
115
200
75
50
110
35
10
4
6
33562
16781
87.8
58.5
367
CWS
5.9-R
M16
15
200
455
35
95
250
75
40
90
55
20
5
7
36010
18005
95.7
63.8
163
CWS
7.6-R
M20
20
200
465
45
95
250
75
40
90
55
20
5
7
39097
19549
95.7
63.8
255
CWS
7.0-R
M24
25
200
480
50
115
230
85
50
110
45
20
5
7
38736
19368
95.7
63.8
367
CWS
7.1-R
M16
15
200
495
35
95
290
75
40
90
55
20
5
7
42160
21080
106.5
71.0
163
CWS
9.2-R
20
200
505
45
95
290
75
40
90
55
20
5
7
45561
22780
106.5
71.0
255
CWS
8.5-R
520
50
115
270
85
50
110
45
20
5
7
45163
22582
106.5
71.0
367
CWS
8.6-R
340
75
40
90
55
20
5
8
50503
25251
120.0
80.0
163
CWS
11.2-R
M20 M24 IPE450
IPE500
HEB220
Welds (mm)
Connection detail (mm)
Endplate: S2 (mm)
IPE220 IPE240 1PE270
IPE300
IPE330
25
200
M16
15
200
545
35
95
M20
20
200
555
45
95
340
75
40
90
55
20
5
8
54076
27038
120.0
80.0
255
CWS
10.5-R
M24
25
200
570
50
115
320
85
50
110
45
20
5
8
53611
26806
120.0
80.0
367
cws
10.6-R
M16
15
200
595
35
100
6 6
9 9
62124
31062
133.4
88.9
163 255
13.8-R
100
20 20
CWS
45
50 50
88.9
605
100 100
133.4
200
40 40
29256
20
80 80
58512
M20
380 380
cws
13.0-R
M24
25
200
620
50
120
360
90
50
120
40
20
6
9
60966
30483
133.4
88.9
367
CWS
13.3-R
15
140
305
35
90
120
60
40
90
25
10
3
5
15736
7868
48.5
32.4
163
EPT
3.0-R
140
325
35
90
140
60
40
90
25
10
4
5
18221
9110
53.0
35.3
163
EPT
3.6-R
160
65
40
90
32
10
4
6
22949
11475
68.3
45.5
163
EPT
4.2-R
M16 M16
15
M16
15
154
355
35
95
M20
20
160
365
45
95
160
65
40
100
30
10
4
6
25668
12834
80.5
53.7
255
CWS
3.8-R
M16
15
170
385
35
95
190
65
40
yo
40
10
4
6
27591
13795
84.0
56.0
163
EPT
5.1-R
M20
20
170
395
45
95
190
65
40
100
35
10
4
6
30438
15219
89.7
59.8
255
cws
4.6-R
M16
15
180
415
35
95
220
65
40
90
45
10
4
6
32296
16148
94.1
62.7
163
EPT
6.1-R
il thaï vsi!l be protected front corrosion this should not cicale difficulties, and indeed it is c
ii be ignored in this siiuatir
.
Resistance Eni -plate: S 235 (mm)
We Ids
Rotational stiffness
(mm)
(mm)
(kNm/rad)
u
aw
af
40
10
4
35
10
4
90
60
20
40
100
55
85
50
120
290
75
40
95
290
75
115
270
85
35
95
340
75
45
95
340
75
50
115
320
85
50
595
35
ITO
380
80
605
45
ITO
380
80
620
50
120
360
90
220
645
35
ITO
430
20
220
655
45
ITO
M24
25
220
670
50
M16
15
220
695
M20
20
220
M24
25
1PE220
M16
IPE240 IPE270
IPE360
1PE400
IPE450
IPE500
IPE550
IPE600
HEB240
Connection detai
IPE300 IPE330
IPE360
1PE4TO
I The boll spaLing d u
Pp
epl
"1
w
wi
y5
220
65
40
ITO
115
200
75
50
120
y5
250
75
40
45
y5
250
75
480
50
115
230
220
495
35
y5
20
220
505
45
25
220
520
50
M16
15
220
545
M20
20
220
555
M24
25
220
570
M16
15
220
M20
20
220
M24
25
220
M16
15
M20
Moment kNm)
Shear (kN)
failure mode
Reference lenglh(m)
Rd
2/3MRd
vRd
17680
98.7
65.8
255
CWS
5.6-R
S
17547
98.7
65.8
367
CWS
5.6-R
S
38126
19063
107.6
71.8
163
CWS
7.2-R
S
7
41066
20533
107.6
71.8
255
CWS
6.7-R
S
5
7
40648
20324
107.6
71.8
367
CWS
6 7-R
S
20
5
7
44y43
22472
119.8
79.9
163
CWS
8.6-R
S
60
20
5
7
48123
24061
119.8
79.9
255
CWS
8.1-R
120
50
20
5
/
4766y
23835
119.8
79.9
367
CWS
8.2-R
40
90
65
20
5
8
54013
27006
135.0
90.0
163
CWS
10.5-R
40
ITO
60
20
5
8
57357
28679
135.0
TO.O
255
CWS
9.9-R
120
50
20
5
8
56826
28413
135.0
90.0
367
cws
10.0-R
40
ITO
60
20
6
9
62949
31474
150.0
100.0
163
cws
12.9-R
40
ITO
60
20
6
9
66998
33499
150.0
100.0
255
cws
12.1-R
50
120
50
20
6
y
66389
33195
150.0
100.0
367
cws
12.2-R
80
40
ITO
60
20
6
y
72138
36069
165.1
110.1
163
cws
15.6-R
430
80
40
ITO
60
20
6
y
76509
38254
165.1
110.1
255
cws
14.7-R
120
410
90
50
120
50
20
6
y
75852
37926
165.1
110.1
367
cws
14.9-R
35
ITO
480
80
40
ITO
60
20
7
10
81922
40y61
180.1
120.1
163
cws
18.9-R
705
45
ITO
480
80
40
ITO
60
20
7
10
86363
43181
180.1
120.1
255
cws
17.9-R
220
720
50
120
460
TO
50
120
50
20
7
10
85637
4281 y
180.1
120.1
367
cws
18.1-R
15
140
305
35
90
120
60
40
TO
s s s s s s s s s s s s s s
25
10
3
5
16934
8467
48.5
32.4
163
EPT
2.7-R
8.6-R
M16
15
140
325
35
90
140
60
40
90
25
10
4
5
19663
9831
53.0
35.3
163
EPT
3.3-R
S
M16
15
154
355
35
95
160
65
40
90
32
10
4
6
24925
12462
68.3
45.5
163
EPT
3.9-R
S
M20
20
160
365
45
95
160
65
40
ITO
30
10
4
6
28382
14191
95.8
63.9
255
cws
3.4-R
10.7-R
M16
15
170
385
35
95
190
65
40
90
40
10
4
6
30110
15055
84.0
56.0
163
EPT
4.7-R
S
95
190
65
40
ITO
35
10
4
6
33781
16890
106.7
71.1
255
cws
4.2-R
S
'Ρ
bp
hp
M20
20
180
425
45
M24
25
ITO
440
50
M16
15
210
455
35
M20
20
210
465
M24
25
210
M16
15
M20 M24
e
P
P
s
j,ini
*j,ini'2
6
35360
6
350y5
5
7
20
5
45
20
90
65
40
ITO
50
M
Code
L
bb
L
bu
M20
20
170
395
45
M16
15
180
415
35
y5
220
65
40
90
45
10
4
6
35384
17692
94.1
62.7
163
EPT
5.6-R
S
M20
20
180
425
45
95
220
65
40
ITO
40
10
4
6
39375
19687
117.5
78.3
255
cws
5.0-R
S
M24
25
190
440
50
115
200
75
50
120
35
10
4
6
39638
19819
117.5
78.3
367
cws
5.0-R
S
M16
15
210
455
35
95
250
75
40
90
60
20
5
/
41983
20991
108.1
72.0
163
EPT
6.5-R
S
M20
20
210
465
45
95
250
75
40
ITO
55
20
5
7
45899
22949
128.1
85.4
255
cws
6.0-R
S
M24
25
210
480
50
115
230
85
50
120
45
20
5
/
46053
23027
128.1
85.4
367
cws
5.9-R
M16
15
220
495
35
95
290
75
40
90
65
20
5
7
49701
24850
121.6
81.1
163
EPT
7.8-R
M 20
20
220
505
45
95
290
75
40
ITO
60
20
5
7
53979
26989
142.6
95.0
255
cws
7.2-R
s s s
and indeed il is common foi rhes
Resistance
M24 1PE450
bp
hp
25
220
520
(mm)
Moment kNm)
Shear (kN)
| vRd
failure mode Code
Reference length(m)
l
w
W1
u
a„.
af
s
j,ini
j,ini'2
MRd
2/3MRd
85
50
120
50
20
5
7
54165
27083
142.6
95.0
367
cws
7.2-R
S
40
20
5
8
60220
30110
141.0
94.0
163
EPT
P
P
Pp
epl
50
115
270
e
Rotational stiffness (kNm/rad)
u
L
bb
L
bu
M16
15
230
545
35
95
340
75
TO
70
9.4-R
S
M20
20
230
555
45
95
340
75
40
ITO
65
20
5
8
64694
32347
160.6
107.1
255
CWS
8.8-R
S
M24
25
230
570
50
115
320
85
50
120
55
20
5
8
64892
32446
160.6
107.1
367
cws
8.7-R
M16
15
240
5y5
35
100
380
80
40
ITO
70
20
6
y
70917
35458
161.2
107.5
163
EPT
1I.4-R
M20
20
240
605
45
100
380
80
40
ITO
70
20
6
y
75913
37957
178.5
119.0
255
cws
10.7-R
M24
25
240
620
50
120
360
90
50
120
60
20
6
9
76115
38058
178.5
119.0
367
cws
10.6-R
M 16
15
240
645
35
ITO
430
80
40
ITO
70
20
6
9
81507
40753
177.5
118.3
163
EPT
13.8-R
M20
20
240
655
45
1(X)
430
80
40
ITO
70
20
6
y
86931
43466
196.5
131.0
255
cws
13.0-R
670
50
120
410
90
50
120
60
20
6
y
87148
43574
196.5
131.0
367
cws
12.9-R
480
80
40
ITO
70
20
7
IO
92820
46410
197.0
131.3
163
EPT
16.7-R
480
80
40
ITO
70
20
7
10
98379
49 ITO
214.3
142.9
255
cws
15.7-R
120
60
20
7
10
98588
49294
214.3
142.9
367
cws
M24
25
240
720
50
120
460
90
50
15.7-R
s s s s s s s s s s
IPE220
M16
15
150
305
35
120
60
40
100
25
10
3
5
17604
8802
52.0
34.7
163
EPT
2.6-R
8.3-R
IPE240
M16
15
150
325
35
TO TO
140
60
40
100
25
10
4
5
20485
10242
56.8
37.9
163
EPT
3.2-R
S
IPE270
M16
15
154
355
35
95
160
65
40
ITO
27
10
4
6
25767
12884
68.3
45.5
163
EPT
3.8-R
S
M20
20
170
365
45
95
160
65
40
110
30
10
4
6
29585
14792
103.4
68.9
255
BFC
3.3-R
10.3-R
M16
15
170
385
35
95
190
65
40
100
35
10
4
6
31248
15624
84.0
56.0
163
EPT
4.5-R
S
395
45
95
190
65
40
110
30
10
4
6
35201
17601
120.7
80.5
255
CWS
4.0-R
S
35
95
220
65
40
ITO
40
10
4
6
36847
18423
94.1
62.7
163
EPT
5.4-R
S
95
220
65
40
110
35
10
4
6
41173
20586
132.9
88.6
255
CWS
4.8-R
S
75
50
120
35
10
4
6
42214
21107
132.9
88.6
• 367
cws
4.7-R
S
43888
21944
108.1
72.0
163
EPT
6.2-R
48164
24082
144.9
96.6
255
CWS
5.7-R
49197
24598
144.9
96.6
367
CWS
5.6-R
s s s s s s s s s s s s
1PE5IX)
IPE550
M24 1PF.6TO
HEB260
'Ρ
Wt Ids
Connection detaii (mm)
Eni -plaie: S 235 (mm)
1PE300
M16
15
240
695
35
M20
20
240
705
45
ITO
M16 M20
IPE360
1PE400
15 20
170 180 180
415 425
45
M24
25
190
440
50
115
M16
15
210
455
35
95
250
75
40
ITO
55
20
5
M20
20
210
465
45
95
250
75
40
110
50
20
5
M24
25
210
480
50
115
230
85
50
120
45
20
5
/ / /
M16
15
220
495
35
95
290
75
40
ITO
60
20
5
7
52158
26079
121.6
81.1
163
EPT
7.4-R
20
220
505
45
95
290
75
40
110
55
20
5
I
56865
28433
161.3
107.5
255
cws
6.8-R
220
520
50
115
270
85
50
120
50
20
5
7
58043
29022
161.3
107.5
367
cws
6.7-R
35
95
340
75
40
100
65
20
5
8
63498
31749
141.0
94.0
163 '
EPT
8.9-R
75
40
110
60
20
5
8
68465
34232
181.7
121.1
255
cws
8.3-R
cws
8.1-R
M24
IPE5TO
20
200
M20
IPE450
240
ITO
M20 IPE330
25
M16
25 15
230
545
M20
20
230
555
45
95
340
M24
25
230
570
50
115
320
85
50
120
55
20
5
8
69794
34897
181.7
121.1
367
M16
15
240
595
35
ITO
380
80
40
100
70
20
6
9
75505
37753
161.2
107.5
163
EPT
10.7-R 10.0-R 9.9-R
M20 M24 *) The bolt spacing di-es not comply witl
20
240
605
45
ITO
380
80
40
110
65
20
6
9
80672
40336
202.0
- 134.7
255
CWS
25
240
620
50
120
360
TO
50
120
60
20
6
9
82135
41068
202.0
134.7
367
cws
raiou thai will bc proiected tn
on tliis should ii
Resistance Eni -plate: S 235
Connection detai
We Ids
Roiational stiffness
(mm)
(mm)
(mm)
(kNm/rad)
'Ρ
e
P
P
Pp
e
pi
u
l
w
|
«!
u
a„,
af
20
6
9
87245
s
j,ini
s
j,ini/2
vRd
failure mode Code
Reference length(m) L
bb
Lbu
M16
15
250
645
35
100
430
80
40
ITO
43623
179.5
119.7
163
EPT
12.9-R
S
M20
20
250
655
45
100
430
80
40
110
70
20
6
9
92789
46395
222.4
148.2
- 255
cws
12.2-R
S
M24
25
250
670
50
120
410
90
50
120
65
20
6
9
94404
47202
222.4
148.2
367
cws
11.9-R
S
M16
15
260
695
35
ITO
480
80
40
ITO
80
20
7
10
99789
49894
201.1
134.0
163
EPT
15.5-R
S
M20
20
260
705
45
100
480
80
40
110
75
20
7
10
105412
52706
242.5
161.6
255 -.-
cws
14.7-R
S
M24
25
260
720
50
120
460
90
50
120
70
20
7
10
107158
53579
242.5
161.6
367
cws
14.4-R
S
1PE220
M16
15
150
305
35
90
120
60
40
ITO
25
10
3
5
17856
8928
52.0
34.7
163
EPI
2.6-R
8.1-R
IPE240
M16
15
150
325
35
90
140
60
40
ITO
25
10
4
5
20815
10407
56.8
37.9
163
EPT
3.1-R
S
M16
15
154
355
35
95
160
65
40
ITO
27
10
4
6
26259
13130
68.3
45.5
163
EPT
3.7-R
S
M20
20
170
365
45
95
160
65
40
110
30
10
4
6
30322
15161
103.4
68.9
255
BFC
3.2-R
10.0-R
M16
15
170
385
35
95
190
65
40
ITO
35
10
4
6
31932
15966
84.0
56.0
163
EPT
4.4-R
S
3.9-R
S
IPE600
IPE270 IPE300 IPE330
IPE360
IPE400
1PE450
IPE500
IPE550
IPE600
HEB3TO
hp
Shear ' (kN)
75
IPE550
HEB280
bp
Moment kNm) M 2/3MRd Rd
IPE220
M20
20
170
395
45
95
ITO
65
40
110
30
10
4
6
36172
18086
132.0
88.0
255
CWS
M16
15
180
415
35
95
220
65
40
ITO
40
10
4
6
37746
18873
94.1
62.7
163
EPT
5.2-R
S
M20
20
180
425
45
y5
220
65
40
110
35
10
4
6
42413
21206
145.3
96.9
255
CWS
4.7-R
S
M24
25
190
440
50
115
200
75
50
120
35
10
4
6
43618
21809
145.3
96.9
367
CWS
4.5-R
M16
15
210
455
35
y5
250
75
40
ITO
55
20
5
45110
22555
108.1
72.0
163
EPT
6.1-R
M20
20
210
465
45
y5
250
75
40
110
50
20
5
/ /
49771
24885
158.4
105.6
255
CWS
5.5-R
M24
25
210
480
50
115
230
85
50
120
45
20
5
7
50989
25495
158.4
105.6
367
CWS
5.4-R
35
95
290
75
40
ITO
60
20
5
7
53763
26882
121.6
81.1
7.2-R
M24
25
240
620
50
M16
15
250
645
35
ITO
430
M20
20
250
655
45
ITO
430
80
40
110
70
20
6
9
97003
48501
243.1
162.0
255
cws
11.6-R
M24
25
250
670
50
120
410
TO
50
120
65
20
6
9
98952
49476
243.1
162.0
367
cws
11.4-R
M16
15
260
695
35
ITO
480
80
40
ITO
80
20
7
10
104105
52052
201.1
134.0
163
EPT
14.9-R
M20
20
260
705
45
ITO
480
80
40
HO
75
20
7
10
110469
55234
265.0
176.7
255
cws
14.0-R
M24
25
260
720
50
120
460
TO
50
120
70
20
/
10
112586
56293
265.0
176.7
367
cws
13.7-R
s s s s s s s s s s s s s s s s s s s
M16
15
150
305
35
TO
120
60
40
ITO
25
10
3
5
18562
928!
52.0
34.7
163
EPT
2.5-R
7.8-R
M16
15
220
495
163
EPT
M20
20
220
505
45
95
290
75
40
110
55
20
5
/
58926
29463
176.3
117.5
255
CWS
6.6-R
M24
25
220
520
50
115
270
85
50
120
50
20
5
7
60322
30161
176.3
117.5
367
CWS
6.4-R
M16
15
230
545
35
95
340
75
40
ITO
65
20
5
8
65684
32842
141.0
94.0
163
EPT
8.6-R
M20
20
230
555
45
95
340
75
40
HO
60
20
5
8
71183
35592
198.6
132.4
255
CWS
8.0-R
M24
25
230
570
50
115
320
85
50
120
55
20
5
8
72769
36385
198.6
132.4
367
CWS
7.8-R
M16
15
240
595
35
100
380
80
40
ITO
70
20
6
9
78355
39177
161.2
107.5
163
EPT
10.3-R
M20
20
240
605
45
100
380
80
40
110
65
20
6
y
84124
42062
220.8
147.2
255
CWS
9.6-R
120
360
TO
50
120
60
20
6
y
85883
42942
220.8
147.2
367 -
cws
9.4-R
80
40
ITO
75
20
6
9
90776
45388
179.5
119.7
163
EPT
12.4-R
*) The holt spacing d « · , nol comply υ,ΐιΐι ι
on that will bc protected li
l i b e ignored m (lus
\
Resistance
(mm) 'Ρ 1PE240 IPE270
IPE3TO
IPE330
IPE360
IPE4TO
M16 M16
IPE500
epl
u
l
w
w
l
υ
a„.
af
s
j,ini
Sj,ini'2
Shear (kN)
vRd
failure mode Code
Reference length(m) L
bb
L
bu
15
150
325
35
TO
140
60
40
ITO
25
10
4
5
21687
10843
56.8
37.9
163
EPT
15
154
355
35
95
160
65
40
ITO
27
10
4
6
27390
13695
68.3
45.5
i 163
EPT
3.6R
S
45
95
160
65
40
110
30
10
4
6
32592
16296
103.4
68.y
255
BFC
3.0R
9.3R
3.0R
9.4R
20
170
15
170
385
35
95
ITO
65
40
ITO
35
10
4
6
33436
16718
84.0
56.0
163
EPT
4.2R
S
95
ITO
65
40
110
30
10
4
6
38982
19491
134.2
8y.5
255
BFC
3.6R
11.3 R
95
220
65
40
ITO
40
10
4
6
39656
19828
94.1
62.7
163
EPT
5.0R
S
65
40
110
35
10
4
6
45829
22915
157.6
105.1
255
EPT
M20
20
170
395
45
M16
15
180
415
35
M20
20
180
425
45
95
220
4.3R
S
M24
25
190
440
50
115
200
75
50
120
35
10
4
6
47471
23736
167.7
111.8
367
CWS
4.2R
13.0R
M16
15
210
455
35
95
250
75
40
ITO
55
20
5
7
47566
23783
108.1
72.0
163
EPT
5.7R
S
M 20
20
210
465
45
95
250
75
40
110
50
20
5
/
53935
26967
179.3
119.5
255
EPT
5.1R
M 24
25
210
480
50
115
230
85
50
120
45
20
5
7
55639
27820
182.8
121.9
36y
CWS
4.9R
M16
15
220
495
35
95
2TO
75
40
ITO
60
20
5
7
56yio
28455
121.6
81.1
163
EPT
6.8R
20
220
505
45
95
2TO
75
40
110
55
20
5
/
64047
32024
201.8
134.6
255
EPT
6.1R
50
115
270
85
50
120
50
20
5
7
66007
33003
203.5
135.7
367
CWS
5.9R
60
135
250
y5
60
130
45
20
5
7
66955
33477
203.5
135.7
477
CWS
5.8R
75
40
ITO
65
20
5
8
69865
34933
141.0
94.0
163
EPT
8.1R
s s s s s s s s s s s s s s s s s s s s s s
M24
25
220
520
M27
30
220
540
M16
15
230
545
35
95
340
M20
20
230
555
45
95
340
75
40
110
60
20
5
8
77651
38826
229.2
152.8
255
CWS
7.3R
M24
25
230
570
50
115
320
85
50
120
55
20
5
8
79899
39949
229.2
152.8
367
CWS
7.1R
M27
30
230
590
60
135
300
95
60
130
50
20
5
8
80972
40486
229.2
152.8
477
CWS
7.0R
M16
15
240
595
35
100
380
80
40
ITO
70
20
6
9
83504
41752
161.2
107.5
163
EPT
9.7R
240
605
45
ITO
380
80
40
110
65
20
6
9
92072
46036
254.8
169.9
255
CWS
8.8R
620
50
120
360
90
50
120
60
20
6
9
94584
47292
254.8
169.9
367
CWS
8.6R
340
ITO
60
140
50
20
6
y
94448
47224
254.8
169.9
477
CWS
8.6R
430
80
40
ITO
75
20
6
9
97102
48551
179.5
119.7
■ 163
EPT
11.6R
70
20
6
9
106451
53226
280.5
187.0
255
CWS
10.6R 10.3R
20 25
240
M27
30
240
640
60
140
M16
15
250
645
35
ITO
M20
20
250
655
45
ITO
430
80
40
110
M24
25
250
670
50
120
410
90
50
120
65
20
6
9
109246
54623
280.5
187.0
367
CWS
30
250
690
60
140
3TO
ITO
60
140
55
20
6
y
109114
54557
280.5
187.0
477
cws
10.3R
35
ITO
480
80
40
ITO
80
20
111774
55887
201.1
134.0
163
EPT
13.8R
45
ITO
480
80
40
110
75
20
10
121547
60774
305.9
203.9
255
cws
12.7R
120
460
90
50
120
70
20
10
124602
62301
305.9
203.9
367
CWS
12.4R
60
140
60
20
/ / / /
10
10
124443
62222
305.9
203.9
477
cws
12.4R
M27 M16
15
260
695
M20
20
260
705
M24
HEB320
Pp
P
P
Moment kNm) M 2/3MRd Rd
M16
M24
IPE600
e
(mm)
M 20
M20
1PE550
hp
Rotational stiffness (kNiii/rad)
365
M20
1PE450
bp
Wi Ids
Connection délai (mm)
Eni plate: S 235
25
260
720
50
M27
30
260
740
60
140
440
ITO
IPE220
M16
15
150
305
35
90
120
60
40
100
25
10
3
5
18683
9342
52.0
34.7
163
EPT
R
7.8R
IPE240
M16
15
150
325
35
90
140
60
40
ITO
25
10
4
5
21864
10932
56.8
. 37.9
163
EPT
3.0R
9.3R
IPE270
M16
15
154
355
35
95
160
65
40
ITO
27
10
4
6
27685
13842
68.3
45.5
163
EPT
3.5R
S
') The bolt spacing does
ι tilat w i l l be protected troni ι
■ι this should nol create di f fie
Ì io bc ignored in this situation
Resistance Em plate: S 235 (mm)
IPE300
IPE330
IPE360
IPE4TO
1PE450
bp
bp
C
P
P
W i Ids
Rotational stiffness
(mm)
(mm)
(kNni/rad)
Pp
epl
u
l
w
w,
u
a,T
a
f
s
j,ini
Sj,ini'2
Moment kNm) 2/3MRd MRd
Shear (kN)
¡ vRd
failure mode Code
Reference length(m) L
bb
L
bu
M20
20
170
365
45
95
160
65
40
110
30
10
4
6
33257
16628
103.4
68.9
. 255
BFC
2.yR
M16
15
170
385
35
95
190
65
40
100
35
10
4
6
33878
16939
84.0
56.0
163
EPT
4.1R
S
M20
20
170
395
45
95
190
65
40
110
30
10
4
6
39870
19935
134.2
89.5
255
BFC
3.5R
11.0R
9.1R
M16
15
180
415
35
95
220
65
40
ITO
40
10
4
6
40270
20135
94.1
62.7
163
EPT
4.yR
S
M20
20
180
425
45
95
220
65
40
110
35
10
4
6
4697y
23490
157.6
105.1
;
255
EPT
4.2R
13.1R
M24
25
190
440
50
115
200
75
50
120
35
10
4
6
48y37
24468
171.8
114.6
' 367
BFC
4.0R
12.6R
M16
15
210
455
35
95
250
75
40
ITO
55
20
3
7
48424
24212
108.1
72.0
163
EPT
5.6R
S
M20
20
210
465
45
95
250
75
40
110
50
20
5
7
55425
27713
179.3
119.5
255
EPT
4.yR
S
M24
25
210
480
50
115
230
85
50
120
45
20
5
7
574y5
28747
199.6
133.1
367
CWS
4.8R
S
M16
15
220
495
35
95
290
75
40
ITO
60
20
5
/
58093
29047
121.6
81.1
163
EPT
6.7R
S
M20
20
220
505
45
95
2TO
75
40
110
55
20
5
7
65991
32995
201.8
134.6
255
EPT
5.yR
S
M24
25
220
520
50
115
270
85
50
120
50
20
5
7
68379
34190
222.1
148.1
367
CWS
5.7R
S
M27
30
220
540
60
135
250
95
60
130
45
20
5
7
69702
34851
222.1
148.1
477
CWS
5.6R
S
M16
15
230
545
35
95
340
75
40
ITO
65
20
5
8
71556
35778
141.0
94.0
163
EPT
7.9R
S
M20
20
230
555
45
95
340
75
40
110
60
20
5
8
80259
40130
232.1
154.7
255
EPT
7.1R
M24
25
230
570
50
115
320
85
50
120
55
20
5
8
83019
41509
250.2
166.8
367
CWS
6.8R
M27
30
230
590
60
135
300
95
60
130
50
20
5
8
84532
42266
250.2
166.8
477
cws
6.7R
M16
15
240
595
35
100
380
80
40
ITO
70
20
6
y
85787
42894
161.2
107.5
163
EPT
9.4R
M20
20
240
605
45
100
380
80
40
HO
65
20
6
y
y5446
47723
26.3.7
175.8
255
EPT
8.5R
M 24
25
240
620
50
120
360
90
50
120
60
20
6
9
y8552
49276
278.2
185.4
367
cws
8.2R
M27
30
240
640
60
140
340
100
60
140
50
20
6
9
yy206
49603
278.2
185.4
477
cws
8.2R
M16
15
250
645
35
100
430
80
40
ITO
75
20
6
y
100021
50010
179.5
119.7
163
EPT
11.3R
M20
20
250
655
45
100
430
80
40
110
70
20
6
y
110625
55312
293.7
195.8
255
EPT
10.2R
410
90
50
120
65
20
6
9
114091
57045
306.2
204.1
367
CWS
9.9R
M24
25
250
670
50
120
M27
30
250
690
60
140
390
100
60
140
55
20
6
9
114834
57417
306.2
204.1
477
CWS
9.8R
M16
15
260
695
35
100
480
80
40
ITO
80
20
V
10
115435
57717
201.1
134.0
163
EPT
13.4R
M20
20
260
705
45
100
480
80
40
110
75
20
7
10
126612
63306
327.8
218.5
255
EPT
12.2R
M24
25
260
720
50
120
460
TO
50
120
70
20
7
10
130419
65209
333.9
222.6
367
CWS
11 9R
M27
30
260
740
60
140
440
ITO
60
140
60
20
/
10
131220
65610
333.9
222.6
477
cws
11.8R
s s s s s s s s s s s s s s s
M16
15
150
305
35
90
120
60
40
ITO
25
10
3
5
18711
9356
52.0
34.7
163
EPT
R
7.8R
IPE240
M16
15
150
325
35
90
140
60
40
ITO
25
10
4
5
21928
10964
56.8
37.9
163
EPT
3.0R
9.3R
1PE270
M16
15
154
355
35
95
160
65
40
ITO
27
10
4
6
27828
13914
68.3
45.5
163
EPT
3.5R
s
M20
20
170
365
45
95
160
65
40
110
30
10
4
6
33664
16832
103.4
68. y
255
BFC
2.9R
9.OR
M16
15
170
385
35
95
190
65
40
ITO
35
10
4
6
34126
17063
84.0
56.0
163
EPT
4.1R
S
IPE5TO
IPE550
IPE600
HEB340
'Ρ
Connection detail
IPE220
IPE3TO •l Hic Nili spaom· di
to he ignored m this
Resistance
M 20 IPE330
IPE360
1PE400
IPE450
IPE500
M16
1PE240 IPE270
IPE300
IPE330 "I The boli spacinc does r
180
15
a„
af
s
j,ini
*j,ini'2
MRd
2/3MRd
vRd
110
30
10
4
6
40447
20223
134.2
89.5
255
BFC
3.5R
100
40
10
4
6
40647
20324
94.1
62.7
163
EPT
4.9R
S
40
lit)
35
10
4
6
47761
23880
157.6
105.1
255
EPT
65
40
65
40
220
65
395
45
95
190
415
35
95
220
pi
Reference lengdi(m)
u
w
Code
L
bb
L
bu
10.8R
20
180
425
45
4.1R
M24
25
190
440
50
115
200
75
50
120
35
10
4
6
4yy43
24972
171.8
114.6
367
BFC
4.0R
12.4R
M16
15
210
455
35
95
250
75
40
ITO
55
20
5
7
48y88
24494
108.1
72.0
163
EPT
5.6R
S
M20
20
210
465
45
95
250
75
40
110
50
20
5
7
56480
28240
179.3
119.5
255
EPT
4.8R
S
M24
25
210
480
50
115
230
85
50
120
45
20
5
7
58815
29408
213.8
142.5
367
CWC
4.6R
S
M16
15
220
495
35
95
290
75
40
ITO
60
20
5
7
58915
29457
121.6
81.1
163
EPT
6.6R
S
M20
20
220
505
45
95
290
75
40
110
55
20
5
7
67416
33708
201.8
134.6
255
EPT
5.8R
S
115
270
85
50
120
50
20
5
7
70123
35061
238.1
158.7
367
CWC
5.5R
35858
239.4
159.6
477
CWC
5.4R
M24
25
220
520
50
M27
30
220
540
60
135
250
95
60
130
45
20
5
7
71717
M16
15
230
545
35
95
340
75
40
ITO
65
20
5
8
72788
36394
141.0
94.0
163
EPT
7.8R
60
20
5
8
82239
41119
232.1
154.7
255
EPT
6.9R
M24
25
250
670
50
120
410
90
50
M27
30
250
690
60
140
390
100
60
140
55
20
6
y
119304
5y652
331.7
221.2
477
CWS
9.5R
M16
15
260
695
35
100
480
80
40
ITO
80
20
7
10
118334
5yi67
201.1
134.0
163
EPT
13.1R
M20
20
260
705
45
100
480
80
40
HO
75
20
/
10
130721
65360
327.8
218.5
255
EPT
11.8R
M24
25
260
720
50
120
460
90
50
120
70
20
7
10
135128
67564
361.7
241.2
367
CWS
11.4R
30
260
740
60
140
440
100
60
140
60
20
7
10
136609
68305
361.7
241.2
477
CWS
11.3R
s s s s s s s s s s s s s s s s s s
150
305
35
90
120
60
40
ITO
25
10
3
5
18719
9360
52.0
34.7
163
EPT
R
7.8R
325
35
90
140
60
40
ITO
25
10
4
5
21966
10983
56.8
37.9
163
EPT
3.0R
9.3R
35
95
160
65
40
ITO
27
10
4
6
27933
13966
68.3
45.5
163
EPT
3.5R
S
40
110
30
10
4
6
34016
17008
103.4
68.9
255
BFC
2.9R
8.9R
56.0
163
EPT
4.1R
S
89.5
255
BFC
3.4R
10.7R
62.7
163
EPT
4.8R
S
M20
20
230
555
45
95
340
75
40
110
M24
25
230
570
50
115
320
85
50
120
55
20
5
8
85386
42693
269.0
179.3
367
CWC
6.6R
M27
30
230
590
60
135
300
95
60
130
50
20
5
8
87224
43612
270.5
180.3
477
CWC
6.5R
M16
15
240
595
35
100
380
80
40
ITO
70
20
6
9
87512
43756
161.2
107.5
163
EPT
9.3R
20
240
605
45
100
380
80
40
110
65
20
6
y
98082
49041
263.7
175.8
255
EPT
8.3R
240
620
50
120
360
90
50
120
60
20
6
y
101645
50822
300.0
200.0
367
CWC
8.0R
240
640
60
140
340
100
60
140
50
20
6
9
102848
51424
301.3
200.9
477
CWS
7.9R
100
430
80
40
ITO
75
20
6
9
102284
51142
179.5
119.7
163
EPT
11.0R
100
430
80
40
110
70
20
6
y
113952
56976
293.7
195.8
255
EPT
9.9R
120
65
20
6
y
117945
58973
330.6
220.4
367
CWC
9.6R
25 30
M16
15
250
645
35
M20
20
250
655
45
M27 IPE220
170
e
failure mode
M 20
M27
HEB360
20
Pp
Shear (kN)
u
w
P
e
Moment kNm)
l
l
P
hp
(mm)
12.9R
M24
IPE6TO
bp
Rotational stiffness (kNm/rad)
95
M20
IPE550
'ρ
Wc Ids
Connection délai (mm)
Eni plaie: S 235 (mm)
M16 M16 M16
15 15 15
150 154
355
M20
20
170
365
45
95
160
65
M16
15
170
385
35
95
190
65
40
ITO
35
10
4
6
34321
17160
84.0
M20
20
170
395
45
95
190
65
40
HO
30
10
4
6
40954
20477
134.2
M16
15
180
415
35
95
220
65
40
ITO
40
10
4
6
40954
20477
94.1
for a connection thai will he protected from corrosion [his should not create difficulties, and indeed il i;
ion for these c rile
ι to be ignored in this site
.
Resistance Connection detai (mm)
Ene -plate: S235 (mm) 'Ρ
IPE360
IPE400
IPE450
IPE5TO
IPE550
1PE600
HEB400
bp
bp
e
P
Ρ
Pp
e
Wt Ids
Rotational stiffness
(mm)
(kNm/rad)
pi
"1
w
Wj
u
a„
af
s
j,ini
Sj,ini'2
MRd
Moment kNm) 2/3MRd
Shear (kN)
i VRd
failure mode Code
Reference length(m) L
bb
L
bu
M20
20
180
425
45
y5
220
65
40
110
35
10
4
6
48454
24227
157.6
105.1
255
EPT
4.1-R
12.7-R
M24
25
190
440
50
115
200
75
50
120
35
10
4
6
5084y
25425
171.8
114.6
367
BFC
3.9-R
12.1-R
M16
15
210
455
35
y5
250
75
40
ITO
55
20
5
7
4y457
24728
108.1
72.0
163
EPT
5.5-R
S
M20
20
210
465
45
y5
250
75
40
110
50
20
5
7
57423
28711
179.3
119.5
255
EPT
4.8-R
S
50
115
230
85
50
120
45
20
5
7
60011
30006
217.7
145.2
M24
25
210
480
367
BFC
4.6-R
14.2-R
M16
15
220
495
35
y5
2TO
75
40
ITO
60
20
5
7
59615
29808
121.6
81.1
163
EPT
6.5-R
S
M20
20
220
505
45
y,5
290
75
40
110
55
20
5
7
68702
34351
201.8
134.6
255
EPT
5.7-R
S
M24
25
220
520
50
115
270
85
50
120
50
20
5
7
71715
35858
253.5
169.0
367
CWC
5.4-R
S
M27
30
220
540
60
135
250
95
60
130
45
20
5
7
73570
36785
254.9
169.9
477
CWC
5.3-R
S
M16
15
230
545
35
y5
340
75
40
ITO
65
20
5
8
73860
36930
141.0
94.0
163
EPT
7.7-R
S
M20
20
2.30
555
45
95
340
75
40
HO
60
20
5
8
84044
42022
232.1
154.7
255
EPT
6.7-R
S
M24
25
230
570
50
115
320
85
50
120
55
20
5
8
87568
43784
286.4
ITO.y
367
CWC
6.5-R
S
M27
30
230
590
60
135
300
95
60
130
50
20
5
8
89720
44860
288.0
192.0
477
CWC
6.3-R
S
M16
15
240
595
35
100
380
80
40
ITO
70
20
6
y
89034
44517
161.2
107.5
163
EPT
9.1-R
S
M 20
20
240
605
45
100
380
80
40
HO
65
20
6
y
100508
50254
263.7
175.8
255
EPT
8.1-R
S
M24
25
240
620
50
120
360
TO
50
120
60
20
6
y
104520
52260
319.3
212.y
367
CWC
7.7-R
S
M27
30
240
640
60
140
340
ITO
60
140
50
20
6
y
106255
53127
321.1
214.1
477
CWC
7.6-R
S
M16
15
250
645
35
100
430
80
40
ITO
75
20
6
y
104304
52152
179.5
119.7
163
EPT
10.8-R
S
M20
20
250
655
45
ITO
430
80
40
110
70
20
6
y
117036
58518
293.y
195.8
255
EPT
9.6-R
S
M24
25
250
670
50
120
410
TO
50
120
65
20
6
y
121550
60775
352.0
234.7
367
CWC
9.3-R
S
M27
30
250
690
60
140
390
ITO
60
140
55
20
6
y
123510
61755
353.9
235.9
477
cwc
9.1-R
S
M16
15
260
695
35
ITO
480
80
40
100
80
20
7
10
120949
60474
201.1
134.0
163
EPT
12.8-R
S
45
ITO
480
80
40
110
75
20
134553
67277
32y.8
218.5
255
EPT
:
M20
20
260
705
11.5-R
S
M24
25
260
720
50
120
460
TO
50
120
70
20
/ /
10 10
139557
69779
385.2
256.8
367
CWC
11.1-R
S
M27
30
260
740
60
140
440
ITO
60
140
60
20
7
10
141710
70855
387.2
258.1
477
CWC
10.9-R
S
IPE220
M16
15
150
305
35
90
120
60
40
ITO
25
10
3
5
18648
9324
52.0
34.7
163
EPT
R
7.8-R
IPE240
M16
15
150
325
35
TO
140
60
40
ITO
25
10
4
5
21932
10966
56.8
37.9
163
EPT
3.0-R
9.3-R
1PE270
M16
15
154
355
35
95
160
65
40
100
27
10
4
6
27983
13992
68.3
45.5
163
EPT
3.5-R
S
M20
20
170
365
45
95
160
65
40
110
30
10
4
6
34460
17230
103.4
68.9
255 ,
BFC
2.8-R
8.8-R
M16
15
170
385
35
95
190
65
40
100
35
10
4
6
34497
17248
84.0
56.0
163
EPT
4.1-R
S
95
ITO
65
40
110
30
10
4
6
41639
20820
134.2
89.5
255
BFC
3.4-R
10.5-R
95
220
65
40
ITO
40
10
4
6
41295
20647
94.1
62.7
163
EPT
4.8-R
S
35
10
4
6
49438
24719
157.6
105.1
255
EPT
4.0-R
12.5-R
35
10
4
0
52168
26084
171.8
114.6
367
BFC
3.8-R
11.8 R
IPE300 IPE330
I Thr Kili sp.i.iii;· do«
M 20
20
170
395
45
M16
15
180
415
35
M20
2(1
180
425
45
y.5
220
65
40
110
M24
25
190
440
50
115
200
75
50
120
Resistance
'ρ 1PE360
IPE4TO
IPE550
IPE6TO
IPE220 IPE240 1PE270 IPE300 IPE330
IPE360
P
P
Pp
epl
"1
»
WJ
u
aw
af
Sj,ini
^j,ini'2
Shear (kN) !
VRd
failure mode Code
Reference length(m) L
bb
L
bu
15
210
455
35
95
250
75
40
ITO
55
20
5
7
50041
25020
108.1
72.0
163
M 20
20
210
465
45
95
250
75
40
110
50
20
5
7
58813
29407
179.3
119.5
255
EPT
4.6-R
S
M24
25
210
480
50
115
230
85
50
120
45
20
5
7
6180y
30904
217.7
145.2
367
BFC
4.4-R
13.8-R
M16
15
220
495
35
95
290
75
40
ITO
60
20
5
7
60562
30281
121.6
81.1
163
EPT
6.4-R
S
20
220
505
45
95
290
75
40
110
55
20
5
7
70665
35333
201.8
134.6
255
EPT
5.5-R
S
220
520
50
115
270
85
50
120
50
20
5
7
74179
37089
275.0
183.3
367
EPT
5.2-R
S
60
135
250
95
60
130
45
20
5
7
76459
38229
279.3
186.2
477 -
BFC
5.1-R
15.9-R
35
95
340
75
40
ITO
65
20
5
8
75406
37703
141.0
94.0
163
EPT
7.5-R
S
75
40
110
60
20
5
8
86887
43443
232.1
154.7
255
EPT
25
M 27
30
220
540
M16
15
230
545
5.5-R
S
M20
20
230
555
45
95
340
6.5-R
S
M24
25
230
570
50
115
320
85
50
120
55
20
5
8
yi042
45521
316.9
211.2
367
EPI
6.2-R
S
M27
30
230
590
60
135
300
95
60
130
50
20
5
8
93718
46859
323.1
215.4
477
CWC
6.0-R
S
M16
15
240
5y5
35
100
380
80
40
ITO
70
20
6
y
91322
45661
161.2
107.5
163
EPI
8.9-R
S
M20
20
240
605
45
100
380
80
40
110
65
20
6
y
104430
52215
263.7
175.8
255
EPT
7.8-R
M24
25
240
620
50
120
360
90
50
120
60
20
6
y
109206
54603
358.3
238.y
367
CWC
7.4-R
M27
30
240
640
60
140
340
ITO
60
140
50
20
6
y
111807
55904
360.3
240.2
477
CWC
7.2-R
M16
15
250
645
35
100
430
80
40
100
75
20
6
y
107435
53717
179.5
119.7
163
EPT
10.5-R
M20
20
250
655
45
100
430
80
40
110
70
20
6
y
122116
61058
293.7
195.8
255
EPT
9.2-R
410
90
50
120
65
20
6
y
127533
63767
395.0
263.3
367
CWC
8.8-R
M24
25
250
670
50
120
M27
30
250
690
60
140
390
ITO
60
140
55
20
6
y
130485
65242
397.2
264.8
477
CWC
8.6-R
M16
15
260
695
35
100
480
80
40
ITO
80
20
/
10
125097
62548
201.1
134.0
163
EPT
12.4-R
M20
20
260
705
45
100
480
80
40
HO
75
20
7
10
140966
70483
327.8
218.5
255
EPT
11.0-R
M24
25
260
720
50
120
460
TO
50
120
70
20
10
147021
73510
432.2
288.2
367
CWC
10.5-R
30
260
740
60
140
440
ITO
60
140
60
20
/ /
10
150297
75149
434.6
289.7
477
CWC
10.3-R
s s s s s s s s s s s
150
305
35
90
120
60
40
ITO
25
10
3
5
18052
9026
52.0
34.7
163
EPT
2.6-R
8.1-R
35
TO
140
60
40
ITO
25
10
4
5
21276
10638
56.8
37.9
163
EPT
3.1-R
S
95
160
65
40
ITO
27
10
4
6
27216
13608
68.3
45.5
163
EPT
3.6-R
S
65
40
110
30
10
4
6
33706
16853
103.4
68.9
255
BFC
2.9-R
9.0-R
M27 HEB450
C
Moment kNm) M 2/3MRd Rd
M16
M24
1PE500
hp
Rotational stiffness (kNm/rad)
EPT
M 20
IPE450
bp
Wi Ids (mm)
Connection detaii (mm)
Eni plate: S 235 (mm)
M16 M16 M16
15 15 15
150 154
325 355
35
:
M20
20
170
365
45
95
160
M16
15
170
385
35
95
190
65
40
100
35
10
4
6
33642
16821
84.0
56.0
163
EPT
4.2-R
S
M20
20
170
395
45
95
190
65
40
110
30
10
4
6
40878
20439
134.2
89.5
255 -
BFC
3.4-R
10.7-R
M16
15
180
415
35
95
220
65
40
ITO
40
10
4
6
40385
20193
94.1
62.7
163
EPT
4.9-R
S
M20
20
180
425
45
95
220
65
40
110
35
10
4
6
48699
24349
157.6
105.1
255
EPT
4.1-R
12.7-R
M24
25
190
440
50
115
200
75
50
120
35
10
4
6
51664
25832
171.8
114.6
367
BFC
3.8-R
12.0-R
35
95
250
75
40
ITO
55
20
5
7
49058
24529
108.1
72.0
163
EPT
5.6-R
S
45
95
250
75
40
110
50
20
5
7
58131
29066
179.3
119.5
255
EPT
4.7-R
S
M16 M20
I The boit spacint· does not comply with nia
15 20
210 210
455 465
:i tliat w i l l be protected tre
il diis should noi create difficulties, and indeed i
for these criteria to be ignored in this situ.
Resistance
IPE400
IPE450
61434
30717
217.7
145.2
59601
29801
121.6
81.1
7
70148
35074
201.8
5
/
74053
37026
20
5
7
76719
65
20
5
8
110
60
20
5
50
120
55
20
95
60
130
50
af
l
w
wi
U
aw
85
50
120
45
20
5
/
75
40
ITO
60
20
5
7
290
75
40
110
55
20
5
115
270
85
50
120
50
20
60
135
250
95
60
130
45
545
35
95
340
75
40
ITO
230
555
45
95
340
75
40
25
230
570
50
115
320
85
30
230
590
60
135
300
«P
bp
bp
M24
25
210
M16
15
220
M20
20
M24
P
P
Pp
epl
480
50
115
230
495
35
95
290
220
505
45
95
25
220
520
50
M27
30
220
540
M16
15
230
M20
20
M24 M27
e
U
s
j,ini
s
Shear (kN) v
Rd
failure mode Code
Reference lengdi(m) L
bb
Lbu
367
BFC
4.4-R
13.9-R
■ 163
EPT
6.5-R
S
134.6
255
EPT
5.5-R
S
275.0
183.3
367
EPT
5.2-R
S
38359
279.3
186.2
477"
BFC
5.1-R
15.8-R
74543
37271
141.0
y4.o
163
EPT
7.6-R
S
8
86691
43346
232.1
154.7
255
EPT
6.5-R
S
5
8
91360
45680
316.9
211.2
367
EPT
6.2-R
S
20
5
8
94526
47263
342.4
228.3
477
CWC
6.0-R
S
M16
15
240
595
35
ITO
380
80
40
ITO
70
20
6
9
90669
45335
161.2
107.5
163
EPT
8.9-R
S
20
240
605
45
ITO
380
80
40
110
65
20
6
y
104733
52366
263.7
175.8
255
EPT
7.7-R
S
M24
25
240
620
50
120
360
90
50
120
60
20
6
y
110155
55077
359.9
23y.y
367
EPT
7.4-R
S
M27
30
240
640
60
140
340
ITO
60
140
50
20
6
y
113684
56842
381.9
254.6
477
CWC
7.1-R
S
MI6
15
250
645
35
ITO
430
80
40
ITO
75
20
6
9
107114
53557
179.5
119.7
163
EPT
10.5-R
S
M20
20
250
655
45
ITO
430
80
40
110
70
20
6
9
123018
61509
293.7
195.8
255
EPT
9.2-R
S
M24
25
250
670
50
120
410
90
50
120
65
20
6
9
129218
64609
400.2
266.8
367
EPT
8.7-R
S
M27
30
250
690
60
140
390
ITO
60
140
55
20
6
9
133250
66625
420.9
280.6
477
CWC
8.5-R
S
M16
15
260
695
35
ITO
480
80
40
ITO
80
20
7
10
125220
62610
201.1
134.0
163
EPT
12.4-R
S
M20
20
260
705
45
ITO
480
80
40
110
75
20
7
10
142611
71306
327.8
218.5
255
EPT
10.8-R
S
M24
25
260
720
50
120
460
90
50
120
70
20
7
10
149601
74800
444.0
296.0
367
EPT
10.3-R
S
M27
30
260
740
60
140
440
ITO
60
140
60
20
7
10
154120
77060
460.6
307.1
477
CWC
10.0-R
S
IPE220
M16
15
160
305
35
90
120
60
40
110
25
10
3
5
18411
9206
55.5
37.0
163
EPT
2.5-R
7.9-R
IPE240
M16
15
160
325
35
90
140
60
40
110
25
10
4
5
21725
10863
60.6
40.4
163
EPT
3.0-R
9.4-R
160
65
40
110
25
10
4
6
27810
13905
71.0
47.3
163
EPT
3.5-R
S
33324
16662
103.4
68.9
255
BFC
2.9-R
9.1-R
IPE550
IPE600
IPE270
IPE3TO
IPE330
1PE360
IPE400 · ) Hie ho
j,ini/2
Moment kNm) M 2/3MRd Rd
M20
IPE5TO
HEB5TO
Rotational stiffness (kNm/rad)
Welds (mm)
Connection délai (min)
Eni plate: S 235 (mm)
1 S p . l . l I l L ' lll-CS IK
M16
15
160
355
35
95
M20
20
180
365
45
95
160
65
40
120
30
10
4
6
M16
15
170
385
35
95
190
65
40
110
30
10
4
6
34239
17119
84.0
56.0
163
EPT
4.1-R
S
M20
20
180
395
45
95
190
65
40
120
30
10
4
6
40527
20263
134.2
89.5
255
BFC
3.5-R
10.8-R
M16
15
180
415
35
95
220
65
40
HO
35
10
4
6
41181
20590
y4.i
62.7
163
EPT
4.8-R
S
M20
20
180
425
45
95
220
65
40
120
30
10
4
6
48214
24107
157.6
105.1
255
EPT
4.1-R
12.8-R
M24
25
200
440
50
115
200
75
50
130
35
10
4
6
51436
25718
171.8
114.6
367
BFC
3.8-R
12.0-R
95
250
75
40
110
50
20
3
7
50164
25082
108.1
72.0
163
EPT
5.4-R
S
M16
15
210
455
35
M20
20
210
465
45
95
250
75
40
120
45
20
5
7
57706
28853
179.3
119.5
255
EPT
4.7-R
S
M24
25
210
480
50
115
230
85
50
130
40
20
5
61102
30551
217.7
145.2
367
BFC
4.5-R
14.0 R
M16
15
220
495
35
95
290
75
40
110
55
20
5
/ /
61090
30545
121.6
81.1
163
EPT
6.4-R
S
[ Lunipl, vwili ni
.111.Il l h . i l
*il
k
ni.ncc.ed
οι Licjir diti
niini Ini illese Lineria m K ι,-ηοιοί ,·
Resistance Connect on detail (mm)
Em -plate: S 235 (mm)
M20
IPE450
hp
e
P
P
Pp
20
220
505
45
95
290
e
pi
75
l
w
40
120
u
(mm)
(kNm/rad)
Moment kNm) M 2/3MRd Rd
Shear (kN)
,
u
aw
af
s
j,ini
^j,ini'2
50
20
5
7
69874
34937
201.8
134.6
5
7
73915
36958
275.0
7
76704
38352
279.3
w
l
vRd
failure mode Code
Reference lengdi(m) L
bb
L
bu
255
EPT
5.6-R
183.3
367
EPT
5.3-R
S
186.2
477
BFC
5.1-R
15.8-R
S
M 24
25
220
520
50
115
270
85
50
130
45
M27
30
220
540
60
1.35
250
y.s
60
140
40
20
5
M16
15
230
545
35
95
340
75
40
110
60
20
5
8
76647
38323
141.0
94.0
163
EPI
7.4-R
S
20
230
555
45
95
340
75
40
120
55
20
5
8
86705
43353
232.1
154.7
255
EPT
6.5-R
S
570
50
115
320
85
50
130
50
20
5
8
91579
45789
316.9
211.2
367
EPT
6.2-R
S
y.s
60
140
45
20
5
8
94920
47460
362.1
241.4
477
CWC
6.0-R
S
80
40
110
65
20
6
y
93851
46925
161.2
107.5
163
EPT
8.6-R
S
60
20
6
y
105165
52582
263.7
175.8
255
E.PT
7.7-R
S
M24
25
230
M27
30
230
590
60
135
300
M16
15
240
595
35
100
380
M20
20
240
605
45
100
380
80
40
120
M 24
25
240
620
50
120
360
TO
50
130
55
20
6
y
110875
55437
359.9
23y.y
367
EPT
7.3-R
M27
30
240
640
60
140
340
ITO
60
140
50
20
6
y
114756
57378
403.7
269.2
477
CWC
7.1-R
M16
15
250
645
35
100
430
80
40
HO
70
20
6
y
111149
55575
179.5
119.7
163
EPT
10.1-R
20
250
655
45
100
430
80
40
120
65
20
6
y
123976
61988
293.7
195.8
255
EPT
9.1-R
250
670
50
120
410
TO
50
130
60
20
6
9
130552
65276
400.2
266.8
367
EPT
8.6-R
6TO
60
140
390
ITO
60
140
55
20
6
9
135018
67509
445.0
296.7
477
CWC
8.4-R
480·
80
40
110
75
20
7
10
130331
65166
201.4
134.3
163
EPT
11.9-R
M16
15
260
6y.5
35
100
M20
20
260
705
45
100
480
80
40
120
70
20
7
10
144222
72111
327.8
218.5
255
EPT
10.7-R
M24
25
260
720
50
120
460
90
50
130
65
20
7
10
151689
75845
444.0
296.0
367
EPT
10.2-R
M27
30
260
740
60
140
440
ITO
60
140
60
20
/
10
156733
78366
487.0
324.7
477
CWC
9.9-R
s s s s s s s s s s
IPE220
M16
15
160
305
35
90
120
60
40
110
25
10
3
5
17894
8947
55.5
37.0
163
EPT
2.6-R
8.1-R
IPE240
M16
15
160
325
35
90
140
60
40
110
25
10
4
5
21145
10572
60.6
40.4
163
EPT
3.1-R
1PE270
M16
15
160
355
35
95
160
65
40
110
25
10
4
6
27119
13560
71.0
47.3
163
EPT
3.6-R
s s
M20
20
180
365
45
95
160
65
40
120
30
10
4
6
32448
16224
103.4
68.9
255
BFC
3.0-R
9.4-R
170
385
35
95
190
65
40
110
30
10
4
6
33450
16725
84.0
56.0
163
EPT
4.2-R
S
190
65
40
120
30
10
4
6
39559
19779
134.2
89.5
255
BFC
3.5-R
11.1-R
220
65
40
HO
35
10
4
6
40307
20153
94.1
62.7
163
EPT
4.9-R
S
40
120
30
10
4
6
47175
23588
157.6
105.1
255
EPT
IPE550
M20 M24 M27 IPEfiOO
HEB550
bp
Rotational stiffness
20
M20
1PE5TO
'ρ
Wi Ids
IPE300 IPE330
IPE360
IPE400
M16
30
15
250
M20
20
180
3y.5
45
95
M16
15
180
415
35
95
M20
20
180
425
45
95
220
65
4.2-R
13.1-R
M24
25
200
440
50
115
200
75
50
130
35
10
4
6
50456
25228
171.8
114.6
367
BFC
3.9-R
12.2-R
M16
15
210
455
35
95
250
75
40
110
50
20
5
7
49178
24589
108.1
72.0
163
EPT
5.6-R
S
M20
20
210
465
45
95
250
75
40
120
45
20
5
7
56592
28296
179.3
119.5
255
EPT
4.8-R
S
M24
25
210
480
50
115
230
85
50
130
40
20
5
7
60094
30047
217.7
145.2
367
BFC
4.5-R
14.2-R
M16
15
220
4y5
35
95
290
75
40
HO
55
20
5
/
60045
30022
121.6
81.1
163
EPT
6.5-R
S
505
45
95
2TO
75
40
120
50
20
5
7
68731
34365
201.8
134.6
255
EPT
5.7-R
S
50
115
270
85
50
130
45
20
5
7
72922
36461
275.0
183.3
367
EPT
5.3-R
S
M20 M24 1 The N i l i spacinc' di>t
25
20 25
220 220
520
connection that w i l l be pioicctcd t
m j indeed it is common lor [he·
Resistance Connection detai (mm)
Ent -plate: S235 (mm)
IPE450
IPE500
IPE550
IPE600
HEB6(X)
Welds
Rotational stiffness
(mm)
(kNm/rad)
75885
37942
279.3
186.2
477
BFC
5.1-R
S
75563
37782
141.0
94.0
163
EPT
7.5-R
S
8
85592
42796
232.1
154.7
255
EPT
6.6-R
S
5
8
90685
45342
316.9
211.2
367
EPT
6.3-R
S
20
5
8
y4264
47132
363.6
242.4
477
BFC
6.0-R
S
65
20
6
9
y2826
46413
161.2
107.5
163
EPT
8.7-R
S
120
60
20
6
9
104200
52100
263.7
175.8
7.8-R
S
7.3-R
S
Ρ
Pp
«pi
"1
ΛΥ
"1
u
aw
af
540
60
135
250
95
60
140
40
20
5
7
545
35
95
340
75
40
HO
60
20
5
8
230
555
45
95
340
75
40
120
55
20
5
25
230
570
50
115
320
85
50
130
50
20
M27
30
230
590
60
135
300
95
60
140
45
M16
15
240
595
35
ITO
380
80
40
110
ITO
380
80
40
bp
hp
M27
30
220
M16
15
230
M20
20
M24
e
Reference length(m)
j,ini/2
P
'Ρ
failure mode
Moment kNm) 2/3MRd MRd
s
j,ini
S
Shear (kN)
vRd
Code
L
bb
L
bu
M20
20
240
605
45
255
EPT
M24
25
240
620
50
120
360
90
50
130
55
20
6
y
110210
55105
359.9
239.9
367
EPT
M27
30
240
640
60
140
340
ITO
60
140
50
20
6
y
114399
57200
422.6
281.7
477
CWC
7.1-R
S
M16
15
250
645
35
ITO
430
80
40
110
70
20
6
y
110261
55130
179.5
119.7
163
EPT
10.2-R
S
M20
20
250
655
45
ITO
430
80
40
120
65
20
6
y
123242
61621
293.7
195.8
255
EPT
9.1-R
S
M24
25
250
670
50
120
410
90
50
130
60
20
6
y
130206
65103
400.2
266.8
367
EPI"
8.7-R
S
M27
30
250
690
60
140
390
ITO
60
140
55
20
6
9
135057
67528
465.8
310.5
477
CWC
8.3-R
S
M16
15
260
695
35
ITO
480
80
40
HO
75
20
7
10
129655
64827
201.4
134.3
163
EPT
11.9-R
S
M20
20
260
705
45
ITO
480
80
40
120
70
20
7
10
143818
71909
327.8
218.5
255
EPT
10.8-R
M24
25
260
720
50
120
460
90
50
130
65
20
7
10
151777
75889
444.0
296.0
367
EPT
10.2-R
M27
30
260
740
60
140
440
ITO
60
140
60
20
7
10
157292
78646
509.8
339.9
477
CWC
9.8-R
s s s
35
90
120
60
40
110
25
10
3
5
17422
8711
55.5
37.0
1PE220
M16
15
160
305
163
EPT
2.7-R
8.4-R
IPE240
M16
15
160
325
35
90
140
60
40
110
25
10
4
5
20611
10306
60.6
40.4
163
EPT
3.2-R
S
IPE270
M16
15
160
355
35
95
160
65
40
HO
25
10
4
6
26476
13238
71.0
47.3
163
EPT
3.7-R
S
M20
20
180
365
45
95
160
65
40
120
30
10
4
6
31631
15816
103.4
68.9
255
BFC
3.1-R
9.6-R
M16
15
170
385
35
95
190
65
40
110
30
10
4
6
32707
16354
84.0
56.0
163
EPT
4.3-R
S
M20
20
180
395
45
95
190
65
40
120
30
10
4
6
38644
19322
134.2
89.5
255
BFC
3.6-R
11.4-R
M16
15
180
415
35
95
220
65
40
110
35
10
4
6
39471
19735
94.1
62.7
163
EPT
5.0-R
S
M20
20
180
425
45
95
220
65
40
120
30
10
4
6
46176
23088
157.6
105.1
255
EPT
4.3-R
S
50
115
200
75
50
130
35
10
4
6
49497
24749
171.8
114.6
367
BFC
4.0-R
12.5-R
IPE300 IPE330
IPE360
IPE4TO
M24
25
200
440
M16
15
210
455
35
95
250
75
40
110
50
20
5
7
48217
24109
108.1
72.0
163
EPT
5.7-R
S
M20
20
210
465
45
95
250
75
40
120
45
20
5
7
55495
27747
179.3
119.5
255
EPT
4.9-R
S
M24
25
210
480
50
115
230
85
50
130
40
20
5
7
59076
29538
217.7
145.2
367
BFC
4.6-R
S
M16
15
220
495
35
95
290
75
40
110
55
20
5
/
58998
29499
121.6
81.1
163
EPT
6.6-R
S
M20
20
220
505
45
95
290
75
40
120
50
20
5
7
67568
33784
201.8
134.6
255
EPT
5.8-R
S
220
520
50
115
270
85
50
130
45
20
5
/
71876
35938
275.0
183.3
367
EPT
5.4-R
S
135
250
95
60
140
40
20
5
7
74980
37490
279.3
186.2
477
BFC
5.2-R
S
95
340
75
40
110
60
20
5
8
74433
37217
141.0
94.0
163
EPT
7.6-R
S
M24 IPE450 *l The K.lt sp.Kiii ; -
25
M27
30
220
540
60
M 16
15
230
545
35
create difficulties. anJ indeed ii
Resistance Connection detail (nun)
End-plate: S235 (mm) Pp
1PE600
') The bolt spacing docs η
"1
"1
af
J
j,mi
^j,ini'2
Shear (kN) VRd
failure mode Code
Refereiice lengdi(m) L
bb
L|JI
M20
20
230
555
45
95
340
75
40
120
55
20
5
8
84397
42199
232.1
154.7
255
6.7-R
S
M24
25
230
570
50
115
320
85
50
130
50
20
5
8
89665
44832
316.9
211.2
367
EPT
6.3-R
S
30
230
590
60
135
300
95
60
140
45
20
5
8
93441
46720
363.6
242.4
477
BFC
6.1-R
S
240
595
35
ITO
380
80
40
110
65
20
6
9
91689
45844
161.2
107.5
163
EPT
8.8-R
S
605
45
ITO
380
80
40
120
60
20
6
9
10.3070
51535
263.7
175.8
255
EPI
7.9-R
S
90
50
130
55
20
6
y
109324
54662
359.9
239.9
367
EPT
M16 M20
IPE550
l'l
Moment kNm) MRd 2/3M R d
EPI'
M27 IPE5TO
c
Rotational stiffness (kNm/rad)
Welds (mm)
15 20
240
M24
25
240
620
50
120
360
7.4-R
S
M27
30
240
640
60
140
340
ITO
60
140
50
20
6
y
113774
56887
441.8
294.5
477
CWC
7.1-R
S
M16
15
250
645
35
ITO
430
80
40
110
70
20
6
y
109185
54593
179.5
119.7
163
EPT
10.3-R
M20
20
250
655
45
ITO
430
80
40
120
65
20
6
9
122248
61124
293.7
195.8
255
EPT
9.2-R
M24
25
250
670
50
120
410
90
50
130
60
20
6
9
129536
64768
400.2
266.8
367
EPT
8.7-R
M27
30
250
690
60
140
390
ITO
60
140
55
20
6
y
134715
67357
487.0
324.6
477
CWC
8.4-R
M16
15
260
695
35
ITO
480
80
40
110
75
20
/
10
128698
64349
201.4
134.3
163
EPT
12.0-R
M20
20
2«)
705
45
ITO
480
80
40
120
70
20
Ί
10
143043
71521
327.8
218.5
255
EPT
10.8-R
120
460
90
50
130
65
20
1
10
151417
75709
444.0
296.0
367
EPT
10.2-R
140
440
ITO
60
140
60
20
7
10
157341
78670
533.0
355.3
477
CWC
y.8-R
s s s s s s s s
M 24
25
260
720
50
M27
30
260
740
60
i to bc ìgnoicd in [his situation.
3. WORKED EXAMPLE
Hand calculation of the stiffness a n d resistance of b e a m to column extended end plate connection M16hr88
25 90 25 35 90
+
+
I
40
( — >
+
+
305
120
+
60
■
'
M
A -.-10 !
L
HEB140
140
Preliminary caculation Column
d,.c =h c -2tf.'Α -2r=\40-2x\2-2x\2
+(lH, + 2 r c ) = 4 2 9 5 . 6 ( 2 x l 4 0 x l 2 ) + (7 + 2 x l 2 ) x l 2 = 1307.6mm2
An. = A L.2¿Vy, w1, m=
e=
0,8/; =
Ί
bc-w 2
= 92mm
907
0.8 χ 12 = 3 \,9mm
2 =
140-90 2
= 25mm
„,,„ = 0.25^=0.25 121^1= 7691 Nmm / ' ■
γ
mm
11 1
Ι Λ-/0
·1
beam h = hh - t lh = 220 9.2 = 210,8/7?/?/
^„ Λι ,/', Λ
McM (class sectionl) =
285406x235 x l Ο
Χ Λ/Ο
M
end plate m = w, Q,%4laf
= 40 0,8 χ V2 χ 5 = 34.34/«/??,
e = ijmm
η η AK
mO 5 )'* 2 3 5
/;/./) = 0,2:> ~ — = 0,25 //?„,„ / Λ /()
ν
.2017Nmm
1.1
344
I mm
■ 60.97 kNm.
Bolts
Ft Rd
0.9fubAs
0.9 χ 800 χ 157 χ IO"3
ï f\íb
1.25
■ 90 A kN
Fr Kd (shear plane passes by threaded part) =
0,6./,/Λ4 ï Μ
Lh = tfc.
0,6 χ 800 χ 157χ IO'3 = 60,3/c/V 1,25
1 0,5(hbnl, + //„,„ ) = 12 +15 + (10 +15) = 39,5 mm
+!ρ+
d =23,16//?//7 COLUMN WEB PANEL IN SHEAR Resistance
0,9Avcfywc
0,9 χ 1307.6 χ 235 χ IO"3
lòy υ»
1.1 χ v3
■.Rd
= 145,2/c/V
ß=l(hyp) V ^
/
,
145 ?
=
^
=
ß
'
■
-
1
Stiffness
/c, =
0.385 Λ,., βh
=
0,385x1307,6
O0OO
= 2.388/77777
X210.8
COLUMN WEB IN COMPRESSION Resistance
V.c
=min
t β, + 2α7 V2 + 2/, + 5(//( + s), tjh +afJ2+
tp + u + S(tfi. + s)
= mm 9.2 + 2 χ 5 xV2 +2 χ 15 + 5(12 + 12);9,2 + 5x -J2 +15 + 10 + 5(12 + 12)= 161,27/77/77
/c. = min 1,0; 1 , 2 5 0 , 5 ^
= l(M
V l'HX
ß=\{hyp) = 0,7
Pc =
^ + 1.3(Mvrw.A,M.J
^1 +1.3 Ixl61,27x :307,6
345
,
fZÃfZ _
1.61.27x92x235 _
V
V 210000x7x7
=
ß...
^/.2 = *,,, P, V . /,, ./n,(. / r Mn = 1 x 0,71 χ 161.27 χ 7 χ 235 χ 1 < % Stiffness
Λ:, =
0Jbcífwcctwc V dc
0,7x161,27x7 =
= 8,589//7//7 92
BEAM FLANGE IN COMPRESSION Resistance
^ . 3 = K-,d % ^ ) =
60.97 o3=289'2^
2108xl
Stiffness /c3=oo BOLTS IN TENSION Resistance F
Rd .4 = 4 A . / w = 4 x 90,4 = 361,6/c7V
Stiffness
A 157 A =3.2 ~ = 3.2x = 12,719/77/7? A, 39,5
COLUMN WEB IN TENSION /?e5/5/o/r7ce
/3t# ,K., = min [4^777 ; 8//7 + 2.5cj ; /J + 4//? + l,25e] = min(4/rx31,9;8x31,9 + 2,5x25;90 + 4x31,9 + l,25x25) = 248,85/??/7i ß = Hhyp)
' " \| 1 + U ( / ? ^ „.,, /„, / Λ,.,)2 ~ \' 1 + ί · 3 ! 2 4 8 ' 8 5 x
P
7
/1306-7)2
^ / , = A V - , Ήν ./'·,, / ï M,, = 0.55 χ 248.85 χ 7 χ 235/1.1 = 204,6ttV
346
=
]71,2^
Stiffness
k, =
WKjfKoK* — d.
0.7x248.85x7 — = 1 3.254/77 777 92
=
COLUMN FLANGE IN TENSION Resistance
/ ί # .Λ,=^/,,,=248.85//7//7 η = min e;l,25m;[bp-w)/2
= min(25; l,25x 31,9 ;25) = 25mm
23.16 e =d 14-
-5,79mm 4
k, = \{hyp) (Sn-2e)lefffclkfcmplfc (δχ 252x5,79Ìx248,85x 1 χ 7691 F/cMM = — V jc^pi.fi =\__ _ _ _ x io'=284,9/(7V 2mn-eK\m + n) 2x31,9x255,79(31,9 + 25) k m l K/f.fc, i.fcpl.j + 4 B,Rd n eff Jet fc 'vPfc" m +n
2
F.fc.Rd.ll
'
F
m Ì n
Rd.6
=
*'fc.Rdjl
*'fc.Rd.l2
'
2 x 248,85χ 1 χ 7691 + 4 χ 90,4 χ 25 χ 103 31,9 + 25
χ 10"' = 226,2 kN
= 226.2kN
Stiffness
0$5lejrfiirfl. kh = —5— 777
0,85x248,85x(l2)J — — — — = 1 1,260/77/77 (31,9) λ
ENDPLATE INTENSION Resistance
V p . ' = m i n 4τυηρ ; Smp + 2.5e/; ; w + 4m + l,25ep ; b = {4π χ 34,34:8 χ 34.34 + 2,5 χ 25;70 + 4 χ 29,34 +1,25 χ 35; 140) = 140/77/7? ; 1,25/τ?,, ] = (25 ; 1.25 χ 34.34) = 25/72/7?
η = min
8/7 2 e „ , / Kn.Rj.i=
2mpnp-eu(mp+np) 2
.'« Rd.2
/??
Kji .„., mpi ρ + 4 niKd "Ρ
'",,+",,
(8χ252χ5,79)χ 140x12017 <
~
X i 1 1
2 x 3 4 . 3 4 x 3 5 5 , 7 9 ( 3 4 . 3 4 + 25) 2 χ 1 4 0 χ 1 2 0 1 7 + 4 χ 9 0 , 4 χ 10 3 χ 25
34.34 + 235
347
10"3 = 231,1 kN
F
RJ.l=min[
F
fp.Rdj'>Fcp.Rd.2\=225¿kN
Stiffness
0 , 8 5 / , „,/ 3 k, =
å
^
J L
0,85χ140χ(ΐ5) 3 = ^—
%
3 ^ = 9.91 5/77/77
(34,34)"
MOMENT RESISTANCE OF THE JOINT
F y w =min[F / w J = 145,2/c/V Plastic design moment resistance :
MRd = FRil h = 145,2 χ 210,8 χ 10"3 = 30,6kNm Elastic moment resistance :
2 2 Me = M, w = χ 30,6 = 20,4kNm STIFFNESS OF THE JOINT Initial stiffness
, Λ^ 210000X 210,8 "xlO" 6 2 SliHi = Eh /\ \k, = = 10617 kNm '■"" tt' ' 1/2.388+1/8.859 + 1/12,719+1/13,254+1/11.268+1/9,915 Secant stiffness
Sj=SJim/2
= 5309kNm
348
CHAPTER 3.a
STIFFNESS AND RESISTANCE
CALCULATION
FOR BEAM-TO-COLUMN JOINTS WITH FLUSH END-PLATE CONNECTIONS
1.
Calculation procedure
2.
Design tables
3.
Application example
349
1. CALCULATION PROCEDURE
Ch.3.a - Beam-to-column joint with flush end-plate
Mechanical characteristics Ultimate stresses
Yield stresses Beam web Beam flange Column web Column flange Endplate Bolts
_vwh
tyfb
1
vfc
'ufe 'up
If hotrolled profiles : fvwc = f fc and f
b
= f 'y lb
Geometrical characteristics Joint
| M = F.h
Column fc
\J
wc
fc
m 0,8 r,
l
w
r"
Avc = Ac 2 bc tfc + ( ^ + 2 rc ) tfc with Ac = column section area Beam
IY
m ■0.8\/2a,
End-plate m
1
«p J? rO.SVTaw 0,8\^2a l
w s = \/2 ac for a welded section
Avc = ( 1\ 2 tfc ) t^
aztVb
r~c
wc
s = rc for a rolled section
wb
J£ w
Bolts d„:
see figure or = d, if no washer
A. :
resistance area of the bolts
352
Ch.3.a - Beam-to-column joint with flush end-plate
RESISTANCE
STIFFNESS Column web panel in shear
0,385 Av
with
0,9 A
V
1
vc
βΛ
β =
J
f yew
/3 yMo
1 for one-sided joint configurations; · 0 for double sided joint configurations symetrically loaded; 1 for double-sided configurations non-symetrically loaded with balanced moments; 2 for double-sided joint configurations non-symetrically loaded with unbalanced moments.
For other values, see 1.2.2.1 in chapter 1.
Column \veb in compression
0,7 b ef/.wctc
FDJ^ - k Rd>2
wc
ρ b „ wc ~c
e/f.wc,c
t f
/Υ„
if λ
< 0,67
wc Jywc
J
**Rd,2 ~
* Alo 7
wc
1
k
wc
P c "eff.wcc
'M-C / y w c ' y
λ,
0 22 (
~γ
if λ J
ith λ
b „
= 0,93
k
wc
> 0,67 wc
d Jf
ejj.wc,c
c
VMc
= min [1,0 ; 1,25 0 , 5 ^ ] WC
L
>
'*'ΎΜΟ
À
wc
i
ï
( *)
J
V
/
J ywc
pc= 1 = Pc, = Pc,
,/β=0 if ß = ι '7 ß = 2 ι
where
ρ, f
cl
i/l
+
1,3 (b ,, ejj.wc ,c
V
Pc; =
1 + 5,2 (b „ 1
o n wc :
b „ e/fwc.c
/ A
wc
/V
v
ejj.wc ,c
t
I A
wc
- ι
-' 5(/, + s)
ρ
je
>
(*) see 1.2.2.2 in chapter 1.
Beam flange in compression
F
w
Mc
353
Rd
f vc '
f vc '
normal stresses in the column web at the root of the fillet radius or of the weld
= t, 12 - a.sil β,
't
1
= McM
l(hb-
U)
: beam design moment resistance
Ch. 3. a - Beam-to-column joint withflushend-plate Bolts in tension
A
k4 = 1,6 -L L
FRÍA
2
=
B
»ith
..Rd
B
tM
=
F,M
t,
ü
r t.Rd
· 9L·A, 'Af*
Column web in tension
*5
0,7 b ,, 1
, t
ejj.wc,{
wc
** Rd,5
cl
~
P< "eff.wcj
w/'í/j
p(= 1
Ύ Mo
'ƒ β = 0
'- P„ = Ρ,.,
1 ι ι
ƒ ι
> »»
W f It f C
'/ß = l '/ß =2
>
/ ~ \
1
—
\-' ,ι
,/l
' 1,3 ν(ό ,,
V η μ
ρ
- 5,2 (b „
V
ef/wc,t
*6
wc
1
-
'
/ Λ ):
r
effwc.t
,/l
Column flange in bending
wc *ywc
c
/ /f ) ;
/
effyvc.t
ve'
wc
vc '
min [ 2nm ; 4m + 1,25e ]
_ °' 85 W , r 'A
m
^«¿,6
m3
i
n
l ? fcJid.tl '■> ric.Rd.t2
(8« 2e ) / _ , fcRd.tl
1
m ,,
,
.
jt
2m/i e (m + rc) k Rd.t: rr
e
fffc,t
'/ö„/c
/C/L. = 1 -- (Vyfc-
8 0
'
m , . k,
2 / „, _
pl fc
£
1 8 0
Ni™™2
a„.fc > / Vffc-
;ƒ σ , > 180 J n.fc
o Iltc :
n
- m i n Γ e ; 1,25m ; e 1 .
'
ρ '
= dw I 4
m , , = 0.25 i , Λ / v . . pi/c
W.<
**«,
(**) see 1 "> ~> 3 in chapter 1
354
t.Rd
(**)
360 ) < 1 N/mm2
normal stresses in the centroïd of the column flange
L
ew
+ A Β ... n
fc
m + «
.
/c -ty/c
' Af o
Ch. 3.a - Beam-to-column joint with flush end-plate End-plate in bending
1.
-
0,85 / „ , tl '
'ffP,t
m
F „ , , = min [ F
Ρ
Rd.l
r»
'
„,, ; F
ep.Rd.l
'
(8n - 2e ) / ,, epRd.X
n
2m . η
ρ
2 /'ffp.t „
_ ep Rd.2
η
pi p
'ffP.t
,
+ 2 Βt Rd .., η ρ +
η
ρ
- min [ e ; 1,25m , ; e 1
m ,
l
.
e (m , + « )
mpip, ρ\
= 0,25 r ƒ p
J
/ γ.,
yp
' Mo
- min LΓ 2Um , ; am , 1 p 1 '
PI
where a s defined in the annexed table
Beam web in tension
k
s = °°
**Λιί,8
"effwb.t
JOINT
wh *ywb
'
FRi = min [ FRi. ]
S.. . = E h1 1 V Mk. i-j
Nominal stiffness :
" eff.wbj
'ffp.t
Initial stiffness : Jjnl
~
li
S.J = S..j.·»·. I 2
ι
Plastic design moment resistance : M
Rd = f M
Elastic moment resistance :
¡MRd
355
'
m,
.
-
m
„,, I
ep.Rd.L
h
Y Ai»
Ch.3.a - Beam-to-column joint with flush end-plate
6 2Π
5 ü,5 M 5,5 I 4,75 4.45
Oí
X 1.3 1.2 1,1
10 0.9 0,8 0,7 0,6 0,5 0,4 0,3 0.2 0,1
0
K -
0,1 0,2 0,3 0,4 0,5 0,6 0.7 0,8 0,9
m pi m . + e pi
m 1
R rO.evTaw
ρ
0,8V~2¡
m P2
λ.
m Ρ 2'
m . + e p\
^
+
ρ
α values to evaluate the dessign resistance of the endplate in tension 356
2. DESIGN TABLES
ß =l Wi
W
Wi
Failure mode
Ρ
+
OO OO' ι—
JZ
_2
ra ca
o
+ + J T>1 U—
ca
C o l u m n w e b in compression
+
't
Jß ~Õ
V
,—h
Η
C o l u m n weh panel in shear
M
'V
vv
Code
Failure mode
CWS
C o l u m n w e b in tension
CWC
Beam flange in compression Bolts in tension
C o l u m n flange in tension
Code
k.. =:
.10
y MO
γ
CWT
' Mb
= ι1 25 ·
CFT
End plate in BFC BT
EPT
tension Beam w e b in tension
BWT
a. Resistance S235 l
HEB 140
HEB 160
b
h
140
206
50
120
50
p
Pp
Rotational stiffness (kNm/ rad)
Moment (kNm)
Shear (kN)
Failure mode
wj
aw
af
°j,ini
^ j , ini'2
MRd
2/3M R d
'Rei
Code
90
25
3
5
5906
2953
20.2
13.5
157
e
l>l
Referenee length(m) L
bb
L
bu
IPE220
M16
15
CFT
7.9R
S
IPE240
M16
15
140
226
50
140
50
90
25
4
5
7164
3582
22.7
15.1
157
CFT
9.1R
S
IPE270
M16
15
140
254
55
160
55
90
25
4
6
8789
4395
25.7
17.1
157
CFT
S
S
IPE220
M16
15
140
206
50
120
50
90
25
3
5
7037
3518
22.7
15.1
157
CFT
6.6R
S
IPE240
M16
15
140
226
50
140
50
90
25
4
5
8584
4292
25.4
16.9
157
CFT
7.6R
S
1PE270
M16
15
154
254
55
160
55
90
32
4
6
10669
5335
29.8
19.9
157
CFT
9.1R
S
M20
20
154
254
55
160
55
90
32
4
6
11928
5964
41.0
27.3
245
CWS
8.2R
S
M16
15
160
284
55
190
55
90
35
4
6
13298
6649
34.5
23.0
157
CFT
10.6R
S
M20
20
160
284
55
190
55
90
35
4
6
14748
7374
46.8
31.2
245
CWS
9.5R
S
M16
15
160
312
55
220
55
90
35
4
6
16040
8020
38.8
25.8
157
CFr
12.3R
S
M 20
20
160
312
55
220
55
90
35
4
6
17688
8844
52.6
35.1
245
CWS
11.2R
S
IPE220
M16
15
140
206
50
120
50
90
25
3
5
7388
3694
24.1
16.1
157
EPT
6.3R
S
IPE240
M16
15
140
226
50
140
50
'70
25
4
5
9044
4522
27.2
18.1
157
EPT
7.2R
S
IPE270
M16
15
154
254
55
160
55
'70
32
4
6
11287
5643
32.4
21.6
157
CFT
8.6R
S
M20
20
154
254
55
160
55
90
32
4
()
12731
6366
43.6
29.1
245
CFT
7.6R
S
M16
15
170
284
55
190
55
90
40
4
6
14185
7093
37.4
24.9
157
CFT
9.9 R
S
M20
20
170
284
55
190
55
90
40
4
6
15837
79 ÍS
50.9
33.9
245
CFT
8.9R
S
M16
15
180
312
55
220
55
90
45
4
6
17229
8615
42.0
28.0
157
CR'
11.5R
M20
20
180
312
55
220
55
90
45
4
6
19090
9545
57.1
38.1
245
CFT
10.4R
s s
M24
20
180
312
65
200
65
110
35
4
6
17012
8506
58.3
38.8
352
CWS
11.6 R
S
342
55
250
55
'XI
45
5
7
20508
10254
46.6
31.0
157
CFT
13.3 R
s
IPE300
1PE330
HEB 180
P
p
Welds (mm)
Connection detail (mm)
Endplate: S235 (mm)
1PE300
1PE330
1PE360
M16
15
180
Resistance
M20
hp
Ρ
Pp
20
180
342
55
250
Shear (kN)
Failure mode
Reference length(m)
\v
"1
a„
af
aS·
■ j,ini
^j,ini'2
MRd
2/3MRd
VRd
55
90
45
5
7
22537
11268
63.4
42.3
245
CFT
12.1R
S
65
110
35
5
7
20303
10152
64.9
43.2
352
CWS
e
pl
Code
L
bb
L
bu
M24
20
180
342
65
13.5R
S
M16
15
180
380
55
290
55
90
45
5
7
24958
12479
52.7
35.2
157
CFT
15.6R
S
M20
20
180
380
.ss
290
55
'XI
45
5
/
27267
13633
71.8
47.9
245
CFT
14.3R
S
M24
20
180
380
65
270
65
110
35
5
7
24827
12414
73.8
49.2
352
CWS
15.7R
1PE220
M16
15
140
206
50
120
50
'70
25
3
5
7955
3977
24.1
16.1
157
EPT
5.9R
IPE240
M16
15
140
226
50
140
50
90
25
4
5
9783
4891
27.2
18.1
157
EPT ·
6.7R
254
55
160
55
90
32
4
6
12271
6136
32.4
21.6
157
EPT
7.9R
32
4
6
14017
7009
46.9
31.2
245
s s s s s s s s s s s s s s s s s s s s s s s s s s s s s s
IPE270
1PE300
IPE330
1PE360
IPE4CX)
1PE450
IPE500
HEB220
bp
Moment (kNm)
230
IPE400
HEB200
'ρ
Rotational stillness (kNm/rad)
Wc Ids (min)
Connection t etail (mm)
Hue plate: S 235 (muil
M16
15
154
M20
20
154
254
55
160
55
90
CFT
6.9R
M16
15
170
284
55
190
55
90
40
4
6
15514
7757
38.9
25.9
157
EPT
9.0R
M20
20
170
284
55
190
55
'Χ)
40
4
6
17534
8767
53.7
35.8
245
CFT
8.0R
M16
15
180
312
55
220
55
'Χ)
45
4
6
18939
9470
44.8
29.9
157
EPT
10.4R
M20
20
180
312
55
220
55
90
45
4
6
21239
10620
60.3
40.2
245
CFT
9.3R
M24
20
180
312
65
200
65
110
35
4
6
19567
9783
69.5
46.3
352
CFT
10.1R
M16
15
200
342
55
250
55
90
55
5
7
22655
11328
50.1
33.4
157
EPT
12.1R
55
90
55
5
7
25187
12594
66.9
44.6
245
CFT
10.8R
M20
20
200
342
55
250
M24
20
200
342
65
230
65
110
45
5
7
23573
11786
79.6
53.0
352
CWS
11.6R
M16
15
200
380
55
290
55
90
55
5
7
27719
13860
56.7
37.8
157
EPT
14.0 R
M20
20
2(X)
380
55
290
55
90
55
.s
7
30632
15316
75.7
50.5
245
CFT
12.7R
M24
20
200
380
65
270
65
110
45
5
7
28916
14458
90.5
60.3
352
CWS
13.4R
M16
15
200
428
55
340
55
90
55
5
8
34464
17232
65.0
43.3
157
EPT
16.4R
M20
20
200
428
55
340
55
90
55
5
8
37829
18915
86.8
57.9
245
CFT
15.0R
M24
20
200
428
65
320
65
110
45
5
8
36022
18011
104.1
69.4
352
CWS
15.7R
200
476
60
380
60
100
50
6
y
40092
20046
71.1
47.4
157
CFT
S
60
380
60
100
50
6
9
44134
22067
95.5
63.6
245
CFT
18.3R
70
360
70
120
40
6
9
40958
20479
111.5
74.3
352
'CFT
19.8R
90
25
3
5
8023
4012
24.1
16.1
157
EPT
M16
15
M20
20
200
476
M24
20
200
476
IPE220
M16
15
140
206
50
120
50
IPE240
M16
15
140
226
50
140
50
90
25
4
5
9896
4948
27.2
18.1
157
EPT
IPE270
M16
15
154
254
55
160
55
90
32
4
6
12458
6229
32.4
21.6
157
EPT
M20
20
160
254
55
160
55
100
30
4
6
14237
7118
47.5
31.7
245
CET
6.8R
M16
15
170
284
55
190
55
90
40
4
6
15814
7907
38.9
25.9
157
EPT
8.9R
M20
20
170
284
55
190
55
100
35
4
6
17887
8943
55.2
36.8
245
CFT
7.8R
M16
15
180
312
55
220
55
90
45
4
6
19378
9689
44.8
29.9
157
EPT
10.2R
M20
20
180
312
55
220
55
100
40
4
6
21785
10893
62.8
41.9
245
CFT
9.1R
IPE300
IPE330
·) The Nili spjJi
aeaic diltkullicv jtiJ itiJcrcJ it
5.8R 6.6R '
7.8R
Resistance Eni -plate: S235 (mm) 'ρ
We Ids
Rotational stiffness
(mm)
(mm)
(kNm/rad)
bp
bp
Ρ
Pp
e
pi
w
"1
aw
af
s
j,ini
Sj,ini'2
Moment (kNm) 2/3MRd MRd
Shear (kN) v
Failure mode
Rd
Code
Refere ice length(m) L
bb
L
bu
M24
20
190
312
65
200
65
120
35
4
6
19792
9896
69.8
46.5
352
,CFT
10.0-R
S
M16
15
210
342
55
250
55
90
60
5
7
23263
11632
50.1
33.4
157
ΈΡΤ
11.7-R
S
M20
20
210
342
55
250
55
KK)
55
5
7
26031
13015
69.6
46.4
245
CFT
10.5-R
M24
20
210
342
65
230
65
120
45
5
7
24008
12004
82.3
54.9
352
CFT
11.4-R
M16
15
220
380
55
290
55
90
65
5
7
28583
14292
56.7
37.8
157
EPT
I3.6-R
M20
20
220
380
55
290
55
100
60
5
/
31798
15899
78.9
52.6
245
CFT
12.2-R
M24
20
220
380
65
270
65
120
50
5
7
29692
14846
95.8
63.9
352
CFT
13.1-R
M16
15
220
428
55
340
55
90
65
5
8
35710
17855
65.0
43.3
157
EPT
15.9-R
M20
20
220
428
55
340
55
ITO
60
5
8
39466
19733
90.4
60.3
245
CFT
14.4-R
M24
20
220
428
65
320
65
120
50
5
8
37200
18600
110.2
73.5
352
CFT
15.2-R
M16
15
220
476
60
380
60
ITO
60
6
9
42225
21112
72.4
48.3
157
EPT
19.2-R
M20
20
220
476
60
380
60
ITO
60
6
9
46815
23408
100.7
67.2
245
CFT
17.3-R
M24
20
220
476
70
360
70
120
50
6
9
44401
22200
123.1
82.1
352
CFT
18.2-R
M16
15
220
524
60
430
60
ITO
60
6
9
50074
25037
80.7
53.8
157
EPT
S
M20
20
220
524
60
430
60
100
60
6
9
55178
27589
112.2
74.8
245
CFT
20.4-R
M24
20
220
524
70
410
70
120
50
6
9
52642
26321
137.6
91.7
352
CFT
21.4-R
M16
15
220
572
60
480
60
ITO
60
7
10
58523
29261
88.9
59.3
157
EPT
S
M20
20
220
572
60
480
60
100
60
7
10
63978
31989
123.7
82.5
245
CFT
S
M24
20
220
572
70
460
70
120
50
7
10
61412
30706
151.9
101.3
352
CFT
S
IPE220
M16
15
140
206
50
120
50
90
25
3
5
8238
4119
24.1
16.1
157
EPT
5.7-R
IPE240
M16
15
140
226
50
140
50
90
25
4
5
10199
5099
27.2
18.1
157
EPT
6.4-R
IPE270
M16
15
154
254
55
160
55
90
32
4
6
12895
6447
32.4
21.6
157
EPT
7.5-R
M20
20
160
254
55
160
55
ITO
30
4
6
15047
7524
50.3
33.5
245
CFT
6.5-R
M16
15
170
284
55
190
55
90
40
4
6
16451
8226
38.9
25.9
157
EPT
8.5-R
M20
20
170
284
55
190
55
ITO
35
4
6
18997
9498
58.2
38.8
245
CFT
7.4-R
M16
15
180
312
55
220
55
90
45
4
6
20252
10126
44.8
29.9
157
EPT
9.8-R
55
220
55
ITO
40
4
6
23241
11620
65.4
43.6
245
CFT
8.5-R
s s s s s s s s s s s s s s s s s s s s s s s s s s s s s s s s
IPE360
1PE400
IPE450
IPE500
IPE550
IPE600
HEB240
Connection detail
IPE300 IPE330
IPE360
1PE4(X)
M20
20
180
312
M24
20
190
312
65
200
65
120
35
4
6
21965
10983
75.3
50.2
352
CFT
9.0-R
M16
15
210
342
55
250
55
90
60
5
7
24419
12209
50.1
33.4
157
EPT
11.2-R
M20
20
210
342
55
250
55
ITO
55
5
7
27890
13945
72.6
48.4
245
CFT
9.8-R
M24
20
210
342
65
230
65
120
45
5
7
26753
13376
87.9
58.6
352
CFT
10.2-R
M16
15
220
380
55
290
55
90
65
5
7
30160
15080
56.7
37.8
157
EPT
12.9-R
M 20
20
220
380
55
290
55
ITO
TO
5
7
34237
17118
82.2
54.8
245
CR'
11.3-R
220
380
65
270
65
120
50
5
7
33206
16603
101.0
67.3
352
CFT
11.7-R
M24 ') Tlir- holi sp.iLitiL' dix
20
ι he igmircd in tins «.iiuaiu
Resistance
1PE450
M16 M20 M24
IPE5TO
1PE550
IPE600
HEB260
IPE220
\\
"1
aw
af
55
90
70
5
8
37902
55
ITO
65
5
8
42725
320
65
120
55
5
8
41857
60
ITO
70
6
9
'ρ
bp
hp
P
Pp
«pi
15
230
428
55
340
20
230
428
55
340
230
428
65
20
94.2
20928
45477
43.3
157
; EPT
15.0R
S
62.8
245
CFT
13.3R
S
116.2
77.5
352
CFT
13.5R
S
22739
72.4
48.3
157
EPT
L
bb
L
bu
476
60
17.8R
S
240
476
60
380
TO
100
70
6
9
50916
25458
105.0
70.0
245
CFT
15.9R
S
M24
20
240
476
70
360
70
120
60
6
9
50176
25088
129.9
86.6
352
CFT
16.1R
S
M16
15
240
524
60
430
TO
ITO
70
6
9
54181
27090
80.7
53.8
157
EPT
20.8R
S
M20
20
240
524
ω
430
60
ITO
70
6
9
60285
30143
117.0
78.0
245
C FI"
18.7R
S
M24
20
240
524
70
410
70
120
60
6
9
59624
29812
145.1
96.7
352
CFT
18.9R
S
M16
15
240
572
60
480
60
ITO
70
7
10
63611
31805
88.9
59.3
157
EPT
S
S
M20
20
240
572
60
480
60
ITO
70
7
10
70197
35098
128.9
85.9
245
CFT
22.0R
M 24
20
240
572
70
460
70
120
60
7
10
69672
34836
160.2
106.8
352
CFT
22.2R
M16
15
150
206
50
120
50
ITO
25
3
5
8076
4038
23.7
15.8
157
EPT
5.8R
ITO
25
4
5
10039
5020
26.7
17.8
157
EPT
6.5R
ITO
27
4
6
12649
6324
30.6
20.4
157
EPT
7.7R
6
15125
7563
51.1
34.1
245
CFT
6.4R
s s s s s s s s s s s s s s s s s s s s s s s s
50
140
1PE270
M16
15
154
254
55
160
55
M20
20
170
254
55
160
55.
110
30
4
M16
15
170
284
55
190
55
ITO
35
4
6
16278
8139
37.2
24.8
157
EPT
8.6R
M20
20
170
284
55
190
55
110
30
4
6
19105
9552
58.3
38.9
245
CFT
7.3R
M16
15
180
312
55
220
55
ITO
40
4
6
20174
10087
43.2
28.8
157
EPT
9.8R
M 20
20
180
312
55
220
55
110
35
4
6
23502
11751
66.3
44.2
245
CFT
8.4R
20
190
312
65
200
65
120
35
4
6
22921
11461
76.9
51.3
352
EPT
8.6R
55
250
55
ITO
55
5
7
24615
12308
50.1
33.4
157
EPT
11.IR
55
250
55
110
50
?
7
28500
14250
74.1
49.4
245
CFT
9.6R
45
5
7
28012
14006
91.6
61.1
352
CFT
9.8R
5
7
30539
15269
56.7
37.8
157
EPT
12.7R
M24 M16
15
210
342
M20
20
210
342
M24
20
210
342
65
230
65
120
M16
15
220
380
55
290
55
ITO
60
M20
20
220
380
55
290
55
110
55
5
/
35139
17570
83.9
56.0
245
CFT
11.1R
M24
20
220
380
65
270
65
120
50
5
7
34895
17448
104.1
69.4
352
CFT
11.IR
15
230
428
55
340
55
ITO
65
5
8
38574
19287
65.0
43.3
157
EPT
14.7R
230
428
55
340
55
110
60
5
8
44070
22035
96.2
64.1
245
CFT
12.9R
120
55
5
8
44166
22083
119.8
79.9
352
CFT
12.8R
M16 M20
IPE550
65.0
Code
240
226
IPE500
18951 21362
M
VRd
^jjini'^
15
150
IPE450
2/3MRd
j,ÌJlÌ
Reference length(m)
20
15
IPE4TO
Rd
S
Failure mode
M20
M16
IPE360
Shear (kN)
M16
IPE240
IPE330
Moment (kNm)
380
50
1PE3TO
Rotational stiffness (kNm/rad)
Wi Ids (nun)
Connection ι etail (nun)
Eni plate: S 235 (nun)
20
M24
20
230
428
65
320
65
M16
15
240
476
60
380
60
ITO
70
6
9
46579
23289
72.4
48.3
157
EPT
17.4R
M20
20
240
476
60
380
60
110
65
6
9
52758
26379
107.2
71.5
245
CFT
15.3R
M24
20
240
476
70
360
70
120
60
6
9
53126
26563
133.9
89.3
352
CFT
15.2R
M16
15
250
524
60
430
60
ITO
75
6
9
55723
27861
80.7
53.8
157
EPT
20.2R
ι The h d t .pjuinL Joes nol m n i p i v vit
r t l i m i llta.1 υill he pmleulcil fron) ι
Resistance EIK
'ρ
Ρ
(mm)
(kNm/rad)
Pp
epl
w
WJ
a, v
110
70
a
Moment (kNm) M 2/3MRd Rd
f
s
j,ini
^j,ini'2
6
9
62729
31364
119.5
Shear (kN)
Failure mode
VRd
Code
Reference lengdi(m) L
bb
L
bu
20
250
524
60
430
79.6
245
CFT
18.0-R
S
M24
20
250
524
70
410
70
120
65
6
9
63334
31667
149.6
99.7
352
CFT
17.8-R
S
M16
15
260
572
60
480
60
ITO
80
7
10
65678
32839
88.9
59.3
157
EPT
23.6-R
S
M20
20
260
572
60
480
60
110
75
7
10
73352
36676
131.6
87.8
245
CFT
21.1-R
S
M24
20
260
572
70
460
70
120
70
7
10
74241
37120
165.1
110.1
352
CFT
20.8-R
S
IPE220
M16
15
150
206
50
120
50
ITO
25
3
5
8022
4011
23.7
15.8
157
EPT
5.8-R
S
1PE240
M16
15
150
226
50
140
50
ITO
25
4
5
9989
4994
26.7
17.8
157
EPT
6.5-R
S
1PE270
M16
15
154
254
55
160
55
ITO
27
4
6
12612
6306
30.6
20.4
157
EPT
7.7-R
S
M20
20
170
254
55
160
55
110
30
4
6
15160
7580
51.6
34.4
245
EPT
6.4-R
S
M16
15
170
284
55
190
55
ITO
35
4
6
16269
8135
37.2
24.8
157
EPT
8.6-R
S
M20
20
170
284
55
190
55
110
30
4
6
19201
9600
59.0
39.4
245
EPT
7.3-R
S
M16
15
180
312
55
220
55
ITO
40
4
6
20211
10105
43.2
28.8
157
EPT
9.8-R
S
M20
20
180
312
55
220
55
110
35
4
6
23681
11841
67.9
45.2
245
CFT
8.3-R
S
M24
20
190
312
65
200
65
120
35
4
6
23186
11593
76.9
51.3
352
EPT
8.5-R
S
M16
15
210
342
55
250
55
ITO
55
5
7
24717
12358
50.1
33.4
157
EPT
11.1-R
S
M20
20
210
342
55
250
55
110
50
5
7
28792
14396
75.7
50.5
245
CFT
9.5-R
S
M24
20
210
342
65
230
65
120
45
5
7
28411
14206
92.7
61.8
352
EPT
9.6-R
M16
15
220
380
55
290
55
ITO
60
5
7
30752
15376
56.7
37.8
157
EPT
12.6-R
M20
20
220
380
55
290
55
110
55
s
7
35608
17804
85.7
57.2
245
CET
10.9-R
M24
20
220
380
65
270
65
120
50
5
7
35504
17752
105.9
70.6
352
C ΓΓ
10.9-R
M16
15
230
428
55
340
55
ITO
65
5
8
38974
19487
65.0
43.3
157
EPT
14.5-R
M20
20
230
428
55
340
55
110
60
5
8
44816
22408
98.3
65.5
245
CFT
12.6-R
M24
20
230
428
65
320
65
120
55
5
8
45100
22550
121.8
81.2
352
CFT
12.6-R
M16
15
240
476
60
380
60
ITO
70
0
9
47198
23599
72.4
48.3
157
EPT
17.2-R
380
60
110
65
6
9
53814
26907
109.5
73.0
245
CFT
15.0-R
s s s s s s s s s s s s s s s s s s
IPE330
IPE360
IJ
IPE400
IPE450
1PE500
IPE550
IPE600
HEB3TO
bp
Rotational stiffness
M20
IPE300
'Jj
bp
We Ids
60
1PE600
HEB280
Connection detail (mm)
-plate: S235 (mm)
M20
20
240
476
60
M24
20
240
476
70
360
70
120
60
6
9
54416
27208
136.1
90.7
352
CFT
14.9-R
M16
15
250
524
60
430
60
ITO
75
6
9
56627
28314
80.7
53.8
157
EPT
19.9-R
M20
20
250
524
60
430
60
110
70
6
9
64175
32088
122.0
81.3
245
CFT
17.6-R
M24
20
250
524
70
410
70
120
65
6
9
65065
32532
152.1
101.4
352
CFT
17.3-R
M16
15
260
572
60
480
60
ITO
80
7
10
66933
33466
88.9
59.3
157
EPT
23.1-R
M20
20
260
572
60
480
60
HO
75
7
10
75258
37629
134.5
89.6
245
CFT
20.6-R
M24
20
260
572
70
460
70
120
70
7
10
76488
38244
167.9
111.9
352
CFr
20.2-R
120
50
ITO
25
3
5
8049
4024
23.7
15.8
157
EPT
5.8-R
140
50
ITO
25
4
5
10046
5023
26.7
17.8
157
EPT
6.5-R
IPE220
M16
15
150
206
50
IPE240
M16
15
150
226
50
■osimi li ns should i i
reale l i l f f k u l l i c s .
,on foi iliese criteria ι
Resistance
IPE270
M16 M20
IPE3TO
1PE330
IPE360
IPE400
IPE450
IPE240 IPE270
254
55
160
170
254
55
160
20
a„.
af
j,ini
55
ITO
27
4
6
12717
6358
30.6
55
110
30
4
6
15560
7780
51.6
55
ITO
35
4
6
16459
8230
S
j,im/2
vRd
Code
20.4
157
EPT
7.6R
s
34.4
245
EPT
6.3R
S
37.2
24.8
157
EPT
8.5R
245
EPT
7.1R
s s s s s s s s s s s s s s s s s s s s s s s s s s s s s s s s
L
bb
170
284
55
170
284
55
190
55
110
30
4
6
19774
9887
59.0
39.4
M16
15
180
312
55
220
55
ITO
40
4
6
20511
10255
43.2
28.8
157
EPT
9.6R
M 20
20
180
312
55
220
55
110
35
4
6
24468
12234
68.9
45.9
245
EPT
8.1R
M 24
20
190
312
65
200
65
120
35
4
6
24253
12127
76.9
51.3
352
EPT
8.2R
M16
15
210
342
55
250
55
ITO
55
5
7
25161
12580
50.1
33.4
157
EPT
10.9R
M 20
20
210
342
55
250
55
110
50
5
7
29849
14924
79.0
52.7
245
CFT
9.2R
120
45
5
7
29824
14912
92.7
61.8
352
EPT
9.2R
56.7
37.8
157
EPT
12.4R
M24
20
210
342
65
230
65
M16
15
220
380
55
290
55
ITO
60
5
7
31424
15712
M20
20
220
380
55
290
55
110
55
5
7
37055
18527
89.5
59.6
245
CFT
10.5R
M 24
20
220
380
65
270
65
120
50
5
/
37410
18705
108.6
72.4
352
EPT
10.4R
M27
25
220
380
75
250
75
130
45
5
7
38246
19123
126.6
84.4
458
CFT
10.2R
M16
15
230
428
55
340
55
ITO
65
5
8
39999
20000
65.0
43.3
157
EPT
14.2R
20
230
428
55
340
55
110
60
5
8
46839
23420
102.5
68.4
245
CFT
12.1R
428
65
320
65
120
55
5
8
47725
23863
126.0
84.0
352
CFT
11.9R
130
50
5
8
48943
24472
147.6
98.4
458
CFT
11.6R
20
230
M 27
25
230
428
75
300
75
M16
15
240
476
60
380
60
ITO
70
6
9
48624
24312
72.4
48.3
157
EPT
16.7R
M20
20
240
476
60
380
60
110
65
6
9
56452
28226
114.3
76.2
245
CFT
14.3R
M24
20
240
476
70
360
70
120
60
6
9
57793
28896
140.8
93.9
352
CFT
14.0R
M27
25
240
476
80
340
80
140
50
6
9
58684
29342
163.3
108.9
458
■; CFT
13.8R
M16
15
250
524
60
430
60
100
75
6
9
58569
29285
80.7
53.8
157
EPT
19.3R
20
250
524
60
430
60
110
70
6
9
67576
33788
127.3
84.9
245
CFT
16.7R
250
524
70
410
70
120
65
6
9
69348
34674
157.3
104.8
352
CFT
16.3R
524
80
390
80
140
55
6
9
70759
35380
185.2
123.5
458
CFT
15.9R
ITO
80
7
10
69491
34746
88.9
59.3
157
EPT
22.3R
20 25
250
M16
15
260
572
60
480
60
M20
20
260
572
60
480
60
110
75
/
10
79530
39765
140.3
93.5
245
CFT
19.5R
M24
20
260
572
70
460
70
120
70
7
10
81802
40901
173.6
115.8
352
CFT
18.9R
M27
25
260
572
80
440
80
140
60
7
10
83710
41855
204.9
136.6
458
CFT
18.5R
M16
15
150
206
50
120
50
ITO
25
3
5
7999
4000
23.7
15.8
157
EPT
5.8R
15
150
226
50
140
50
ITO
25
4
5
9996
4998
26.7
17.8
157
EPT
6.5R
15
154
254
55
160
55
ITO
27
4
6
12675
6338
30.6
20.4
157
EPT
7.7R
170
254
55
160
55
110
30
4
6
15640
7820
51.6
34.4
245
EPT
6.2R
M16 M16 M20
·) The holt spjdiiL' do<
154
»1
pi
15
M27
IPE220
15
w
e
Reference lengüi(m)
20
M24
HEB320
P
Failure mode
M16
M20
IPE600
hp
Shear (kN)
M20
M24
IPE550
bp
Moment (kNm) 2/3MRd MRd
190
M20
1PE500
Pp
'ρ
Rotational stiffness (kNm/rad)
Wc Ids (mm)
Connection ι etail (mm)
Eni plate: S 235 (mm)
20
sion ilii> :..:: I n
L
bu
Resistance Ene -plate: S 235 (mm) 'ρ 1PE300
We Ids
Rotational stiffness
(mm)
(mm)
(kNm/rad)
bp
bp
P
Pp
55
190
w
W]
aw
55
100
35
e
pi
a
Moment (kNm) 2/3MRd MRd
f
Sj,ini
Sj,ini'2
4
6
16436
8218
37.2
Shear (kN)
Failure mode
Reference length(m)
VRd
Code
'-bb
24.8
L
bu
M16
15
170
284
157
EPT
8.5-R
S
M20
20
170
284
55
190
55
110
30
4
6
19917
9959
59.0
39.4
245
EPT
7.0-R
S
M16
15
180
312
55
220
55
100
40
4
6
20520
10260
43.2
28.8
157
EPT
9.6-R
S
M20
20
180
312
55
220
55
110
35
4
6
24696
12348
68.9
45.9
245
EPT
8.0-R
M24
20
190
312
65
200
65
120
35
4
6
24653
12327
76.9
51.3
352
EPT
8.0-R
M16
15
210
342
55
250
55
100
55
5
7
25217
12608
50.1
33.4
157
EPT
10.8-R
M20
20
210
342
55
250
55
110
50
5
7
30190
15095
82.3
54.9
245
EPT
9.1-R
M24
20
210
342
65
230
65
120
45
5
7
30381
15191
92.7
61.8
352
EPT
9.0-R
M16
15
220
380
55
290
55
ITO
60
5
7
31567
15783
56.7
37.8
157
EPT
12.3-R
M20
20
220
380
55
290
55
110
55
5
7
37571
18786
93.4
62.2
245
EPT
10.3-R
M24
20
220
380
65
270
65
120
50
5
7
38205
19103
108.6
72.4
352
EPT
10.2-R
M27
25
220
380
75
250
75
130
45
5
/
39349
19674
132.5
88.3
458
CFT
9.9-R
M16
15
230
428
55
340
55
100
65
5
8
40291
20146
65.0
43.3
157
EPT
14.1-R
M20
20
230
428
55
340
55
110
60
5
8
47628
23814
107.1
71.4
245
EPT
11.9-R
M24
20
230
428
65
320
65
120
55
5
8
48881
24441
128.3
85.6
352
EPT
11.6-R
M27
25
230
428
75
300
75
130
50
5
8
50496
25248
154.1
102.7
458
CFT
11.2-R
M16
15
240
476
60
380
60
100
70
6
9
49096
24548
72.4
48.3
157
EPT
16.5-R
M20
20
240
476
60
380
60
110
65
6
9
57544
28772
119.3
79.5
245
EPT
14.1-R
M24
20
240
476
70
360
70
120
60
6
9
59339
29670
145.7
97.1
352
EPT
13.6-R
M27
25
240
476
80
340
80
140
50
6
9
60972
30486
171.1
114.0
458
CFT
13.3-R
M16
15
250
524
60
430
60
ITO
75
6
9
59283
29641
80.7
53.8
157
EPT
19.0-R
M20
20
250
524
60
430
60
110
70
6
9
69058
34529
132.9
88.6
245
;EPT
16.3-R
M24
20
250
524
70
410
70
120
65
6
9
71377
35688
162.7
108.5
352
EPT
15.8-R
M27
25
250
524
80
390
80
140
55
6
9
73681
36841
193.4
128.9
458
CFr
15.3-R
M16
15
260
572
60
480
60
ITO
80
7
10
70506
35253
88.9
59.3
157
EPT
21.9-R
M20
20
260
572
60
480
60
110
75
7
10
81469
40735
146.5
97.7
245
EPT
19.0-R
M24
20
260
572
70
460
70
120
70
7
10
84394
42197
179.7
119.8
352
EPT
18.3-R
M27
25
260
572
80
440
80
140
60
7
10
87357
43679
214.0
142.6
458
CFT
IPE220
M16
15
150
206
50
120
50
ITO
25
3
5
7925
3963
23.7
15.8
157
EPT
IPE240
M16
15
150
226
50
140
50
ITO
25
4
5
9915
4957
26.7
17.8
157
EPT
6.6-R
IPE270
M16
15
154
254
55
160
55
ITO
27
4
6
12589
6294
30.6
20.4
157
EPT
7.7-R
M 20
20
170
254
55
160
55
110
30
4
6
15619
7810
51.6
34.4
245
EPT
6.2-R
M16
15
170
284
55
190
55
ITO
35
4
(1
16350
8175
37.2
24.8
157
EPT
8.6-R
M20
20
170
284
55
190
55
110
30
4
6
19929
9964
59.0
39.4
245
EPT
7.0-R
s s s s s s s s s s s s s s s s s s s s s s s s s s s s s s s
IPE330
IPE360
IPE400
IPE450
IPE5TO
IPE550
IPE6fX)
HEB340
Connection detail
IPE3TO
I The boti stuens dix
ininn dir illese trilei
17.7-R '
5.9-R
Resistance
'Ρ IPE330
1PE360
IPE4TO
1PE450
\v
W]
aw
a
f
s
j,ini
^j,ini'^
vRd
Code
L
bb
312
55
220
55
100
40
4
6
20445
43.2
28.8
157
EPT
9.7R
s
180
312
55
220
55
110
35
4
6
24756
12378
68.9
45.9
245
"EPT
8.0R
S
M24
20
190
312
65
200
65
120
35
4
6
24831
12415
76.9
51.3
352
EPT
8.0R
S
M16
15
210
342
55
250
55
100
55
5
7
25164
12582
50.1
33.4
157
EPT
10.9R
M20
20
210
342
55
250
55
110
50
5
7
30318
15159
82.3
54.9
245
EPT .
9.0R
M 24
20
210
342
65
230
65
120
45
5
7
30660
15330
92.7
61.8
352
EPT
8.9R
55
100
60
5
7
31565
15783
56.7
37.8
157
EPT
12.3R
s s s s s s s s s s s s s s s s s s s s s s s s s s s s s s s
M16
15
220
380
55
290
M20
20
220
380
55
290
55
110
55
5
/
37817
18908
93.4
62.2
245
EPT
10.3R
M24
20
220
380
65
270
65
120
50
5
7
38646
19323
108.6
72.4
352
EPT
10.1R
M27
25
220
380
75
250
75
130
45
5
7
39996
19998
136.7
91.1
458
CFT
9.7R
M16
15
230
428
55
340
55
100
65
5
S
40388
20194
65.0
43.3
157
EPT
14.0R
M 20
20
230
428
55
340
55
110
60
5
8
48068
24034
107.1
71.4
245
EPT
11.8R
M24
20
230
428
65
320
65
120
55
5
8
49583
24791
128.3
85.6
352
EPT
11.4R
25
230
428
75
300
75
130
50
5
8
51472
25736
158.7
105.8
458
CFT
11.0R
240
476
60
380
60
100
70
6
9
49317
24659
72.4
48.3
157
EPT
16.4R
476
60
380
60
110
65
6
9
58209
29104
119.3
79.5
245
EPT
13.9R
476
70
360
70
120
60
6
9
60333
30166
145.7
97.1
352
EPT
13.4R
80
340
80
140
50
6
9
62494
31247
176.5
117.7
458
CFT
13.0R
100
75
6
9
59682
29841
80.7
53.8
157
EPT
18.9R
M16
15 20 20 25
240 240 240
476
M16
15
250
524
60
430
60
M20
20
250
524
60
430
60
110
70
6
9
70020
35010
132.9
88.6
245
EPT
16.1R
M 24
20
250
524
70
410
70
120
65
6
9
72744
36372
162.7
108.5
352
EPT
15.5R
M27
25
250
524
80
390
80
140
55
6
9
75696
37848
199.2
132.8
458
CFT
14.9R
M16
15
260
572
60
480
60
100
80
7
10
71132
35566
88.9
59.3
157
EPT
21.7R
M20
20
260
572
60
480
60
110
75
7
10
82790
41395
146.5
97.7
245
ÍEPT
18.7R
20
260
572
70
460
70
120
70
7
10
86208
43104
179.7
119.8
352
EPT
17.9R
260
572
80
440
80
140
60
7
10
89949
44974
220.4
146.9
458
CFT
17.2R
206
50
120
50
100
25
3
5
7850
3925
23.7
15.8
157
EPT ·
5.9R
100
25
4
5
9829
4914
26.7
17.8
157
EPT
6.7R
M16
25 15
150
IPE240
M16
15
150
226
50
140
50
IPE270
M16
15
154
254
55
160
55
100
27
4
6
12496
6248
30.6
20.4
157
EPT
7.8R
M20
20
170
254
55
160
55
110
30
4
6
15581
7790
51.6
34.4
245
EPT
6.2R
15
170
284
55
190
55
100
35
4
6
16252
8126
37.2
24.8
157
EPT
8.6R
170
284
55
190
55
110
30
4
6
19915
9957
59.0
39.4
245
EPT
7.0R
55
220
55
ITO
40
4
6
20351
10176
43.2
28.8
157
EPT
9.7R
55
110
35
4
6
24780
12390
68.9
45.9
245
EPT
8.0R
M16 M20
1PE330
bu
180
M27
IPE300
L
15
M24
IPE220
epl
Reference lengtli(m)
20
M27
HEB360
Pp
Failure ilode
M 20
M24
1PETO0
Ρ
Shear (kN)
M16
M20
1PE550
bp
Moment (kNm) 2/3MRd MRd
10223
M27 1PE5TO
"Ρ
Rotational stiffness (kNm/rad)
Wc Ids (nun)
Connection t etail (mm)
Ene plate: S 235 (mm)
M16 M20
20 15 20
180 180
312 312
55
220
ted h u m a i r u i s i i n i lilis s
:|[¡es, and indeed il i
ι he ignored in this situaiir
Resistance Connection detail (mm)
Ene -plate: S 235 (mm)
1PE360
1PE400
IPE450
IPE5TO
IPE550
'Ρ
bp
bp
P
Pp
epl
w
W!
a„.
M24
20
190
312
65
200
65
120
35
4
M16
15
210
342
55
250
55
100
55
M20
20
210
342
55
250
55
110
M24
20
210
342
65
230
65
M16
15
220
380
55
290
(kNm/rad)
Moment (kNm) 2/3MRd MRd
Shear (kN)
Failure mode
Reference lengtli(m)
vRd
Code
51.3
352
EPT
7.9-R
S
50.1
33.4
157
EPT
10.9-R
S
15198
82.3
54.9
245
EPT
9.0-R
S
30879
15440
92.7
61.8
352
EPT
8.8-R
7
31521
15761
56.7
37.8
157
EPT
12.3-R
s s s s s s s s s s s s s s s s s s s s s s s s s s s s s s s
a
s
j,ini
Sj,ini'2
6
24965
12482
76.9
5
7
25082
12541
50
5
7
30397
120
45
5
7
55
100
60
5
f
L
bb
M20
20
220
380
55
290
55
110
55
5
7
37994
18997
93.4
62.2
245
EPT
10.2-R
M24
20
220
380
65
270
65
120
50
5
7
39007
19504
108.6
72.4
352
EPT
10.0-R
M27
25
220
380
75
250
75
130
45
5
7
40548
20274
139.3
92.9
458
EPT
9.6-R
M16
15
230
428
55
340
55
ITO
65
5
8
40421
20210
65.0
43.3
157
EPT
14.0-R
M20
20
230
428
55
340
55
110
60
5
8
48412
24206
107.1
71.4
245
EPT
11.7-R
M24
20
230
428
65
320
65
120
55
5
8
50174
25087
128.3
85.6
352
EPT
11.3-R
M27
25
230
428
75
300
75
130
50
5
8
52319
26160
163.5
109.0
458
CFT
10.8-R
M16
15
240
476
60
380
60
ITO
70
6
9
49452
24726
72.4
48.3
157
EPT
16.4-R
M20
20
240
476
60
380
60
110
65
6
9
58748
29374
119.3
79.5
245
EPT
13.8-R
M24
20
240
476
70
360
70
120
60
6
9
61186
30593
145.7
97.1
352
EPT
13.2-R
M27
25
240
476
80
340
80
140
50
6
9
63848
31924
182.2
121.5
458
CFT
12.7-R
M16
15
250
524
60
430
60
ITO
75
6
9
59966
29983
80.7
53.8
157
EPT
18.8-R
M20
20
250
524
60
430
60
110
70
6
9
70823
35412
132.9
88.6
245
EPT
15.9-R
M24
20
250
524
70
410
70
120
65
6
9
73936
36968
162.7
108.5
352
EPT
15.3-R
M27
25
250
524
80
390
80
140
55
6
9
77507
38753
205.2
136.8
458
CFT
14.5-R
480
60
ITO
80
7
10
71611
35805
88.9
59.3
157
M16
15
260
572
60
EPT
21.6-R
M20
20
260
572
60
480
60
110
75
7
10
83916
41958
146.5
97.7
245
EPT
18.4-R
M24
20
260
572
70
460
70
120
70
7
10
87809
43905
179.7
119.8
352
EPT
17.6-R
M27
25
260
572
80
440
80
140
60
7
10
92298
46149
227.1
151.4
458
CFT
16.8-R
IPE220
M16
15
150
206
50
120
50
100
25
3
5
7688
3844
23.7
15.8
157
EPT
6 IR
IPE240
M16
15
150
226
50
140
50
ITO
25
4
5
9641
4820
26.7
17.8
157
EPT
6.8-R
15
154
254
55
160
55
ITO
27
4
6
12283
6141
30.6
20.4
157
EPT
7.9-R
170
254
55
160
55
110
30
4
6
15428
7714
51.6
34.4
245
EPT
6.3-R
55
190
55
ITO
35
4
6
16012
8006
37.2
24.8
157
EPT
8.8-R
39.4
245
EPT
7.1-R
IPE600
HEB400
Rotational stiffness
Welds (mm)
IPF.270
M16 M20
IPE3TO IPE330
IPE360 Ί The N i l i spadini' dix
20
M16
15
170
284
M20
20
170
284
55
190
55
110
30
4
6
19778
9889
59.0
M16
15
180
312
55
220
55
ITO
40
4
6
20098
10049
43.2
28.8
157
EPT
9.8-R
M20
20
180
312
55
220
55
HO
35
4
6
24681
12340
68.9
45.9
245
EPT
8.0-R
M 24
20
190
312
65
200
65
120
35
4
6
25036
12518
76.9
51.3
352
EPT
7.9-R
M16
15
210
342
55
250
55
ITO
55
5
7
24825
12412
50.1
33.4
157
EPT
11.0-R
ι M Ì I I lx- protected f u m i corrosion tins sluiuid n
L
bu
Resistance Connection detail (mm)
End-plate: S235 (mm)
Pp M20 1PE4TO
IPE450
HEB450
IPE220 1PE240 IPE270
IPE360
'j.ini
Sj,ini'2
Failure mode Code
Reference lengtli(m) L
bb
55
250
55
110
50
5
7
30358
15179
82.3
54.9
245
.EPT
65
120
45
5
7
31060
155.30
92.7
61.8
352
EPT
8.8-R
S
55
ITO
60
5
7
31297
15649
56.7
37.8
157
EPT
12.4-R
S
s s s s s s s s s s s s s s s s s s s s s s s s s s s s s s s
9.0-R
210
342
65
220
380
55
290
M20
20
220
380
55
290
55
110
55
5
/
38084
19042
93.4
62.2
245
EPT
10.2-R
M 24
20
220
380
65
270
65
120
50
5
7
39386
19693
108.6
72.4
352
.EPT
9.9-R
M 27
25
220
380
75
250
75
130
45
5
7
41211
20606
139.3
92.9
458
EPT
9.4-R
M16
15
230
428
55
340
55
ITO
65
5
8
40286
20143
65.0
43.3
157
EPT
14.1-R
M20
20
230
428
55
340
55
110
60
5
8
48736
24368
107.1
71.4
245
EPT
11.6-R
230
428
65
320
65
120
55
5
8
50891
25446
128.3
85.6
352
EPT
11.IR
230
428
75
300
75
130
50
5
8
53431
26715
165.8
110.5
458
EPT
10.6-R
60
380
60
ITO
70
6
9
49447
24724
72.4
48.3
157
EPT
16.4-R
9
59361
29681
119.3
79.5
M16
20 25 15
240
476
M20
20
240
476
60
380
60
111)
65
6
245
EPT
13.6-R
M24
20
240
476
70
360
70
120
60
6
9
62304
31152
145.7
97.1
352
EPT
13.0-R
M27
25
240
476
80
340
80
140
50
6
9
65773
32887
183.3
122.2
458
EPT
12.3-R
M16
15
250
524
60
430
60
ITO
75
6
9
60171
30086
80.7
53.8
157
EPT
18.7-R
20
250
524
60
430
60
110
70
6
9
71840
35920
132.9
88.6
245
EPT
15.7-R
410
70
120
65
6
9
75590
37795
162.7
108.5
352
EPT
14.9-R
390
80
140
55
6
9
80173
40086
210.7
140.5
458
EPT
14.1-R
7
10
72100
36050
88.9
59.3
157
EPT
21.5-R
M24
20
250
524
70
M27
25
250
524
80
M16
15
260
572
TO
480
60
ITO
80
M20
20
260
572
60
480
60
110
75
7
10
85439
42719
146.5
97.7
245
EPT
18.1-R
M24
20
260
572
70
460
70
120
70
7
10
90122
45061
179.7
119.8
352
EPT
17.2-R
M27
25
260
572
80
440
80
140
60
7
10
95855
47928
237.7
158.5
458
CFT
16.1-R
M16
15
150
206
50
120
50
ITO
25
3
5
7328
3664
23.7
15.8
157
EPT
6.4-R
15
150
226
50
140
50
ITO
25
4
5
9200
4600
26.7
17.8
157
EPT
7.1-R
15
154
254
55
160
55
ITO
27
4
6
11743
5871
30.6
20.4
157
EPT
8.3-R
55
160
55
110
30
4
6
14810
7405
51.6
34.4
245
EPT
6.6-R
55
190
55
ITO
35
4
6
15334
7667
37.2
24.8
157
EPT
9.2-R
190
55
110
30
4
6
19039
9520
59.0
39.4
245
EPT
7.4-R
4
6
19285
9642
43.2
28.8
157
EPT
10.3-R 8.3-R
M16 M16 M16
20 15 20
170 170 170
254 284 284
55
M16
15
180
312
55
220
55
ITO
40
M20
20
180
312
55
220
55
110
35
4
6
23818
11909
68.9
45.9
245
EPT
M24
20
190
312
65
200
65
120
35
4
6
24328
12164
76.9
51.3
352
EPT
8.1-R
M16
15
210
342
55
250
55
ITO
55
3
7
23858
11929
50.1
33.4
157
EPT
11.5-R
M20
20
210
342
55
250
55
110
50
5
7
29360
14680
82.3
54.9
245
EPT
9.3-R
210
342
65
230
65
120
45
5
7
30252
15126
92.7
61.8
352
EPT
9.0-R
M24 1 The boli spatuii' dot
af
Shear (kN) VRd
15
M20 IPE330
I»1
Moment (kNm) MRd 2/3MRd
20
M20 IPE3TO
(kNm/rad)
M24
M20
1PE600
342
(mm)
M16
M27
IPE550
210
R o t a t i o n a l stiffness
230
M24
IPE5TO
20
C
Welds
20
I he piotectcd fun
usimi (his shimld noi create ditti, ulti
S
Resistance Connection detail (mm)
Ene -plate: S 235
(mm) P
bp
hp
P
Pp
epl
w
w,
aw
M16
15
220
380
55
290
55
100
60
M20
20
220
380
55
290
55
110
55
M24
20
220
380
65
270
65
120
250
75
130
l
IPE400
(kNm/rad)
Moment (kNm)
f
s
j,ini
Sj,ini'2
MRd
5
7
30166
15083
56.7
5
7
36960
18480
93.4
50
5
7
38497
19249
108.6
45
5
7
40505
20253
139.3
a
Shear (kN)
Failure mode
Reference lengtli(m)
vRd
Code
37.8
157
EPT
12.9-R
62.2
245
EPT
10.5-R
72.4
352
EPT
10.1-R
s s s
92.9
458
EPT
2/3MRd
L
bb
L
bu
M27
25
220
380
75
9.6-R
S
M16
15
230
428
55
340
55
100
65
5
8
38966
19483
65.0
43.3
157
EPT
14.5-R
S
M20
20
230
428
55
340
55
110
60
5
8
47495
23747
107.1
71.4
245
EPT
11.9-R
S
M24
20
230
428
65
320
65
120
55
5
8
49958
24979
128.3
85.6
352
EPT
11.3-R
S
M27
25
230
428
75
300
75
130
50
5
8
52762
26381
165.8
110.5
458
EPT
10.7-R
S
M16
15
240
476
60
380
60
100
70
6
9
47964
23982
72.4
48.3
157
EPT
16.9-R
S
M20
20
240
476
60
380
60
110
65
6
9
58052
29026
119.3
79.5
245
EPT
13.9-R
S
M24
20
240
476
70
360
70
120
60
6
9
61387
30693
145.7
97.1
352
EPT
13.2-R
S
M27
25
240
476
80
340
80
140
50
6
9
65597
32799
183.3
122.2
458
EPT
12.3-R
S
M16
15
250
524
60
430
60
100
75
6
9
58559
29280
80.7
53.8
157
EPT
19.3-R
S
M20
20
250
524
60
430
60
110
70
6
9
70523
35261
132.9
88.6
245
EPT
16.0-R
S
M24
20
250
524
70
410
70
120
65
6
9
74774
37387
162.7
108.5
352
EPT
15.1-R
S
M27
25
250
524
80
390
80
140
55
6
9
80285
40143
210.7
140.5
458
EPT
14.0-R
S
M16
15
260
572
60
480
60
100
80
7
10
70381
35190
88.9
59.3
157
EPT
22.0-R
S
M20
20
260
572
60
480
60
110
75
7
10
84172
42086
146.5
97.7
245
EPT
18.4-R
S
M24
20
260
572
70
460
70
120
70
7
10
89487
44744
179.7
119.8
352
EPT
17.3-R
S
M27
25
260
572
80
440
80
140
60
7
10
96367
48184
239.6
159.7
458
EPT
16.1-R
S
IPE220
M16
15
160
206
50
120
50
110
25
3
5
7185
3592
23.4
15.6
157
EPT
6.5-R
S
1PE240
M16
15
160
226
50
140
50
110
25
4
3
9040
4520
26.3
17.5
157
EPT
7.2-R
S
1PE270
M16
15
160
254
55
160
55
110
25
4
6
11518
5759
29.6
19.7
157
EPT
8.4-R
M20
20
180
254
55
160
55
120
30
4
6
14706
7353
51.1
34.1
245
EPT
6.6-R 9.3-R
s s s s s s s s s s s s
IPE450
1PE500
IPE550
IPE600
HEB5TO
Rotation il stiffness
Wc Ids (mm)
IPE300 IPE330
IPE360
IPE400
M16
15
170
284
55
190
55
110
30
4
6
15016
7508
35.3
23.5
157
EPT
M 20
20
180
284
55
190
55
120
30
4
6
18943
9472
58.5
39.0
245
EPT
7.4-R
M16
15
180
312
55
220
55
110
35
4
6
18968
9484
41.3
27.5
157
EPT
10.4-R
M20
20
180
312
55
220
55
120
30
4
6
23634
11817
65.9
43.9
245
EPT
8.4-R
65
2TO
65
130
35
4
6
23959
11979
75.5
50.4
352
EPT
8.3-R
M24
20
200
312
M16
15
210
342
55
250
55
110
50
5
7
23814
11907
49.8
33.2
157
EPT
11.5-R
M20
20
210
342
55
250
55
120
45
5
7
29352
14676
80.5
53.6
245
EPT
9.3-R
M24
20
210
342
65
230
65
130
40
5
7
29762
14881
88.1
58.8
352
EPT
9 2-R
M16
15
220
380
55
290
55
110
55
5
7
30173
15086
56.6
37.8
157
EPT
12.9-R
M20
20
220
380
55
290
55
120
50
5
7
37157
18579
92.9
61.9
245
EPT
10.5-R
Resistance
l
IPE450
IPE5TO
IPE550
IPE600
hp
e
Ρ
Pp
65
pi
l
a„
af
s
j,ini
Sj,ini'2
130
45
5
7
38047 40215
w
w
M
Shear (kN)
Failure mode
Reference length(m)
Rd
2/3MRd
vRd
Code
19023
103.9
69.2
352
'EPT
10.2R
s
20108
133.4
88.9
458
EPT
9.7R
S
L
bb
L
bu
M24
20
220
380
65
M27
25
220
380
75
250
75
140
40
5
7
M16
15
230
428
55
340
55
110
60
5
8
39075
19537
65.0
43.3
157
EPT
14.5R
S
M 20
20
230
428
55
340
55
120
55
5
8
47906
23953
106.9
71.3
245
EPT
11.8R
M 24
20
230
428
65
320
65
130
50
5
8
49638
24819
123.6
82.4
352
EPT
11.4R
M27
25
230
428
75
300
75
140
45
5
8
52635
26317
159.5
106.4
458
EPT
10.8R
15
240
476
60
380
60
110
65
6
9
48245
24123
72.4
48.3
157
EPT
16.8R
M20
20
240
476
60
380
60
120
60
6
9
58723
29362
119.3
79.5
245
EPT
13.8R
M24
20
240
476
70
360
70
130
55
6
9
61328
30664
141.3
94.2
352
EPT
13.2R
140
50
6
9
65093
32546
183.3
122.2
458
EPT
12.4R
s s s s s s s s s s s s s s s s
M16
M 27
25
240
476
80
340
80
M16
15
250
524
60
430
60
110
70
6
9
59045
29522
80.7
53.8
157
EPT
19.1R
M 20
20
250
524
60
430
60
120
65
6
9
71523
35761
132.9
88.6
245
EPT
15.8R
M24
20
250
524
70
410
70
130
60
6
9
75176
37588
161.2
107.5
352
EPT
15.0R
M27
25
250
524
80
390
80
140
55
6
9
79943
39972
210.7
140.5
458
EPT
14.1R
M16
15
260
572
60
480
60
110
75
7
10
71190
35595
88.9
59.3
157
EPT
21.7R
M20
20
260
572
TO
480
60
120
70
7
10
85618
42809
146.5
97.7
245
EPT
18.1R
20
260
572
70
460
70
130
65
7
10
90274
45137
179.7
119.8
352
EPT
17.1R
260
572
80
440
80
140
60
7
10
96274
48137
239.6
159.7
458
EPT
16.1R
50
120
50
110
25
3
5
6929
3464
23.4
15.6
157
EPT
6.7R
110
25
4
5
8723
4361
26.3
17.5
157
EPT
25
M27 IPE220
bp
Moment (kNm)
270
M24
HEB550
P
Rotational stiffness (kNm/rad)
We Ids (mm)
Connection ι e lai I (nun)
Eni plate: S 235 (nun)
15
M16
160
206
IPE240
M16
15
160
226
50
140
50
7.5R
s
IPE270
M16
15
160
254
55
160
55
110
25
4
6
11128
5564
29.6
19.7
157
EPT
8.7R
M20
20
180
254
55
160
55
120
30
4
6
14200
7100
51.1
34.1
245
EPT
6.8R
M16
15
170
284
55
190
55
110
30
4
6
14523
7261
35.3
23.5
157
EPT
9.7R
M 20
20
180
284
55
190
55
120
30
4
6
18323
9162
58.5
39.0
245
EPT
7.7R
M16
15
180
312
55
220
55
110
35
4
6
18364
9182
41.3
27.5
157
EPT
10.8R
M20
20
180
312
55
220
55
120
30
4
6
22899
11450
65.9
43.9
245
EPT
8.6R
20
200
312
65
200
65
130
35
4
6
23283
11641
75.5
50.4
352
EPT
8.5R
55
250
55
110
50
5
7
23067
11533
49.8
33.2
157
EPT
11.8R
55
250
55
120
45
5
/
28470
14235
80.5
53.6
245
EPT ,
9.6R
40
5
7
28964
14482
88.1
58.8
352
EPT
9.4R
56.6
37.8
157
EPT
13.3R
s s s s s s s s s s s s s s
IPE300
IPE330
M24 IPE360
IPE400
M16
15
210
342
M20
20
210
342
M24
20
210
342
65
230
65
130
M16
15
220
380
55
290
55
110
55
3
/
29279
14640
M20
20
220
380
55
290
55
120
50
5
7
36120
18060
92.9
61.9
245
EPT
10.8R
20
220
380
65
270
65
130
45
5
7
37110
18555
103.9
69.2
352
EPT
10.5R
220
380
75
250
75
140
40
5
7
39294
19647
133.4
88.9
458
EPT
9.9R
M24 M27 ■l The M t spacim· d ^ s noi comply with ma
25
n thai will he protected iron
,iim this should not c
ι m he ignored in this .situation
Resistance Connection ι etail (mm)
Ene -plate: S 235 (mm) 2 " 2 w
i Λλ Λ, —
w
„i
" ,
=
+t?
38,66 = 0.607 38.66 + 25 35.14 38,66 + 25
/·
-.jinni
η ς , 3
α =5.13 (see the a t t a c h e d chart).
t; f (I5) 2 x235 mp ,p„ = 0,25 - ^ = 0.25 ^ ¿ = 12017 Nmm I mm y 11 I MC
l 1
'
Bolts
0g^_0,9xg00xl57».0'_ 9 0 i 4 i w Y Mb
!25
r. , , , , , J J 0,6/,Λ 0.6 χ 800 χ 157 χ 10~3 „ , „ , „ F,, ω (shear plane passes bv threaded part) = ———— = — = 6Q.3kN Y MI, 125 Lh = t/c +tp+ 0,5(hholl + hml ) = 12 +15 + i (10 +15) = 39.5mm 1/ =23.16/77777 COLUMN WEB PANEL IN SHEAR Resistance
VwM=
09Λ,,Λ», _ 0 , 9 χ 1 3 0 7 . 6 χ 2 3 5 χ 10"
^r,«„
V3xi,i
- = U52kN
ß=\{hyp) V „, 145.2 Flin=^Æ- = = 145.2/c/V '"" β 1 Stiffness
0,385 v4re. 0.385x1307,6 /c, = β—— ; = 3.044mm h = 1x165,4
389
COLUMN WEB IN COMPRESSION Resistance 0 ">
t
Λ\.IfMrx= — + af y¡2+tp+5(tfí. +/;)= — + 5 x 7 2 + 1 5 + 5x(l2 + 12) = 146,67mm . σ„,
k = min 1,0; 1,25 0,57
= \{hyp)
./ vue1
Λ, = 0 , 9 3 j ^ y F/i
= 0 , 9 3 j 1 4 6 6 7 , x 9 2 ^ 2 j 5 = 0.52 s 0,67 210000x7x7 τ =0,75
A =
l + 1.3(/?è //iixc /' M ,/^,)"
y 1 + 1,3(1x146,67x7 1307,6)
F«äi = km pc Kff,wcx tm ƒ„,, / γ A,„ = 1 χ 0,74 χ 146,67 χ 7 χ 235 χ 10"3/ΐ,1 = 163A2kN Stiffness
*
-
,
=
0,7V,c. c ',c
0,7x146,67x7
c/f
92
■
= 7,812mm
BEAM FLANGE IN COMPRESSION Resistance
Stiffness k, =cc BOLTS IN TENSION Resistance
FKr/, = 2 5, ω = 2 χ 90,4 = 1SQMN Stiffness
A-, =1.6 4c = 1,6 x — = 6,359mm U 39,5
390
COLUMN WEB INTENSION Resistance
bcff
WJ
= minpTzw;4m + l,25e] = min (2πχ 31,9;4 χ 31,9 + 1,25x25) = 158,85 mm
ß-'{hyp) Ρ,
τ = 0,72 \ί 1 + 1,3(1 χ 158,85x7/1307,6)
l + lißbe/f^ttJA vc)2
FRÍ¡,
= Ρ, V « , t »t Ut-1Y
MO
= 0,72 χ 185,85 χ 7 χ 235 χ 10" 3 /!,! = 170,6kN
stiffness
=
°>7beff.t, eff„cltwc d
=
_0.7x158.85x7 _ = 8,460mm 92
COLUMN FLANGE IN TENSION Resistance hjj jc t = °ef/ we / = 185.85mm
/7 = min e : 1,25m;[b p - w) I 2J = min (25 ; 1,25 χ 31.9 ; 25) = 25mm cj„ = cF / 4 =
Ffc I(ll „ = 1
23.14
= 5,79mm
(8n-2e)k,lerrfclm,fc 8x252x5,79x185,85x1x7691 ; / / ?— = : 7 τ — χ 10' = 181,9kN 2mn-ew(m + n) 2x31.9x255,79(31,9 + 25) ^K.ffjc,kjcmpLfc
1
fc.llil.i2
+ 2BlRdn
2x 185,85x 1 χ7691 + 2χ90,4χ ΙΟ3 χ25 31,9 + 25
m +n
F
Rti.e = min[ F/cRilll ■ FfcMj2
\ = 122AkN
Stiffness k, =
0,85/., ,,.,/' 0,85x185,85x(l2) 3 t - = ; ~r = 7,188mm (31,9)3 m
ENDPLATE IN TENSION Resistance l
e/f.p.,=min
Timp\ , ';ampi
■ τη\η(2π χ38,66;5,13x 38,66) = 198.3mm
391
ιΛ _ 3 xlO"·1 = \22A kN
Fep Rd
= min(25;l,25x38,66;25) = 25mm
ep;l25mpì:e
n = min
%np-le»)lcjj.p,,mPiv 8x252x5,79x198,3x12017 ,=^ '-— ' - { =X'- -, r χ 10"3 = 287.ΜΛ'
2mpìnp-eH(mpì+np)
'
2L
#/
F„,,, Ί = e M 2 " ·
2x38.66x25 5,79(38.66 + 25)
m , +25 / f t ,/ì 2 χ 198,3x12017 +2 χ 90.4 χ IO3 χ 25 ρ/ ^-^ = · χ 10-1 = 145,9kN mp]+np 38,66 + 25
FRdl =min[ F,p/W , ;F, /)/W2 ]= 145,9/t/V Stiffness /t7 =
0,85/„,/3 %¿L-L
0.85x198,3(15)3 -L— ^ _ L = 9.849mm =
mpi
(38,66)'
BEAM WEB IN TENSION Resistance VH*.'=V,./=198'5/WW
Fp,,, = K,,,., F , fyt ΙΥ v* =198,5 χ 5,9 χ 235 χ 10"3/ΐ,1 = 2 4 9 , 9 ^ Stiffness k% = c o
MOMENT RESISTANCE OF THE JOINT
F/(í/ = min[F /(í/ ,] = 1 2 2 , 4 ^ Plastic design moment resistance :
MRd = FRd h = 122,6 χ 170.4 χ 10"3 = 2Q,25kNm Elastic moment resistance :
2 Me = M„, = 13,5/cF/m π
¡Ut
STIFFNESS OF THE JOINT initial stiffness :
S
, ^ 210000x(l65.4) : xl0 6 =Elr l\\lk = — = 5906kNm jj ' ' 1/3.044+1/7.812 + 1/6.359 + 1/8.460+1/7.188 + 1/9.849
Secant stiffness : S / = S / , „ , / 2 = 2953 r Wm
39:
CHAPTER 3.b
STIFFNESS AND RESISTANCE
CALCULATION
FOR BEAM-TO-COLUMN JOINTS WITH FLUSH END-PLATE CONNECTIONS
1.
Calculation procedure
2.
Design tables
3.
Application example
393
1. CALCULATION PROCEDURE
Ch. 3. b - Beam-to-column joint with flush end-plate
Mechanical characteristics Ultimate stresses
Yield stresses Beam web Beam flange Column web Column flange Endplate Bolts
'ylc 'up
If hotrolled profiles : fvwc
a n (
fyfc
t fywb
—
fyfti
Geometrical characteristics Joint \ M = F. h
>
; i . L^_ Column t
fc
\J
wc
2i
a
.f
m 0,8r c ¡w
L Γ*
d ■
c Γ
c
\ u.o vz a c w s = v'2 ac
ι,
for a welded section
'
m
End-plate pJ / 0.8^F2a w
fb
U
+
m P2'
'wb ι
ι,
L
0,8 vTa t. 1
j
m
A v c = ( h c 2 tfc ) t,vc
ep r
s = rc for a rolled section
[e
\
H
h,
Avc = Ac 2 bc tfc + ( twc + 2 rc ) tlc with Ac = column section area Beam
fc
1
Bolts dw :
see figure or = d, if no washer
A,. :
resistance area of the bolts
d
396
t
*
Cli. 3. b - Beam-to-column joint withflushend-plate
RESISTANCE
STIFFNESS Column web panel in shear
0,385 A
with
v
0,9 A
V
P*
β
f vc
'
J
yew
'■ ν/3 γ.„„
1 for onesided joint configurations; 0 for double sided joint configurations symetrically loaded; 1 for doublesided configurations nonsymetrically loaded with balanced moments; 2 for doublesided joint configurations nonsymetrically loaded with unbalanced moments.
For other values, see 1.2.2.1 in chapter 1.
Column web in compression
0,7 b Cff.WC,C
F„,_ = k tia,2
WC
ρ b„
wc 'c
tf
eff.wc,c
/y„
wc
J
ywc
if λ J
* Mo
< 0,67 wc
'
1 'Rd,!'
wc Pc
"tff.wc.c
0 22 t* ~ ~
'wc J ywcl^
λ WC
if λ J
•Uh λ
b „
= 0,93
ejj.wc.c
\
'l'^Mo
λ wc
> 0,67 WC
'
d fJ
E t
c 7
y\vc
WC
\
kwc= min [1,0 ; 1,25 0 , 5 ^ ]
(+)
J VW
pe= 1
,/β = 0
= Pel = Pc2 where
'/P=l ' / ß =2 pc¡ 1 + 1,3 (b „ v
t
ejj.wc ,c
Ι Α )
wc
2
ve '
Pc2
1 + 5,2 (b „ v
o n wc :
effvc.c
t. + a,J 2 + t "f
'fb fb
ft
ρ
t
ejj wc ,c
I A f
wc
normal stresses in the column web at the root of the fillet radius or of the weld
+ min (H ; aJl f ν
+ ί ) + 5(ί, + s) ρ'
ν
fc
'
(*) see 1.2.2.2 in chapter 1.
Beam flange in
k} - °°
F
«,,3 = McM
I ( V
V
compression M c Rd : beam design moment resistance
397
vc '
Cli. 3. b - Beam-to-column joint withflushend-plate Bolts in tension
A k4 = 1,6 -!■
F
Rä,4
=
B
2
,.Rä
»
Column web in tension
•
B
=F,Mä
t.Rä
A °-9L· y
M
ρ
Ì t h
"b ¡Mb
-
■'
0,7 b „ , t *S
_
'
ejj.wc,(
wc
^ Rd.S
h
~ Ρ t "cff.wcj
'wc Jywc
'
TAf»
wc
with
;ƒ P = 0
p(= 1
'= P„
'/ß = i
-P,2
180 N/mm2
o n fc :
w, =V,,
fc
Imn - e (m + «) 2 1... m ,, k, + 2 Β u. η efffc.t pife fc 1 Rd m + n
= ( 2J / , - 180 - σ , ) / v(2f.-
M'
K
.
/ƒ σ , < 180 A'/m/ίΓ
kr = 1
e
mplfc
1
Ch.3.b - Beam-to-column joint with flush end-plate End-plate in bending
/,
_
0,85 / , , , / 3 '
7
'ffP,' P 3 m pi
FRd1
= min [ FepMi
; FpJM2 ]
(8« - le ) l „ p
-
P
ep.Rd.]
w'
π
2m , η pi
ρ
ρ
m .
effp.t pip , . e (m , + η ) IV
/) Ι
_ en/M.2
m , + ρ\
η
- min [ e ρ
m ,
= 0,25 Γ f
pi p
effp.t
Ρ
ρ
η ρ
, ; e 1
; 1,25m
L
/»I J
I yp
yk, ' Mo
- min [ 2nm , ; am , 1
where α is defined in the annexed table Beam web in tension
ks
= °°
Γ RJ,S ~ "eff.wbj
b
eff»b.t
S
FRd
. = E h1 1 Y ¡"i
l/k.
wb Jywb ' y Mo
effp.t
Initial stiffness :
[ FRi.
= min
M
*t
=
F
Rä
JOINT S. = S.. . 1 2
]
Plastic design moment resistance :
Nominal stiffness :
Elastic moment resistance :
399
ρ'
2 1,. m . + 2 Β ... η .' WP —h
+ +
aw
M^ %
t J a
Code
Beamflangein compression
BFC
M
Bolts in tension
BT
M
End plate in tension
3"-
)
Beam web in tension
ΎΜΟ
110 125
EPT BWT
f
Connection detail (mm)
End-plate: S235 (mm)
S235
Failure m o d e
t
Rotational stiffness (kNm/rad)
Welds (mm) Ήν
iL
a
f
S
j.ini
S
¡4ni / 2
Resistance Moment (kNm) M Kd 2/3M Rd
Shear
Failure mode
Reference length(m)
ML 'Rd
Code
s s s
IPE220
M16
15
140
206
50
120
50
90
25
3
5
15433
5144
24.1
16.1
157
EPT
1PE240
M16
15
140
226
50
140
50
90
25
4
5
20098
6699
27.2
18.1
157
EPT
1PE270
M16
15
154
254
55
160
55
90
32
4
6
26826
8942
32.4
21.6
157
EPT
154
254
55
160
55
90
32
4
6
42892
14297
53.8
35.9
245
EPT
7.1-R
55
90
40
4
6
36564
12188
38.9
25.9
157
EPT
12.0-R
M20 IPE300
IPE330
IPE360
IPE400
1PE450
M16
15
170
284
55
190
M20
20
170
284
55
190
55
90
40
4
6
57607
19202
64.3
42.8
245
EPT
7.6-R
M16
15
ISO
312
55
220
55
90
45
4
6
47398
15799
44.8
29.9
157
EPT
13.0-R
M20
20
180
312
55
220
55
90
45
4
6
74007
24669
73.8
49.2
245
EPT
8.3-R
200
65
110
35
4
6
62600
20867
78.5
52.3
352
EPT
9.9-R
250
55
90
60
5
7
60854
20285
50.1
33.4
157
EPT
14.0-R
90
60
5
7
93626
31209
82.5
55.0
245
EPT
9.1-R
85645
28548
96.8
64.5
352
EPT
10.0-R
M24
20
180
312
65
M16
15
210
342
55
M20
20
210
342
55
250
55
M24
20
210
342
65
230
65
110
50
5
7
M16
15
220
380
55
290
55
90
65
5
7
78661
26220
56.7
37.8
157
EPT
15.4-R
290
55
90
65
5
7
120698
40233
93.4
62.3
245
EPT
10.1-R
270
65
110
55
5
7
113428
37809
112.7
75.1
352
EPT
10.7-R
130
45
5
7
118284
39428
139.3
92.9
458
M20
20
220
380
55
M24
20
220
380
65
M27
25
220
380
75
250
75
EPT
10.3-R
M16
15
230
428
55
340
55
90
70
5
8
104399
34800
65.0
43.3
157
EPT
17.0-R
230
428
55
340
55
90
70
5
8
159614
53205
107.1
71.4
245
EPT
11.1-R
65
320
65
110
60
5
8
152172
50724
130.4
86.9
352
EPT
11.6-R
54059
165.8
110.5
109-R
M20 M24
IPE500
20
20 20
230
428
M27
25
230
428
75
300
75
130
50
5
8
162176
458
EPT
M16
15
240
476
60
380
60
100
70
6
9
118633
39544
72.4
48.3
157
EPT
S
476
60
380
60
100
70
6
9
187003
62334
119.3
79.5
245
EPT
13.5-R
M20
20
240
") Tl« bolt irpacinfc do« not conchy with nvodmum ml
cria, for ■ connoti«! thai will he picrteried from tonoston Ih« iliould not creale difficulties, and indeed it it common for these criteri» to be ignored in this liinalion.
(mm)
(mm)
(mm)
°w
e
J!L
M24
IPE550
240
476 476
70 SO
360 340
"r
S
jr'"i
Resistance Moment
1M¿L
M Rd
OEM
2/3M Rd
Shear
ML
Failure mode
'Rd
Code
Reference length(m)
70
120
60
176462
58821
145.7
97.1
352
EPT
14.3-R
80
14(1
50
190544
63515
183.3
122.2
458
EPT
13.3-R
49674
80.7
53.8
157
EPT
M27
25
240
M16
15
250
524
60
430
60
100
75
149023
20
250
524
60
430
60
100
75
233999
78000
132.9
88.6
245
EPT
15.1-R
410
70
120
65
222310
74103
162.7
108.5
352
EPT
15.9-R
390
SO
140
55
245405
81802
210.7
140.5
458
EPT
14.4-R
SO
10
188438
62813
59.3
157
EPT
M20
1PE600
20
Rotational stiffness (lcNm/rad)
Welds
Connection detail
End-plate: S235
M24
20
250
524
70
M27
25
250
524
SO
M16
15
260
572
60
480
60
100
20
260
572
60
480
60
100
SO
10
291826
97275
146.5
97.7
245
EPT
16.6-R
20
260
572
70
460
70
120
70
10
280299
93433
179.7
119.8
352
EPT
17.2-R
260
572
80
440
SO
140
60
10
314622
104874
239.6
159.7
458
EPT
15.4-R
M20 M24 M27
25
44-
·) Tte boll sparii« d o a not comply with m u i m i m criteni
ft» · connection lha will be prelected ftom common Ihil should not crate difficullies, m l indeed it is common Tor these criteri« lo be ignored m Ulis .iüjatio!
YVj W W[
+-+
+
Failure m o d e
Code
Beam flange in compression
BFC
Bolts in tension
BT
+
End plate in
% e
+
Pi
+
Beam web in tension
Welds (mm)
Connection detail (mm)
End-plate: S235 (mm)
S235
tension
a
!nL IPE220
M16
w
Rotational süfïness (kNm/rad)
a
f
S
j,ini
1M¿L
ΎΜΟ
= 110
TMb = 1-25
EPT BWT
Resistance Moment (kNm) M Rd
Shear
Failure mode
2/3M Rd
'Rd
Code
Reference length(m)
15
140
206
50
120
50
90
25
3
5
15433
5144
27.1
18.0
163
EPT
S
226
50
140
50
90
25
4
5
20098
6699
30.5
20.3
163
EPT
s
IPE240
M16
15
140
IPE270
M16
15
154
254
55
160
55
90
32
4
6
26826
8942
36.8
24.5
163
EPT
S
M20
20
154
254
55
160
55
90
32
4
6
42892
14297
60.3
40.2
255
BWT
7.1-R
M16
15
170
284
55
190
55
90
40
4
6
36564
12188
44.5
29.7
163
EPT
12.0-R
M20
20
170
284
55
190
55
90
40
4
6
57607
19202
73.0
48.7
255
EPT
7.6-R
220
55
90
45
4
6
47398
15799
51.5
34.3
163
EPT
13.0-R 8.3-R
44-
IPE300
IPE330
IPE360
IPE400
M16
15
180
312
55
M20
20
180
312
55
220
55
90
45
4
6
74007
24669
84.3
56.2
255
EPT
M24
25
180
312
65
200
65
110
35
4
6
76838
25613
102.2
68.2
367
BWT
8.0-R
M16
15
210
342
55
250
55
90
60
5
7
60854
20285
57.6
38.4
163
EPT
14.0-R
M20
20
210
342
55
250
55
90
60
5
7
93626
31209
94.2
62.8
255
EPT
9.1-R
65
110
50
5
7
101226
33742
132.0
88.0
367
EPT
8.4-R
43.5
163
EPT
15.4-R
M24
25
210
342
65
230
M16
15
220
380
55
290
55
90
65
5
7
78661
26220
65.2
M20
20
220
380
55
290
55
90
65
5
7
120698
40233
106.7
71.1
255
EPT
10.1-R
220
380
65
270
65
110
55
5
7
132799
44266
153.1
102.1
367
EPT
9.1-R
75
250
75
130
45
5
7
134515
44838
175.2
116.8
477
BWT
9.0-R
70
5
8
104399
34800
74.7
49.8
163
M24 M27 IPE450
220
380
M16
15
230
428
55
340
55
EPT
17.0-R
M20
20
230
428
55
340
55
90
70
5
8
159614
53205
122.2
81.5
255
EPT
11.1-R
25
230
428
65
320
65
110
60
5
8
177216
59072
177.1
118.1
367
EPT
10.0-R
428
75
300
75
130
50
5
8
182736
60912
221.1
147.4
477
EPT
9.7-R
100
70
6
9
118633
39544
83.3
55.5
163
EPT
S
100
70
6
9
187003
62334
136.2
90.8
255
EPT
13.5-R
M27
") The bolt spacing
30
90
M24
IPE500
25
30
230
M16
15
240
476
60
380
60
M20
20
240
476
60
380
60
d o c not comply with nurimum criteri», tc . ccwct.on that will be protected from corrosion thi. should nol crate dUTrcllies. „ d indeed it i. common for Uvee criteri, to be .gnored in Ihi. ritutfion.
Resistance
'Sv
^El M24 M27 1PE550
M16 M20 M24 M27
Ι1Έ600
25 30 15
240 240 250
476 476 524
ML
Failure mode
'Rd
Code
Reference length(m)
70
120
60
211574
70525
197.8
131.9
367
EPT
12.0-R
SO
340
80
140
50
219603
73201
244.8
163.2
477
EPT
11.5-R
430
60
100
75
149023
49674
92.8
61.8
163
EPT
S
233999
78000
151.8
101.2
255
EPT
15.1-R
265560
88520
221.0
147.3
367
EPT
13.3-R
280.8
187.2
477
EPT
12.6-R
102.2
68.2
163
EPT
60
250
524
60
430
60
100
25
250
524
70
410
70
120
65
524
S ■ ./2
Shear
360
20
250
S¡¡¿"iL
Moment (kNm) M Rd 2/3M Rd
70
75
30
Rotational stiffness (kNm/rad)
Welds (mm)
Connection detail (mm)
End-plate: S235 (nun)
SO
390
SO
140
55
280319
93440
60
100
80
10
188438
62813
M16
15
260
572
60
480
M20
20
260
572
60
-ISO
60
100
80
10
291826
97275
167.3
111.5
255
EPT
16.6-R
70
460
70
120
70
10
330442
110147
244.0
162.7
367
EPT
14.6-R
10
353714
117904
318.5
212.3
477
EPT
13.7R
M24 M27
25 30
260 260
572 572
·) The bolt spacing doe. not comply with maximum criteria.
80
440
80
140
60
for a comedión that will be protected from corrosion this should not crate difficn Itie», md indeed ,1 is common for these criteria to be ¡gnored in this situation
3. WORKED EXAMPLE
Hand calculation of the stiffness and resistance of beam to beam flush e n d plate connection M16hr8.8
25 90 25 50
H
+
15
V
V
(—h
+
120; 50 ;
15
206
M
Ml , IPE220
+> +
t j
τ—
ÍPE220
*
140 Preliminary caculation beam
t.
h = hh-^-p
9,2
50 = 165,4mm
= 220-
McK¡¡ (class section 1) =
Wphvfvh 285406x235x1 Ο 1.1
Χ.\/0
= 60,97kNm
end plate w -1
m..
^ - 0,8Vïa . = 9 0
Ί
^ ,9 0.8 χ 42 χ 3 = 38.66mm
m
ni = Ρ -t β 0,8V2ar = 50109,2 0,8 V2 χ 5 = 35,14mm
bp-w 14090 e „ = —— = = 25mm ρ
o
\ =
m. mpi+ep
38.66 = 0.607 38.66 + 25
Λ=
™n-> m
55.14 : 0,5552 38,66 + 25
p\
?
+e
p
a = 5.13 (see the attached chart).
t;fv„ (I5) 2 x235 m.,.. = 0.25 ^ = 0,25 ^ = 12017Nmm I mm 'pi.ρ 1.1 y Λ/Ο
45:
Bolts
_
0ÆtA y
J-9
800 » 157χ IQ'
=goMN
1,25
Uh
r- , , , u *u ■ , 0·6/; n.fc
o n fc :
normal stresses in the centroïd of the column flange
n = min [ e ; 1,25m ; (b - w)/2 ] e
=d H'
I4
M'
" W = °·25 Ve /,/c ' YM„
v, = 6
(**) see 1.2.2 ,3 in chapter 1.
478
.#c,
Ch.5 - Beam-to-column joint withflangecleats Flange cleat in bending
1
eff. a,t
a
FMi7
= rain [ F i J M i I ; FaJtda
]
(%n - 2e ) / „ , m ,
F aRd.i
v
a
w'
2m n
-
effa.t v
aa
w
a
= min f e
t.Rd
; l,25m
|
0,25 ί ; ƒya
pia
B,„.
pia
eff.a.t
n
a' 2
2 / ,, . m ,
F a.Rd,2
pi.a
e (m + n ) n
a
/ γ' M»
t„ , = b / 2 ef] α,t
Flange cleats in bearing
2 4 K. K, f b
ta J ita
a
d
= 10 α f
d t
a J mx
Ι Ί. a
ΙΛ
(non preloaded bolts) K
= min [ 0,25 — +
0,5 ;
0,25 — + 0,375 ; 1,25 ] d
α
= min [ L
α
Pb 0
K ta
_. j_ . Λ»
3 rf ' 3
rfn
4 ' ƒ
0
o/- 1,0
^ uà
= min L[1,5 —=— ; 2,5 ] '
,
,
,
j
d,,,< X
M16
d for M16 bolts
Bolts in shear
16 ƒ „ rf2
ί"«.. = 4 μ/.*^./Y*
(connection to beam) (non preloaded
μ =
0,6 for strength grades 4.6, 5.6 and 8.8 0,5 for strength grades 4.8, 5.8 and 10.9
bolts)
Beam flanges in bearing
2 4 Khb Kin> l/b Jfuíh u/b d
F
10
M,.0 =
(non preloaded bolts)
e
K,
= min [ 0.25 — +
*
0,5 ;
rf
3
0.25 — + 0.375 ; 1,25 ]
rf K . φ,
min [1,5 -?— d
bi
α Λ = min [
; 2,5 ]
Mit,
479
% f u/b
Pb
d
o ' 3 ¿o
d
'/b I
ΥΛ
J_ .
fb
4
ft,
'
or
1,0
Ch.5 Beam-to-column joint with flange cleats
F
Initial stiffness :
Rd = min [ F W i l 1
10
S.. , = Ε h2 1 V l/Ar, ri
Nominal stiffness :
JOINT
Plastic design moment resistance : M
Ri
=
F
«¿
Sj = ^ „ , / 2
Elastic moment resistance :
480
*
2. DESIGN TABLES
β=1 ΥΛ/Ο=1·10
Υ Λ« = 1 2 5 lo w3
C
ψ.
E o U
ra
Jfí
cu
ca
MRd V R d
Failure mode
Code
Failure mode
Code
Failure mode
Code
Column web panel in shear
CWS
Column web in tension
cwr
Bolts in shear
BS
CWC
Column flange in tension
CFT
BFC
Flange cleat in tension
FCT
BT
Flange cleat in bearing
FCB
Column web in compression Beam Hange in compression Bolts in tension
Beam Hange in bearing
BFB
Resistance
DC
S235
Rotational stiffness (kNm/rad)
Connection detail (mm)
Cleats: S235 (mm)
IJ
La t la x t a HbB140
HEB 160
»2
w3
«'b
wc
Sj,ini
Sj,ini/2
Shear (kN) VRd
140
50
90
40
60
80
8
2683
1341
19.9
13.2
12 i
90
40
70
80
8
3140
1570
21.4
14.2
121
Failure mode Code
Reference length(m) Lbb
Lbu
FCT
S
FCT
S
s s
IPE22Ü
MR,
130x65x12
IPE240
M16
130x65x12
140
50
1PE270
M16
130x65x12
140
50
90
40
70
80
8
3837
1919
23.6
15.7
121
FCT
S
S
M20
160x80x14
140
60
115
45
75
80
10
5251
2625
29.4
19.6
188
FCT
S
IPE220
M16
130x65x12
160
50
90
40
60
80
8
2803
1402
22.7
15.1
121
FCT
S
IPE240
M16
130x65x12
160
50
90
40
70
80
8
3289
1645
24.4
16.3
121
FCT
S
IPE270
M16
130x65x12
160
50
90
40
70
80
8
4031
2016
27.0
18.0
121
FCT
S
M 20
160x80x14
160
60
115
45
75
90
10
5575
2788
33.6
22.4
188
FCT
S
M16
130x65x12
160
50
90
40
75
80
8
4861
2431
29.5
19.7
121
FCT
M20
160x80x14
160
60
115
45
80
90
10
6682
3341
36.8
24.5
188
FCT
M16
130x65x12
160
50
90
40
75
80
8
5809
2905
32.1
21.4
121
FCT
M20
160x80x14
160
60
115
45
85
90
10
7941
3971
39.9
26.6
188
FCT
IPE220
M16
130x65x12
180
50
90
40
60
80
8
2846
1423
25.5
17.0
121
FCT
IPE240
M16
130x65x12
180
50
90
40
70
80
8
3342
1671
27.5
18.3
121
FCT
IPE270
M16
130x65x12
180
50
90
40
70
80
8
4101
2051
30.3
20.2
121
FCT
M20
160x80x14
180
60
115
45
75
90
10
5727
2863
37.8
25.2
188
FCT
M16
130x65x12
180
50
90
40
75
80
8
4951
2476
33.2
22.1
121
FCT
s s s s s s s s s
s s s s s s s s s s s s s s
1ΡΕ300
1PE330
HEB 180
wl
Moment (kNm) MRd 2/3MRd
IPE300
Resistance
1PE330
IPE360
1PE400
HEB200
Moment (kNm) 2/3MRd MRd
L a x la x ta
ba
wl
"'2
«3
wb
Wc
g
Sj,ini
Sj,ini/2
M20
160x80x14
180
«1
115
45
80
90
10
6875
3437
41.4
M16
130x65x12
180
50
90
40
75
80
8
5925
2963
36.1
M20
160x80x14
180
85 85
90 100
10 10
44.9
29.9
180
45 55
4093
150x100x14
115 105
8185
M24
60 60
8255
4127
36.1
M16
130x65x12
180
50
90
40
80
80
7042
3521
M20
160x80x14
180
60
115
45
85
90
8 10
9681
4840
M24
150x100x14
180
60
105
55
90
100
10
9733 8540
Shear (kN)
Failure mode
Reference length(m)
VRd
Code
Lbb
lbu
27.6
188
FCT
S
s
24.1
121
FCT
S
s
FCT
24.1
188 271
s
39.0
26.0
121
FCT
48.4
32.3
188
FCT
s s s
4866
38.8
25.9
271
FCT
4270
42.8
28.5
121
FCT
2.8-P
2.8-P
s s
FCT
S
s
M16
130x65x12
180
50
90
40
85
80
8
M 20
160x80x14
180
60
115
45
90
90
10
11670
5835
53.1
35.4
188
FCT
S
5845
42.5
28.3
271
FCT
S
M 24
150x100x14
180
60
105
55
95
100
10
11691
IPE220
M16
130x65x12
200
50
90
40
60
80
8
2894
1447
27.3
18.2
121
FCT
S
1PE240
M16
130x65x12
200
50
90
40
70
80
8
3403
1702
29.4
19.6
121
FCT
S
IPE270 IPF.300 IPE330
IPE360
IPE400
IPE450
s
s s
130x65x12
200
50
90
40
70
80
8
4183
2091
32.5
21.6
121
FCT
160x80x14
200
ω
115
45
75
90
10
5912
2956
42.0
28.0
188
FCT
S S
M16
130x65x12
200
50
90
40
75
80
8
5058
2529
35.5
23.7
121
FCT
S
M20
160x80x14
200
60
115
45
80
90
10
7112
3556
46.0
30.6
188
FCT
S
M16
130x65x12
200
50
90
40
75
80
6063
3031
38.6
25.7
121
FCT
M20 M24
160x80x14
200
60
115
45
85
90
8 10
8487
4244
49.9
33.3
188
FCT
150x100x14
2(X)
110 80
10 8
26.7
50
85 80
40.1
130x65x12
55 40
4308
M16
105 90
8615
200
ω
7219
3609
41.7
27.8
271 121
FCT FCT
160x80x14
200
60
115
35.9
188
FCT
M24
150x100x14
10 10
53.8
105
90 110
5032
60
85 90
10065
200
45 55
s s s s
10185
5093
43.2
28.8
27-,
FCT
M16
130x65x12
200
50
90
40
85
80
8
8773
4387
s
45.8
30.5
121
FCT
2.8-P
2.8-P
M20
160x80x14
200
60
115
45
90
90
10
12166
6083
59.0
39.3
188
FCT
S
55
95
110
10
12267
6134
47.2
31.5
271
FCT
S
s
121
FCT
3.2-P
3.2-P
s
S
S
s s s s
s s s s
s s
M 24
150x100x14
200
60
105
M16
130x65x12
200
50
90
40
85
80
8
10938
5469
50.9
34.0
M20
160x80x14
200
60
115
45
95
90
10
15074
7537
65.5
43.7
188
FCT
S
7573
52.4
34.9
271 121
FCT FCT
S 3.8-P
3.8-P
50
105 90
55 40
100 90
110 80
10 8
15146 13382
6691
56.1
37.4
200
60
115
45
95
90
10
18335
9167
72.1
48.1
188
FCT
2.8-P
2.8-P
150x100x14
200
60
105
55
100
110
10
18372
9186
57.5
38.3
271
FCT
2.8-P
2.8-P
M16
130x65x12
220
60 70
90 90
18.7 .
1723
30.1
20.1
FCT FCT
S S
S
3446
121 121
130x65x12
220
50
90
40
70
90
8 8 8
28.0
220
40 40
1464
130x65x12
90 90
2928
M16 M16
50 50
4238
2119
33.3
22.2
121
FCT
s
S
150x100x14
200
60
M16
130x65x12
200
M20
160x80x14
M24 IPE220 IPE240 IPE270
s s
M16
M24 IPE500
s
M20
M20
HEB220
(mm)
(mm)
S235
Rotation 1 stillness (kNm/rad)
Connection t elail
Cleats: S235
s
s
Resistance S235
La x la x ta
1PE300 1PE330
IPE360
1PE400
1PE450
IPE500
wl
»2
w3
"b
aj.ini
a
J>im'·
Moment (kNm) MRd 2/3MRd
Shear (kN) VR
Failure mode
Reference length'm)
Code
Lbb
Lbu
S
s
M20
160x80x14
220
60
115
45
75
100
10
6005
3003
46.3
30.8
188
FCT
M16
130x65x12
220
50
90
40
75
90
8
5129
2564
36.4
24.3
121
FCT
M20
160x80x14
220
60
115
45
80
100
10
7232
3616
50.6
33.7
188
FCT
S
S
M16
130x65x12
220
50
90
40
75
90
6154
3077
39.6
26.4
121
FCT
S
M20
160x80x14
220
60
115
45
85
100
8 10
8641
4320
54.9
36.6
188
FCT
S
M24
150x100x14
220
60
105
55
85
120
10
8807
4403
44.1
29.4
271
FCT
M16
130x65x12
220
50
90
40
80
90
8
7335
3668
42.8
28.5
121
FCT
s s s s
s s s s s s
s
S
M20
160x80x14
220
60
115
188
FCT
105
10 10
39.5
60
100 120
59.2
220
85 90
5130
150x100x14
45 55
10260
M24
10426
5213
47.5
31.6
271
FCT
M16
130x65x12
220
50
90
40
85
90
8
8924
4462
47.0
31.3
121
FCT
2.7-P
2.7-P
M20
160x80x14
220
60
115
45
90
100
10
12420
6210
64.9
43.3
FCT
S
M24
150x100x14
220
60
105
34.6
90
11142
5571
52.2
34.8
121
FCT
s
S S
50
10 8
52.0
220
120 90
6288
130x65x12
95 85
12576
M16
55 40
188 271
3.2-P
3.2-P
M20
160x80x14
220
60
115
45
95
100
10
15416
7708
72.1
48.1
188
FCT
S
M24
150x100x14
220
60
105
55
100
120
10
15554
7777
57.6
38.4
271
FCT
M16
130x65x12
220
50
90
40
90
90
13651
6825
57.5
38.3
121
FCT
3.7-P
3.7-P
M20
160x80x14
220
60
115
45
95
100
8 10
s s
18785
9393
79.3
52.9
188
FCT
2.7-P
2.7-P
9451
63.2
42.1
271
FCT
2.7-P
2.7-P
FCT
s
M24
150x100x14
220
60
105
55
100
120
10
18901
M16
130x65x12
220
50
90
40
95
90
16351
8176
62.8
41.8
121
FCT
4.3-P
4.3-P
22386
11193
86.5
57.6
188
FCT
3.1-P
3.1-P
M20
160x80x14
220
60
115
45
100
100
8 10
M24
150x100x14
220
60
105
55
110
120
10
22474
11237
68.8
45.9
271
FCT
3.1-P
3.1-P
M16
130x65x12
90 115
40 45
95 100
90 100
8 10
9696
68.0
45.4
5.0-P
5.0-P
26420
13210
93.7
62.4
121 188
FCT
160x80x14
50 60
19392
M20
220 220
FCT
3.7-P
3.7-P
M24
150x100x14
220
60
105
55
110
120
10
26477
13239
74.5
49.6
271
FCT
3.7-P
3.7-P
IPE220
M16
130x65x12
240
50
90
40
60
90
2960
1480
28.7
19.1
121
FCT
S
IPE240
M16
130x65x12
240
50
90
40
70
90
8 8
3485
1743
30.9
20.6
121
FCT
1PE270
M16
130x65x12
240
50
90
40
70
90
8
4291
2145
34.1
22.7
121
FCT
M20
160x80x14
240
60
115
33.6
188
FCT
50
90
10 8
50.5
240
100 90
3061
130x65x12
75 75
6122
M16
45 40
5198
2599
37.3
24.9
121
s s s
S S
FCT
S
M20
160x80x14
240
60
115
45
80
100
10
7383
3692
55.2
36.8
188
FCT
S
130x65x12
240
50
90
40
75
90
6245
3122
40.6
27.1
121
FCT
M20
160x80x14
240
60
115
45
85
100
8 10
s
M16
8835
4418
59.9
39.9
188
FCT
S S
S S
M 24
150x100x14
240
60
105
55
85
120
10
9121
4560
48.1
32.1
271
FCT
S
S
M16
130x65x12
240
50
'X)
40
80
90
8
7453
3726
43.8
29 2
121
FCT
S
S
IPE550
IPE600
HEB240
Rotational stiffness (kNm/rad)
Connection detail (mm)
Cleats: S235 (mm)
1PE300 IPE330
IPE360
"
S S S
Resistance
M 20
M24 IPE400
IPE450
IPE500
IPE550
Shea": (kN)
Moment (kNm)
Lbb
Lbu
43.0
188
FCT
S
S
34,5
271
FCT
S
S
48.1
32.1
121
FCT
2.7-P
2.7-P
6373
70.8
47.2
188
FCT
S
S
6538
56.7
37.8
FCT
S
S
35.7
271 121
FCT
3.1-P
3.1-P
S
wl
w2
W3
wb
wc
g
Sj,ini
Sj.ini/2
MRd
2/3MRd
160x80x14
240
60
115
45
85
100
10
10510
5255
64.6
150x100x14
240
60
105
55
'XI
120
10
10820
5410
51.8
40
85
90
8
9080
4540
45
90
100
10
12747
M16
130x65x12
240
50
M20
1 «1x80x14
240
60
115
Reference length(m)
Code
ba
90
Failure mode
VRd
La x la x ta ■
240
60 50
105 90
55 40
95 85
120 90
10 8
13076 11357
5679
53.5
240
60
115
45
95
100
10
15860
7930
78.7
52.4
188
FCT
S
62.8
41.9
271
FCT
S
S
58.9
39.3
121
FCT
3.6-P
3.6-P 2.6-P
M24
150x100x14
240
M16
130x65x12
M20
160x80x14
M24
150x100x14
240
60
105
55
100
120
10
16213
8106
M16
130x65x12
240
50
90
40
90
90
8
13940
6970
,
M20
160x80x14
240
60
115
45
95
100
10
19374
9687
86.5
57.7
188
FCT
2.6-P
M24
150x100x14
240
60
10 8
46.0
8364
64.3
42.9
FCT FCT
2.6-P
16728
271 121
2.6-P
50
120 90
69.0
240
100 95
9877
130x65x12
55 40
19753
M16
105 90
4.2-P
4.2-P
45 55 40
100 110 95
100 120 90
10 10 8
23141
11571
94.3
62.9
3.0-P
11771
75.1
50.1
FCT FCT
3.0-P
23542
3.0-P
3.0-P
M20
160x80x14
240
M 24
150x100x14
240
60 60
M16
130x65x12
240
50
115 105 90
19876
9938
69.7
46.5
188 271 121
FCT
4.9-P
4.9-P
M20 M24
160x80x14
240
60
115
45
100
100
10
27379
13690
102.2
68.1
188
FCT
3.5-P
3.5-P
150x100x14
240
60
105
55
110
120
10
27807
13904
81.2
54.2
271
FCT
3.5-P
3.5-P
M16
130x65x12
260
50
90
40
60
100
2984
1492
29.4
19.6
121
FCT
IPE240
M16
130x65x12
260
50
90
40
70
100
8 8
3516
1758
31.6
21.1
121
FCT
S S
S S
1PE270
M16
130x65x12
260
50
90
40
70
100
8
4332
2166
34.9
23.3
121
FCT
S
S
M20
160x80x14
260
60
115
45
75
110
10
6195
3097
54.7
36.4
188
FCT
S
130x65x12
260
50
90
40
75
100
8
5251
2626
38.2
25.5
121
FCT
S S
M20
160x80x14
260
60
115
45
80
110
10
7477
3739
59.8
39.8
188
FCT
M16
130x65x12
260
50
90
40
75
100
8
6313
3156
41.6
27.7
121
FCT
S S
M20
160x80x14
260
60
115
45
85
110
10
8957
4479
64.8
43.2
188
FCT
S
S S
M24
150x100x14
260
60
105
55
85
120
10
9303
4651
52.1
34.7
271
FCT
S
S
260
50
90
40
80
100
7540
3770
44.9
29.9
121
FCT
115
45
85
110
10667
5334
69.9
46.6
188
FCT
105
55
90
120
8 10 10
11050
5525
56.1
37.4
271
FCT
S S S
S S S
4598
49.3
32.9
IPE600
HEB260
(mm)
(mm)
S235
Rotational stiffness (kNm/rad)
Connection ί etail
Cleats: S235
1PE220
IPE300
IPE330
IPE360
1PE400
IPE450
M16
M16
130x65x12
M20
160x80x14
260
60
M24
150x100x14
260
60
S S
M16
130x65x12
260
50
90
40
85
100
8
9196
121
FCT
2.6-P
2.6-P
M20
160x80x14
260
60
115
45
90
110
10
12952
6476
76.7
51.2
188
FCT
S
M24
150x100x14
260
60
105
55
95
120
10
13371
6686
61.4
40.9
271
FCT
S S
M16
130x65x12
260
50
90
40
85
100
11515
5757
54.8
36.5
121
FCT
3.1-P
3.1-P
M20
160x80x14
260
60
115
45
95
110
8 10
16140
8070
85.2
56.8
188
FCT
S
S
S
Cleats: S235 (mm)
S235
IPE500
1PE550
La x la x ta
ba
wl
»2
M24
150x100x14
260
60
M16
130x65x12
260
50
M20
160x80x14
260
M24
150x100x14
260
M16
130x65x12
260
Rotational stiffness (kNm/rad)
Resistance Failure mode
Reference length(m)
j,im'
Moment (kNm) MRd 2/3MRd
16605
8302
68.1
45.4
271
FCT
S
S
14150
7075
60.3
40.2
121
FCT
3.6-P
3.6-P
19748
9874
93.7
62.5
188
FCT
2.6-P
2.6-P
20264
10132
74.7
49.8
271
FCT
S
S
8500
65.9
43.9
121
FCT
4.1-P
4.1-P
w3
wb
105
55
100
120
10
90
40
90
100
8
60
115
45
95
110
10
60
105
55
100
120
10
50
90
40
95
100
8
16999
3j,im
a
Shear (kN) VRd
Code
Lbb
Lbu
M20
160x80x14
260
60
115
45
100
110
10
23623
11812
102.2
68.1
188
FCT
3.0-P
3.0-P
M24
150x100x14
260
60
105
55
110
120
10
24187
12094
81.4
54.2
271
FCT
2.9-P
2.9-P
M16
130x65x12
260
50
90
40
95
100
8
20224
10112
71.4
47.6
121
FCT
4.8-P
4.8-P
M20
160x80x14
260
60
115
45
100
110
10
27994
13997
110.7
73.8
188
FCT
3.5-P
3.5-P
M24
150x100x14
260
60
105
55
110
120
10
28618
14309
88.0
58.7
271
FCT
3.4-P
3.4-P
IPE220
M16
130x65x12
280
50
90
40
60
100
8
2994
1497
30.1
20.1
121
FCT
S
S
IPE240
M16
130x65x12
280
50
90
40
70
100
8
3528
1764
32.4
21.6
121
FCT
S
S
IPE270
M16
130x65x12
280
50
90
40
70
100
8
4348
2174
35.8
23.8
121
FCT
S
S
M20
160x80x14
280
60
115
45
75
110
10
6232
3116
56.5
37.7
188
FCT
S
S
M16
130x65x12
280
50
90
40
75
100
8
5274
2637
39.1
26.1
121
FCT
S
S
M20
160x80x14
280
60
115
45
80
110
10
7526
3763
61.8
41.2
188
FCT
S
S
M16
130x65x12
280
50
90
40
75
100
8
6343
3171
42.5
28.4
121
FCT
S
S
M20
160x80x14
280
60
115
45
85
110
10
9022
4511
67.0
44.7
188
FCT
S
S
M24
150x100x14
280
60
105
55
85
120
10
9414
4707
56.1
37.4
271
FCT
S
S
M16
130x65x12
280
50
90
40
80
100
8
7580
3790
45.9
30.6
121
FCT
S
S
M20
160x80x14
280
60
115
45
85
110
10
10752
5376
72.3
48.2
188
FCT
S
S
M24
150x100x14
280
60
105
55
90
120
10
11191
5596
60.4
40.3
271
FCT
S
S
M16
130x65x12
280
50
90
40
85
100
8
9250
4625
50.5
33.6
121
FCT
2.6-P
2.6-P
M20
160x80x14
280
60
115
45
90
110
10
13065
6533
79.3
52.9
188
FCT
S
S
M24
150x100x14
280
60
105
55
95
120
10
13553
6777
66.1
44.1
271
FCT
S
S
M16
130x65x12
280
50
90
40
85
100
8
11591
5795
56.1
37.4
121
FCT
3.1-P
3.1-P S
IPE600
HEB280
Connection detail (mm)
IPE300 1PE330
IPE360
IPE400
IPE450
IPE500
IPE550
M20
160x80x14
280
60
115
45
95
110
10
16297
8148
88.1
58.7
188
FCT
S
M24
150x100x14
280
60
105
55
100
120
10
16848
8424
73.3
48.9
271
FCT
S
S
M16
130x65x12
280
50
90
40
90
100
8
14255
7127
61.8
41.2
121
FCT
3.6-P
3.6-P
M20
160x80x14
280
60
115
45
95
no
10
19960
9980
96.9
64.6
188
FCT
2.5-P
2.5-P
M24
150x100x14
280
60
105
55
100
120
10
20584
10292
80.5
53.6
271
FCT
S
S
M16
130x65x12
280
50
90
40
95
100
8
17137
8569
67.4
45.0
121
FCT
4.1-P
4.1-P
M20
160x80x14
280
60
115
45
100
no
10
23901
11950
105.6
70.4
188
FCT
2.9-P
2.9-P
M24
150x100x14
280
60
105
55
110
120
10
24595
12297
87.6
58.4
271
FCT
2.9-P
2.9-P
Resistance S235
w]
La x la x ta
w'2
«3
Moment (kNm) MRd 2/3MRd
wb
sj.ini
10202
73.1
aj,im'
Shear (kN)
Failure mode
Reference length(m)
VRd
Code
Lbb
Lbu
48.7
M16
130x65x12
280
50
'X)
40
95
KW
8
20404
121.
FCT
4.7-P
4.7-P
M20
160x80x14
280
60
115
45
1(X)
110
10
28353
14176
114.4
76.3
188
FCT
3.4-P
3.4-P
M24
150x100x14
280
60
105
55
110
120
10
29132
14566
94.8
63.2
271
FCT
3.3-P
3.3-P
1PE220
M16
130x65x12
300
50
90
40
60
100
8
3008
1504
30.8
20.5
121
FCT
S
S
1PE240
M16
130x65x12
300
50
90
40
70
100
8
3547
1773
33.1
22.1
121
FCT
S
S
IPE270
M16
130x65x12
3(X)
50
90
40
70
100
8
4374
2187
36.6
24.4
121
FCT
S
S
M20
160x80x14
300
60
115
45
75
110
10
6297
3148
57.4
38.3
188
FCT
S
S
M16
130x65x12
300
50
90
40
75
100
8
5307
2654
40.0
26.7
121
FCT
S
160x80x14
300
60
115
45
80
no
10
7612
3806
62.8
41.9
188
s
M20
FCT
S
S
M16
130x65x12
300
50
'X)
40
75
UX)
8
6388
3194
43.5
29.0
121
FCT
S
S
M20
160x80x14
300
60
115
45
85
110
10
9133
4566
68.1
45.4
188
FCT
M24
300
60
105
55
85
120
10
9583
4791
60.1
40.1
271
FCT
M16
130x65x12
300
50
90
40
80
100
8
7639
3820
47.0
31.3
121
FCT
M20
160x80x14
300
60
115
45
85
110
10
10896
5448
73.5
49.0
188
s s s
S
150x100x14
FCT
S
M24
150x100x14
300
60
105
55
90
120
10
11406
5703
64.7
43.2
271
FCT
S
S
M16
130x65x12
300
50
90
40
85
100
8
9329
4665
51.6
34.4
121
FCT
2.6-P
2.6-P
M20
160x80x14
300
60
115
45
90
110
10
13256
6628
80.6
53.7
188
FCT
S
S
M24
150x100x14
300
60
105
55
95
120
10
13831
6915
70.9
47.2
27!
FCT
S
S
200x100x16
300
65
150
65
95
130
12
17777
8889
82.2
54.8
35
FCT
S
S
M16
130x65x12
300
50
90
40
85
100
8
11703
5852
57.4
38.3
121
FCT
3.0-P
3.0-P
M20
160x80x14
300
60
115
45
95
110
10
16559
8280
89.5
59.7
188
FCT
S
S
100
120
10
17221
8610
78.5
52.4
271
FCT
S
S
IPE600
HEB300
Rotational stiffness (kNm/rad)
Connection detall (mm)
Cleats S235 (nini)
1PE300 IPE330
IPE360
IPE400
M27 IPE450
1PE500
1PE550
S
s
M24
150x100x14
300
60
105
55
M27
200x100x16
300
65
150
65
110
130
12
21956
10978
90.8
60.6
352
FCT
S
S
M16
130x65x12
300
50
90
40
90
100
8
14409
7205
63.2
42.1
121
FCT
3.5-P
3.5-P
M20
160x80x14
300
60
115
45
95
110
10
20313
10156
98.4
65.6
188
FCT
S
S
M24
150x100x14
300
60
105
55
100
120
10
21074
10537
86.2
57.5
271
FCT
S
S
M27
200x100x16
300
65
150
65
110
130
12
26668
13334
99.5
66.4
352
FCT
S
S
M16
130x65x12
300
50
90
40
95
100
8
17342
8671
69.0
46.0
121
FCT
4.1-P
4.1-P
M20
160x80x14
300
60
115
45
100
110
10
24359
12179
107.4
71.6
188
FCT
2.9-P
2.9-P
300
60
105
55
110
120
10
25218
12609
93.9
62.6
271
FCT
2.8-P
2.8-P
65
150
65
120
130
12
31708
15854
108.2
72.1
352
FCT
S
S
40
95
100
8
20671
10335
74.8
49.8
121
FCT
4.7-P
4.7-P
45
100
110
10
28942
14471
116.3
77.5
188
FCT
3.3-P
3.3-P
55
110
120
10
29921
14960
101.5
67.7
271
FCT
3.2-P
3.2-P
M24 M27 1PE600
S
150x100x14 200x100x16
300
M16
130x65x12
300
50
90
M20
160x80x14
300
60
115
M24
150x100x14
300
60
105
Resistance S235
HEB320
La x la x ta
ba
wl
»3
»b
Sj.ini
°J,ini'-
Moment (kNm) MRd 2/3MRd
Shear (kN) VRd
Failure mode
Reference length! m)
Code
Lbb
Lbu
FCT
S S S
S S S
M27
200x100x16
300
65
150
65
120
130
12
37380
18690
116.9
77.9
IPE220
M16
130x65x12
300
50
352 121
50
8 8
20.5
300
100 100
30.8
130x65x12
60 70
1504
M16
40 40
3008
IPE240
90 90
3548
1774
33.1
22.1
121
FCT FCT
IPE270
M16
130x65x12
300
50
90
40
70
100
8
4376
2188
36.6
24.4
121
FCT
S
S
M20
160x80x14
300
60
115
45
75
110
10
6312
3156
57.4
38.3
188
FCT
S
S
M16
130x65x12
300
50
90
40
75
100
8
5312
2656
40.0
26.7
121
FCT
S
S
M20
160x80x14
3(X)
60
115
45
80
110
10
7633
3817
62.8
41.9
188
FCT
S
S
M16
130x65x12
300
50
90
40
75
100
8
6395
3197
43.5
29.0
121
FCT
S
S
M20
160x80x14
300
60
115
45
85
110
10
9163
4581
68.1
45.4
188
FCT
S
S
M24
150x100x14
300
60
105
55
85
120
10
9627
4814
60.1
40.1
271
FCT
S
S
M16
130x65x12
300
50
90
40
80
100
8
7650
3825
47.0
31.3
121
FCT
S
S
M20 M24
160x80x14
300
60
115
45
85
110
10
10937
5468
73.5
49.0
188
FCT
150x100x14
300
60
105
55
90
120
10
11466
5733
64.7
43.2
271
FCT
S S
S S
M16
130x65x12
300
50
90
40
85
100
8
9347
4673
51.6
34.4
121
FCT
2.6-P
2.6-P
M20
160x80x14
300
60
115
45
90
110
10
13314
6657
80.6
53.7
188
FCT
S
S
M24
150x100x14
300
60
105
55
95
120
10
13911
6956
70.9
47.2
271
FCT
S
S
M27
200x100x16
300
65
150
65
95
130
12
17931
8966
82.2
54.8
352
FCT
S
S
M16
130x65x12
300
50
90
40
85
100
8
11732
5866
57.4
38.3
12'
FCT
3.0-P
3.0-P
IPE300 IPE330
1PE360
IPE400
IPE450
IPE5IX)
1PF.550
IPE600
HEB340
Rotational stiffness (kNm/rad)
Connection detail (mm)
Cleats: S235 (mm)
IPF220
M20
160x80x14
300
45 55
95 100
110 120
10 10
89.5
59.7
S
S
17335
8667
78.5
52.4
188 271
FCT
M24
115 105
8322
300
60 60
16645
150x100x14
FCT
S
S
M27
200x100x16
300
65
150
65
110
130
12
22168
11084
90.8
60.6
352
FCT
S
S
M16
130x65x12
300
50
90
40
90
100
14452
7226
63.2
42.1
12!
FCT
3.5-P
3.5-P
M20
160x80x14
300
60
115
45
95
110
8 10
20434
10217
98.4
65.6
18.5
FCT
S
S
10616
86.2
57.5
271
FCT
S
S
13476
99.5
66.4
FCT
S
S 4.0-P
M24
150x100x14
3(X)
60
105
55
100
120
10
21231
M27
2(X)xlO0xl6
3(X)
130x65x12
300
150 90
65 40
110 95
130 100
12 8
26953
M16
65 50
17404
8702
69.0
46.0
352 121
FCT
4.0-P
12262
107.4
71.6
188
FCT
2.9-P
2.9-P
62.6
271
FCT
2.8-P
2.8-P
M20
160x80x14
3(X)
60
115
45
100
110
10
24524
M24
150x100x14
300
60
105
55
110
120
10
25427
12714
93.9
M27
200x100x16
300
65
150
65
120
130
12
32077
16039
108.2
72.1
352
FCT
S
S
M16
130x65x12
300
50
90
40
95
100
8
20757
10378
74.8
49.8
121
FCT
4.7-P
4.7-P
M20
160x80x14
300
60
115
45
100
110
10
29162
14581
116.3
77.5
188
FCT
3.3-P
3.3-P
M24
150x100x14
3(X)
60
105
55
110
120
10
30195
15098
101.5
67.7
271
FCT
3.2-P
3.2-P
M27
200x100x16
300
65
150
65
120
130
12
37854
18927
116.9
77.9
352
FCT
M16
130x65x12
300
50
90
40
60
1(X)
8
3006
1503
30.8
20.5
121
FCT
S S
S S
Resistance
S235
wl
La x la x ta IPE240 IPE270
IPE330
1PE360
IPE400
1PE450
IPE500
wl,
aj,ini
3
J,mi'
MRd
2/3MRd
Shear (kN) VR-1
Failure mode
Reference lengdi(m)
Code
Lbb
Lbu
130x65x12
3(X)
40
70
100
8
3546
1773
33.1
22.1
121
FCT
S
S
M16
300
50 50
90
130x65x12
90
40
70
100
8
4375
2187
36.6
24.4
121
FCT
S
S
160x80x14
300
60
115
45
75
110
10
6318
3159
57.4
38.3
188
FCT
S
S
300
50
90 115
40 45
75 80
100 110
8 10
5312
2656
40.0
26.7
3822
62.8
41.9
FCT FCT
S
7644
121 188
S S
90 115 105
40 45 55
75 85 85
100 110 120
8 10 10
6397
3198
43.5
29.0
9179
4589
68.1
45.4
9654
4827
60.1
40.1
121 188 271
FCT FCT FCT
50
90
40
80
100
8
7655
3827
47.0
31.3
121
FCT
115 105
45 55
85 90
110 120
10 10
10960
5480
73.5
49.0
11502
5751
64.7
43.2
188 271
FCT FCT
M16
130x65x12
M20
160x80x14
300
60
M16
130x65x12
M20
160x80x14
300 300
50 60
M24
150x100x14
300
60
s s s s s s s
S
s s s s s
M16
130x65x12
M20
160x80x14
300 300
M24
150x100x14
300
60 60
M16
130x65x12
300
50
90
40
85
100
8
9355
4678
51.6
34.4
121
FCT
2.6-P
2.6-P
M20 M24
160x80x14
3«)
60
115
45
90
110
10
13349
6675
80.6
53.7
188
FCT
150x100x14
300
60
105
55
95
120
10
13963
6981
70.9
47.2
271
FCT
200x100x16
M16
130x65x12
300 300 300
s s
M27
s s s
65
150
65
95
130
12
18033
9016
82.2
54.8
352
FCT
90 115
40 45
85 95
100 110
8 10
11748
5874
57.4
38.3
3.0-P
8350
89.5
59.7
105 150 90
55 65 40
100 110 90
120 130 100
10 12 8
17411
8705
78.5
52.4
22312
11156
90.8
60.6
7240
63.2
s s s
S S S
14479
FCT FCT FCT FCT FCT
3.0-P
16700
121 188
S
M20
160x80x14
M 24
150x100x14
M27
200x100x16
300 300
130x65x12
300
50 60 60 65 50
42.1
27; 352 121
3.5-P
3.5-P
160x80x14
300
60
115
45
95
110
10
20515
10258
98.4
65.6
188
FCT
S
S
300
60
105
55
100
120
10
21339
10669
86.2
57.5
27-
FCT
S
S
65
110
130
12
27150
13575
99.5
66.4
352
FCT
M16 M20 M24
150x100x14
M27
200x100x16
300
65
150
S
S
M16
130x65x12
50
90
40
95
100
8
17444
8722
69.0
46.0
121
FCT
4.0-P
4.0-P
M20 M24
160x80x14
300 300
71.6
2.8-P
2.8-P
32338
16169
108.2
72.1
FCT FCT FCT
2.9-P
62.6
188 271 352
2.9-P
93.9
65
10 10 12
107.4
300
110 120 130
12787
200x100x16
100 110 120
25574
M27
45 55 65
12319
300
115 105 150
24638
150x100x14
60 60
S
S
M16
130x65x12
300
50
90
40
95
100
8
20815
10408
74.8
49.8
121
4.6-P
4.6-P
M20 M24 M27
160x80x14
300
60
115 105
45 55
100 110
110 120
10 10
29318
14659
116.3
77.5
3.3-P
3.3-P
30391
15195
101.5
67.7
188 271
FCT FCT FCT
3.2-P
3.2-P
200x100x16
130 100
12 8
116.9
77.9
IPE220
120 60
19098
130x65x12
65 40
38195
M16
150 90
3004
1502
30.8
20.5 .
352 121
FCT FCT
S S
1PE240
M16
130x65x12
70 70
100 100
8 8
33.1
22.1
IPE270
40 40
1772
130x65x12
90 90
3544
M16
4373
2187
36.6
24.4
121 121
FCT FCT
S S S S
IPE550
IPE600
HEB360
w3
Moment (kNm)
M16 M20
IPE300
Rotational stiffness (kNm/rad)
Connection d etail (mm)
Cleats: S235 (mm)
150x100x14
300 300
60 65
300 300 300
50 50 50
S S
Resistance Cleats: S235 (mm)
S235
La x la x ta
1PE300
1PE330
IPE360
1PF.400
1PE450
wl
w2
«3
Si.i 'J,un
wb
(kN) VRd
Code
Lbb
Lbu
Reference length(m)
300
60
115
45
75
110
10
6323
3161
57.4
38.3
188
FCT
S
S
130x65x12
300
50
90
40
75
100
8
5311
2656
40.0
26.7
121
FCT
S
S
M20
160x80x14
300
60
115
45
80
110
10
7651
3826
62.8
41.9
FCT
M16 M20
130x65x12
90 115 105
40 45 55
75 85 85
100
3198
43.5
29.0
FCT
9191
4595
68.1
45.4
FCT
S
S S S
120
8 10 10
6397
150x100x14
50 60 60
S S
M24
300 300 300
188 121 188
9676
4838
60.1
40.1
271
FCT
S
S
M16
130x65x12
300
50
90
40
80
100
8
7657
3828
47.0
31.3
121
FCT
S
S
M20 M24
160x80x14
85 90 85 90
10 10 8 10
5489
73.5
49.0
11533
5766
64.7
43.2
S S
S S
9361
4681
51.6
34.4
188 271 121
FCT FCT
130x65x12
45 55 40 45
10979
M16
115 105 90 115
no
150x100x14
300 300 300
FCT
2.6-P
2.6-P
13378
6689
80.6
53.7
188
FCT
S
S
FCT FCT FCT
S S
S S
3.0-P
3.0-P
FCT
S
S
S S
S
3.5-P
3.5-P
S
S S
160x80x14
no
■
M20
160x80x14
300
60 60 50 60
M24 M27 M16 M20
150x100x14
300
60
105
55
95
120
10
14007
7003
70.9
47.2
200x100x16
300 300 300
65 50 60
150 90 115
65 40 45
95 85 95
130 100 110
12 8 10
18120
9060
82.2
54.8
11759
5880
57.4
38.3
16745
8373
89.5
59.7
271 352 121 188
60 65 50 60 60
105 150 90 115 105
55 65 40 45 55
100 110 90 95 100
120 130 100 110 120
10 12 8 10 10
17476
8738
78.5
52.4
271
FCT
22436
11218
90.8
60.6
352 121 188 271
FCT FCT FCT FCT FCT FCT FCT FCT
130x65x12 160x80x14
120 100
no
M27 M16 M20 M24
200x100x16
150x100x14
M27
200x100x16
300
65
150
65
110
130
M16 M20
130x65x12
90 115 105
40 45 55
95 100 110
no
150x100x14
50 60 60
100
M24 M27
300 300 300
200x100x16
300
65
150
65
M16
130x65x12
300
50
90
M20
160x80x14
300
60
M24
150x100x14
300
60
M27
200x100x16
300
65
IPE220
M16
130x65x12
300
IPE240
M16
130x65x12
IPE270
M16
130x65x12
M20 M16
IPE3(X)
Failure mode
160x80x14
300 300 300 300 300
IPE600
She;,r
M16
150x100x14
IPE550
aj.iru'.
Moment (kNm) MRd 2/3MRd
M20
M24 IPE500
HEB400
Rotational stiffness (kNm/rad)
Connection detail (mm)
S
14500
7250
63.2
42.1
20584
10292
98.4
65.6
21432
10716
86.2
57.5
12
27322
13661
99.5
66.4
17476
8738
69.0
46.0
24734
12367
107.4
71.6
120
8 10 10
25701
12850
93.9
62.6
352 121 188 27!
120
130
12
32567
16284
108.2
72.1
352
FCT
S
S
40
95
100
8
20863
10431
74.8
49.8
121
FCT
4.6-P
4.6-P
115
45
100
no
10
29452
14726
116.3
77.5
188
FCT
3.3-P
3.3-P
105
55
no
120
10
30562
15281
101.5
67.7
271
FCT
3.2-P
3.2-P
150
65
120
130
12
38496
19248
116.9
77.9
352
FCT
S
S
50
90
40
60
100
8
2998
1499
30.8
20.5
121
FCT
S
S
300
50
90
40
70
100
8
3538
1769
33.1
22.1
121
FCT
S
S
50
90
40
70
100
8
4367
2184
36.6
24.4
121
FCT
160x80x14
300 300
ω
115
45
75
110
10
6324
3162
57.4
38.3
FCT
S
130x65x12
300
50
90
40
75
100
8
5305
2653
40.0
26.7
188 121
S S
FCT
S
S
130x65x12 160x80x14
160x80x14
S S
S
4.0-P
4.0-P
2.8-P
2.8-P
S
S
S
Resistance S235
La x la x ta
IPE330
1PE360
IPE400
IPF.450
1PE500
IPE550
IPE600
HEB450
Rotational stiffness (kNm/rad)
Connection de (mm)
Cleats: S235 (mm)
w3
ba
wb
Moment (kNm)
Sj.ini
3j,ini'
MRd
2/3MRd
Shear (kN) VRd
10
7657
3828
62.8
41.9
Failure mode Code
Reference length(m) Lbb
Lbu
M20
160x80x14
300
60
115
45
80
110
188
FCT
S
S
M16
130x65x12
300
50
90
40
75
100
8
6392
3196
43.5
29.0
12!
FCT
S
S
M20
160x80x14
300
60
115
45
85
110
10
9202
4601
68.1
45.4
188
FCT
S
S
M24
150x100x14
3(X)
60
105
55
85
120
10
9703
4851
60.1
40.1
271
FCT
S
130x65x12
3(X)
50
90
40
80
100
8
7654
3827
47.0
31.3
121
FCT
s
M16
S
S
M20
160x80x14
300
60
115
45
85
110
10
10998
5499
73.5
49.0
188
FCT
S
S
M24
150x100x14
300
60
105
55
90
120
10
11572
5786
64.7
43.2
27!
FCT
S
S
M16
130x65x12
300
50
90
40
85
100
8
9363
4681
51.6
34.4
121
FCT
2.6-P
2.6-P S
M20
160x80x14
3(X)
60
115
45
90
110
10
13412
6706
80.6
53.7
188
FCT
S
M24
150x100x14
300
ω
105
55
95
120
10
14065
7033
70.9
47.2
271
FCT
S
S
M27
200x100x16
300
65
150
65
95
130
12
18242
9121
82.2
54.8
352
FCT
S
S
M16
130x65x12
300
50
90
40
85
100
8
11769
5885
57.4
38.3
121
FCT
3.0-P
3.0-P
M20
160x80x14
300
60
115
45
95
110
10
16803
8402
89.5
59.7
188
FCT
S
S
M 24
150x100x14
300
60
105
55
100
120
10
17566
8783
78.5
52.4
271
FCT
S
S
M27
200x100x16
300
65
150
65
110
130
12
22615
11307
90.8
60.6
352
FCT
S
S
M16
130x65x12
300
50
90
40
90
100
8
14521
7261
63.2
42.1
121
FCT
3.5-P
3.5-P
M20
160x80x14
300
60
115
45
95
110
10
20675
10338
98.4
65.6
188
FCT
S
S
M24
150x100x14
300
60
105
55
100
120
10
21564
10782
86.2
57.5
271
FCT
S
s
M27
200x100x16
300
65
150
65
110
130
12
27574
13787
99.5
66.4
352
FCT
S
S
M16
130x65x12
300
50
90
40
95
100
8
17514
8757
69.0
46.0
121
FCT
4.0-P
4.0-P
M20
160x80x14
300
60
115
45
100
110
10
24869
12434
107.4
71.6
188
FCT
2.8-P
2.8-P
M24
150x100x14
300
60
105
55
110
120
10
25886
12943
93.9
62.6
271
FCT
S
S
M27
200x100x16
300
65
150
65
120
130
12
32909
16454
108.2
72.1
352
FCT
S
S
M16
130x65x12
300
50
90
40
95
100
8
20924
10462
74.8
49.8
121
FCT
4.6-P
4.6-P
M20
160x80x14
300
60
115
45
100
110
10
29642
14821
116.3
77.5
188
FCT
3.3-P
3.3-P
110
120
10
30815
15408
101.5
67.7
271
FCT
3.1-P
3.1-P
M24
150x100x14
300
60
105
55
M27
200x100x16
300
65
150
65
120
130
12
38951
19475
116.9
77.9
352
FCT
S
S
IPE220
M16
130x65x12
300
50
90
40
60
100
8
2979
1489
30.8
20.5
121
FCT
S
S
IPE240
M16
130x65x12
300
50
90
40
70
100
8
3515
1758
33.1
22.1
121
FCT
S
S
M16
130x65x12
300
50
90
40
70
100
8
4340
2170
36.6
24.4
121
FCT
S
S
M20
160x80x14
300
60
115
45
75
110
10
6287
3144
57.4
38.3
188
FCT
S
M16
130x65x12
300
50
90
40
75
100
8
5274
2637
40.0
26.7
121
FCT
S
M20
160x80x14
300
60
115
45
80
110
10
7615
3807
62.8
41.9
188
FCT
S
130x65x12
300
50
90
40
75
100
8
6355
3178
43.5
29.0
121
FCT
S
s s s s
1PE270 1PE300 IPE330
M16
Resistance S235
IPE360
1PE400
1PE450
IPE500
1PE550
IPE600
HEB500
Connection detail (mm)
Cleats: S235 (mm)
Rotational stiffness (kNm/rad)
Moment (kNm)
Shear (kN)
Si.i 'J,ini
aj.mi'.
MRd
2/3MRd
10
9155
4577
68.1
10
9672
4836
60.1
100
8
7611
3805
85
no
10
10945
55
90
120
10
90
40
85
100
60
115
45
90
300
60
105
55
95
300
65
150
65 40
La x la x ta
ba
wl
w2
w3
wb
M20
160x80x14
300
60
115
45
85
110
M24
150x100x14
300
60
105
55
85
120
M16
130x65x12
300
50
90
40
80
M20
160x80x14
300
60
115
45
M24
150x100x14
300
60
105
M16
130x65x12
300
50
M20
160x80x14
300
M24
150x100x14
M27
200x100x16
Failure mode
Reference lengüi(m)
VRd
Code
Lbb
Lbu
45.4
188
FCT
S
S
40.1
271
FCT
S
S
47.0
31.3
121
FCT
S
S
5472
73.5
49.0
188
FCT
S
S
11540
5770
64.7
43.2
271
FCT
S
S
8
9313
4656
51.6
34.4
121
FCT
2.6P
2.6P
no
10
13353
6676
80.6
53.7
188
FCT
S
S
120
10
14033
7017
70.9
47.2
271
FCT
S
S
95
130
12
18228
9114
82.2
54.8
352
FCT
S
S
85
100
8
11711
5856
57.4
38.3
121
FCT
3.0P
3.0P
M16
130x65x12
300
50
90
M20
160x80x14
300
60
115
45
95
110
10
16740
8370
89.5
59.7
188
FCT
S
S
M24
150x100x14
300
60
105
55
100
120
10
17538
8769
78.5
52.4
271
FCT
S
S
M27
200x100x16
300
65
150
65
110
130
12
22617
11308
90.8
60.6
352
FCT
S
S
M16
130x65x12
300
50
90
40
90
100
8
14456
7228
63.2
42.1
121
FCT
3.5P
3.5P S
M20
160x80x14
300
60
115
45
95
no
10
20612
10306
98.4
65.6
188
FCT
S
M24
150x100x14
300
60
105
55
100
120
10
21545
10773
86.2
57.5
271
FCT
S
S
M27
200x100x16
300
65
150
65
no
130
12
27602
13801
99.5
66.4
352
FCT
S
S
M16
130x65x12
300
50
90
40
95
100
8
17444
8722
69.0
46.0
12¡
FCT
4.0P
4.0P
M20
160x80x14
300
60
115
45
100
no
10
24810
12405
107.4
71.6
18 ;
FCT
2.8P
2.8P
M24
150x100x14
300
60
105
55
no
120
10
25882
12941
93.9
62.6
271
FCT
S
S
M27
200x100x16
300
65
150
65
120
130
12
32972
16486
108.2
72.1
352
FCT
S
S
M16
130x65x12
300
50
90
40
95
100
8
20849
10425
74.8
49.8
121
FCT
4.6P
4.6P
M20
160x80x14
300
60
115
45
100
no
10
29593
14796
116.3
77.5
188
FCT
3.3P
3.3P
no
120
10
30833
15417
101.5
67.7
271
FCT
3.1P
3.1P S
M24
150x100x14
300
60
105
55
M27
200x100x16
300
65
150
65
120
130
12
39062
19531
116.9
77.9
352
FCT
S
1PE220
M16
130x65x12
300
50
90
40
ω
no
8
2992
1496
30.8
20.5
121
FCT
S
S
IPE240
M16
130x65x12
300
50
90
40
70
110
8
3531
1765
33.1
22.1
121
FCT
S
S
IPE270
M16
130x65x12
300
50
90
40
70
no
8
4361
2180
36.6
24.4
121
FCT
S
S
M20
160x80x14
300
60
115
45
75
120
10
6313
3157
57.4
38.3
188
FCT
S
S
M16
130x65x12
300
50
90
40
75
no
8
5301
2650
40.0
26.7
121
FCT
S
S
M20
160x80x14
300
60
115
45
80
120
10
7649
3825
62.8
41.9
188
FCT
S
S
M16
130x65x12
300
50
90
40
75
no
8
6390
3195
43.5
29.0
121
FCT
S
S
M20
160x80x14
300
60
115
45
85
120
10
9200
4600
68.1
45.4
188
FCT
S
S
M24
150x100x14
300
60
105
55
85
130
10
9708
4854
60.1
40.1
271
FCT
S
S
IPE300
1PE330
Resistance
1PE360
IPE400
IPE450
IPE500
La x la x ta
ba
wl
w'2
w3
wb
wc
M16
130x65x12
300
40
80
110
160x80x14
300
50 60
90
M20
115
45
85
120
M24
150x100x14
300
60
M16
130x65x12
300
50
105 90
55 40
90 85
130 110
10 8
M20
160x80x14
300
60
115
45
90
120
M24
150x100x14
300
60
105
55
95
M27
200x100x16
300
65
150
65
3(X)
50
90
40
115
M16
130x65x12
Moment (kNm) MRd 2/3MRd
Sj.ini
Sj,ini/2
8
7655
3828
47.0
10
11004
5502
73.5
11587
5793
64.7
43.2
9371
4685
51.6
10
13433
6716
130
10
14098
95
140
12
85
110
8
45
95
120
10
g
Shear (kN)
Failure mode
Reference length(m)
VRd
Code
Lbb
Lbu
31.3
121
FCT
49.0
188
FCT
S S
34.4
271 121
FCT FCT
2.6-P
s s s
80.6
53.7
188
FCT
S
7049
70.9
47.2
271
FCT
S
18316
9158
82.2
54.8
352
FCT
S
11790
5895
57.4
38.3
121
FCT
3.0-P
16852
8426
89.5
59.7
188
FCT
S
S
2.6-P
s s s
3.0-P
s
M20
160x80x14
300
60
M24
150x100x14
300
60
105
55
100
130
10
17631
8815
78.5
52.4
271
FCT
S
M27
200x100x16
65
150
65
110
140
12
22744
11372
90.8
60.6
352
FCT
S
S S
M16
130x65x12
300 300
50
90
40
90
110
8
14562
7281
63.2
42.1
121
FCT
3.5-P
3.5-P
10382
98.4
65.6
188
FCT
S
S
57.5
271
FCT
S
S
M 20
160x80x14
3(X)
60
115
45
95
120
10
20764
M24
150x100x14
300
60
105
55
100
130
10
21674
10837
86.2
M27
200x100x16
300
65
150
65
110
140
12
27781
13890
99.5
66.4
352
FCT
S
S
M 16
130x65x12
300
50
8 10
46.0
4.0-P
4.0-P
25010
12505
107.4
71.6
121 188
FCT
60
110 120
69.0
300
95 100
8790
160x80x14
40 45
17581
M20
90 115
FCT
2.8-P
2.8-P
M 24
150x100x14
300
60
105
55
110
130
10
26055
13027
93.9
62.6
271
FCT
S
S
M27
200x100x16
300
65
150
65
120
140
12
33212
16606
108.2
72.1
352
FCT
S
S
M16
130x65x12
300
50
90
40
95
110
8
21025
10512
74.8
49.8
121
FCT
4.6-P
4.6-P
M20
160x80x14
300
60
115
45
100
120
10
29855
14927
116.3
77.5
188
FCT
3.2-P
3.2-P
M24
150x100x14
300
60
105
55
110
130
10
31063
15531
101.5
67.7
271
FCT
3.1-P
3.1-P
M27
200x100x16
300
65
150
65
120
140
12
39382
19691
116.9
77.9
352
FCT
IPE220
M16
130x65x12
300
50
90
40
60
110
2976
1488
30.8
20.5
121
FCT
M16
130x65x12
300
50
90
40
70
110
3512
1756
33.1
22.1
121
FCT
S S S
S S
IPE240
8 8
M16
130x65x12
300
50
90
40
70
110
8
4338
2169
36.6
24.4
121
FCT
S
S
160x80x14
300
60
115
45
75
120
10
6279
3139
57.4
38.3
188
FCT
S
S
M16
130x65x12
300
50
8 10
26.7
S
S
7609
3804
62.8
41.9
121 188
FCT
60
110 120
40.0
300
75 80
2637
160x80x14
40 45
5274
M20
90 115
FCT
S
S
6358
3179
43.5
29.0
S
4576
68.1
45.4
121 188
FCT
9152
FCT
s s s s
S S
IPE550
IPE600
HEB550
(mm)
(mm)
S235
Rotational stiffness (kNm/rad)
Connection c e tail
Cleats: S235
IPE270
M20 IPE300 IPE330
IPE360
M16
130x65x12
300
50
M20
160x80x14
300
60
90 115
40 45
75 85
110 120
8 10
M 24
150x100x14
300
60
105
55
85
130
10
9669
4835
60.1
40.1
271
FCT
8 10
7618
3809
47.0
31.3
10949
5474
73.5
49.0
121 188
FCT FCT
M16
130x65x12
300
50
M20
160x80x14
300
60
90 115
40 45
80 85
110 120
S
S S S
Resistance Cleats: S235 (mm)
S235
Rotational stiffness
(mm)
(kNm/rad)
Moment (kNm)
Failure mode
Reference length(m)
Sj,ini/2
MRd
2/3MRd
Shear (kN) VR ι
11543
5772
64.7
43.2
271
FCT
S
S
9326
4663
51.6
34.4
121
FCT
2.6-P
2.6-P
10
13369
6685
80.6
53.7
188
FCT
S
S
10
14049
7024
70.9
47.2
271
FCT
S
S
140
12
18260
9130
82.2
54.8
352
FCT
S
S
110
8
11738
5869
57.4
38.3
121
FCT
3.0-P
3.0-P
95
120
10
16779
8389
89.5
59.7
188
FCT
S
S
100
130
10
17577
8788
78.5
52.4
271
FCT
S
S
110
140
12
22687
11344
90.8
60.6
352
FCT
S
S
40
90
no
8
14501
7250
63.2
42.1
121
FCT
3.5-P
3.5-P
45
95
120
10
20682
10341
98.4
65.6
188
FCT
S
S
105
55
100
130
10
21617
10809
86.2
57.5
271
FCT
S
S
65
150
65
no
140
12
27726
13863
99.5
66.4
352
FCT
S
S
300
50
90
40
95
8
17512
8756
69.0
46.0
121
FCT
4.0-P
4.0-P
160x80x14
300
60
115
45
100
no 120
10
24922
12461
107.4
71.6
188
FCT
2.8-P
2.8-P
150x100x14
3(X)
60
105
55
no
130
10
25998
12999
93.9
62.6
271
FCT
S
S
200x100x16
300
65
150
65
120
140
12
33167
16583
108.2
72.1
352
FCT
S
S
M16
130x65x12
300
50
90
40
95
20948
10474
74.8
49.8
121
FCT
4.6-P
4.6-P
M20
160x80x14
300
60
115
45
100
no
8
120
10
29762
14881
116.3
77.5
188
FCT
3.2-P
3.2-P
M24
150x100x14
300
60
105
55
130
10
31009
15505
101.5
67.7
271
FCT
3.1-P
3.1-P
M27
200x100x16
300
65
150
65
120
140
12
39351
19675
116.9
77.9
352
FCT
S
S
IPE220
M16
130x65x12
300
50
90
40
60
2960
1480
30.8
20.5
12,
FCT
S
S
IPE240
M16
130x65x12
300
50
90
40
70
8
3494
1747
33.1
22.1
121
FCT
S
S
1PE270
M16
130x65x12
300
50
90
40
70
no no no
8 8
4316
2158
36.6
24.4
121
FCT
S
S
M20
160x80x14
3(X)
60
115
45
75
120
10
6245
3122
57.4
38.3
188
FCT
M16
130x65x12
300
50
90
40
75
110
8
5247
2624
40.0
26.7
121
FCT
M20
160x80x14
300
60
115
45
80
120
10
7569
3784
62.8
41.9
188
FCT
M16
130x65x12
300
50
90
40
75
6327
3163
43.5
29.0
121
FCT
M20
160x80x14
300
60
115
45
85
no
8
120
10
9105
4553
68.1
45.4
188
FCT
M24
150x100x14
300
60
105
55
85
130
10
9631
4815
60.1
40.1
271
FCT
M16
130x65x12
300
50
90
40
80
no
8
7580
3790
47.0
31.3
121
FCT
M20
160x80x14
300
60
115
45
85
120
10
10893
5447
73.5
49.0
188
FCT
M24
150x100x14
300
60
105
55
90
130
10
11498
5749
64.7
43.2
271
FCT
s s s s s s s s s
S
M16
130x65x12
300
50
90
40
85
110
8
9282
4641
51.6
34.4
121
FCT
2.6-P
IPE400
1PE450
IPE500
IPE550
1PE600
HEB6O0
Connection c e tail
IPE300 1PE330
IPE360
IPE4(X)
La χ la x t a
ba
wl
w2
M24
150x100x14
300
60
M16
130x65x12
300
50
M20
160x80x14
300
M24
150x100x14
M27
w3
wb
Wc
g
Sj.ini
105
55
90
130
10
90
40
85
60
115
45
90
no
8
120
300
60
105
55
95
130
200x100x16
300
65
150
65
95
M16
130x65x12
300
50
90
40
85
M20
160x80x14
300
60
115
45
M24
150x100x14
300
60
105
55
M27
200x100x16
300
65
150
65
M16
130x65x12
300
50
90
M20
160x80x14
300
60
115
M24
150x100x14
300
60
M27
200x100x16
300
M16
130x65x12
M20 M24 M27
no
Code
Lbb
Lbu
S S S S S S S S 2.6-P
Resistance
S235
La x la x 'a
IPF450
1PE500
IPE550
IPE600
Rotational stiffness (kNm/rad)
Connection detail (mm)
Cleats: S235 (mm)
w3
ba
»1,
=>j,ini
a
j , i n i II
Moment (kNm) MRd 2/3MRd
Shear (kN) VR.-I
M20 M24
160x80x14
300
60
115
45
90
120
10
150x100x14
3(X)
47.2
300 300
18199
9100
82.2
54.8
11684
5842
57.4
38.3
M20 M24 M27
120
10 12 8 10
70.9
130x65x12
95 95 85 95
6999
200x100x16
55 65 40 45
130 140
M16
105 150 90 115
13998
M27
16702
8351
89.5
59.7
150x100x14
60 65 50 60 60
105 150
55 65
100 110
130 140
10 12
17518
8759
78.5
52.4
22622
11311
90.8
60.6
271 352
160x80x14 200x100x16
300 300 300
110
8
14437
7219
63.2
42.1
121
120 130
10 10
20594
10297
98.4
65.6
21553
10777
86.2
57.5
188 271
65 50
150 90
65 40
110 95
140 110
12 8
27659
13829
99.5
66.4
300
17440
8720
69.0
46.0
300 300 300
60 60 65
115 105 150
45 55 65
100 110 120
120 130 140
10 10 12
24826
12413
107.4
71.6
25930
12965
93.9
62.6
33102
16551
108.2
72.1
300 300 300 300
50 60 60
90 115 105
40 45 55
95 100
8 10 10
20867
10433
74.8
49.8
29657
14829
116.3
77.5
lit)
110 120 130
30940
15470
101.5
65
150
65
120
140
12
39293
19647
116.9
200x100x16 130x65x12
M20 M24 M27
160x80x14 150x100x14
M16 M20 M24 M27
160x80x14 150x100x14 200x100x16
FCT FCT
90
M16
130x65x12
FCT
95 100
150x100x14
S S
188 271 352 121 188
40
M24 M27
S S
53.7
45 55
300 300 300
Lbu
80.6
90
3(X)
160x80x14
Lbb
6652
115 105
130x65x12
M 20
Reference lengtli(m)
Code
13304
60 60
M16
200x100x16
65 50
lit)
Failure mode
FCT FCT FCT FCT FCT
S
S
3.0-P
3.0-P
S
S
S S
S S
3.5-P
3.5-P
FCT FCT FCT
S S
S S
S
S
FCT
4.0-P
4.0-P
188 271 352
FCT
2.8-P
2.8-P
FCT FCT
S
S
67.7
121 188 271
77.9
352
FCT FCT FCT FCT
352 121
S
S
4.6-P
4.6-P
3.3-P
3.3-P
3.1-P
3.1-P
S
S
ß =i
bo wc
k,
wb
=1
kfc=l w3
c
e
o U
ΥΛΛ = 1 2 5
:L to
JZ
MRd VRd
ra O)
ca
ca
Failure mode
Code
Failure mode
Code
Failure mode
Code
Column web panei in shear
CWS
Column web in tension
CWT
Bolts in shear
BS
CWC
Column flange in tension
CFT
BFC
Flange cleat in tension
FCT
BT
Flange cleat in bearing
FC Β
Column web in compression Beam flange in compression Bolts in tension
Beam flange in bearing
BFB
Resistance
HEB 140
HEB 160
L a x la x t a
ba
wl
w2
»3
wl,
wc
Sj,ini
Sj,ini/2
Moment (kNm) MRd 2/3MRd
Shear (kN) VRri
Failure mode
Reference length(m)
Code
Lbb
Lbu
IPE220
M16
130x65x12
140
50
90
40
60
80
8
2786
1393
20.4
13.6
125
FCT
S
S
IPE240
M16
130x65x12
140
50
90
40
70
80
8
3262
1631
21.9
14.6
125
FCT
S
s
1PE270
M16
130x65x12
140
50
90
40
70
80
8
3987
1993
24.2
16.1
125
FCT
S
S
M20
160x80x14
140
60
115
45
75
80
10
5422
2711
29.8
19.9
196
FCT
S
IPE220
M16
130x65x12
160
50
90
40
60
80
8
2916
1458
23.3
15.5
125
FCT
S
1PE240
M16
130x65x12
160
50
90
40
70
80
8
3424
1712
25.0
16.7
125
FCT
S
IPE270
M16
130x65x12
160
50
90
40
70
80
8
4197
2098
27.7
18.4
125
FCT
S
M20
160x80x14
160
60
115
45
75
90
10
5769
2884
34.1
22.7
196
FCT
S
M16
130x65x12
160
50
90
40
75
80
8
5062
2531
30.3
20.2
125
FCT
S
M20
160x80x14
160
60
115
45
80
90
10
6915
3458
37.2
24.8
196
FCT
S
M16
130x65x12
160
50
90
40
75
80
8
6052
3026
32.9
21.9
125
FCT
S
M20
160x80x14
160
60
115
45
85
90
10
8221
4110
40.4
26.9
196
FCT
S
IPE220
M16
130x65x12
180
50
90
40
60
80
8
2962
1481
26.2
17.5
125
FCT
S
IPE240
M16
130x65x12
180
50
90
40
70
80
8
3481
1741
28.2
18.8
125
FCT
S
1PE270
M16
130x65x12
180
50
90
40
70
80
8
4273
2136
31.1
20.7
125
FCT
S
M20
160x80x14
180
60
115
45
75
90
10
5931
2966
38.3
25.5
196
FCT
S
M16
130x65x12
180
50
'X)
40
75
80
8
5160
2580
34.1
22.7
125
FCT
s
s s s s s s s s s s s s s s
1PE3IX)
1PE330
HEB 180
Rotational stiffness (kNm/rad)
Connection detail (mm)
Cleats: S235 (mm)
IPE300
Resistance S235
IPE360
IPE4(X)
HEB200
IPE220 IPE240 IPE270 1PE300 IPE330
IPE360
IPE400
1PE450
IPE500
HEB220
1PE220
w3
wl
La x la x ta
IPE330
Rotational stiffness (kNm/rad)
Connection detail (mm)
Cleats: S235 (mm)
"b
Moment (kNm)
Shear (kN)
aj.im
Sj,ini'2
MRd
2/3MRd
VRd
7122
3561
41.9
27.9 24.7
Failure mode
Reference lengtli(m)
Code
Lbb
Lbu
196
FCT
125
FCT
S S
S S
s s s s s
M20
160x80x14
180
60
115
45
80
90
10
M16
130x65x12
180
50
90
40
75
80
6178
3089
37.0
M20
160x80x14
180
60
115
45
85
90
8 10
8482
4241
45.5
30.3
196
FCT
S
M 24
150x100x14
180
60
55 40
85 80
100 80
10 8
8452
4226
37.0
24.7
FCT
S
7348
3674
40.0
26.6
282 125
FCT
45
85
90
10
10039
5019
49.0
32.7
196
FCT
M16
130x65x12
180
50
105 90
M20
160x80x14
180
60
115
M 24
150x100x14
180
60
105
55
90
100
10
9969
4985
39.9
26.6
282
FCT
S S S
M16
130x65x12
180
50
90
40
85
80
8
8913
4457
43.9
29.3
125
FCT
2.7-P
2.7-P
M20
160x80x14
180
60
115
45
90
90
10
12102
6051
53.8
35.9
196
FCT
S
S
M24
150x100x14
180
60
105
55
95
100
10
11976
5988
43.7
29.1
282
FCT
S
S
M16
130x65x12
200
50
90
40
60
80
8
3015
1507
29.1
19.4
125
FCT
S
S
M16
130x65x12
200
50
90
40
70
80
8
3548
1774
31.3
20.9
125
FCT
S
S
M16
130x65x12
200
50
8 10
23.0
6130
3065
42.6
28.4
125 196
FCT
60
80 90
34.6
200
70 75
2180
160x80x14
40 45
4361
M20
90 115
S S
M16
130x65x12
200
50
90
40
75
80
8
5275
2638
37.9
25.2
125
FCT
M20
160x80x14
200
60
115
45
80
90
10
7377
3688
46.5
31.0
196
FCT
M16
130x65x12
200
50
90
40
75
80
8
6328
3164
41.1
27.4
125
FCT
45
85
90
10
8808
4404
50.5
33.7
196
FCT
s s s s s s s s s s
FCT
s s s s s s s s
M20
160x80x14
200
60
115
M24
150x100x14
200
60
105
55
85
110
10
8830
4415
41.2
27.4
282
FCT
M16
130x65x12
200
50
90
40
80
80
8
7542
3771
44.4
29.6
125
FCT
M20
160x80x14
200
60
115
45
85
90
10
10452
5226
54.5
36.3
196
FCT
M24
150x100x14
200
60
105
55
90
110
10
10444
5222
44.3
29.5
282
FCT
M16
130x65x12
200
50
90
40
85
80
8
9168
4584
48.8
32.5
125
FCT
2.6-P
2.6-P
M20
160x80x14
200
60
115
39.8
S
105
12581
6291
48.5
32.3
196 282
FCT
60
10 10
59.8
200
90 110
6318
150x100x14
90 95
12636
M24
45 55
FCT
S
S S
M16
130x65x12
200
50
90
40
85
80
8
11435
5717
54.3
36.2
125
FCT
3.1-P
3.1-P
M20
160x80x14
200
60
115
45
95
90
10
15659
7830
66.4
44.2
196
FCT
S
S
M24
150x100x14
200
60
105
55
100
110
10
15535
7768
53.8
35.8
282
FCT
S
S
M16
130x65x12
200
50
90
39.8
19051
9526
73.0
48.7
FCT FCT
3.6-P
115
125 196
3.6-P
60
8 10
59.7
200
80 90
6998
160x80x14
90 95
13995
M20
40 45
2.7-P
2.7-P
M24
150x100x14
200
60
105
55
100
110
10
18848
9424
59.0
39.3
282
FCT
2.7-P
2.7-P
M16
130x65x12
220
50
90
40
60
90
1526
32.0
21.3
125
FCT
40
70
90
8 8
3052
90
3594
1797
34.4
22.9
125
FCT
S S
S S
90
40
70
90
8
4421
2211
38.0
25.4
125
FCT
S
S
IPE240
M16
130x65x12
220
50
IPE270
M16
130x65x12
220
50
Resistance S235
IPE300 IPE330
IPE360
IPE400
IPE450
MRd
2/3MRd
6231
3115
46.8
31.2
5353
2676
41.6
27.8
10
7506
3753
51.2
8
6427
3214
45.2
100
10
8973
4486
55.6
85
120
10
9032
4516
40 45
80 85
90 100
8 10
7669
55
90
120
ba
wl
»2
M20
160x80x14
220
60
115
45
75
100
10
M16
130x65x12
220
50
90
40
75
90
8
M20
160x80x14
220
60
115
45
80
100
M16
130x65x12
220
50
90
40
75
90
M20
160x80x14
220
60
115
45
85
M24
150x100x14
220
60
105
55
M16
130x65x12
M20
160x80x14
220 220
50 60
90 115
M24
150x100x14
220
60
105
M16 M20 M24 M16 M20 M24
130x65x12 160x80x14
220 220
50 60
90 115
Moment (kNm)
Sj,ini/2
L a x la x ta
wl,
40 45
85 90
90 100
196
FCT
S
S
125
FCT
S
S
34.1
196
FCT
S
S
30.2
FCT
S
S
37.0
125 196
FCT
S
S
45.3
30.2
282
FCT
S
S
3834
48.9
32.6
125
FCT
S
S
10663
5332
59.9
39.9
196
FCT
S
S
10
10698
5349
48.7
32.5
282
FCT
S
S
8 10
9333
4667
53.7
35.8
2.6-P
6455
65.7
43.8
FCT FCT
2.6-P
12910
125 196
6453
53.4
35.6
282
FCT
S S
S S
125 196 282
FCT
3.0-P
3.0-P
FCT FCT
S S
S
125 196
FCT
3.5-P
3.5-P
2.6-P
2.6-P
60 50
105 90
55 40
95 85
120 90
10 8
11658
5829
59.7
39.8
60 60
115 105
45 55
95 100
100 120
10 10
16029
8014
73.0
48.7
150x100x14
220 220
15965
7982
59.1
39.4
160x80x14
M16
130x65x12
220
50
90
40
90
90
8
14290
7145
65.7
43.8
160x80x14
220
60
115
45
95
100
10
19538
9769
80.3
53.5
150x100x14
60 50 60
105 90 115
55 40 45
100 95 100
120 90 100
10 8 10
9703
64.9
43.3
ΊΟ",
17121
8561
71.7
47.8
125
FCT FCT FCT
160x80x14
220 220 220
19405
1PE550
M20 M24 M16
23285
11643
87.6
58.4
150x100x14
220
60
105
55
110
120
10
23075
11537
70.7
47.1
196 282
130x65x12
220
50
90
40
95
90
8
20313
10157
77.7
51.8
160x80x14
220 220 240 240
60
115 105 90 90
45 55 40 40
100 110 60 70
100 120 90 90
10 10 8 8
130x65x12
Reference length(m) Lbb
220 220
130x65x12
Failure mode Code
12906
150x100x14
Shear (kN) VRd
IPE500
M20 M24
Lbu
s
2.6-P
2.6-P
4.1-P
4.1-P
FCT FCT
3.0-P
3.0-P
3.1-P
3.1-P
125 196 282
FCT FCT FCT
4.8-P
4.8-P
3.5-P
3.5-P
3.6-P
3.6-P
FCT FCT
S
S S
1PE220
M16 M20 M24 M16
IPE240
M16
1PE270
M16
130x65x12
240
50
90
40
70
90
8
4479
2239
40.2
26.8
125
FCT
S S
M20
160x80x14
240
60
115
45
75
100
10
6357
3178
51.1
34.1
196
FCT
S
S
M16 M20
130x65x12
240
50
90
40
75
90
8
5428
2714
44.0
29.3
125
FCT
S
160x80x14
240
60
115
45
80
100
10
7669
3834
55,8
37.2
196
130x65x12
75 85 85 80
90 100 120 90
8 Κ) Κ) 8
47.8
31.9
60.6
40.4
125 196
9362
4681
49.4
32.9
282
FCT FCT
130x65x12
40 45 55 40
4591
240
90 115 105 90
9183
150x100x14
50 60 60 50
3263
M20 M24
240 240 240
6526
160x80x14
S S S
S S
M16
FCT FCT
7797
3898
51,6
34.4
125
FCT
IPE600
HEB240
Rotational stiffness (kNm/rad)
Connection detail (mm)
Cleats: S235 (mm)
IPE300 IPF330
IPF.360
M16
150x100x14 130x65x12 130x65x12
ω
50 50
27488
13744
94.8
63.2
27190
13595
76.5
51.0
3086
1543
33.8
22.5
3637
1818
36.3
24.2
125 125
S
S
S S S
S
S
Resistance
S235
La x la x ta
1PF.4(X)
IPF450
IPE500
HEB260
J,mi'
MRd
2/3MRd
10934
5467
65.4
43.6
196
11113
5557
53.2
35.4
Si'J, uu
w'3
wb
115
45
85
100
10
105
55
90
120
10
wl
Shear (kN) VRd
a
Failure mode
Reference lenglh(m)
Code
Lbb
Lbu
FCT FCT
S
282
S
S S
160x80x14
M24
150x100x14
240 240
60 60
M16
130x65x12
240
50
90
40
85
90
8
9504
4752
56.7
37.8
125
FCT
2.6-P
2.6-P
M 20
160x80x14
240
60
115
45
90
100
10
13264
6632
71.7
47.8
196
FCT
S
S
M24
150x100x14
240
60
105
55
95
120
10
13434
6717
58.2
38.8
282
FCT
S
M16
130x65x12
240
50
90
40
85
90
8
11893
5947
63.0
42.0
125
3.0-P
3.0-P
240 240 240
60 60 50
115 105 90
45 55 40
95 100 90
100 120 90
10 10 8
16509
8254
79.6
53.1
16660
8330
64.5
43.0
S S
s
14607
7304
69.4
46.3
196 282 125
FCT FCT FCT FCT
3.5-P
3.5-P
240 240 240
60 60 50
115 105 90
45 55 40
95 100 95
100 120 90
10 10 8
20176
10088
87.6
58.4
70.8
47.2
FCT FCT
2.5-P
10152
S
S
17534
8767
75.7
50.5
196 282 125
2.5-P
20304
FCT
4.0-P
4.0-P
240 240
60 60 50
115 105 90
45 55 40
100 110 95
100 120 90
10 10 8
24103
12052
95.5
63.7
2.9-P
2.9-P
12101
77.1
51.4
2.9-P
10423
82.1
54.7
FCT FCT
2.9-P
20845
196 282 125
FCT
24202
4.6-P
4.6-P
60
115
45
100
100
10
28527
14264
103.4
69.0
3.4-P
60 50
105 90
55 40
110 60
120 100
10 8
28595
14297
83.4
55.6
FCT FCT
3.4-P
240 260
3.4-P
3.4-P
3112
1556
34.5
23.0
196 282 125
S
90 90 115 90 115
40 40 45 40 45
70 70 75 75 80
100 100 110 100 110
8 8 10 8 10
3670
1835
37.1
24.7
4523
2262
41.0
27.3
6435
3217
55.3
36.9
5486
2743
44.9
29.9
125 125 196 125
S S S
160x80x14
260 260 260
FCT FCT FCT FCT
S
7770
38S5
60.5
40.3
l'6
FCT FCT
M20
160x80x14
M 24
150x100x14
M16
130x65x12
M20
160x80x14
M 24
150x100x14
M16
M20 M24
150x100x14
M16
130x65x12
M20
160x80x14
M24
150x100x14
IPE220
M16
130x65x12
IPE240
M16
130x65x12
IPE270
M16 M20
130x65x12
IPE600
ba
Moment (kNm)
M 20
130x65x12
IPE550
Rotational stiffness (kNm/rad)
Connection detail (mm)
Cleats: S235 (mm)
160x80x14
240 240
s S
IPE300
M16
130x65x12
260
160x80x14
260
IPE330
M20 M16
50 50 60 50 60
130x65x12
50 60
90 115
40 45
75 85
100 110
8 10
6601
3300
48.8
32.5
S
4657
65.7
43.8
125 196
FCT
9314
FCT
S
60
105
55
85
120
10
9554
4777
53.5
35.7
282
8 10 10
7893
3947
52.7
35.1
FCT FCT
11103
5552
70.8
47.2
125 196
11356
5678
57.6
38.4
282
s s s s
S S
IPE360
1PE400
IPE450
M20
160x80x14
260 260
M24
150x100x14
260
M16
130x65x12
260
M20
160x80x14
260
50 60 60
90 115 105
40 45 55
80 85 90
100 110 120
FCT
S S S S
S S S S S S S
M24
150x100x14
260
M16
130x65x12
260
50
90
40
85
100
8
9630
4815
57.8
38.6
125
FCT
2.5-P
2.5-P
M20
160x80x14
260
60
115
45
90
110
10
13487
6743
77 7
51.8
196
FCT
S
S
M24
150x100x14
260
60
105
:o
95
120
10
13745
6872
63.1
42.0 .
282
FCT
S
S
M16
130x65x12
260
50
'X)
40
85
100
8
12066
6033
64.3
42.9
125
FCT
2.9-P
2.9-P
M20
160x80x14
260
60
115
45
95
110
10
16813
8406
86.3
57.5
196
FCT
S
S
FCT
Resistance S235
1PE500
1PE550
IPE600
HEB280
Connection detail (mm)
Cleats: S235 (mm)
Rotational stiffness (kNm/rad)
Moment (kNm)
Shear (kN)
Failure mode
Reference length(m)
La x la x ta
ba
wl
w2
w3
wb
wc
g
Sj,ini
Sj,ùu72
MRd
2/3MRd
Vpd
Code
M24
150x100x14
260
60
105
55
100
120
10
17074
8537
69.9
46.6
282
FCT
S
S
M16
130x65x12
260
50
90
40
90
100
8
14838
7419
70.8
47.2
125
FCT
3.4P
3.4P S
Lbb
Lf,u
M20
160x80x14
260
60
115
45
95
no
10
20581
10291
94.9
63.2
196
FCT
S
M24
150x100x14
260
60
105
55
100
120
10
20844
10422
76.7
51.1
282
FCT
S
s
M16
130x65x12
260
50
90
40
95
100
8
17833
8916
77.3
51.5
125
FCT
4.0P
4.0P
M20
160x80x14
260
60
115
45
100
no
10
24626
12313
103.5
69.0
196
FCT
2.9P
2.9P
M24
150x100x14
260
60
105
55
no
120
10
24885
¡2442
83.5
55.7
282
FCT
2.8P
2.8P
M16
130x65x12
260
50
90
40
95
100
8
21228
10614
83.8
55.9
125
FCT
4.6P
4.6P
M20
160x80x14
260
60
115
45
100
no
10
29195
14598
112.1
74.7
196
FCT
3.3P
3.3P
M24
150x100x14
260
60
105
55
no
120
10
29452
14726
90.4
60.2
282
FCT
3.3P
3.3P
IPE220
M16
130x65x12
280
50
90
40
60
100
8
3123
1561
35.2
23.5
125
FCT
S
S
IPE240
M16
130x65x12
280
50
90
40
70
100
8
3684
1842
37.8
25.2
125
FCT
S
S
IPE270
M16
130x65x12
280
50
90
40
70
100
8
4542
2271
41.8
27.9
125
FCT
S
S
M20
160x80x14
280
60
115
45
75
no
10
6475
3237
59.6
39.7
196
FCT
S
S
M16
130x65x12
280
50
90
40
75
100
8
5511
2755
45.8
30.5
125
FCT
S
S
M20
160x80x14
280
60
115
45
80
no
10
7824
3912
65.2
43.4
196
FCT
S
S
M16
130x65x12
280
50
90
40
75
100
8
6634
3317
49.7
33.2
125
FCT
S
S
M20
160x80x14
280
60
115
45
85
no
10
9384
4692
70.7
47.1
196
FCT
S
S
M24
150x100x14
280
60
105
55
85
120
10
9671
4835
57.6
38.4
282
FCT
S
S
M16
130x65x12
280
50
90
40
80
100
8
7937
3968
53.7
35.8
125
FCT
S
S
M 20
160x80x14
280
60
115
45
85
no
10
11195
5597
76.3
50.8
196
FCT
S
S
M24
150x1 (Xix 14
280
ω
105
55
90
120
10
11505
5753
62.0
41.4
28.2
FCT
S
S
M16
130x65x12
280
50
90
40
85
100
8
9690
4845
59.0
39.3
125
FCT
2.5P
2.5P
M20
160x80x14
280
60
115
45
90
no
10
13609
6805
83.7
55.8
196
FCT
S
S
M24
150x1 (Xix 14
280
60
105
55
95
120
10
13937
6969
67.9
45.3
282
FCT
S
S
M16
130x65x12
280
50
90
40
85
100
8
12150
6075
65.6
43.7
125
FCT
2.9P
2.9P
M20
160x80x14
280
60
115
45
95
no
10
16983
8492
92.9
61.9
196
FCT
S
S
100
120
10
17332
8666
75.3
50.2
282
FCT
S
S
90
100
8
14953
7476
72.2
48.2
125
FCT
3.4P
3.4P
IPE300
1PE330
IPE360
1PE400
IPE450
IPE500
IPF550
M24
150x100x14
280
60
105
55
M16
130x65x12
280
50
90
40
M20
160x80x14
280
60
115
45
95
no
10
20812
10406
102.2
68.1
196
FCT
S
S
M24
150x100x14
280
60
105
55
100
120
10
21183
10592
82.6
55.1
282
FCT
S
S
M16
130x65x12
280
50
90
40
95
100
8
17985
8992
78.8
52.6
125
FCT
3.9P
3.9P
M 20
160x80x14
280
60
115
45
100
110
10
24928
12464
111.4
74.3
196
FCT
2.8P
2.8P
M24
150x100x14
280
60
105
55
110
120
10
25316
12658
90.0
60.0
282
FCT
2.8P
2.8P
Resistance S235
IPE600
HEB300
IPE220 IPE240 IPE270 1PE300 IPE330
21427
10
29586
110
120
10
40
60
100
90
40
70
50
90
40
300
60
115
130x65x12
300
50
90
160x80x14
300
60
130x65x12
300
50
160x80x14
300
150x100x14
100
105
55
50
90
300
50
M16
130x65x12
300
M20
160x80x14
M16 M20
Reference length(m)
VRd
Code
Lbb
Lbu
10713
85.5
57.0
125
FCT
4.5-P
4.5-P
14793
120.7
80.5
196
FCT
3.3-P
3.3-P
29997
14999
97.3
64.9
282
FCT
3.2-P
3.2-P
8
3138
1569
35.9
23.9
125
FCT
S
S
100
8
3704
1852
38.6
25.7
125
FCT
S
S
70
100
8
4569
2284
42.6
28.4
125
FCT
S
S
45
75
110
10
6545
3273
63.9
42.6
196
FCT
S
S
40
75
100
8
5548
2774
46.7
31.1
125
FCT
S
S
115
45
80
110
10
7916
3958
69.8
46.5
196
FCT
S
S
90
40
75
100
8
6682
3341
50.7
33.8
125
FCT
S
S
60
115
45
85
110
10
9504
4752
75.8
50.5
196
FCT
S
S
300
60
105
55
85
120
10
9849
4925
61.7
41.2
282
FCT
S
S
300
50
90
40
80
100
8
8001
4001
54.8
36.5
125
FCT
160x80x14
300
115
45
85
110
10
11351
5675
81.7
54.5
196
FCT
150x100x14
300
60
105
55
90
120
10
11733
5866
66.5
44.3
282
FCT
130x65x12
300
50
90
40
85
100
8
9777
4889
60.2
40.1
125
FCT
160x80x14
300
60
115
45
90
110
10
13816
6908
89.6
59.8
196
FCT
M24
150x100x14
300
60
105
55
95
120
10
14231
7116
72.8
48.5
282
FCT
M27
200x100x16
300
65
150
65
95
130
12
18275
9138
84.5
56.4
367
FCT
M16
130x65x12
300
50
90
40
85
100
8
12273
6137
66.9
44.6
163
FCT
s s s s s s s
S
60
2.9-P
2.9-P
115
45
95
110
10
17268
8634
99.6
66.4
196
FCT
55
100
120
10
17726
8863
80.6
53.8
282
FCT
s
s
105
S
S
110
130
12
22578
11289
93.5
62.3
367
FCT
S
S
125
FCT
3.3-P
3.3-P
M16
130x65x12
280
M20
160x80x14
280
50
90
60
115
M24
150x100x14
280
60
M16
130x65x12
3(X)
M16
130x65x12
M16
M16
M16
130x65x12
M20
160x80x14
300
60
M24
150x100x14
300
60
-
S S S S
s s
M27
200x100x16
300
65
150
65
M16
130x65x12
300
50
90
40
90
100
8
15123
7561
73.7
49.1
M20
160x80x14
300
60
115
45
95
110
10
21196
10598
109.5
73.0
196
FCT
S
S
M24
150x100x14
300
60
105
55
100
120
10
21702
10851
88.5
59.0
282
FCT
S
S
M27
200x100x16
300
65
150
65
110
130
12
27432
13716
102.4
68.3
367
FCT
S
S
M16
130x65x12
300
50
90
40
95
100
8
18210
9105
80.4
53.6
125
FCT
3.9-P
3.9-P
M20
160x80x14
300
60
115
45
100
110
10
25427
12713
119.4
79.6
196
FCT
2.8-P
2.8-P
150x100x14
300
60
105
55
110
120
10
25977
12989
96.4
64.3
282
FCT
S
S
200x100x16
300
65
150
65
120
130
12
32622
16311
111.3
74.2
367
FCT
S
S
90
40
95
100
8
21721
10861
87.1
58.1
125
FCT
4.5-P
4.5-P
M24 M27 IPE600
8
110
95
45
Failure mode
She.,r (kN)
2/3MRd
w'3
M20
IPE550
100
40
Moment (kNm) MRd
«2
M24
IPE500
Sj,ini/2
wl
M20
1PE450
Sj,ini
Wc
ba
M24
IPE400
g
wb
La x la x ta
M20 IPE360
Rotational stiffness (kNm/rad)
Connection c e tail (mm)
Cleats: S235 (mm)
M16
130x65x12
300
50
M20
160x80x14
300
60
115
45
100
110
10
30228
15114
129.3
86.2
196
FCT
3.2-P
3.2-P
60
105
55
110
120
10
30835
15417
104.3
69.5
282
FCT
3.1-P
3.1-P
M24
150x100x14
300
Resistance S235
M27 HEB320
La x la x ta
ba
wi
w2
»3
wb
200x100x16
300
65
150
65
120
130
50
90
40
60
100
IPE220
M16
130x65x12
300
IPE240
M16
130x65x12
40
70
100
M16 M20
130x65x12
50 50
90
IPE270
300 300
90
40
70
100
160x80x14
300
60
115
45
75
M16
130x65x12
300
50
90
40
75
no
M20
160x80x14
300
60
115
45
80
M16
130x65x12
300
50
90
40
75
IPE300 IPE330
IPE360
1PE400
IPE450
1PE51X)
1PE550
IPE600
I1EB340
Rotational stiffness (kNm/rad)
Connection detail (mm)
Cleats: S235 (mm)
IPE220
M20
160x80x14
300
60
115
45
85
M24
150x100x14
300
60
105
55
85
Moment (kNm) MRd 2/3MRd
Sj.ini
Sj,ini/2
12
38468
19234
120.3
80.2
8 8 8 10
3138
1569
35.9
23.9
3704
1852
38.6
25.7
4571
2286
42.6
28.4
6562
3281
63.9
Shear (kN) VRd
Failure mode
Reference length(m)
Code
Lbb
Lbu
367
FCT FCT
125 196
FCT
42.6
FCT
S S S S S
S
125 125
s s s s s s s s s s s s
FCT
100
8
5552
2776
46.7
31.1
125
FCT
S
no
10
7939
3969
69.8
46.5
196
FCT
S
8 10
6690
3345
50.7
33.8
125
FCT
9537
4768
75.8
50.5
196
FCT
S S
10
9896
4948
61.7
41.2
282
FCT
S
100
8
8014
4007
54.8
36.5
125
FCT
S
no
10
11396
5698
81.7
54.5
196
FCT
S
120
10
11795
5898
66.5
44.3
282
FCT
S
100
no 120
S S
s S
M16
130x65x12
300
50
90
40
80
M20
160x80x14
300
60
115
45
85
M24
150x100x14
300
60
105
55
90
M16
130x65x12
300
50
90
40
85
100
8
9796
4898
60.2
40.1
125
FCT
S
M20
160x80x14
300
60
10 10
59.8
196
FCT
S
60
110 120
89.6
300
90 95
6940
150x100x14
45 55
13879
M24
115 105
14316
7158
72.8
48.5
282
FCT
M27
200x100x16
300
65
150
65
95
130
12
18438
9219
84.5
56.4
367
FCT
M16
130x65x12
300
50
90
40
85
100
8
12305
6152
66.9
44.6
125
FCT
s s 2.9-P
M20
160x80x14
300
60
115
45
95
17361
8681
99.6
66.4
196
FCT
M24
150x100x14
300
120 130
10 12
17847
8924
80.6
53.8
282
FCT
300
55 65
100
200x100x16
105 150
S S
M27
60 65
no
10
22802
11401
93.5
62.3
367
FCT
S
M16
130x65x12
300
50
90
40
90
100
8
15171
7585
73.7
49.1
125
FCT
s s s
3.3-P
3.3-P
M20
160x80x14
300
60
115
45
95
110
10
21328
10664
109.5
73.0
196
FCT
S
M24
150x100x14
3(X)
60
105
55
100
120
10
21869
10935
88.5
59.0
282
FCT
S
M27
200x100x16
300
65
150
65
110
130
12
27733
13867
102.4
68.3
367
FCT
S
s s
18278
9139
80.4
53.6
125
FCT
3.9-P
3.9-P
no
2.9-P
S
M16
130x65x12
300
50
90
40
95
100
8
M20
160x80x14
300
60
115
45
1ÍX)
no
10
25607
12803
119.4
79.6
196
FCT
2.8-P
2.8-P
120
10
26199
13100
96.4
64.3
282
FCT
S
120
130
12
33013
16506
111.3
74.2
367
FCT
S
100
8
21817
10908
87.1
58.1
125
FCT
s s
4.4-P
4.4-P
no
10
30469
15234
129.3
86.2
196
FCT
3.2-P
3.2-P
120
10
31126
15563
104.3
69.5
282
FCT
3.1-P
3.1-P
M24
150x100x14
300
60
105
55
M27
200x100x16
300
65
150
65
M16
130x65x12
300
50
90
40
95
M 20
160x80x14
300
60
115
45
100
M24
150x100x14
300
60
105
55
110
M27
200x100x16
300
65
150
65
120
130
12
38971
19485
120.3
80.2
367
FCT
S
S
M16
130x65x12
300
50
90
40
60
100
8
3136
1568
35.9
23.9
125
FCT
S
S
no
Resistance
S235
La x la x ta
ba
wl
w2
w3
wl,
Wc
g
Sj,ini
Sj,ini; = ^ — ^ - 0.8 χ 15 = 29mm bc-wc 160-90 e=— -= = 35mm Ί
m '"pife
Ί
=0^5 υ
· —
¿tn^Æ.^ 0.25 χ = 9026 Nmm I mm γ
1.1
Λ/Ο
Beam
t f 14 h = hh + w, + ^ = 270 + 45 + —
M CM,,, v(class section 1) =
li7,,/,,,/',,, y
= 3 2 2 λ?7/77
=
483997x235x10"" 1
/ Λ/0
512
1 11 ·
= 103,4 KNm
Flange cleats
g =1 Omm g>OAtu : ma = vt', - 0,5 ta = 4 5 - 0.5(14) = 38 mm e„ = / -vi\ = 8 0 - 4 5 = 35 mm t2 f 142 x^35 = 0.25 -2^2- = 0.25 =— = 10468 Nmm I mm v 11
mPla
1 i
-
I Mo
Bolts
^
/
= ^ ^ Α = ° · 9 χ 8 0 0 χ 2 4 5 = ΐ4ΐ.ι^ Y M,,
1-25
4 = /fc + tu + 0,5(hbo„ + h ) = 13 +14 + 0,5 (13 +18) = 42,5 mm dv = d j =29,26 mm COLUMN WEB PANEL IN SHEAR Resistance
Vm β-\
Rd
0.9 Arcfvcv _ 0,9x1759x235 χ 10"3 =- - y c w = ^ ^ = 1 9 5 , 3 kN ν'3;/Λ/„ v'3xl,l {hypothesis)
V„ia 195.3 Fl
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