THE STATIC STRENGTH OF I-BEAM TO RECTANGULAR
HOLLOW SECTION COLUMN CONNECTIONS
THE STATIC STRENGTH OF I-BEAM TO RECTANGULAR
HOLLOW SECTION COLUMN CONNECTIONS
PROEFSCHRIFT
ter verkrijging van de graad van doctor
aan de Technische Universiteit Delft,
op gezag van de Rector Magnificus Prof.dr.ir. J. Blaauwendraad,
in het openbaar te verdedigen ten overstaan van een commissie,
door het College voor Promoties aangewezen,
op vrijdag 5 december 1997 te 13:30 uur
door
Li Hua Lu
civiel ingenieur
Dit proefschrift is goedgekeurd door de promotor Prof.dr.ir. J. Wardenier Sainenstelling promotiecommilssie Rector Magnificus, Prof.dr.ir. J. Wardenier, Profit J.W.B. Stark, Prof.drir. J.C. Walraven,
Prof. L.A.G. Wagemans,
Profit B. Boon,
Prof ir. H.H. Snijder, Prof. dr.ir: R.S. Puthli,
ISBN 90-407-1603-X
Copyright CD 1997 by L.H. Lu All rights reserved.
No part of this material' protected by this copyright notice may be reproduced or
utilized in any form or by any means, electronic or mechanical, including
photocopying, recording or by any information storage and retrieval system, withoutpermission from the publisher: Delft University Press
Mekelweg 4 2628 CD Delft The Netherlands Telephone: +31(0)15 278 32 54 Telefax: +31(0)15 278 1661 E-mail: DUP@DUP.TUDelft.NL Voorzitter TU Delft TU Delft TU Delft TU Delft TU Delft TU Eindhoven University of Karlsruhe
ACKNOWLEDGEMENTS
The research presented in this thesis has been carried out at the Faculty of Civil
Engineering of Delft University of Technology, sponsored by Commission Beek, TUDelft and Comite International pour le Developpement et Etude de la Construction Tubulaire within the CIDECT programme SAX.
The author would like to express her gratitude to her colleagues of the group "Steel
Structures" of the Delft University of Technology for their encouragement throughout
the research. Particular acknowledgement is due to Mr. A. verheul and Mr. H.L.N.
Munter for their work regarding the experiments and due to the staff the Steel
Structures Laboratory of TNO Building and Construction Research.The author appreciates the support of her colleagues of the group "Bouwspeurwerk"
of the Ministry of public Works. Transport and Water Management, The Netherlands. Thanks are expressed to the European Coal and Steel Community, Rijkswaterstaat, Van
Leeuwen Buizen for using the experimental results of ECSC Project 7210-SA/611. Appreciation is also extended to Stichting Nationale Computerfaciliteiten (NCF) for
their financial support for using the CRAY YMP9814256 and IBM Nederland NV for
making available an IBM RS/6000 model 350 workstation for a period of two years in the framework of a study contract.
KEYWORDS
Static strength, Welded and bolted connections, I-beam to RHS column connections, Experimental tests, Numerical modelling, FE analyses, Analytical models.
CONTENTS
SUMMARY 1
LIST OF SYMBOLS 2
1 INTRODUCTION 5
1.1 THE USE OF HOLLOW SECTIONS 5
1.2 DESIGN OF TUBULAR STRUCTURES 5
1.3 AIM OF THE RESEARCH 6
1.4 RESEARCH PROGRAMME 6
1.5 OUTLINE OF THE THESIS 9
LITERATURE STUDY 11
2.1 INTRODUCTION 11
2.2 RELEVANT EXPERIMENTAL AND ANALYTICAL
RESEARCH 12
2.2.1 Plate to RHS column connections 13
2.2.2 I-beam to RHS column connections 15
2.3 DESIGN CODES AND RECOMMENDATIONS 16
3 EXPERIMENTAL RESEARCH 19
3.1 INTRODUCTION 19
3.2 RESEARCH PROGRAMME 19
3.3 MEASURED DIMENSIONS OF THE SPECIMENS 21
3.4 MECHANICAL PROPERTIES 27
3.4.1 Steel members 27
3.4.2 Welding material 27
3.4.3 Reinforced concrete 27
3.5 TEST RIG AND TESTING PROCEDURES 28
3.5.1 Axially loaded plate or I-beam to RHS column
connections (series 1 and 2) 28
3.5.2 I-beam to RHS column connections loaded by in-plane
bending moments (series 3 and series 4) 32
3.6 DEFINITION OF VARIOUS CHARACTERISTICS 35
3.6.1 Displacement of the connection 35
3.6.2 Moment and rotation of the connection 36
3.6.3 Deformation limit for the ultimate load capacity 39
3.6.4 Definition of the ultimate load 41
...
...
. . . ....
2 .... . . . ..... .
. ....
. . . . . ....
....
3.7 RESULTS OF THE EXPERIMENTS 41 3.71 Axially loaded plate to RHS column connections (series
1) 44
3.7:2 Axially loaded 1-beam to RHS column connections
(series 2) 44
3.7.3 Welded I-beam to RHS column connections loaded by
in-plane bending moments (series 3) 46
3.7.4 Bolted I-beam to RHS column connections loaded by in
plane bending moments (series 4) ,47
3.8 DISCUSSION OF THE EXPERIMENTAL RESULTS 50
3.8.1 The influence of p 52
3.8.2 The multiplanar loading effect , ,, a .. . . 53
3.8.3 The interaction effect
3.8.4 The influence of a steel floor ...
. 543.8.5 Effect of concrete filling in column ... . 54
3.8.6 Effect of a composite floor 54
.3.9 COMPARISON OF THE EXPERIMENTAL:RESULTS WITH
EXISTING STRENGTH FORMULAE .
...
543.9.1 Plate to RHS column connections 55.
3.9.2 Axially loaded I-beam to RHS column connections . . . ., 56
3.9.3 I-beam to RHS column connections loaded by in-plane
bending moments 56
4
CALIBRATION OF NUMERICAL MODELS WITH THEEXPERIMENTS 59
4.1 INTRODUCTION 59
4.2 NUMERICAL MODELLING 59
4.2.1 Finite element meshes 60
4.2.2 Finite element type 60
4.2.3 Modelling of the material properties .... a ., 62
4.2.4 Simulation of loading 66
4:3 NUMERICAL SIMULATIONS OF THE EXPERIMENTS 66
4.3,1 Modelling of the welds 67
4.3.2 Modelling of concrete filling in the column ... . ,... 68'
4.3.3 Modelling of the composite floor . .
...,
, 684.3.4 Modelling of the slip of the bolts 68
4.4 CALIBRATION OF THE NUMERICAL RESULTS WITH
THE EXPERIMENTAL RESULTS, ,70
3
AXIALLY LOADED PLATE TO REIS COLUMN CONNECTIONS5.1 INTRODUCTION 81
5.2 RESEARCH PROGRAMME... 81
53
5.3 MAIN CHARACTERISTICS OF THE NUMERICAL
MODELLING 83
5.4 FINITE ELEMENT ANALYSES 85
5.5 VALIDATION OF THE CIDECT DESIGN FORMULAE 91
5.6 ANALYTICAL MODEL 93
5.6.1 Failure modes 93
5.6.2 Yield line model 95
5.6.3 Chord side wall failure 95
5.7 COMPARISONS OF THE NUMERICAL RESULTS WITH
THE ANALYTICAL MODEL 96
5.8 ULTIMATE MEAN STRENGTH FORMULAE FOR
UNIPLANAR CONNECTIONS 98
5.9 ULTIMATE MEAN STRENGTH FORMULAE FOR
MULTIPLANAR CONNECTIONS 99
5.9.1 Multiplanar geometrical effect 99
5.9.2 Multiplanar loading effect 100
6 AXIALLY LOADED I-BEAM TO RHS COLUMN
CONNECTIONS 103
6.1 INTRODUCTION 103
6.2 RESEARCH PROGRAMME 103
6.3 FINITE ELEMENT ANALYSES 106
6.4 ANALYTICAL MODELS 113
6.4.1 Failure modes 113
6.4.2 Yield line model 114
6.4.3 Chord side wall failure 116
6.5 COMPARISON OF THE NUMERICAL RESULTS WITH
THE ANALYTICAL MODELS 117
6.6 ULTIMATE STRENGTH FORMULAE FOR UNIPLANAR
CONNECTIONS 118
6.7 ULTIMATE STRENGTH FORMULAE FOR MULTIPLANAR
CONNECTIONS [20
6.7.1 Multiplanar geometrical effect 121
6.7.2 Multiplanar loading effect LIE
7 I-BEAM TO RHS COLUMN CONNECTIONS LOADED BY
IN-PLANE BENDING MOMENTS 125
7.1 INTRODUCTION 125
7.2 RESEARCH PROGRAMME 125
7.3 FINITE ELEMENT ANALYSES 128
7.4 ANALYTICAL MODELS 138
7.4.1 Failure modes 138
7.4.2 Yield line model 139
. . .
...
. . . .... .... .
.. ...
. .... ...
. . . . . .. ...
. .7.5 COMPARISON OF THE NUMERICAL RESULTS WITH
THE ANALYTICAL MODELS 121.1
7.6 ULTIMATE MEAN STRENGTH FORMULAE FOR
UNIPLANAR CONNECTIONS 442
7.6.1 Strength formulae excluding the effect of pre-loading in
the columns 142
7.6.2 The effects of pm-loading in the columns .
17
ULTIMATE MEAN STRENGTH FORMULAE FORMULTIPLANAR CONNECTIONS ...
. 1477.7.1 Multiplanar geometrical effect 147
7.7.2 Multiplanar loading effect . . . 148
8 BOLTED I-BEAM TO RHS COLUMN CONNECTIONS WITH
A COMPOSITE FLOOR LOADED, BY IN-PLANE BENDING
MOMENTS 51,
81
INTRODUCTION ... .
.. ...
. . . 1518.2 ANALYTICAL MODELS, 152
8.2.1 Failure modes 152
8.2.2 Failure of the slab . ,
..
1538.2.3 Column face yielding 155
8l3 COMPARISON OF THE NUMERICAL RESULTS WITH
THE ANALYTICAL MODELS 156
8.4 DISCUSSION OF THE NUMERICAL RESULTS ..., . . 157
8.5 DESIGN ASPECTS 160
9 THE EFFECT 'OF' CONCRETE FILLING IN THE RHS
COLUMNS
9.1 INTRODUCTION . 161
9.2 RESEARCH PROGRAMME .. . . .
....
1619.3 FINITE ELEMENT ANALYSES 163
94
ANALYTICAL MODELS 1669.5 COMPARISON OF THE NUMERICAL RESULTS WITH
THE ANALYTICAL MODELS AND THE EXISTING
FORMULAE .167"
9,6 'COMPARISON OF THE NUMERICAL RESULTS WITH THE ULTIMATE STRENGTH FORMULA FOR AXIALLY
LOADED PLATE TO RHS COLUMN CONNECTIONS -..-. .. 170
TO, SUMMARY AND CONCLUSIONS .
10.1 INTRODUCTION . 173
10.2 GENERAL CONCLUSIONS 1173
10.3 DETERMINATION OF THE DESIGN STRENGTH 180'
144
161
10.3.2 Comparison of experimental results, with the
ultimate strength formula 1,81
10.3.3 Determination of the joint factor . . .., . .41,82
/04 SUMMARY OF THE ULTIMATE STRENGTH FORMULAE .... 1,84
10.4.1 Axially loaded plate to RHS column connections . . 184
10.4.2 Axially loaded connections 'between plates with
two levels and RHS columns
/87
Axially loaded I-beam to REIS column
connections (with a web at the connection) . . 189 110.4.4 I-beam to RHS column connections loaded by
in-plane bending moments 19'1
10.4.5 Bolted I-beam to RHS column connections with a composite floor loaded by in-plane bending
moments ... ...
...
. . 19411 BIBLIOGRAPHY
.. 197
11.1' INTRODUCTION
... 4.
. . . 19711.2 EXPERIMENTAL RESEARCH
. .,
.... , .
. . . 197'11.3 NUMERICAL RESEARCH . 200
11.4 DESIGN CODES AND RECOMMENDATIONS . . . 203
11.5 FINITE ELEMENT ANALYSES PROGRAM .
,.. .. ... 204
SAMEWATTING
CURRICULUM VITAE 206,
SUMMARY
Semi-rigid connections between I-beams and rectangular hollow section columns offer
economical advantages for a wide range of applications in onshore and offshore
structures. However, insufficient information is
available for design of 'these
connections. In order to obtain more insight into the static behaviour of the connections
and to form a basis for the !design, experimental and numerical investigations have
been carried out.
From the experimental research
bake information on the static
behaviour of1
multiplanar connections under different loading cases has been obtained. It has been shown that the strength of the connections is influenced by both the geometrical
parameters, such as ifs, 2y, 11 etc. and the loading conditions.
In order to establish the basic' mean ultimate strength formulae which cart serve as a
basis for design recommendations, an extensive parameter study is required. To
perform parametric studies, the finite element analyses method has been chosen because it is cheaper than executing experiments. In order to form a sound basis for
the numerical models, calibration of the numerical models has been carried out using the experimental results. Good agreement has been obtained between the numerically determined results and results from the experiments.
Based on these well calibrated numerical models, the parametric study has been carried
out using finite element analyses. Different geometries and loading cases have been investigated. Further, analytical models have been developed for different failure
modes. Based on the numerical results and the formulae based on the analytical
models, basic ultimate mean strength formulae have been derived for both uniplanar and multiplanar connection. The multiplanar loading effects, the effects of concrete filling of the column and the effects of a composite floor on the static strength of the. connections have been taken into account.
LIST OF SYMBOLS
a,b constant used in the Ramberg-Osgood relationship throat thickness of the welds, i=1...3
ah, horizontal weld sizes, i=1....4
vertical weld sizes, i=1....4
too width of the RHS column
width of the plate
be effective plate width
ber effective width for punching shear
diameter of CHS
fe concrete cube crashing strength
ft concrete splitting strength
fy yield stress of the material
yield stress of the RHS member
fy., yield stress of the plates or the flanges of an I-beam
fy,c1 yield stress of the cleat angle
fy.r yield stress of the reinforcement
yield stress of the web of an I-beam
fe ultimate tensile stress of the material
f(c) effect function of concrete filling in the column f(J) multiplanar load effect function
f(ni) the effect function of the pre-loading in the column
f(n) the effect function of the maximum compression stress in the column
fail)
interaction of the web of an I-beamh, depth of an I-beam
hc, height of the cleat angle
hin
h = h,-t,
hi distance between the reinforcement in the slab and the bottom flange of I-beam
the stiffness of the spring elements length of the RHS column
length of the plate of I-beam
pre-loading ratio in the column, ni=N0pIN0,p1
maximum compression stress in the column, n=isli/No.p,
r, inside radii of the corner of the RHS column outside radii of the corner of the RHS column
to wall thickness of the RES column
t, thickness of the plate or the flanges of an I-beam tc thickness of corner of the RHS column
tc, thickness of the cleat flange
thickness of the web of an I-beam Ao cross section area of the column
Ang cross section area of the reinforcement bars 08
An, cross section area of the reinforcement bars 06 COV coefficient of variation
deformation of the spring
elastic modulus of the concrete
F1,F2 vertical loads on the ends of the in-plane and out-of-plane I-beams
load ratio between out-of-plane and in-plane brace, J=F2/F1 or N2/N1
moments at the column face
MoM2 moments at the column face of the in-plane and out-of-plane I-beams.
M1=F1*11 and M2=F2*11
M .u.exp experimentally determined connections strength for connections loaded
by in-plane bending moments
M Lux( ultimate strength of the bolted connections with a composite floor
determined by the slab failure criterion
Maud) ultimate strength on the in-plane I-beams for uniplanar I-beam to RHS
column connections loaded by in-plane bending moments
MI .u,xxb ultimate strength of multiplanar connections between I-beams and RHS
columns loaded by in-plane bending moments
experimentally determined ultimate strength for connections loaded by in-plane bending moments
numerically determined ultimate strength for connections loaded by in-plane bending moments
No the maximum axial load in the column N0 applied at the top of the column
the full plastic resistance of the column
axial loads on the in-plane and out-of-plane plates or I-beams NI* the CIDECT design strength for plate to RHS column connection
experimentally determined connections strength for axially loaded.
connections
Niuri ultimate strength of the reinforcement within the effective width of the
slab
ultimate strength for axially loaded uniplanar plate to RHS column
connections
NI,u,xxp ultimate strength for axially loaded multiplanar plate to RHS column
connections
ultimate strength for axially loaded uniplanar I-beam to RHS column
connections
NI .u.xxbax ultimate strength for axially loaded multiplanar I-beam to RHS column
connections
experimentally determined ultimate strength of the connection
Nn,
numerically determined ultimate strength of the connectionNd design load
N, load at serviceability limit Nu load at ultimate limit
1
standard deviation of the variable, Q2.1n(V12+1)
Qr, Q,,2=1n(Vr,2+1)
Qs Q52=ln(V52+1)
R2 correlation coefficient
R,..R
regression constantsRd design strength of the connection Rk characteristic strength of the connection
Rim mean value of the design model
variation of yield stress
Vr coefficient of variation of the design model
coefficient of variation for the dimensions and material properties
variation of column thickness Vs variation of the design model
weighting factor of the Vr,
a.6 weighting factor of the Vs
width ratio between plate and RHS column b,/b
Pei width ratio between cleat flange and RHS column ',Ail 27 width to thickness ratio of RHS column Nit,
action load factor
Yin partial safety factor for the resistance
A indentation of RHS column face
Ab deformation of the bolts in the bottom flange
Eo reference strain used in the Ramberg-Osgood relationship
maximum strain of the material engineering strain
CT
E no tensile strain normal to the crack of the concrete
true strain
reference stress used in the Ramberg-Osgood relationship
at
engineering stresstrue stress
I-beam depth to RHS column width ratio hi/b
ratio between the height of the cleat angle and width of the RHS
column h1/130wavelength of the deformation
thickness ratio of I-beam's flange and RHS column t,/to
average rotation of the beams at the column face in the same plane
CHS circular hollow section RHS rectangular hollow section
CIDECT
Comite International pour
le Developpement etl'Etude de
laConstruction Tubulaire
ECSC European Coal and Steel Community
FE finite element
V
V
1
INTRODUCTION
1.1 THE USE OF HOLLOW SECTIONS
In recent years the use of steel hollow sections has increased, as she structural
advantages of hollow sections have become apparent to most designers.
Compared to open sections, tubular sections (circular hollow sections CHS and
rectangular hollow sections RHS) provide the most efficient use of a steel cross section in resisting compression, tension, bi-axial bending and torsion. Hollow sections offerconsiderable advantages for multiplanar connections compared to open section
members, which are optimal for framing systems in one plane. Further, they are easierto pick up and more stable to erect due to their greater lateral strength. As a
consequence, handling and erection costs are saved. The internal void of the hollow sections gives possibilities for heating and ventilation of buildings by water or aircirculation. By filling the tubular sections with concrete, the stiffness and strength of she connections and also the fire resistance can be increased. Protection costs are
appreciably lower for hollow section than for other sections due to a smaller surface
provided that the ends of the hollow sections are closed.
The rectangular hollow section (RHS), as the youngest member in the family of steel
hollow sections, has proved to be an excellent structural element for a wide range of applications e.g. industrial buildings, towers, barriers,
cranes, jibs, and also for
mechanical equipment, agricultural applications, etc. Theyare easier to connect thanCHS members, which require specialized profile cutting which is more expensive than
the straight cuts required for RHS.
1.2 DESIGN OF TUBULAR STRUCTURES
In the design of steel structures, it is still customary to consider the connections as pin-ended or rigid. Pin-pin-ended connections lead to fabrication friendly designs but heavier beams, while rigid connections result in material savings at the expense of fabrication
costs. The most economical solution is to consider a fabrication friendly semi-rigid
connection, taking the structural moment resistance and the flexibility of theconnection into account for the design of a structure..
Semi-rigid connections are very attractive for use in industrial buildings, 'but also offer advantages for other structures e.g. offshore structures. One example is the connection
between I-section beams and CHS or RHS columns in
a framed structure. The elements are optimally used, with the beams taking the bending moments and shear forces, while the tubular columns are predominantly loaded in compression.The strength of unstiffened semi-rigid connections between structural hollow sections depends on the geometry of the structural members to be connected. As a consequence
the selection of the members may depend on the connection strength. It is therefore very important that the designer has a good knowledge of the connection behaviour, so that an optimum design can be obtained.
During the last 30 years, extensive experimental and numerical research have been
carried out in a number of institutes for different types of semi-rigid tubular
connections. Considerable information is available for tubular connections made of
CHS and RHS members. Design recommendations can be found in Eurocode 3 [D3], CIDECT design guides [D7,D81, IIW [D6], AWS [D2], AD [D1] etc. However, very limited information is available for connections between 1-beams and RHS columns. The existing CIDECT design formulae for plate to RHS column connections [D7], as
given by Wardenier [E30], are based on limited test data of axially tension loaded uniplanar connections with a small range of geometrical parameters. For multiplanar connections, no multiplanar geometrical and loading effects have been taken into
account. Also no composite action in the column has been studied. More information
on the static strength of semi-rigid I-beam to RHS column connections is therefore required urgently. To fill this gap, an extensive experimental and numerical research programme has been set up in the present project.
1.3 AIM OF THE RESEARCH
The aim of this research is to determine the static strength of the connections between I-beams and RHS columns and to develop the basic ultimate strength formulae which
are used as basis for design recommendations. It is also intended to show the effects
of the reinforced concrete infill in the columns (composite columns) and the influence
of a steel floor on composite steel-concrete floor on the connection behaviour. With this aim, experimental research and numerical research have been carried out.
The experimental work has been performed in the framework of ECSC project 72
10-SA/611 at Delft University of Technology and TNO Building and Construction
Research in The Netherlands. The numerical investigations have been carried out in the programme "Constructieve vaardigheden bij het detailleren van staal-beton verbindingen voor civiele constructies en gebouwen" sponsored by Commission Beek at Delft University of Technology.The experimental results have been used for the calibrations of numerical models in
which material and geometrical non-linearities are included. Based on well calibrated
numerical models, parameter studies have been carried out using finite element
analyses. The numerical results have been used for determination of the basic ultimate strength formulae for the considered connections.1.4 RESEARCH PROGRAMME
The complete research programme consists of 5 steps:
1 A review of literature studies, to consider existing information and design rules
2 Experimental investigations, including simple detail tests, interaction tests and complete connection tests
3 Calibration of the numerical models with the experiments
4
Numerical parameter studies using finite element analyses based on the
calibrated numerical models5 Analysis of the numerical results and proposal of the basic ultimate strength
formulae as basis for design recommendations
Four types of connections are considered in the present research (see table 1.1): axially loaded plate to RHS column connections, with and without concrete filling in the column
axially loaded I-beam (with and without a web) to RHS column connections, with and without concrete filling in the column
I-beams welded to RHS column connections with and without a steel floor
loaded by in-plane bending moments
I-beams bolted to RHS column connections with a composite floor loaded by
in-plane bending moments
By analysing the connection behaviour in this systematic way, the contribution of the main connection components on the connection behaviour has been determined, i.e:
the influence of the flange of the I-beam
the interaction between the top and bottom flanges of the I-beam the influence of a steel floor or a composite floor
the effect of a reinforced concrete in the RHS column
the multiplanar loading effect
All these effects combined, result in a description of the behaviour of a complete
Table 1.1 The connections considered in the present project
Connections uniplanar connection null planar connection
axially loaded plate to RHS column connections N i ,... (xp) N 1 N2
I
N7 -___. ... (xxp)axially loaded 1-beam to RHS column connections N1 ----... or without a web with a web (xbax)
+
..4.L
..._ N1 N1 ..--(xxbax) Al.... '-... I-beam to RHS column connections loaded by in-plane bending moments (xb) tNo 11111111% %Pi00,
4111111411 bolted I-beam to RHS column connections with a composite floor (xxb_.,) . .0 . . ' . I . 4 II . . I1.5 OUTLINE OF THE THESIS
In order to obtain a basic acknowledgement, a brief summary of the literature study with respect to the static behaviour of semi-rigid connections with RHS columns is given in chapter 2. including experimental and numerical research work.
In chapter 3, the experimental work is described and the results obtained from the
experiments are shown.
Chapter 4 describes the calibration of the numerical models against the experiments.
The most important aspects regarding the numerical modelling are discussed.
Based on well calibrated numerical models, extensive parameter studies have been carried out using finite element analyses. A wide range of geometrical parameters of the connections and various loading conditions has been covered. The results of the numerical parameter studies are presented in chapter 5 to chapter 7 separately for
different types of welded connections. Analytical models for several failure modes have
been developed. Based on the numerical results and the analytical models, the basic
ultimate strength formulae have been established. The influence of the concrete filling
in the columns and the multiplanar loading effects have been taken into account.
In chapter 8, the behaviour of bolted connections between l-beams and RHS columns with a composite floor is studied. The influence of the concrete filling in the columns
and the influence of the multiplanar loading is shown.
In chapter 9, the effects of the concrete in the columns on the connection behaviour are shown for different types of connections under different loading conditions. The summaries and final conclusions arc given in chapter 10.
2
LITERATURE STUDY
2.1 INTRODUCTION
From the sixties to the eighties, extensive experimental research has been performed on different types of connections using rectangular hollow section (RHS) members.
The investigations have been primarily focused on welded uniplanar connections where RHS was used both for chords and braces, such as X-, T- and K-joints in RI-IS. Those
connections have been tested with axial loading, in-plane bending and out-of-plane
bending moments. Based on the test data and theoretical analyses, basic design
formulae for the static strength of the connections have been developed which have
been later implemented in several design recommendations, such as: IIW, Eurocode 3,
CIDECT design guides and AU etc. The experimental and analytical work regarding
welded connections in structural hollow sections before 1982 has been summarized by
Wardenier in [E30]. An extensive list of literature on experimental, analytical and numerical research on the static behaviour of connections between plates or 1-beams and RHS columns is given in chapter 11.
In comparison with studies of connections in RHS, tests on welded connections between plates or 1-beams and RHS columns were very limited. Until 1981, only 16
test data were available for uniplanar plate to RHS column X-joints and 10 for
uniplanar I-beam to RHS column T-joint. No test data existed for multiplanar
connections.In 1992, 62 uniplanar I-beam to RHS column T-joints loaded by in-plane bending moments have been published by Ligocki [E17]. The results of the tests have been included in the data bank of connections [E26].
In 1994, the first 19 test data were available for multiplanar X-joints between plates
or I-beams and RHS columns [E28]. These tests were carried out in the ECSC project
'Semi-rigid connections between 1-beams and tubular columns'. The results of the experiments are discussed in chapter 3 of this thesis.
Further, from 1968 to 1994, a significant number of tests have been carried out in
Japan and Singapore on X- and T-joints between plates or I-beams and RHS columns
with internal or external stiffeners. A brief summary is given below.
In Japan:
A complete review of the test data on I-beam to CHS and RHS column connections with exterior diaphragms in moment resisting frames carried out in Japan have been
The simple tests simulated a simple diaphragm to column connection under axial
loading. A total of 60 tests for CHS columns and 58 tests for RHS columns have been performed. Further connections with I-beams subjected to in-plane bending moments
have been tested. The number of the tests is 12 for CHS columns and 7 for RHS columns. Also tests with I-beams subjected to asymmetrical bending moment have been performed. The number of the tests is 27 for CHS columns and 30 for RHS
columns. Based on the test results, strength formulae for the ultimate load capacity and
the yielding load capacity have been derived. Details of the tests can be found in the
references [E1,E2,E7,E9,E10,E14 to E16, E20 and E32}.
In Singapore:
Experiments on externally stiffened connections between I-beams and box columns have been performed by Shanmugam et al [E22,E23]. Different types of the external stiffeners have been used: triangular plates, angle stiffeners and T-stiffeners. The
influence of those stiffeners on the static behaviour of connections have been shown.
Finite element analyses on those types of connections have been performed by Ting
et al [N27,N28].
2.2 RELEVANT EXPERIMENTAL AND ANALYTICAL RESEARCH
Since the present work is concentrated on connections between plates or I-beams and
RHS columns without use of external stiffeners, only test results for welded
connections have been summarised in the following sections.The results of the Polish tests have not been included in this section because the RHS
columns used in those tests are made by joining two U-profiles together, which may differ to the columns considered in the present work.
From the previous research, it has been found that in many cases the load-deformation
curves do not show a peak load. In order to determine the ultimate load capacity, a deformation criterion has to be chosen. To solve this problem, a deformation limit has been discussed and evaluated in [N11) (A description of the deformation limit is given in section 3.6.3). It has been shown that a deformation limit of 3%b0(d0) based on the
local deformation of the column face is an appropriate choice for tubular joints. Therefore, throughout this thesis, the deformation limit of 3%bo has been used.
For axially loaded connections, this deformation limit is taken at the intersection of the
column face. For I-beam to RHS column connections loaded by in-plane bending
moments, this deformation limit is taken at the intersection of the column face and the compression loaded flange of an I-beam.
S TELL INGEN
behorende bijj het proefschrifi
The static strength of I-beam to
rectangular hollow section column connections:
vanL.H. Lu
Bij het bepalen van de "bezwijksterkte" van verbindingen dient een international aanvaard vervormingscriterium gebruikt to worden. Een lolcale vervorming van
3% van de breedte of diameter van de randstaaf
een goede keuze voorbuisverbindingen..
Het is noodzakelijk am op korte terniijn Internationale overeenstemming to
bereiken voor de evaluatie van numerieke resultaten (zoals de stijfheiden sterkte van verbindingen) naar richtlijnen.
Voor eon goede benadering van de sterkte zou er voor elk type verbinding en
elk belastingsgeval eon aparte formule gegeven moeten worden, doch dit maakt
de richtlijnen zo gecoinpliceerd dat de constructeurs "door de bomen het bos.
niet meer zien".
4i Elk numeriek model dient gccalibreerd te worden met experimentele resultaip.
ria.twit 14-ta
6 %rr
I t3Cr uo. At
ottie
Dat ondanks uitgebreide en ingewilckelde procedures bij grote infrastructurele
projecten toch nog verkeerde beslissingen worden genomen komt doordat de keuzes voor de toekomst gemaakt worden met de kennis van heden.
6. De promotie van staal-beton constructies heeft de afgelopen 25 jaar op het ,gebied van bruggen en viaducten in Nederland niet het gewenste result aat
gehad.
7'. Het gevaar, veroorzaalct door de plaatsing van paaltjes midden op een fietspad
met het doel autoverkeer to weren, is groter dan bet gevaar dat autoverkeer zou
opleveren..
Slecht systeembeheer veroorzaakt meer vertrag ng dan een langzame computer, is
9. Biji afspraken tothhet regell moeten 'zijn dat deze Inlet door de 'telefoon worden onderbroken.
111
lEen mens is
als staal :na langdurig onderhevig 'te zijn geweest aan
spanningswisselingen komt de vermoeidheid opzetten; ,doorbelasten kan tot
'breuk leiden.
2.2.1 Plate to RHS column connections
Experiments to determine the effective width criterion for the welded connections
between plates and box sections have been carried out by V.d. Elzen [E5], De Geeter [E8] and Rolloos [E21]. In those tests, the influence of the corner radius of the column
and the influence of width ratios pd.() was not considered. In order to determine the effective width of brace cross walls in RHS joints and for I-beam to RHS column connections, welded plate to RHS chord connections for various width ratios f3 and various chord slenderness 2i have been investigated by Wardenier and Davies et al
[E29,E30,E3,E4]. Based on the test data and theoretical analyses, it was indicated by Wardenier [E30] that design of these connections can be based on the effective width criterion, the chord punching shear criterion and the chord wall bearing criterion. The
strength formulae have been established by Wardenier and further adopted in the
CIDECT design guide [D7].
The connection strength for the welded plate to RHS column connections by Wardenier are summarised in table 2.1 and 2.2. Some of the results deviate somewhat from those
given in [E29] due to the fact that here the deformation limit of 3%b0 has been used while in [E29] peak loads were used.
Note:
peak load obtained before 3%b0 ** P-5-2 has extra thick weld sizes
Table 2.1 Summary of the test results for plate to RHS connections [E29] (fillet welds)
Table 2.2 Summary of the test results for plate to RHS connections [E291 (butt
welds) Test specimens chord ho x 110 x to [mm] plate b1 x t/ [nun] 0 27 fl, [1\1 /gin) 2] Nu ,xu [keN] P-1 180.1x179.7x6.2 180.5x6.4 1.00 28.6 335.7 187.0 * P-2 179.7 x180.1x6.1 160.2x6.4 0.89 175.5 P-3 180.0x180.0x6.0 140.0x6.4 0.78 110.9 P-4 179.8x179.6x6.0 109.7x6.4 0.61 93.8 P-5 180.9x180.8x9.3 160.0x9.1 0.89 20.5 259.1 255.1 P-5-2 ** 180.8x180.8x9.3 160.0x9.1 0.89 380.8 P-6 180.9x181.0x9.0 140.0x9.0 0.78 216.4 * P-7 180.8x180.9x9.0 110.0x9.0 0.61 134.2 P-8 180.8x181.4x13.4 160.0x12.0 0.89 14.4 253.6 436.4 P-9 180.9x180.7x13.3 140.0x12.0 0.78 400.9 P-10 180.9x181.1x13.4 110.0x12.0 0.61 305.0 Test specimens chord bo x ho x to [mm] plate bi x ti [mm] 13 2y fy0 [N/mm2]
Nu.p
[1(N] P-2-II I 80.2x179.8x6.0 160.0x6.4 0.89 28.6 335.7 178.9 P-4-11 180.6x179.2x6.1 110.2x6.5 0.61 97.3 P-741 181.0x180.8x9.1 110.1x9.1 0.61 20.5 259.1 174.0 P-8-11 180.9x180.4x 13.5 160.2x11.8 0.89 14.4 253.6 458.2 P-10-I1 180.8x180.6x13.4 110.1x12.1 0.61 300.0 * I2.2.2 I-beam to RHS column connections
Until 1981, a total of 10 uniplanar I-beam to RHS column 1-joints loaded by in-plane
bending moments have been tested in Japan [E15]. The test results provided useful information on the behaviour of unstiffened RHS moment connections. Kanatani indicated that generally four local failure modes, i.e. chord face yielding, chord side wall failure, local buckling of brace flanges and punching shear, can be expected for
this type of connection. The relationship between the failure modes and the
dimensional parameters of the specimens has been investigated. The experimentalresults have been compared with the empirical formulae (see E14,E16,D1), predicting the ultimate connection strength of plate to column connections. It was found that for 3.1.0, the empirical formulae are applicable, but for p<1.0, the strength of the 1-beam connections is overestimated by those formulae.
A theoretical push-pull yield line model has been assumed by Szlendak 1E25] to
predict the joint strength. The theoretical predications agreed well with the test results of Kanatani.
The connection strengths of the Japanese tests are summarised in table 2.3. Some of
the results deviate somewhat from those given in [EIS] due to the fact that here a local
Note:
peak load 'obtained before 3%130
Table 2.3 Summary of the test results for 1-beam to RHS connections [E15]
i3
DESIGN CODES AND RECOMMENDATIONSBased on the test results and theoretical analyses, a number of design recommendations
have been established for welded hollow section connections, such as: IIW [D6],
Eurocode 3 [D3], CIDECT design guides [137,D8], All [D1], etc. The first IIW design
recommendations were published in 1981 and the updated version in 1989. These updated design recommendations have been further adopted for Eurocode 3 for the
European countries and Canada The Japanese design recommendations AU for tubular connections are. in line with the IIW recommendations.
Since very limited information is available for connections between plates or 1-beams and RHS columns, the design formulae given by Wardenier [E30], which were based
on the limited test data, have been adopted in the CIDECT design guide [D7]. The Japanese design recommendations for tubular connections (AU) only give design
Test specimens Chord 'bo x ho x to [mm] 1 1-beam til x in, x t, x ti [mm] 13 2y fYO [N/mm2]i Mu,exp [1c.Nm]; H f 200x200x6 148x100x6x9 0.50 33.3 383 8.4 H 2 300x150x6.5x9 0.75 ___ 42.2 I H:3 300x200x6x9 1.00 91.6 ii
H4
400x200x8x13 1.00 106.7 * H 5 200x200x9 448x100x6x9 0.50 22.2 340 19.5 H 6 300x150x6.5x9 0.75 76.0 1 H 7 300x200x6x9 1.00 137.7 ._ 1 H 8 200x200x12 I 148x100x6x9 0.50 I 167 378i ' 3118 1 I H 9 II I 300x150x6.5x9 0.75 1 122.7li io
1 1 300x200x6x9 1.00 1 I I 187.0 1 Iformulae for connections with exterior diaphragms. Therefore, throughout the present
work only CIDECT design formulae have been used for comparison.
CIDECT design formulae are only given for uniplanar plate to RHS column
connections loaded in tension with a small range of geometries. For multiplanar connections, no information is available for the multiplanar geometrical and loading
effects. The CIDECT design formulae for uniplanar connections may lead to an unsafe
design for multiplanar connections with a negative load ratio.
In the CIDECT design guide, for I-beam to RHS column connections loaded by
in-plane bending moments, the strength of the connection is obtained by multiplying the
axial resistance of plate to RHS column connection by the beam depth (h1-t1)
[E30,D7]. No further information is given for multiplanar connections.3
EXPERIMENTAL RESEARCH
3.1 INTRODUCTION
As mentioned in chapter 1, information on the static behaviour of connections between
I-beams and RHS columns is very limited compared to information on other types of
connections, such as RHS to RHS connections. The existing design formulae [E30,D7] are based on limited test data of axially tension loaded uniplanar plate to RHS column
connections. No test results are available for multiplanar connections. In order to get insight into the multiplanar geometrical and loading effects, experiments have been
carried out on multiplanar connections.
3.2 RESEARCH PROGRAMME
The experimental research programme is summarized in table 3.1. It consists of 19 test specimens divided into four test series (series 1 to series 4). Series 1 consists of eight simple tests (IR 1 to 1R8) between plates and RHS columns with axial loading on the plates. Series 2 (2R1 to 2R3) are interaction tests, three multiplanar connections with two levels of plates (I-beam flanges only, no web at the connection) with axial loading on the flanges. Series 3 considers four complete tests (3R1 to 3R4) on I-beams welded to RHS columns loaded by in-plane bending moments, one of them (3R2) has a 5 mm
thick steel floor. Series 4 consists of four complete tests (4R1 to 4R4) on I-beams bolted to RHS columns with a composite floor comprising a deep steel deck and a concrete slab, loaded by in-plane bending moments. The rectangular hollow section
(RHS) columns are in some cases filled with reinforced concrete in order to study the influence of the composite action of the column. These connections are shown in table 3.1 with a shaded area inside the columns. The details of the design of concrete filled
columns and composite floor have been reported in (E28].
Three loading cases (J=0,+1 and -1, J=1\12/N1 or J=F2/F1) have been considered to
investigate the multiplanar loading effects. The loads on each test specimen are shown in table 3.1.
N1 ...
1}:°
N1 1R2 N1 ...i1,-...:7 Ni 1R3 i}....lir NI N1 air 1R4 NI eV (3 =0.4 # =0.4 /3 =0.57 # =0.57 1R5Ifl
1R6 1R7fl
1R8N2."
NI N2 "lb 41. NI N N2 all' NW Or ie. off Nsiofriir
111. NI N2 N1 N2 N1 N2 NI N2 N2/Ni =-1 p =0.4 N2/Ni= + 1 # =0.4 N2/Ni= - 1 p 0.57 N2/Ni= + 1 # =0.57 2R1 2R2 2R3 ar,,,,1
I
1-le
N1 atss:F N1 off Ni Iwo NIoff1
I
if_ Ni 41111L #
=0.4 'de' (3 =0 . 4 -# =0.57 3R1 3R2m
-4111111111110-____Ar...aw,.. 3R 3 1 1lip
411.
3R4I
I 12"me.
IF
11 Fi4Lel
F1 F2el
111
-fl =O.4 F ft =0.4 --1 fl ---0.4 F241 = + 1 # =0.4 4 k 1 _Am . ' . ' . ill I I I I I I I I 11 Ie
m 1:- ' - - " 4R2 --...01 I I I I I I I I I I I I I Icli ir. " . . " ' 4R3 F...ta
. - . - - ' I I I I I I I I ll I I I i 1 0 I 7 ' ' ' ' ' ' . . . .te-t
4F2 4R4 F Am., 1 1 I "e---ir I.
i ... 2 (3 =0.4 fl =O.4 F241 =+ 1 F p = 0 .4 F2/Fi = + 1 )3 =0.4 -1 -$ ri3.3 MEASURED DIMENSIONS OF THE SPECIMENS
In figure 3.1 the configuration of an I-beam to RHS column connection and the main
geometrical parameters of the connections are shown. The nominal sizes and the
non-dimensional parameters of the test specimens are given in table 3.2. For all test
specimens, rectangular hollow section with nominal dimensions of 300x300x10 mm
is used for the column. The length of the RHS column 10
is 1800 mm. The reinforcements in the columns and of the composite floor are shown in figure 3.2.Jo
II
Figure 3.11 Configurations and non-dimensional parameters of the connections.
301 30 compositecolumn 0.300..300.10 (Fe51 0) 8020 (8500H) 08 (85000 Concrete 035/45 75 110150CRS 75
Figure 1 The arrangement of the reinforcenientS,
111=
/ b,
= be, / to,= t
/ toii = h / 6,
composite floor so 16-150-R allkil r4 I I 6-150 v.; be, be ot Ii to t 38 4For test series 1 to series 3, the plates and flanges of 1-beams are directly welded to
the column with butt welds and the webs of the I-beams are welded to the column on
both sides of the web with fillet welds. For the bolted connections (series 4), angle
cleats and web plates are provided to bolt the I-beams to the RHS columns. The cleats
are 160x80x10 mm angle sections, 120 mm long, with 6 013 mm holes provided for the M12-10.9 bolts. The web plate size is 180x81x6 mm, providing 3018 mm bolt holes for M16-8.8 bolts (see figure 3.3).
300
Figure 3.3 Details of bolted connections
For numerical modelling, careful measurements of the actual dimensions and the mechanical properties of the test specimens have been carried out. The details of the measurements have been reported in [E281. The average values of the measured dimensions of each specimen are summarized in table 3.3 to table 3.6.
Since the connection behaviour is sensitive to the weld geometry, the weld sizes were measured for each welded specimen individually (see figure 3.4). The average values of the measured horizontal leg lengths ah, and vertical leg lengths a to 4), which represent the actual weld sizes on plates, I-beams and columns are summarized in table
3.7.
Note:
(CC) concrete filled column
(SF) a steel floor
KT) N, in tension
Table 3.2 Nominal dimensions and loading cases for test specimens with an RHS column of 300*300*10, 1800 mm long Test specimens Configuration N2/NI or Nominal dimensions Non-dimensional parameters bixt, (plates) or bixt,xh, (I-beams) 1, I mm I 13 2y 't 11 I mm] IR 1 0 I 20x 10 615 0.4 30.01.00 1R2 (CC)
fl
0 (T) 120x10 615 0.4 1.00 1R3 N7-- NI 0 170x12 780 0.57 1.20 I R4 (CC)Nifl
..."'N2 0 170x12 780 0.57 1.20 1R5 LJ -1 120x10 615 0.4 1.00 1R6 +1 170x10 615 0.4 1.00 1R7 -1 120x12 780 0.57 1.20 1R8 +1 170x12 780 0.57 1.20 2R1 0 120x10x240 600 0.4 30.00.98 0.8 2R2 (CC) 0 (T) 120x10x240 600 0.4 0.98 0.8 2R3 II II 0 170x12x360 800 0.57 1.27 1.2 --ir; ...- --vl °raft - --(J.PE 240 resp. ...._ IPE 360) 3R1 0 120x10x240 1200 0.4 10.00.98 0.8 3R2 (SF) .1I
F2 0 120x10x240 1200 0.4 0.98 0.8 3R3 111111111111010-' -1 120x10x240 I 200 0.4 0.98 0.8 3R4 21
+1 120x10x240 1200 0.4 0.98 0.8 opE 240) 4R1 F F1 0 120x10x240 1200 0.4 30.00.98 0.8 4R2 (CC) I 0 120x10x240 1200 0.4 0.98 0.8 4R3 -,,....----_____"'Ilk to -
+1 120x10x240 1200 0.4 0.98 0.8 4R4 ---' -+1 120x 10x240 1200 0.4 0.98 0.8 tN -(IPE 240) F2/F, I I H ' "Table 3.3 Average values of measured dimensions and material properties for test series I Test specimens Measured dimensions [mm] Measured material properties I[19/mm2] fy.0 2R1 300.0 9.74 120.0 9.74 242.1 453.0 I 420.0 480.0
Table 3.4 Average values of measured dimensions and material properties for test series 2 Test specimens Measured dimensions [rnm] Measured material properties [NI/mm2] ' b, II to 6 I
b
t,f
fy,,it
299.9 9.82 119.6 9.89 434.0 398.0 1R2 I 299.9 9.82 119.6 9.89 434.0 398.0 1R3 1 299.9 9.82 170.0 11.53 434.0 392.0 1R4 I 299.9 9.82 170.0 11.53 ' 434.0 392.0 1R5 I 299.9 9.82 1 120.5 10.03 434.0 388.0 i 1R6 299.9 9.82 I 120.5 10.03 434.0 388.0 1R7 299.9 9.82 170.0 11.53 434.0 392.0 1R8 300:0 11 9.74 170.0 11.53 453.0 , 392.0 2R2 300.0 9.74 120.0 9.74 I 242.1 449.0 II 420.0 480.0 2R3i 300.0 , 9.74 169.2 12.89 363.4 I 453.0 404.0 I 442.0 I be to b, ti h,Table 3.5 Average values of measured dimensions and material properties for test series 3
Table 3,:6 Average values of measured dimensions and material !properties, for test
series 4 Test specimens Measured dimensions [mm] i Measured material properties IN/mm21 be I t0 b, it, fyi, i 3R1 300 9.76 119.7 9.72 6.64 241.9 439 421 470 3R2 300 9.76 119.7 9.72 6.64 1 241.9 439 421 355
_
3R3 300 9.76 119.0 9.63 i 6.57 241.8 387 419 473 3R4 300 9.76 119.0 9.63 6.57 2411.8 1 387 419 1 473 Test specimens Measured dimensions [mm] , Measured material properties [14/mm2] RHS I-beam cleat b,t
b,ç
h,k,
Ed v,o f,1 fy!,, 4121300 9.76 119.6 9.72 6.48 242.2 79.0
10.4 439
431 490 377 4R2300 9.96 119.6 9.72 6.48 242.2 79.0
10.4 439 431 490 377 4R3300 9.88 120.3 9.83 6.53 242.2 79.0
10.4 438
432 503
377 4R4300 9.88 120.3 9.83 6.53 242.2 79.0
10.4 438 432 503
377r
B B
{-1
A
TEA
B-B
column wallah3 I-beam 'Range'
Figure 3.4 Weld measurements,
Table 3.7 Average values of the measured weld sizes
column wall
I-beam web
114
C-C
A-A
Connections ahl
a,
a,,2 a33 ay3 ah4 daN41R1 12.3 10.7 6.5 6.2 9.6 11.4 1R2 13.2 8.9 6.6 6.1 9.3 10.1 --1R3 13.9 9.4 7.0 6.4 9.7 12.9 --1R4 15.5 9.8 6.5 6.2 12.7 12.4 IRS 13.0 11.0 6.5 6.2 10.8 11.1 I 1R6 1 12.4 10.1 6.8 6.0 10.2 10.1 1R7 14.9 9.4 6.9 5.7 10.3 9.5 --1R8 14.6 7.8 6.4 5.3 11.1 11.4 2R1 13.6 9.3 6.9 5.9 9.5 12.1 --2R2 14.3 9.7 7.6 6.7 10.0 11.8 I 2R3 16.8 10.4 7.6 5.7 14.5 153 3R1 14.9 10.7 7.8 7.4 14.5 13.2 7.1 6.3 3R2 12.0 9.3 7.1 7.4 14.5 13.2 6.9 6.1 3R3 15.3 9.3 7.0 7.0 11.1 11.9 6.9 6.1 3R4 , 14.1 9.8 6.9 9.0 10.1 11.8 6.9 6.5 av4 ahi av1 v2 -- ---- ----
--3.4 MECHANICAL PROPERTIES
3.4.1 Steel members
The RHS columns used for the tests are hot finished with steel grade S355. The WE 240 and IPE 360 beams are Fritenar M 355 offshore steels. The plates and steel floor
are grade St52-3 according to DIN 17100. The actual mechanical properties fy (yield stress), fu (ultimate stress), e (permanent elongation) and Iv (constriction or necking) of the above mentioned steel members have been measured and reported in [E281. The
average values of measured yield stress for the steel members are also given in table
3.3 to 3.6.
3.4.2 Welding material
The butt welds of all test specimens are welded with basic electrodes, trade name Kryo
1, electrode size 03.2 (nominal mechanical properties being fy=470 N/mm2, fu=520 N/mm2, e=31%). For the fillet welds, basic electrodes with trade name Safdry 52, electrode size 05.0 (nominal mechanical properties being fy=408 N/mm2, fu=511
N/mm2, E=34%) have been used.
3.4.3 Reinforced concrete
For the reinforced concrete infill of the RHS columns, the concrete strength class of C35/45 is used. The reinforcements 020 is Grade B500H.
The concrete strength class C20/25 is used for the composite floor. The reinforcements
06 are cold formed plain bars of grade B500N and the reinforcements 08 are hot finished bars of grade B500H. The mechanical properties of the steel reinforcements and concrete are given in table 3.8.
Note:
measured for B500H 020 bars fy= 565 N/mm2, fu= 644 N/mm2, E= 9%
measured for B500N 08 bars fy= 570 N/mm2, 645 N/mm`. E= 24%
measured for B500H 06 bars fy= 615 N/mm=, fu= 627 N/mm2. s= 17% Table 3.8 Material properties of the concrete and reinforcements
3.5 TEST RIG AND TESTING PROCEDURES
3.5.1 Axially loaded plate or I-beam to RHS column connections (series 1 and 2)
A schematic drawing of the test rig for series 1 and series 2 with axial loading on the braces is shown in figure 3.5. The RHS columns were always positioned horizontally
and the plates or 1-beams loaded by N, (in-plane) were positioned vertically. During
the testing, the column was maintained horizontal by using a servo controlled hydraulic
jack to displace the column vertically at one end of the column. The lateral
displacement of the loaded plates and beams was prevented by using lateral supportsat one-third and two-third of the length of the members. This avoids buckling of these members under compression loading.
The axial load in the vertical direction N, was applied vertically on the lower member using a servo controlled hydraulic jack, while the upper member was pin-supported to the reaction frame. For multiplanar loading cases, load N2 (out-of-plane) was applied
by means of a hydraulic jack mounted in an independent frame in the horizontal direction along the horizontal members. Sections I-I and II-II of figure 3.5 show the
Test specimen Material properties [N/mm=1 Reinforcements Concrete Column ( I) Floor (2) Column (C35/45) Floor (C20/25) fc f, Er 1R2 B500H 56.5 4.82 25100 1R4 B500H 49.5 4.15 27000 2R2 B500H 54.7 3.88 27200 4R1 B500H/N 37.64 3.58 36500 4R2 B500H B500H/N ---- 40.64 3.79 36500 4R3 B500H/N 60.3 4.00 40.18 3.84 36447 4R4 B500H B500H/N 57.7 5.12 28100 40.18 3.84 36447 (1) i(2) f, I , ,
1
situation for compression and tensile loads in the horizontal members respectively. The
ends of the horizontal members when loaded, were also adjustable supported in the same way as used for the column to avoid eccentric loading during testing.
Figure 3.6 shows the test rig for the tests 2R1 and 2R2 with only in-plane, 1-beams
loaded in tension and compression.
:I!
Mb! et
10-11
Figure 3.5 Test rig for series if and 2
ii
I
sominamintappisitsmagm
ais
!fl
ir 4a
a 1 1 1-1..i'I"
x a1
Imoissisismonine
.
+Figure 3.6a Test specimen 2111 ii the meat rig 4
-vI
,j
ail. 1.
41
if I_El
:-.
11711
---7.----0
a 'I.
*Al
.2°,Iv- ..
7..,...---..".,,,,,4
I
pl.
,
. 1 ...,..,. ...,-._a
ab I
.n_- 71-,
r-
1 1.4 I '1 ,v
3,51 I-beam to RHS column 'connections loaded by in-plane, bending moments
(series 3 and series 4)
The test rigs used for test specimens loaded by in-plane bending moments are
schematically shown in figure 3.7 for F2/F1=0 and +1 and figure 3.8 for FIF1=-1. The test specimens were positioned in the test rig with the RHS column always in a vertical position.For the loading cases F2/F1=0 and 1, the same test rig as shown in figure 3.7 is used. The test specimens were supported at the ends of the 1-beams. With F2/F1=0, the ends
of the out-of-plane beams were free (see figure 3.9a). The load was applied in
compression to the column bottom through the servo controlled hydraulic jack.
TUT SPEalatrl A hive raw bang TEST SPECIMEN load Weal tte
ra.
rammil
I SIDS AA. tetrad spade SECT1011 B-S Lateral supports Rate beaters Shea Note:For 3RJ and 3R2 with F.,/F1=0, the ends of the out-of-plane beams. wernifreet
For test specimen 3R3 loaded with , the test rig arrangement has been changed.
The in-plane beams were pulled downwards at their ends by a servo controlled
hydraulic jack and spreader beam system, the reactions were taken by tension bars from the top of the test rig frame to the ends of the out-of-plane beams (see figure 3.9b). The forces F, and reactions F2 on the in-plane and out-of-plane beams were transmitted through roller bearings to ensure only vertical loading obtained. Hinges were provided at the ends of all the tension bars.
For all test specimens, lateral displacements of the column were prevented by using lateral supports in two directions. Lateral displacements of the I-beams were also prevented by using lateral supports at the flanges of the loaded beams.
Figure 3.8 Test rig for 3R3 with F21F1=-1
-roo. o.arra =°^4"Y I e
1111111
PrImorr bem, LatAral eupportsa
I
II °
-4-w
1an!
1.L.ul b. 3R3 with F2/F,=-1Figure 3.9 Test specimens 3R2 and 3R3 in the test rigs ,LoiiLt -....,,,,,..;1/40, liii-ul
La.: tia
. C.? -: -.-1,... . ' Y - - \ . . . 77r - i.
.
e.
I
, ,.. if ... Ti.... i1
. I --.-........-.. ....-.-..
_.,.., :fp 'I i.
. e.
1 1...,.
u_
et a. III-
Ililt
_
a. 3R2 with F2/F1=0 g. 13.6 DEFINITION OF VARIOUS CHARACTERISTICS
Throughout this thesis, the connection behaviour has been presented in a
load-displacement curve for an axially loaded connection and a moment-rotation curve for a connection loaded by bending moments. The definition of the load (moment) and thedisplacement (rotation) of the connections has been given in the following sections
16.1 Displacement of the connection
The measurements for all, axially loaded test specimens (series ) and 2) are shown in
figures 3.10' and 3.11.
For all axially 'loaded connections, the load of the 'connection is the average value of
the loads on two plates or I-beams in the same plane. The displacement of the
connection represents the average value of the indentations into the column face of thetwo plates or I-beams in the same plane, i.e.: A=(2*s3+s4+s5)/8 (see figures 3.10 for series I)
A=(2*s3+s4+s5+2*s7+s8+s9)/16 (see figure 3.11 for series 2)
Isoa (1R1 to 1R4) 2000 (1R5 to IRS)
!it
a(IRS to R0) 1^II
ii
1(1R1 to 1R2) 20Rt tok$R8),1 11(1R5 to IRS IVO Notes: 191 3.41,5 :Vertical deformation ,(1R4 to 1R8)2) 6,7.8 : Horizontal deformation (1R1,1R5 to IRS)
3)1 6.9 : Horizontal deformation of plate centre line, front and rear face (1R2 to 1R4)
Figure 340 Typical schematic details of transducers: for series P
10020.600 plate 1(1R1 to 1R4) 120700650 plate ,(1R5 to 1RB) RHS 300.300.10 cc :5 22 ir-15 re re
6(10) PE 240
PE 360
VIEW A-A
HS 300.300.10
Figure 3.11 Typical schematic details of transducers for series 2
3.6.2 Moment and rotation of the connection
For connections loaded by in-plane bending moments, the moment at the column face
has been used, which is obtained by multiplying the reaction force at a beam support
by the distance between the support and the column face. The moment of the
connection is the average value of the moments for the two beams in the same plane (on either side of a column).
In figures 3.12 and 3.13, the measurements for all test specimens loaded by in-plane bending moments (series 3 and 4) are shown. Two methods can be used to calculate the beam rotation. The first is by using the two vertical displacements of the beam
divided by the distance between them. The second is by adding the column
indentations at the upper and lower flanges of the beam divided by the distance
between the measurement points. The two methods give almost the same results. Throughout the present work, the first method is used to calculate the connection rotation. Since the elastic deformation of the beam is small it is further neglected in the analysis. The rotation of the connection is the average value of the two beam rotations in the same plane (on either side of a column).
A
7
Ann
VIEW AA
Notes:
All transducer measurements are along beam centrelines
RHS 300*30010
Figure 3.12 Typical schematic details of transducers for series 3
Unloaded IPE 240
2) Deflection of loaded beams at locations 3, 4, 7 and 8
2) Deflection of unloaded beams at locations 1, 2, 5 and 8
3) Deformation of column at locations 9, 10, 11 and 12
1 5 1
40
21 Loaded IPE 240
6I
A
48 47 Concrete floor 7'9 T 40738r i
1.
35038r
350 VIEW AA 40 only for 4R1. 4R2 T 405 406 6C only for 4R3, 4R4T --I 30
405 195 RHS 3004.300.10 50 1144Figure 3,13 Typical schematic details of transducers for series 4
63 45 44" 195 31 400 32
3.6.3 Deformation limit for the ultimate load capacity
In many cases the load-deformation curves do not show a peak load. In order to determine the ultimate load capacity, a deformation criterion is required.
For tubular connections, several ultimate deformation limits are available, such as the deformation limit given by Yura [E31] for CHS joints, the deformation limit given by
Korol and Mirza [N6] for RHS T-joints loaded by axial compression, and the
deformation limit suggested by Lu [N9] for uniplanar I-beam to RHS column
connections loaded by in-plane bending moments. However, these deformation limitsare only valid for certain cases. Adopting a deformation limit which can be used for all types of tubular joints is desirable.
To solve this problem, an extensive investigation has been carried out on different types of tubular joints [NH]. Based on the experimental and numerical results, an ultimate deformation limit of 3%b0(d0) has been selected for tubular connections. Verification of this deformation limit has been done by checking various types of
tubular joints: axially loaded plate to tubular column (CHS,RHS) connections [N4.N81,
I-beam to tubular column (CHS,RHS) connections loaded by in-plane bending
moments [N3,N5,N7,N9], X-joints in CHS and X-joints in RHS members loaded by
in-plane bending moments [N24,N25,N29,N30], X-and T-joints in RHS loaded by axial compression in braces [N32].
Theoretically, the designer could use the load-displacement diagram of connections for design and check the ultimate and serviceability criteria, but this is rather complicated
for practical design. To avoid this, a procedure to define the ultimate strength of the connection has been carried out. In general, a connection can be considered to have failed if a maximum load is reached or if an adopted deformation limit is reached. If no deformation limit is used, an additional serviceability limit criterion has to be
adopted for design. For axially loaded hollow section joints, an indentation of 1%b0(d0)
at the chord face is generally used as the serviceability deformation limit as given in
the IIW 11D6].
In most cases, the behaviour of tubular connections tends to be flexible with a large
deformation. The strength of the connection increases with increasing deformations of the connections (see figures 3.15 to 3.18). This phenomenon has been obtained also for other types of tubular joints, e.g. X-joints in CHS [N24,N25,N29,N30], plate or I-beam to CHS column connection [N3,N5], and X- and T-joints in RHS [N32]. For different
types of joints under different loading cases, it has been found that failure of the
connection is mainly related to the plastification of the chord face around the
intersection of brace and chord. Therefore a local indentation of the chord face at theintersection has been proposed as the deformation limit to determine the design load
From the experimental and the numerical load-displacement curves, it has been found
that for connections where a peak load is obtained, a corresponding local indentation
of the chord face at the intersection varies between 2.5%-4%b0(d0), as shown by Van
der Vegte [N31], De Winkel [N3] and Yu [N32]. Furthermore, in the experiments of
this programme [E28], initial cracking started at joint deformations exceeding 3%130. Therefore, a local deformation limit of 3%130(d0) at the intersection of the chord face has been suggested as the ultimate deformation limit. To verify this deformation limit,
the FE results for different types of connections have been used to check both the serviceability and the ultimate strength (see Nil).
For hollow section connections, the deformation at serviceability should satisfy the requirements of the structure.
If the load on the connection belonging to the
serviceability of 1%b0(d0) (Nr) multiplied by the appropriate load factor for the limit state (ye) results in a load exceeding that belonging to the ultimate design strength (No),than Nd will be governing, i.e. the serviceability limit is not critical. According to Eurocode 3 [D3], considering the combination of the different unfavourable action
loads on the structures, the minimum value of ye should be taken as 1.35. If the
ultimate loads N at the deformation limit from the numerical analyses would be
considered as the characteristic values, the design loads can be obtained by dividing
the characteristic values by yr. For different failure modes, yr, varies from 1.0 to 1.25 as suggested by WardeniertE30]. For plastification, y, is taken as 1.1. Based on these
arguments, the ratio between the ultimate load and the serviceability load i(Nr/Ns)
should be less than 1.5. In this case, the check at serviceability can be ignored.
Otherwise, the strength of these connections is determined by the serviceability
criterion.A
[mm]
Figure ,3.14 Deformation limit
Severiceability N,, Ultimate limit d Ns 1 N
After checking the strength at this deformation limit and the strength at serviceability
for different types of the connections (the details has been described in Nil), it has been found that the deformation limit of 3%b0(d0) based on the local deformation of the column face is an appropriate choice. Therefore, this deformation limit of 3%b0
based on the local deformation of the column face has been used throughout this thesis.
3.6.4 Definition of the ultimate load
For the determination of the ultimate strength capacity of connections, the following
considerations have been taken into account:
For connections where a maximum load is obtained before the deformation limit of 3%130, the maximum load is taken as the ultimate strength of the connection. For connections without a maximum load or with a maximum load but obtained
after the deformation limit of 3%b0, the ultimate strength is taken at the
deformation limit of 3%b0.For axially loaded connections, this deformation limit is taken at the intersection of the column face. For I-beam to RHS column connections loaded by in-plane
bending moments, this deformation limit is taken at the intersection of the column face and the compression loaded flange of an I-beam.
3.7 RESULTS OF THE EXPERIMENTS
For axially loaded connections (series 1 and 2), testing was stopped when the total
column indentation reached approximately 10% of the column width, so that
information on the deformation capacity and failure modes was obtained. For
connections subjected to in-plane bending moments (series 3 and 4), testing was
stopped when the average beam rotation reached approximately 0.15 radians if no peak load was obtained earlier.
The load-displacement curves obtained from the experiments of series 1 are shown in
figure 3.15 for each group of connections with the same 13
values. The load-displacement curves obtained from the experiments of series 2 are given in figures3.16. The moment-rotation curves for series 3 and 4 are shown in figures 3.17 and 3.18 respectively.
goo. 400.
T2
o. -_r
Deformatic .limit of 3 l' bn lESTSERIES 121=30
. _ _.
_-.
_ 1 ....
.
...
-1R1 C.-_ . ... i 600. 400! i Deformation limit of 3 TESTSERIES 1 /3=0.57 11R4 , ifl
I I27=30
, 1R3 N2/N1=0air"
1 1R4 .Willi
Al
.. ...j
..1R7 1 1 - -N2/N1=0(0 1R1 N2/N1=-1 1R0,---
N2/N1=+11 I if 71 . 20: 3o. 40.---
A [mm]
1101 20. 40.A [mm],
Figure 115 Load-disritacement curves for series.
600. 800. n 1R1 N2/N1=0 N2/N1=-1 t N2/N1=+1 30.
500.
Figure 3 ii6 Load-displacement curves for series 2
100. 1000, 750. 250. DO. 50. 0, 0. 0. 10. 20. 30.
A [mm]
Figure 3.17 Moment-rotation curves for series 3
40. Deformcrti n limit of 3 1 TEST SERIES 2 N2/N1=0
