INELASTIC PERFORMANCE OF STEEL/CONCRETE COMPOSITE … · This thesis deals with the behaviour of Partially Encased Composite (PEC) and Concrete Filled Tubes (CFT) subject to cyclic

INELASTIC PERFORMANCE OF

STEEL/CONCRETE COMPOSITE

MEMBERS

A thesis submitted for the degree of

Master of Philosophy

By

Xiao Ban

Department of Civil and Environmental Engineering

Imperial College London

February 2012

2

Abstract

This thesis deals with the behaviour of Partially Encased Composite (PEC) and

Concrete Filled Tubes (CFT) subject to cyclic loading by means of experimental and

numerical investigations. It addresses a number of design and assessment issues

regarding the ductility capacity and ultimate response of PEC and CFT beam-column

elements.

Experimental results from ten tests including seven cyclic tests on PEC members and

three cyclic tests on CFT members are presented. The set-up, instrumentation and

member configuration are described followed by a full description of the experimental

results. The composite members were subjected to cyclic gradually increasing lateral

displacements along with varying levels of axial load simulating various gravity

effects. Particular attention was given to the ultimate failure mode. To this end, in

order to enhance their ductility, six of the seven PEC specimens were provided with

special transverse links with the purpose of delaying the onset of local buckling. The

effects of these improved details are discussed with regards to their influence on

ductility as well as other structural response parameters.

Numerical Finite Element models developed to simulate the response of the

specimens are proposed and validated against the experimental results. This allowed

for a more detailed assessment of local buckling effects in composite members.

Furthermore, the FE models were used to conduct parametric studies on key design

aspects related to the stiffness, capacity and ductility of composite members.

Based on the experimental results and numerical studies, the implications of the

finding of this work on design consideration for PEC members and CFT members are

discussed.

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Declaration

I confirm that this thesis is my own work. In it, I give references and citations

whenever I refer to, describe or quote from the published, or unpublished, work of

others.

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Acknowledgement

I would like to thank my first supervisor Prof. Ahmed Y. Elghazouli, for giving me

the opportunity to study in Imperial College London. I would also like to thank Dr.

Christian Malaga-Chuquitaype for your patient and kind assistance. It is my privilege

to work under your supervision.

The experimental work was carried out in the Structures Laboratory in Skempton

Building. I believe the work would not have been completed without the hard work of

Leslie Clark, Ron Millward, Stef Algar, Trevor Strickland and Delroy Hewitt. I would

especially like to thank Leslie and Ron for their very hard work, dedication to this

project, and always encouraging me during the whole time. The time spending in the

Structures Laboratory was a previous memory for me.

I also would like to thank the staff and students in Skempton Building, in particular:

Fionnuala Ni Dhonnabhain, Mukesh Kumar, Yanzhi Liu, Osofero Adelaja I, Arash

Soleiman Fallah, Mahmud Ashraf, and all other fellow researchers in Room 424. All

of you provided an inspiring and happy working environment.

I thank my parents for always encouraging me to pursue my dreams and giving me

confidence to face difficulties.

Finally, I would like to acknowledge the scholarship from the Chinese Scholarship

Council to support me complete the work here.

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Table of Contents Notation ..................................................................................................................................... 7

List of Figures ........................................................................................................................... 9

List of Tables ........................................................................................................................... 12

Chapter 1. Introduction ..................................................................................................... 13

1.1 Background ................................................................................................................... 13

1.2 Objectives and scope ..................................................................................................... 14

1.3 Outline of the thesis ....................................................................................................... 14

Chapter 2. Literature Review ............................................................................................ 16

2.1 Introduction ................................................................................................................... 16

2.2 Concrete Filled Steel members ...................................................................................... 16

2.3 Partially Encased Composite members ......................................................................... 20

2.4 Modelling of composite members ................................................................................. 22

2.4.1 Concrete damage plasticity model .......................................................................... 23

2.4.2 Steel models subjected to cyclic loading ................................................................ 26

2.5 Concluding remarks....................................................................................................... 28

Chapter 3. Experimental Methodology ............................................................................. 29

3.1 Introduction ................................................................................................................... 29

3.2 Testing arrangement ...................................................................................................... 29

3.3 Instrumentation and measurements ............................................................................... 32

3.4 Load application ............................................................................................................ 34

3.5 Description of specimens .............................................................................................. 35

3.5.1 Specimen details ..................................................................................................... 35

3.5.2 Material properties.................................................................................................. 38

3.5.3 Preparation of the specimens .................................................................................. 40

Chapter 4. Experimental Results ....................................................................................... 42

4.1 Introduction ................................................................................................................... 42

4.2 Partially encased composite members ........................................................................... 42

4.3 Concrete filled steel members ....................................................................................... 52

4.4 Observations and discussions ........................................................................................ 56

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4.4.1 Moment-rotation hysteresis .................................................................................... 56

4.4.2 Ductility .................................................................................................................. 61

4.4.3 Dissipated energy ................................................................................................... 64

4.4.4 Fracture life ............................................................................................................ 67

4.4.5 Strain measurements ............................................................................................... 68


Chapter 5. Numerical Simulation ...................................................................................... 73

5.1 Introduction ................................................................................................................... 73

5.2 Development of FE models ........................................................................................... 74

5.2.1 General ................................................................................................................... 74

5.2.2 Element type and mesh size ................................................................................... 74

5.2.3 Constitutive material relationships ......................................................................... 75

5.2.4 Boundary conditions and displacement history ...................................................... 76

5.3 Validation ...................................................................................................................... 77

5.3.1 Load-displacement response .................................................................................. 77

5.3.2 Forces in PEC transverse links ............................................................................... 83


Chapter 6. Sensitivity Studies and Design Implications ................................................... 91

6.1 Introduction ................................................................................................................... 91

6.2 Stiffness considerations ................................................................................................. 91

6.3 Moment capacity ........................................................................................................... 93

6.4 Ductility considerations ................................................................................................. 98

6.5 Concluding remarks..................................................................................................... 103

Chapter 7. Conclusions and Suggestions for Future Work ............................................. 104

7.1 Conclusions ................................................................................................................. 104

7.2 Suggestions for future work ........................................................................................ 106

References ............................................................................................................................. 108

Appendix A Supplementary Experimental Results for PEC members ................................. 113

Appendix B Supplementary Experimental Results for CFT members .................................. 128

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Notation

Symbols

a length of buckle wave Ac effectively confined concrete area Acc overall confined area of cross-section b width of flange outstand c flange outstand (box width) C kinematic hardening modulus Ck initial kinematic hardening modulus D distance between links E modulus of elasticity Ecc modulus of elasticity for concrete Etotal total dissipated energy fc un-confined concrete compressive strength fcc concrete compressive strength F yield surface pressure k buckling coefficient My1 yield moment My2 ultimate moment Mmax,Rd Maximum design value of the resistance moment in the presence of a

compressive normal force n axial load ratio N number of back stress P axial load Pu nominal section capacity t thickness of flange or square box

8

Greek Symbols

α back stress δy estimated yield displacement δy1 yield displacement δy2 ultimate displacement εc un-confined concrete compressive strain εcc confined concrete compressive strain εcr critical buckling strain εy yield strain εpl equivalent plastic strain rateν Poisson’s ratio μ ductility ratio σ y yield stress σu ultimate stress γk kinematic hardening rate λp plate slenderness parameter

9

List of Figures Figure 1.1 Composite beams before pouring of concrete ........................................................ 13

Figure 1.2 Typical cross section of composite column ........................................................... 14

Figure 2.1 Concrete filled steel member with new confinement [23] .................................... 18

Figure 2.2 Concrete filled steel members with stiffeners [24] ................................................ 19

Figure 2.3 Effectively confined area in a PEC section. ........................................................... 24

Figure 2.4 Confined and unconfined concrete model [57]. ..................................................... 25

Figure 3.1 General view of the test-rig .................................................................................... 30

Figure 3.2 Details of the test-rig (mm) .................................................................................... 31

Figure 3.3 Details of load transfer section (mm) ..................................................................... 31

Figure 3.4 Layout of instrumentation for CFT specimens (mm)............................................. 33

Figure 3.5 Layout of instrumentation for PEC specimens (mm)............................................. 33

Figure 3.6 Specimens IC3, IC4 and IC5 .................................................................................. 34

Figure 3.7 Specimens IC2, IC6 and IC7 .................................................................................. 34

Figure 3.8 Protection of strain gauges on links ....................................................................... 34

Figure 3.9 Loading protocol considered in the cyclic tests [62].............................................. 35

Figure 3.10 Specimen detailing ............................................................................................... 37

Figure 3.11 Specimen with transverse bars - outside welded links (IC3) ............................... 37

Figure 3.12 Specimen with improved detailing – inside welding (IC4 and IC5) .................... 38

Figure 3.13 Coupon test .......................................................................................................... 38

Figure 3.14 Partially encased specimens prior to concrete casting ......................................... 40

Figure 3.15 Casting of the PEC members ............................................................................... 41

Figure 3.16 Casting of the CFT members ............................................................................... 41

Figure 4.1 Load-displacement response for IC1 ..................................................................... 43

Figure 4.2 View of IC1 after the test ....................................................................................... 44


Figure 4.4 Failure mode for IC2 .............................................................................................. 45


Figure 4.6 Fracture of flanges for IC3 ..................................................................................... 46


Figure 4.8 Fracture of flanges for IC4 ..................................................................................... 48


Figure 4.10 Fracture of flanges and concrete cracking in IC5 ................................................ 49

Figure 4.11 Load-displacement response for IC6 ................................................................... 50

Figure 4.12 Fracture of the transverse bars and flanges in IC6 ............................................... 50

Figure 4.13 Load-displacement response for IC7 ................................................................... 51

Figure 4.14 Fracture of the transverse bars and flanges in IC7 ............................................... 52

Figure 4.15 Load-displacement response for SY0 .................................................................. 53

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Figure 4.16 Fracture of steel tube for SY0 .............................................................................. 53


Figure 4.18 Fracture of steel tube for SY1 .............................................................................. 54


Figure 4.20 Fracture of flanges for SY2 .................................................................................. 55

Figure 4.21 Moment-rotation response of all specimens ........................................................ 61

Figure 4.22 Load-displacement envelope curves .................................................................... 64

Figure 4.23 Energy dissipation of composite members .......................................................... 67

Figure 4.24 Displacement versus strain for transverse links: IC2 ........................................... 70






Figure 5.1 Mesh sensitivity study for composite members ..................................................... 75

Figure 5.2 Concrete damage plasticity material model for unconfined concrete .................... 76

Figure 5.3 Concrete damage plasticity material model for confined concrete ........................ 76

Figure 5.4 Energy history of the numerical analysis of PEC member .................................... 77

Figure 5.5 Comparison of hysteretic curves for IC1 from FE simulation and experiment ..... 78





Figure 5.10 Comparison of hysteretic curves for IC6 from FE simulation and experiment ... 81

Figure 5.11 Comparison of hysteretic curves for IC7 from FE simulation and experiment ... 81

Figure 5.12 Comparison of hysteretic curves for SY0 from FE simulation and experiment .. 82



Figure 5.15 Axial loads in selected links for IC2 .................................................................... 84

Figure 5.16 Location of links for IC2 ...................................................................................... 84










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Figure 6.1 Experimental secant stiffness of PEC member (Cont’d) ....................................... 92

Figure 6.2 Moment-displacement response for PEC members with different link spacing .... 95

Figure 6.3 Moment-displacement response for PEC members with different axial load ........ 96

Figure 6.4 Moment-displacement response for CFT members ............................................... 98

Figure 6.5 Buckling coefficient versus aspect ratio [74] ......................................................... 99

Figure 6.6 Influence of flange slenderness on normalized critical strain for PEC members . 101

Figure 6.7 Influence of flange slenderness on normalized critical strain for CFT members 103

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List of Tables Table 3.1 Summary of experimental programme .................................................................... 36

Table 3.2 Summary of steel section properties........................................................................ 39

Table 3.3 Summary of link material properties ....................................................................... 39

Table 3.4 Concrete mix design ................................................................................................ 39

Table 3.5 Concrete strength ..................................................................................................... 39

Table 4.1 Summary of results .................................................................................................. 61

Table 4.2 Comparison of ductility levels (positive direction) ................................................. 64

Table 4.3 Comparison of ductility levels (negative direction) ................................................ 64

Table 4.4 Summary of member test results ............................................................................. 68

Table 6.1 Details of steel profiles of PEC members used in Figure 6.6 ................................ 100

Table 6.2 Details of steel profiles of CFT members used in Figure 6.7 ................................ 102

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Chapter 1. Introduction

1.1 Background

Composite members, like those presented in Figure 1.1, which are built using various

combinations of steel and concrete, can result in stiffer, stronger and higher ductility

structures compared to steel and reinforced concrete. Composite members include

composite beams, special beam-column connections and composite columns. In

general, composite columns are categorised into three types: 1) concrete filled 2)

partially encased and 3) fully encased composite members, as can be seen in Figure

1.2.

Only partially encased composite (PEC) members and concrete filled steel tube (CFT)

members are studied in this thesis. PEC members consist of H or I profile steel

sections and concrete encased between the flanges. Most of the previous research into

PEC or CFT members has focused on the behaviour of composite members

particularly in terms of local buckling behaviour. To fully utilize the advantages of

PEC members, additional research, particularly on ductility and energy dissipation is

required.

Figure 1.1 Composite beams before pouring of concrete

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(a) Fully encased composite members

(b) Partially encased composite members

(c) Concrete filled rectangular members

(d) Concrete filled circular members

Figure 1.2 Typical cross section of composite column

1.2 Objectives and scope

The main objectives of this research are:

(1) Study the ultimate load, ductility and failure mode of PEC and CFT members;

(2) Assess means of enhancing the ductility of PEC configuration, and provide

information necessary for their assessment and design;

(3) Propose suitable numerical models to simulate the behaviour of composite

members

In order to achieve the above objectives, a total of seven PEC columns and three CFT

members were constructed and tested under cyclic loading with axial loads in the

range of 0% to 20% of the nominal plastic load of the members. These studies were

complemented with finite element simulations, parametric analyses and design-

oriented discussions.

1.3 Outline of the thesis

The performance of PEC and CFT members under cyclic loading is investigated

herein. This chapter provides the background and purpose of the research.

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A literature review, which serves as a background for the topic is presented in Chapter

2. The review mainly covers research on the experimental study of PEC members and

CFT members. In addition, an overview of numerical models for concrete and steel

members is also presented in Chapter 2.

Chapter 3 outlines the experimental set-up and details of the PEC and CFT specimens.

A description of the instrumentation and general loading protocol is also included.

Chapter 4 presents and discusses the observations and results of the tests. A direct

assessment of the influence of several parameters including the levels of axial load,

the configuration of PEC and CFT members and the effect of improved detailing is

performed.

Chapter 5 describes the finite element models employed to simulate the behaviour of

PEC and CFT composite members. The purpose is to provide detailed insight into the

nonlinear inelastic behaviour of composite members through verification against

experimental results.

In Chapter 6, parametric studies are presented in order to investigate the behaviour of

composite members beyond the tested range. Based on the findings from the

experimental and analytical studies, several design implications are also discussed.

The final chapter summarises the findings from the current study and proposes

recommendations for future research.

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Chapter 2. Literature Review

2.1 Introduction

Composite members are constructed by various combinations of steel and concrete to

use the beneficial properties of both materials. To this end, Concrete Filled Tubes

(CFT) members have many advantages: the steel tube provides confinement and thus

increases the stiffness and strength and ductility of the whole member. Meanwhile,

the concrete reduces the possibility of local buckling of the tube. In addition, the steel

tube eliminates the use of formwork during its construction. On the other hand,

compared with CFT, the advantage of employing PEC member is that conventional

beam-to-column connections can be employed.

2.2 Concrete Filled Steel members

Observation of the structural performance after the Great Kanto earthquake in 1923 in

Japan revealed that structures incorporating composite sections sustained significantly

less damage than those utilizing only steel or concrete elements [1, 2]. This lead to a

number of investigations on the benefits of composite construction for seismic

resistance [3-10].

In Japan, researchers carried out extensive investigations on composite structures

beginning in the late 1980’s and early 1990’s [11-13]. Meanwhile, work in Europe

focused on the adoption of concrete-filled tubes as composite beams for long span

structures and bridge pier applications [14-16]. In America, the use of composite

construction dates back to the late nineteenth century with the majority of research on

composite members performed in the mid-twentieth century. In China, investigations

on composite members started from last century primarily in response to the

requirement for taller buildings in seismic areas [17-20]. The cyclic behaviour of

rectangular composite concrete-filled steel section members has been extensively

studied and significant experimental results are available [7, 21-25]. Several

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investigations have been carried out to study the parameters which influence the

capacity, stiffness or ductility of composite members. The parameters studied include

axial load levels, the width-to-thickness ratio and the material properties. Research

has also been performed on innovative details designed to enhance the ductility of

concrete filled steel members [7, 23, 24].

Varma et al. [26] investigated the behaviour of high strength square concrete filled

steel tube members subjected to constant axial load and cyclically varying flexural

loading. The steel was made from either normal or high strength material. A high

stress concrete (110Mpa) was selected. The key parameters studied included the

effects of the width-to-thickness ratio, the yield stress of the steel tube, and the level

of axial load. A total of eight cyclic specimens were tested. It was found that crushing

of concrete and local buckling in the steel tube significantly affected the cyclic

strength and stiffness of the CFT specimens. The flexural stiffness of section under

cyclic loading was dominated by the flexural energy dissipated in the plastic hinge

region. The authors concluded that the cyclic curvature ductility decreased with an

increase of the axial load level. At lower axial load levels, cyclic curvature ductility

decreased with an increase in the steel tube ratio or the steel strength. At higher axial

load levels, the change of steel tube ratio and steel strength did not have a notable

influence on the cyclic curvature ductility.

Inai et al. [27] investigated the behaviour of concrete-filled circular and square steel

tubular beam columns with different material strengths. The main test parameters

included steel strength (400, 590, and 780 MPa), diameter to thickness ratio of steel

tube, and concrete strength (40 and 90 MPa). The specimens were tested under

constant axial compression and cyclic horizontal load with incrementally increasing

lateral deformation. The test results showed that higher strength and thicker steel

tubes gave better overall behaviour of the member. However, higher strength concrete

had an adverse effect on the behaviour.

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Mao and Xiao [23] proposed confining elements for square CFT like those shown in

Figure 2.1 in order to improve the confinement of the concrete core and to delay or

inhibit local buckling. Additional transverse reinforcement was designed for the

potential plastic hinge zones as also shown in Figure 2.1. It was found that such

lateral confinement allows CFT columns to develop large ductility capacities suitable

for earthquake resistant design. It was also shown that the improved detail did not

alter significantly the stiffness or load carrying capacity of a CFT member. Therefore,

it was suggested that standards for the design of conventional CFTs should also be

used in the case of this new member detail.

Figure 2.1 Concrete filled steel member with new confinement [23]

Zhang et al. [24] explored alternative methods to improve the ductility of CFT

columns. Six square columns with longitudinal stiffeners on each of the inner faces of

the steel tube and three columns with two longitudinal stiffeners on opposite inner

faces were tested under constant axial load combined with cyclic lateral

displacements. The cross section of this new member is shown in Figure 2.2. It was

found that the four-stiffener columns had better ductility than the two-stiffener

columns. The parameters studied included the axial load level and steel tube section

types. The axial load level ranged from 30% to 60% of the nominal plastic sectional

19

load. The results indicated that the CFT columns under an axial load below 50% of

the nominal plastic sectional load exhibited better ductility and energy dissipation

capacity. However, the displacement ductility decreased significantly with an increase

in the axial load level above this range.

Figure 2.2 Concrete filled steel members with stiffeners [24]

Liu et al. [25] performed a comprehensive parametric study on the behaviour of

square CFT beam-columns subjected to biaxial moment. Nine tests on beam-column

members were studied under combined constant axial load and cyclic lateral load. The

parameters studied included the effects of axial load ratio, width-to-thickness ratio,

concrete compressive strength and slenderness ratio. The axial load ratio studied

ranged from 35% to 58% of the nominal plastic sectional load while the width-to-

thickness ratios examined were in the range of 31.1 to 56.6. Tests including high

strength concrete and normal strength concrete were reported. As expected, the

experimental results indicated that the ductility and energy dissipation ability of

biaxial loaded square CFT columns decreased with increasing the axial load ratio.

Also, their ductility and energy dissipation ability of CFT members decreased as the

concrete compressive strength increased. It was illustrated that specimens with normal

strength concrete can have better performance than those with high strength concrete

in terms of seismic design.

The above discussion has presented results from various studies on CFT members.

The influence of parameters such as applied axial load, slenderness ratio, types of

material and level of axial loads on the ductility and strength have been studied.

20

2.3 Partially Encased Composite members

Partially encased composite members, consisting of a thin-walled rolled or welded I

or H-shaped steel section with concrete in the areas between the flanges, have

received significant attention recently. Some of the first studies on examining the

inelastic seismic behaviour of partially encased members were undertaken at Imperial

College London [4, 28, 29].

Elnashai and Broderick [4] studied the behaviour of partially encased composite

members via cyclic and pseudo-dynamic tests. These tests included seven beam-

column members of the same configuration, transverse links along their height. 6 mm

diameter steel rods were welded between opposing flanges on both sides of the

column before casting the columns. In order to utilize the benefits of links efficiently,

the links were distributed more densely within the expected plastic hinge zone, at 40

mm spacing, whereas 80 mm spacing was used elsewhere over the member length. It

was concluded that the links were effective in delaying or inhibiting flange local

buckling. The member performance subjected to these loading conditions was

compared to previous tests by Elnashai et al. [30] in which the columns had four 10

mm diameter longitudinal reinforcing bars tied with 6 mm diameter stirrups in

addition to the transverse links. It was concluded that the capacity of the PEC

members with the additional reinforcing bars was slightly higher than the PEC

members with the transverse links only.

Tremblay et al. [31] performed axial load tests on six PEC stub columns. Each

column had a larger square cross-section (either 300 mm × 300 mm or 450 mm × 450

mm) and a length that was five times the cross-section dimension. The main

parameters examined in this group of test were the spacing of the links (varied from

half of the cross-section depth to the full cross-section depth), and the flange b/t ratio

(in the range of 23.2 to 35.4). It should be noted that b/t ratios of PEC tested by

21

Tremblay [31] were much higher than that of PEC columns fabricated from standard

shapes, which makes the sections more susceptible to local buckling.

Chicoine et al. [32] performed axial load tests on five 600 mm × 600 mm × 3000 mm

PEC columns. In this group of tests, the columns had 16 mm diameter links, spaced at

either 300 mm or 600 mm. The effects of additional reinforcement consisting of

reinforcing bars and stirrups were also studied. The observed failure mechanism was

consistent with previous tests. Local buckling happened at round 75% of the peak

load in specimens when the link spacing was equal to the column depth. For the

columns with link spacing equal to 0.5b, in which d was equal to the width of

outstanding flange, the flanges did not buckle until the peak load and the PEC

member performed a more ductile behaviour. It was suggested that the PEC columns

should be designed with a link spacing of 0.5b. The authors concluded that increased

confinement of the concrete was provided by the closer spaced bars. They also

pointed out that the increase in link stresses was nearly proportional to the decrease in

link spacing.

More recently, Treadway [33] carried out experiments to compare the effect of

concrete confinement and local buckling among three different sections, including

HEA140, HEA200 and HEA240. Transverse links were also employed within the

potential plastic region to delay or inhibit local buckling. It was demonstrated that the

onset of local buckling resulted in a reduction in moment capacity. This phenomenon

was more pronounced in the case of presence of axial loading because of the sudden

release of confinement. The links were effective in delaying local buckling; however,

the poor welding quality affected their performance. It was found from the

experiments that the failure of the links occurred at the interface between the links and

the flanges.

The above discussion highlights the development of PEC members. The influence of

parameters such as slenderness ratio, the type of loading and the details of links on

section behaviour was reported. Also, it has also been illustrated that the types of links

22

used in previous studies failed at an early stage so it is necessary that new types of

links be tested in order to effectively improve the ductility of the PEC members.

2.4 Modelling of composite members

ABAQUS [34] has been widely used to study the complex behaviour of composite

members [35-40]. Han et al [37, 41] developed models in ABAQUS/Standard to

study the behaviour of CFT members subjected to shear and constant axial

compression. An elastic-plastic model was used to describe the constitutive behaviour

of the steel, while the damage plasticity model was selected for the concrete. Contact

interactions were found to be an important aspect for the finite element modelling of

composite steel-concrete beam models. Surface-based interaction was used with a

constant pressure model in the normal direction, and Coulomb friction in the

tangential direction between the inner surface of steel tube and the concrete.

Begum et al. [42] also adopted the damage plasticity model to simulate the concrete

behaviour and applied ABAQUS/Dynamic strategy to enhance the calculation time.

ABAQUS/Dynamic is a finite element analysis product that simulates brief transient

dynamic events, such as ballistic impact or quasi-static problems. The

ABAQUS/Dynamic solution method was originally developed for dynamic problems,

in which the inertia plays a prominent role. Therefore, the dynamic explicit method

was able to predict results beyond the peak load. The stub column test results [31, 32]

were compared to numerical models. The numerical simulations were found to be in

good agreement even within the post-peak stages and the failure mechanism observed

during the tests was well represented. As an extension of the previous research,

Begum et al. [43] used FE models to predict the effect of different link spacing on the

performance of PEC columns. In addition, the model was capable to determine the

individual contributions of the concrete and steel to the total member capacity.

Ellobody and Young [44] developed nonlinear 3-D finite element model to investigate

the inelastic behaviour of pin-ended axially loaded concrete encased steel composite

23

columns. The model considers the material properties of the steel and concrete,

interfaces between the steel and concrete and the effect of concrete confinement. The

same authors [45] also employed the division of the cross-section of concrete into

three different zones based on the research by Sheikh et al. [46] and Mander et al. [47].

These models were developed using ABAQUS and validated against published

experimental results.

2.4.1 Concrete damage plasticity model

The nonlinearity of concrete under compression could be simulated by approaches

based on the concept of either damage or plasticity, or a combination of both of them.

Plasticity is generally characterised as the unrecoverable deformation after load

removal. Damage is defined by a reduction of elastic constants. Furthermore,

unloading stiffness degradation and cumulated deformation have been observed in

concrete compression tests. This suggests that plasticity models should be combined

with damage models to correctly represent the nonlinear behaviour of concrete. It was

noted that concrete damage plasticity model could simulate the composite members

well for low confinement levels [48].

In composite members, like PEC or CFT, the triaxial confinement effects provided by

the steel member can considerably enhance the concrete response. The effects of

confinement could be represented within a uniaxial stress-strain curve by means of an

increase in the compressive strength as well as the corresponding level of strain. A

significant number of investigations have been conducted in order to investigate the

confinement effect in composite members [49-54]. Hu et al. [54] proposed the

material constitutive models for CFT columns and verified the material models in

ABAQUS against experimental results. Hu et al. [54] pointed out that the tube would

provide a large confining effect to the concrete especially when the width-to-thickness

ratio b/t is less than 30 for square CFT columns.

24

Mirza [55] studied the effect of confinement on the variability of the ultimate strength

of composite members. Idealised stress-strain curves for concrete were proposed

based on assumed zones of concrete confinement for the cross-section, as illustrated

in Figure 2.3. The concrete part of the section is divided into two parts: 1) unconfined

concrete and 2) partially confined concrete. In general, for PEC sections, as the most

effectively confined zones are those close to the web and flanges shown in Figure 2.3,

a parabolic surface can be assumed to define the boundary between the effectively-

confined and the unconfined concrete [29].

Figure 2.3 Effectively confined area in a PEC section.

Schneider [56] performed a calibration of analytical models for CFT members. A

typical representation of the stress-strain relationship of unconfined concrete and

confined concrete is shown in Figure 2.4 [57]. Based on this study, the three-

dimensional concrete material model available in ABAQUS material library was

developed to simulate concrete with uniaxial strain.

25

Figure 2.4 Confined and unconfined concrete model [57].

The uniaxial compressive strength and the corresponding strain for the unconfined

concrete are fc and εc, respectively. It can be observed from Figure 2.4 that when

concrete is subjected to laterally confining pressure, the uniaxial compressive strength

fcc and the corresponding strain εcc are much higher than those of unconfined concrete.

It can also be appreciated from Figure 2.4 that the stress-strain curve of confined

concrete is composed of three main parts. The first part defines a linear relationship of

the confined concrete. The proportional limit stress could be estimated as 0.5fcc while

the initial Young’s modulus of the confined concrete could be defined as

MPafEcc cc4700 [58].

The second partition of the stress-strain curve describes the nonlinear portion before

the concrete reaches its maximum strength, beginning from 0.5fcc and reaching up to

fcc. This relationship can be estimated by the expression proposed by Saenz [59] as:

32 )())(12())(2(1cccccc

E

cc

RRRR

Ef

(2-1)

Where RE, R, Rσ and Rε are defined as:

cc

ccccE f

ER

(2-2)

RR

RRR E 1

)1(

)1(2

(2-3)

26

4 RR (2-4)

The third part of the curve depicted in Figure 2.4 starts from the maximum confined

concrete stress fcc and ends at fu=rk3fcc. When the stress decreases at fu, the

corresponding strain εu is equal to 11εc. r (a parameter which relates to the concrete

strength) could be taken as 1.0 and 0.5 for concrete cube strength of 30 MPa and 100

MPa, respectively [66]. Linear interpolation was suggested for concrete cube

strengths between 30 MPa and 100 MPa [54]. In general, the parameters fl and k3

depend on the width-thickness ratio, cross section and steel stiffness.

2.4.2 Steel models subjected to cyclic loading

Kinematic and isotropic hardening models are typically adopted to simulate the

inelastic behaviour of materials that are subjected to cyclic loading. In the following,

the main characteristics of these models are summarized.

Yield Surfaces

The kinematic hardening models applied to represent the performance of steel

subjected to cyclic loading are pressure-independent plasticity models. Such pressure-

independent yield surface is defined by the following function:

0)( 0 fF (2-5)

Where σ0 is the yield stress, f(σ-α) is the equivalent Von Mises stress or Hill’s

potential with respect to the back stress α, and F is yield surface pressure.

Hardening

The linear kinematic hardening model has a constant hardening modulus, and the

nonlinear isotropic/kinematic hardening model has both nonlinear kinematic and

nonlinear isotropic hardening components. The evolution law of the linear kinematic

hardening model consists of a hardening component that describes the translation of

27

the yield surface in stress space through the back stress, . When temperature

dependence is omitted, this evolution law conveys to the linear Ziegler hardening law

[60] as:

plC

)(1

0 (2-6)

Where pl is the equivalent plastic strain rate and C is the kinematic hardening

modulus. In this model the equivalent stress defining the size of the yield surface ( 0 )

remains constant, 0

0 , where 0

is the equivalent stress defining the size of the

yield surface at zero plastic strain.

The evolution law for the nonlinear isotropic/kinematic hardening model consists of a

nonlinear kinematic hardening component and an isotropic hardening component. The

former hardening component model describes the translation of the yield surface in

stress space through the back-stress. The latter describes the change of the equivalent

stress defining the size of the yield surface as a function of plastic deformation. The

kinematic hardening component is defined as a combination of a purely kinematic

term and a relaxation term, which introduces the nonlinearity. And the overall back-

stress is computed from the following relation:

N

kk

1

(2-7)

where N is the number of back-stress, and Ck and γk are material parameters that must

be calibrated from cyclic test data. Ck is the initial kinematic hardening modulus, and

γk is a parameter that determines the rate at which the modulus decreases with

increasing plastic deformation.

The isotropic hardening behaviour of the model defines the evolution of the yield

surface size, 0 , as a function of the equivalent plastic strain, pl :

28

)1(00 plbeQ

(2-8)

where Q|∞ and b are material constants and σ|0 is the yield stress at zero equivalent

plastic strain.

2.5 Concluding remarks

Previous research on the behaviour of composite members presented the favourable

performance of this type of member in comparison with bare steel or reinforced

concrete. The majority of available research studies have focused on assessing the

strength of PEC or CFT members under different loading conditions, with particular

attention to the response under combined lateral cyclic loading in combination with

gravity action.

Considering the practical and constructional advantages offered by PEC and CFT

members, their use has been increasing significantly. However, existing studies did

not cover PEC members with different transverse links, which are especially

important to enhance the performance of PEC members. Inelastic behaviour of CFT

and PEC members under extreme loading conditions has been reviewed in this

chapter.

29

Chapter 3. Experimental Methodology

3.1 Introduction

This chapter describes the arrangement used for testing composite members under

combined axial and cyclic lateral loads. The experimental set-up, specimen details,

material properties and loading procedures are described herein. In total, ten

specimens were tested, including CFT as well as PEC details with different section

configurations and varying levels of axial load.

3.2 Testing arrangement

Figure 3.1 presents a general view of the testing arrangement. The experimental set-

up was designed to apply lateral displacements on the tip of a vertical cantilever

member while at the same time imposing constant axial loads at the top of the

specimen. Accordingly, a self-reacting rig was used in order to achieve the proposed

idealised loading conditions as shown in Figure 3.2. The specimens were welded to a

350mm×350mm×30mm thick plate, which in turn was bolted to a

500mm×500mm×50mm thick plate attached to the self-reacting. Detailed numerical

simulation of the set-up using ABAQUS confirmed the rigidity of the bottom plates

hence providing fixed boundary conditions. A base plate of

1200mm×1200mm×50mm was stressed to the frame using 4 bolts of 35 mm diameter.

Figure 3.3 shows the details of the load transfer system used at the top of the

specimens in order to accommodate large lateral displacements as well as different

levels of axial load. A hydraulic actuator operating in displacement control was used

to apply lateral displacements at the top of the cantilever member. The horizontal

actuator had a static capacity of ± 250 kN and a maximum stroke of ± 125 mm. The

back of the horizontal actuator was firmly connected to the reaction frame by means

of 500mm×500mm×75mm plates and hinges. The maximum capacity of the hinges

connected to the horizontal actuator was 300 kN.

30

Axial loads were applied through a 500 kN vertical actuator and were kept constant

throughout the test. The maximum capacity of the hinges connecting the vertical

actuator was 500 kN. Careful consideration was given to the out-of plane deformation

of the rig assemblage and its verticality was constantly monitored during the tests by

means of laser indicators, LVDT transducers and inclinometers attached to the faces

of the specimen.

Figure 3.1 General view of the test-rig

Left SideRight Side

Displacement Direction

31

Lateral Actuator

Axial Actuator

Test Specimen

Figure 3.2 Details of the test-rig (mm)

Hinge 1

Hinge 2

Load cell

(a) Axial actuator detail

Hinge 2Hinge 1 Load cell Lateral Actuator

(b) Lateral actuator detail

Figure 3.3 Details of load transfer section (mm)

32

The design of all test rig partitions containing pins, hinges, plates, actuators and welds

was carried out in accordance with Eurocode 3 [61] provisions and considered the

safety factors used for the laboratory testing at Imperial College London. High

strength steel (Grade S460) was used for hinges as well as bottom plates of the

specimens in order to accommodate the large forces involved. Full penetration groove

welds of 18 mm were utilized throughout.

3.3 Instrumentation and measurements

Lateral displacements and the corresponding forces were recorded by the

displacement transducer and local cell incorporated within the horizontal actuator.

Similarly, the load cell mounted on the vertical actuator measured the axial loads

imposed onto the specimen. The variation of the vertical force at large lateral

displacements was around 10%.

The verticality of the specimen, against deformations in the non-loading direction was

continuously monitored through inclinometers attached to it, while another

inclinometer was placed at the face of the specimen to confirm the in-plane (loading

direction) deformations. Four linear variable displacement transducers (LVDT) were

employed to measure the deformation of the bottom plate of the specimen. Three

draw wire transducers (DWT) were located at the top, middle and bottom of the

specimen to measure the horizontal displacements.

Strain gauges were used to monitor the strains at selected locations in the face of the

CFT columns (Figure 3.4) and PEC columns (Figure 3.5). Additional strain gauges

were used in the case of PEC specimens with transverse links. These strain gauges

were placed at the middle of the link in the bottom pair. Polymer coating was used to

prevent moisture contamination and limit the possible slip in those cases as shown in

Figure 3.8.

33

SG18 SG17

SG20 SG19

SG22 SG21

SG24 SG23

SG26 SG25

SG28 SG27

Top box

Bottom box

Figure 3.4 Layout of instrumentation for CFT specimens (mm)

Top flange

SG17SG18SG20SG19SG21

SG23SG24 SG22

SG30SG31SG32

SG27SG29SG26SG28 SG25

Bottom flange

Figure 3.5 Layout of instrumentation for PEC specimens (mm)

34

TopBottom

40@12

Figure 3.6 Specimens IC3, IC4 and IC5

TopBottom

60@8

Figure 3.7 Specimens IC2, IC6 and IC7

Figure 3.8 Protection of strain gauges on links

3.4 Load application

The axial loading was applied first and kept constant throughout the test. For

specimens tested under pure bending conditions (i.e. no-axial load) a nominal near

zero load of 9 kN was applied at the top in order to prevent actuator instabilities.

A set of cyclic lateral displacements was imposed on the tip of the cantilever

specimen. The cyclic protocol shown in Figure 3.9 was used based on the

recommendations provided by ECCS [62], where δ is the applied displacement and δy

35

is the estimated yield displacement. After completing the first test, it was found that

the δy applied in the experiment was underestimated. In order to keep all the

experiments the same, the estimated δy was kept constant for all other tests.

The loading rate was kept at about 0.1 mm per second up to the 15th cycle, after which

it was increased to 0.4 mm per second. After the maximum displacement was reached,

all the specimens were subjected to additional displacement reversals at amplitudes of

120 mm up to the point when fatigue fracture occurred in one of the steel faces. For

specimen IC5, due to experimental constrains, additional displacement cycles at ±9δy

were used instead until fracture occurred.

0 5 10 15 20 25-16

-12

-8

-4

0

4

8

12

16

y

Cyclics

Figure 3.9 Loading protocol considered in the cyclic tests [62]

3.5 Description of specimens

3.5.1 Specimen details

In total, ten composite members were tested, including three CFT members and seven

PEC members. All the specimens were 1440 mm long and fixed at the base. After

adding the thickness of the top and end plates, the physical length of the specimens

was 1500 mm. Class 1 sections, according to Eurocode 8 [63], was used in all cases.

Table 3.1 gives a summary of the experimental series. The axial load (P) applied in

each test is also listed in Table 3.1 as a function of the nominal section capacity (Pu).

36

All three CFT members employed hot rolled SHS 180×6.3 (Square Hollow Section)

are referred to as SY0, SY1 and SY2 in Table 3.1. In the case of PEC members, UC

152×23 (Universal Columns) were used. Members were provided with conventional

detailing in accordance with European practice. Stirrups with diameter of 8 mm and

40 mm spacing were employed in all specimens in the bottom 480 mm. The stirrup

separation was increased to 80 mm for the rest of the member length. In order to study

the effects of steel links in preventing the occurrence of flange local buckling, details

of transverse link were tested as depicted in Figure 3.10 (c) and (d). Longitudinal 8

mm bars were placed in Specimens IC2 and IC3 as shown in Figure 3.10 (c). On the

other hand, Specimens IC4, IC5, IC6 and IC7 employed I shaped steel plates (8 mm

by 6 mm) welded to the inside of the beam. Two different types of link spacing were

studied, 40 mm in Specimens IC4 and IC5, and 60 mm for Specimens IC6 and IC7.

Table 3.1 Summary of experimental programme

Specimen Section details Axial load

ratio Axial load

Additional welded links

Detail

P/Pu (kN)

SY0 SHS 180×6.3 0 0 -

Figure 3.10 (a) SY1 SHS 180×6.3 10% 220 -

SY2 SHS 180×6.3 20% 440 -

IC1 UC 152×23 10% 125 - Figure 3.10 (b)

IC2 UC 152×23 10% 125 8@60 Figure 3.10 (c)

IC3 UC 152×23 10% 125 12@40

IC4 UC 152×23 10% 125 12@40

Figure 3.10 (d) IC5 UC 152×23 20% 250 12@40

IC6 UC 152×23 10% 125 8@60

IC7 UC 152×23 20% 250 8@60

37

(a) Detail of square CFT member (SY0,

SY1 and SY2)

(b) Detail of conventional PEC member

(IC1)

(c) Detail of PEC member with transverse

bars (IC2 and IC3)

(d) Detail of improved PEC member

(IC4, IC5, IC6 and IC7)

Figure 3.10 Specimen detailing

Figure 3.11 Specimen with transverse bars - outside welded links (IC3)

38

(a) (b)

Figure 3.12 Specimen with improved detailing – inside welding (IC4 and IC5)

3.5.2 Material properties

Steel of nominal Grade S355 was adopted for all specimens. At least three coupon

tests were conducted on all the steel sections used and the average results are

summarized in Table 3.2, where σy refers to the yield stress and σu refers to the

ultimate stress. Similarly, Table 3.3 gives the material properties of the reinforcement

bars used in Specimens IC2, IC3, IC4, IC5, IC6 and IC7.

The concrete mixes employed are reported in Table 3.4. Specimens SY0, SY1, SY2,

IC1, IC2 and IC3 were cast from Mix A while specimens IC4, IC5, IC6 and IC7 were

cast from Mix B. The aggregate size of both mix designs was 9 mm, and the

corresponding mean strengths of test results are summarised in Table 3.5.

Figure 3.13 Coupon test

39

Table 3.2 Summary of steel section properties

Specimen Flange Web SHS 180 Concrete

σy

(MPa)

σu

(MPa)

σy

(MPa)

σu

(MPa)

σy

(MPa)

σu

(MPa)

fc

(MPa)

SY0

-

-

-

-

434

532

48.5

SY1 43.6

SY2 45.4

IC1

458

575

447.5

575.7

-

-

43.6

IC2 42.6

IC3 50.3

IC4

401

558.4

411

555.6

-

-

41.2

IC5 40.3

IC6 45.6

IC7 42

Table 3.3 Summary of link material properties

Specimen σy σu

MPa MPa

Bar 335 463.5

I-section link 500 667.9

Table 3.4 Concrete mix design

Constituent Mix A Mix B

Cement 1 1

Aggregate 2.75 2.39

Sand 1.56 2.05

Plasticizer 0.004 0.005

Table 3.5 Concrete strength

Specimen SY0 SY1 SY2 IC1 IC2 IC3 IC4 IC5 IC6 IC7

fc (MPa) 48.5 43.6 45.4 43.6 42.6 50.3 41.2 40.3 45.6 42

40

3.5.3 Preparation of the specimens

As noted previously, the use of PEC members eliminates the need for formwork.

Accordingly, the sides of the PEC specimens were cast horizontally one day apart.

The difference in compressive strength was minimal on the day of testing which took

place at least after 20 days when the concrete had achieved at least 95% of the design

strength in all cases. Additional cubes were tested after 7 days to control the curing

process. The cast specimens were placed on a vibration table for concrete compaction

as shown in Figure 3.14.

The CFT members were cast vertically and required a minimal amount of form work

on the open end. The concrete was poured into the specimen from a 20 mm diameter

hole in the top plates of the square members as shown in Figure 3.16. The main

results and observations of the 10 specimens described above are presented in Chapter

4.

Figure 3.14 Partially encased specimens prior to concrete casting

41

Figure 3.15 Casting of the PEC members

Figure 3.16 Casting of the CFT members

42

Chapter 4. Experimental Results

4.1 Introduction

In this chapter, the experimental results of seven partially encased composite

members and three concrete filled steel members are presented. As explained in the

previous chapter, special attention was placed to the effects of varying axial loads and

improve section details with additional links. The tests were conducted under

gradually-increasing displacement cycles in order to examine the advantages offered

by the use of new PEC configurations in the ductility and fatigue life performance.

The following sections present the results and observations of PEC specimens

together with a description of the experimental results for the CFT members.

Supplementary results including transducer strain gauge readings and flange/box

strain gauge readings are presented in this chapter and Appendices, respectively.

4.2 Partially encased composite members

Apart from the conventional PEC detail, additional tests were performed in order to

study the improvement on their cyclic performance provided by transverse links

between the steel flanges. To this end, steel bars acting as transverse links were

provided in two PEC specimens through holes placed in the flanges and welded on the

outside (Figure 3.11). Nevertheless, it was found that fracture initiated around the

welding in the hole area due to stress concentration around the heat weakened zone.

Therefore, an improved link detail was designed via the provision of steel plates as

shown in Figure 3.12. In total, seven tests were carried out on PEC specimens under

cyclic lateral displacements at the top of the cantilever member. Five specimens were

tested with an axial load of 125 kN representing about 10% of the nominal plastic

section capacity of the composite cross-section. Another two specimens were tested

with an axial load of 250 kN which corresponding to approximately 20% of the

nominal plastic sectional capacity as described in Chapter 3. In the following parts,

43

detailed description of the test results is presented and discussed, with emphasis on

design parameters and ductility considerations.

IC1

Specimen IC1 was tested under a constant axial load of 125 kN (10% of nominal

plastic sectional capacity). Figure 4.1 depicts the corresponding hysteretic curve while

Figure 4.2 presents a view of Specimen IC1 after the test. As shown in Figure 4.1, the

member started yielding at a load of about 57.6 kN. Small cracking of concrete was

observed in the tensile side starting from the eighth increment of loading

corresponding to a displacement of around 48 mm. Local buckling was noticed at the

first 96 mm excursion, and the concrete confinement was released gradually from that

point onwards. This led to a gradual and continual decrease in capacity in subsequent

cycles. At the 23rd and 25th cycles (of 10δy amplitude), large buckling deformations

appeared on both sides of the specimen as shown in Figure 4.2. The half wavelength

of the flange buckles was approximately 140 mm. Figure 4.2 also shows the extent of

local buckling as well as the spalling of the concrete.

-200 -150 -100 -50 0 50 100 150 200-100

-80

-60

-40

-20

0

20

40

60

80

100

Lo

ad

(kN

)

Displacement (mm)

left side local buckling

Figure 4.1 Load-displacement response for IC1

44

Figure 4.2 View of IC1 after the test

IC2

Apart from the conventional reinforcement detailing used in standard PEC members,

Specimen IC2 was provided with additional 8 mm transverse bars welded to the

flanges within the expected plastic zone at the bottom of the cantilever specimen. For

IC2, the spacing of the welded links was about 60 mm in the vertical direction and a

total of eight link pairs were used. The member was subjected to a constant axial load

which was also equal to 125 kN. Figure 4.3 presents the hysteretic response of

Specimen IC2 whereas its failure mode is depicted in Figure 4.4. It can be appreciated

from Figure 4.3 that the load displacement relationship started deviating from

linearity at about 30 mm with 59 kN of lateral load. The first cracking of steel was

observed at a displacement of approximately 96 mm. The second cracking of steel

happened in the opposite face at a displacement of around 120 mm. At the second

cycle of 120 mm, the two cracking of steel around the holes linked together and

induced a whole fracture of one flange as shown in Figure 4.4 (b). In subsequent

cycles, progressive concrete deterioration took place causing considerable loss in

load-carrying capacity. The large drop in load was a consequence of both cracking of

concrete and fracture of the flange as depicted in Figure 4.4. The

45

-200 -150 -100 -50 0 50 100 150 200-100

-80

-60

-40

-20

0

20

40

60

80

100

Lo

ad

(kN

)

Displacement (mm)

cracking of steel

cracking of steel


(a) (b)

Figure 4.4 Failure mode for IC2

IC3

The section detail of Specimen IC3 was identical to the previous model IC2 except

that the spacing of the transverse welded bars was reduced to 40 mm. Therefore, the

number of transverse links increased to twelve. Specimen IC3 was tested with a

constant axial load of 125 kN. The experimentally observed hysteresis loops are

presented in Figure 4.5. The load-displacement response for this specimen was similar

to Specimen IC2 with initial yielding occurring at a load of about 48 kN and a

displacement of around 24 mm. The crack pattern observed in the flanges of IC3 was

also similar to IC2. Importantly, no signs of local buckling were observed during the

46

whole test. Fracture initiated in the right side flange between two welded bars at the

first cycle with a displacement of 80 mm. The failure of IC3 was also due to the

fracture at the right face of flange. Premature fracture of the flanges prevented

significant enhancement in ductility. Reduction in capacity occurred after local

buckling in IC1, unlike IC2 and IC3 which failed by welding rather than local

buckling.

-200 -150 -100 -50 0 50 100 150 200-100

-80

-60

-40

-20

0

20

40

60

80

100

Loa

d (k

N)

Displacement (mm)

cracking of concrete

cracking of steel


Figure 4.6 Fracture of flanges for IC3

47

IC4

The difficulties associated with welding the buckling-prevention transverse links that

lead to the initiation of fracture near the hole area described previously, motivated the

design of an improved transverse link alternative used in Specimens IC4, IC5, IC6

and IC7. In particular, as described in the previous chapter, Specimen IC4 was

provided with novel transverse plate links (Figure 3-12 (b)) spaced at 40 mm. The test

on Specimen IC4 was carried out under a constant axial load of 125 kN. Figure 4.7

presents the observed load-displacement hysteresis while a view of the specimen at

the end of the test is presented in Figure 4.8. As shown in Figure 4.7, the maximum

lateral load was around 63 kN at a lateral displacement of 75 mm. Concrete crushing

occurred at a displacement of almost 100 mm. Because of the close distribution of

transverse links, no local buckling was observed throughout the test. However, at a

displacement of 120 mm, fracture occurred at the bottom of the flange above the weld

between the specimen and the 30 mm thick bottom plate. This fracture corresponded

to a clear reduction in the load in the load-displacement curve.

-200 -150 -100 -50 0 50 100 150 200-100

-80

-60

-40

-20

0

20

40

60

80

100

Lo

ad

(kN

)

Displacement (mm)

crushing of concrete


48

Figure 4.8 Fracture of flanges for IC4

IC5

Specimen IC5 had the same characteristics as IC4, but with an increase in axial load

to 250 kN corresponding to about 20% of the nominal plastic cross-section capacity.

It is obvious from Figure 4.9 that the P-Δ effect induced notable negative post-elastic

stiffness. The cracking of concrete happened at a displacement of around 72 mm

while the onset of local buckling took place at a displacement slightly above 80 mm.

Fracture was observed at the right side of the steel flange during the first cycle of 120

mm. This test demonstrates that closely spaced transverse links coupled with an

improved welding detail could delay the occurrence of local buckling effectively. The

failure of the composite member was induced by fracture of the flange during the 17th

cycle at around 90 mm. This fracture occurred near the welding area and it can be

attributed to the stress concentration and material hardening near the weld-affected

zone. Nevertheless, no fracture was found in the links themselves or at the welds area

between the links and flanges.

49

-200 -150 -100 -50 0 50 100 150 200-100

-75

-50

-25

0

25

50

75

100

Loa

d (k

N)

Displacement (mm)

cracking of concrete cracking

of steel


Figure 4.10 Fracture of flanges and concrete cracking in IC5

IC6

Specimen IC6 was almost identical to IC4 and IC5, but the buckling-prevention

transverse links were spaced at a distance of 60 mm. Figure 4.11 presents the

hysteretic response of Specimen IC6 in terms of its load-displacement curves and

Figure 4.12 depicts its observed failure mode. As indicated in Figure 4.11, initial

yielding occurred at a load around 40 kN (corresponding to 25 mm). Concrete

cracking started to occur at a displacement of around 72 mm whereas local buckling

took place at the second cycle of displacement of 120 mm. Two links were broken at

50

the seventh cycle of 120 mm. The improved link detailed facilitated the welding

process and thus no weld fracture took place, instead fracture happened within the

link itself. At the ninth cycle of 120 mm, the steel flange fractured on right and left

faces. The effectiveness of the improved welded links on delaying local buckling can

be clearly established by comparing Figure 4.11 with the load-displacement response

of IC2 in Figure 4.3, which was made of similar material and had the same axial load.

It is obvious that the ductility of IC6 was significantly enhanced reaching the 25th

cycle while IC4 failed at the 17th cycle.

-200 -150 -100 -50 0 50 100 150 200-100

-75

-50

-25

0

25

50

75

100

Load

(kN

)

Displacement (mm)


link breaks

local buckling


Figure 4.12 Fracture of the transverse bars and flanges in IC6

51

IC7

Specimen IC7 was fabricated with transverse links spaced 60 mm apart and was

tested with a constant axial load equal to 250 kN (equivalent to 20% of nominal

plastic cross-section capacity). The load-displacement hysteresis for this specimen is

presented in Figure 4.13. Concrete cracking initiated at a displacement of 72 mm,

which was almost the same as previous specimens. The onset of local buckling

occurred at the peak of the second cycle of 120 mm. The load-displacement response

was similar to IC5. The failure of IC7 was due to the fracture of the right side flange.

The ductility of IC7 was higher than that of IC5. This was because the intensive

transverse links in IC5 induced earlier fracture of the flange.

-200 -150 -100 -50 0 50 100 150 200-100

-75

-50

-25

0

25

50

75

100

local buckling

Load

(kN

)

Displacement (mm)



52

Figure 4.14 Fracture of the transverse bars and flanges in IC7

Because of the vulnerable welding between the flange and the links of IC2 and IC3,

the failure of these two specimens occurred earlier than expected. In order to improve

the behaviour of PEC members, a new type of link was used in IC4, IC5, IC6 and IC7.

This new type of link effectively delayed local buckling of the flanges of PEC

members.

4.3 Concrete filled steel members

The concrete filled steel specimens consisted of SHS 180×180×6.3. Three tests were

conducted with an axial load of 0, 220 and 440 kN corresponding to 0, 10% and 20%

of the squash load for the composite section, respectively. In general, once local

buckling occurred, high stresses and strains developed in the corner areas. After a few

cycles of successive inelastic buckling and tensile yielding, cracks initiated in the

steel tube at one of the bottom corners in all specimens. The experimental results and

main observations from each test are given below.

SY0

Specimen SY0 was tested under gradually increasing cyclic displacement at the top of

specimen but without axial loads. The force-displacement curves are presented in

Figure 4.15. Local buckling of the tube occurred, at a displacement of about 72 mm.

The reductions of the load capacity may be attributed to the local buckling of steel

accompanied by some deterioration of the concrete in compression. The half wave

length of the square section was about 140 mm, as shown in Figure 4.16. The first and

53

second fracture happened at amplitudes of ±6δy and ±8δy, respectively. The

unloading branches were largely parallel to each other regardless of the level of

displacement.

-200 -150 -100 -50 0 50 100 150 200-150

-100

-50

0

50

100

150

Lo

ad (

kN)

Displacement (mm)

local buckling

Figure 4.15 Load-displacement response for SY0

Figure 4.16 Fracture of steel tube for SY0

SY1

For test SY1, a constant axial load of 220 kN representing about 10% of the cross-

section squash capacity was used. The load versus displacement relationship of

54

specimen SY1 is given in Figure 4.17. In this test, a peak load of 65 kN was reached

at a displacement of 30 mm. The onset of local buckling occurred at a displacement

approaching 48 mm. With an increase in the level of deformation, the load reduced

gradually with increasing displacement due to the second-order effect induced by the

axial load. The half-length of the tube buckles was approximately 100 mm. Fracture

firstly happened at the front left corner at the 25th cycle. After that, the load reduced

quickly. Figure 4.18 shows the fracture of steel tube as well as crushing of the

concrete inside.

-200 -150 -100 -50 0 50 100 150 200-100

-75

-50

-25

0

25

50

75

100

Load

(kN

)

Displacement (mm)

local buckling


Figure 4.18 Fracture of steel tube for SY1

55

SY2

Specimen SY2 was tested with a constant axial load of 440 kN representing about 20%

of the nominal plastic cross-section capacity. The force-displacement hysteretic loops

for Specimen SY2 are presented in Figure 4.19. The peak load of SY2 was similar to

that of SY1 (i.e. 70 kN at 24 mm). Following the peak load, the slope of the curve

reduced significantly because of the obvious second order effect caused by the higher

axial load. The half wavelength of flange buckling was about 90-120 mm. A view of

SY2 after testing is shown in Figure 4.20.

-200 -150 -100 -50 0 50 100 150 200-150

-100

-50

0

50

100

150

Lo

ad

(kN

)

Displacement (mm)

local buckling


Figure 4.20 Fracture of flanges for SY2

56

4.4 Observations and discussions

4.4.1 Moment-rotation hysteresis

The moment-rotation hysteretic loops for all the composite members are presented in

Figure 4.21. Table 4.1 presents the yield moment (My1) and ultimate moment (My2),

as well as corresponding displacements (δy1 and δy2, respectively), as extracted from

the experimental results.

It can be appreciated from the figures that the degradation of the stiffness is not as

significant as the degradation in the capacity for all the specimens. In the case of IC2

and IC3, the degradation of capacity is marked in the last cycle due to the sudden

fracture of the flange. On the other hand, the capacities of IC4, IC5, IC6 and IC7

decreased gradually. It can be concluded that the configuration of PEC members with

I-section transverse links have better performance on capacity than that of PEC

members with bars, because the drop in capacity is controlled in the former

configuration. On the other hand, for CFT members SY0, SY1 and SY2, the

degradation of capacity is evident from the 8th cycle due to the earlier local buckling

of the flange.

-0.12 -0.08 -0.04 0.00 0.04 0.08 0.12-150

-100

-50

0

50

100

150

Mo

me

nt

(kN

m)

Rotation (mrad)(a) IC1

Figure 4.21 Moment-rotation response of all specimens (Cont’d)

57

-0.12 -0.08 -0.04 0.00 0.04 0.08 0.12-150

-100

-50

0

50

100

150

Mom

ent (

kNm

)

Rotation (mrad)(b) IC2

-0.12 -0.08 -0.04 0.00 0.04 0.08 0.12-150

-100

-50

0

50

100

150

Mom

ent (

kNm

)

Rotation (mrad)(c) IC3


58

-0.12 -0.08 -0.04 0.00 0.04 0.08 0.12-150

-100

-50

0

50

100

150

Mom

ent (

kNm

)

Rotation (mrad)(d) IC4

-0.12 -0.08 -0.04 0.00 0.04 0.08 0.12-150

-100

-50

0

50

100

150

Mom

ent (

kNm

)

Rotation (mrad)(e) IC5


59

-0.12 -0.08 -0.04 0.00 0.04 0.08 0.12-150

-100

-50

0

50

100

150

Mom

ent (

kNm

)

Rotation (mrad)(f) IC6

-0.12 -0.08 -0.04 0.00 0.04 0.08 0.12-150

-100

-50

0

50

100

150

Mo

me

nt

(kN

m)

Rotation (mrad)(g) IC7


60

-0.12 -0.08 -0.04 0.00 0.04 0.08 0.12-200

-150

-100

-50

0

50

100

150

200

Mom

ent (

kNm

)

Rotation (mrad)(h) SY0

-0.12 -0.08 -0.04 0.00 0.04 0.08 0.12-200

-150

-100

-50

0

50

100

150

200

Mom

ent (

kNm

)

Rotation (mrad)(i) SY0


61

-0.12 -0.08 -0.04 0.00 0.04 0.08 0.12-250

-200

-150

-100

-50

0

50

100

150

200

250

Mom

ent (

kNm

)

Rotation (mrad)(j) SY2

Figure 4.21 Moment-rotation response of all specimens

Table 4.1 Summary of results

Specimen δy1 (mm) My1 (kNm) δy2 (mm) My2 (kNm) IC1 24.6 74.5 92.7 114.6 IC2 21.9 77.0 89.1 117.5 IC3 24.9 76.3 89.4 117.0 IC4 23.1 78.6 115.3 118.8 IC5 23.1 63.0 69.2 91.4 IC6 24.5 74.7 69.0 106.2 IC7 21.9 66.7 68.4 95.8 SY0 22.2 114.0 92.0 151.6 SY1 21.9 113.0 37.5 139.8 SY2 22.7 118.9 35.4 142.2

4.4.2 Ductility

The ductility ratio is an important factor to assess structural performance, especially

in the seismic assessment of composite sections. The ductility ratio could be defined

as μ=δμ/δy, where δμ is the ultimate displacement taken as the displacement where the

load degrades below 80% of the maximum capacity, and δy is the yield deformation.

Figures 4.22 presented the envelopes of the load-displacement curves for the

specimens described above. The load-displacement envelope curves were obtained by

connecting the peak branches of the third cycle of hysteretic loops at each loading

increment in order to reflect adequately the degradation effects. It is important to note

62

that specimen IC3 fractured before the load decreased below 80% of its maximum

capacity, so of IC3 was not reported. Also, in the case of Specimens IC4, IC6 and

SY0, when the stroke reached the maximum displacement, the loads did not drop to

80% of the maximum loads.

Table 4.2 and Table 4.3 present the ductility of all specimens in the positive and

negative directions. The effect of different types of links on the force-displacement

envelope curves also could be studied with reference to Figure 4.22.

The effect of the axial load level on the ductility is also shown in Table 4.2.

Specimens IC2, IC3, IC4 and IC6 were all subjected to 10% of the nominal plastic

cross-section capacity, while IC5 and IC7 were subjected to 20% of the nominal

plastic cross-sectional capacity. The increase of the level of axial load causes a

reduction in the member ductility.

-150 -100 -50 0 50 100 150-100

-80

-60

-40

-20

0

20

40

60

80

Load

(kN

)

Displacement (mm)

IC1 IC2 IC3

(a)

Figure 4.22 Load-displacement envelope curves (Cont’d)

63

-150 -100 -50 0 50 100 150-100

-75

-50

-25

0

25

50

75

100

Load

(kN

)

Displacement (mm)

IC1 IC4 IC6

(b)

-150 -100 -50 0 50 100 150-80

-60

-40

-20

0

20

40

60

80

Load

(kN

)

Displacement (mm)

IC5 IC7

(c)

Figure 4.22 Load-displacement envelope curves (Cont’d)

64

-150 -100 -50 0 50 100 150-120

-80

-40

0

40

80

120

Load

(kN

)

Displacement (mm)

SY0 SY1 SY2

(d)

Figure 4.22 Load-displacement envelope curves

Table 4.2 Comparison of ductility levels (positive direction)

Specimen IC1 IC2 IC3 IC4 IC5 IC6 IC7 SY0 SY1 SY2

y (mm) 23.7 23.4 23.2 23.2 23.6 22.8 23.7 23.7 23.2 24.0

(mm) 110.1 114.8 >120 >120 94.6 >120 105.4 >120 95.0 60.0

μ 4.65 4.91 >5 >5 4.01 >5 4.44 >5 4.10 2.5

Table 4.3 Comparison of ductility levels (negative direction)

Specimen IC1 IC2 IC3 IC4 IC5 IC6 IC7 SY0 SY1 SY2

y (mm) -24 -23.8 -24.2 -23.2 -24.5 -23 -23.2 -23.3 -23.5 -23.7

(mm) -118 -91 >-120 >-120 -90 >-120 -105 >-120 -96.0 -62.0

μ 4.92 3.78 >5 >5 3.67 >5 4.52 >5 4.09 2.62

4.4.3 Dissipated energy

The capacity of structural members to dissipate energy is an important factor in the

evaluation process. Therefore, the dissipated energy in every cycle was calculated

from the lateral load versus lateral displacement curve as the area bounded by the

hysteretic hoop in each cycle and the corresponding results are presented in Figure

4.23. Figure 4.23 (a) compares the accumulation of hysteretic energy dissipation of

65

three partially encased composite specimens IC1, IC2 and IC3 which have the same

section configuration and are subjected to the same axial load, the main difference

being the presence and spacing of transverse links. There is no obvious distinction

between the three specimens in the elastic stage. The cumulative energy of IC1 and

IC2 was almost the same, which was a slightly higher than that of IC3. Furthermore,

the adoption of bar links through holes resulted in earlier fracture of flanges in the

case of specimen IC3, so the total cumulative energy of IC3 was smaller than that of

IC1 and IC2. The ultimate cumulative energies of IC1, IC2 and IC3 were 75 KJ, 90

KJ and 50 KJ, respectively.

Figure 4.23 (b) and (c) describes the results of hysteretic energy dissipation of the

four improved partially encased composite members IC4, IC5, IC6 and IC7. It is

evident from the figure that the adoption of new links enhanced the energy dissipation.

Moreover, the early fracture of the flange was prevented by the new links. The energy

dissipation of IC6 and IC7 was higher than that of IC4 and IC5. The closely spaced

links in IC4 and IC5 induced higher stress concentrations and earlier fracture of the

flange.

The influence of the axial load level on the energy absorption as a function of the

accumulated displacement in CFT members is shown in Figure 4.23 (d). It can be

seen that the axial load level has minor influence on the energy dissipation when the

members are in the elastic stage. Once the members enter into the inelastic stage, a

higher axial load level would decrease the energy dissipation due to negative post-

elastic stiffness. The earlier fracture of the members with higher axial loads also

resulted in the decrease of the total dissipated energy.

66

0 1000 2000 3000 4000 50000

20

40

60

80

100

120

140

160

180

Cu

mu

lativ

e E

ne

rgy

(KJ)

Cumulative Displacement (mm)

IC1 IC2 IC3

(a)

Figure 4-23 Energy dissipation of composite members (Cont’d)

0 1000 2000 3000 4000 50000

20

40

60

80

100

120

140

160

180

Cu

mu

lativ

e E

ne

rgy

(KJ)


IC1 IC4 IC6

(b)

0 1000 2000 3000 4000 50000

20

40

60

80

100

120

140

160

180

Cu

mu

lativ

e E

ne

rgy

(KJ)


IC5 IC7

(c)

67

0 1000 2000 3000 4000 50000

20

40

60

80

100

120

140

160

180

Cu

mu

lativ

e E

nerg

y (K

J)


SY0 SY1 SY2

(d)

Figure 4.23 Energy dissipation of composite members

4.4.4 Fracture life

In the case of CFT members, high stress and strains developed in the corner areas,

while in the case of PEC members, high stress and strains developed in the bottom of

the specimens or the flange buckling area. Strain concentration in the bottom area, the

flange or the corner of the steel tube led to crack initiation in the steel after a few

cycles of successive inelastic buckling. These cracks grew into larger opening and

propagated quickly under cyclic loads. Tests were terminated only after the specimens

fractured.

It has also been found from the test that once an opening was formed it grew quickly

into a whole fracture for PEC members. On the other hand, the CFT members could

sustain a number of additional cycles following corner fracture.

Table 4.3 lists the number of cycles at which local buckling, initial fracture and final

failure of specimen occurred. The number of cycles to initial opening of IC2 and IC3

were less than that of IC4, IC5, IC6 and IC7. Although the occurrence of local

buckling of CFT members was earlier than that of PEC members, the failure number

of CFT members was larger than that of PEC members. This was partly due to the

positive effect of concrete in CFT members. The concrete which was inbounded in the

steel tube could perform better confinement effect.

68

Table 4.4 Summary of member test results

Specimen identification

Number of cycle to

Local buckling Initial opening Failure of specimenIC1 12 23 25 IC2 No local buckling 16 19 IC3 No local buckling 15 20 IC4 No local buckling 17 18 IC5 No local buckling 17 20 IC6 18 23 25 IC7 18 24 24 SY0 12 24 25 SY1 10 25 29 SY2 11 21 23

4.4.5 Strain measurements

As explained in the previous chapter, most of the strain gauges were located in the

expected plastic hinge region of the members. In the case of PEC members, a number

of gauges were placed on the flanges as well as on the transversal buckling-prevention

links. In the case of CFT members, strain gauges were distributed along the external

faces of the SHS section to obtain an estimate of the extent of the plastic hinge zone.

A brief discussion of the strain gauge measurements is given here with reference to

Figures 4.24 to 4.29.

All the transverse links in IC2 and IC3 behaved as expected until fracture happened at

the welds. The transverse bars did not fracture during the whole experiment.

According to the results from material tests, the yield strain of bars in IC2 and IC3 is

0.16. In IC2, all the stain gauges exceeded the yield strain. In specimen IC3, the strain

values of G33 and G35 were in the plastic stage. On the other hand, the strain values

of G34 and G36 were still in the elastic stage.

For PEC members with I-shaped links from IC4 to IC7, the yield strain of I-section

links was 0.23. For Specimen IC4 and IC5, all the transverse links were still in the

elastic stage. It is possible because IC4 and IC5 fractured earlier, the effect of links

did not perform eventually.

69

For Specimen IC6 and IC7, all the strains entered into the plastic stage except for G36

in IC6. It was because the link with G36 fractured earlier, the stain value of G36 was

still in the elastic stage. It could also be seen from the figures that the strain value of

links which were spaced at 60 mm was larger than that of links spaced at 40 mm. This

was attributed to the flanges of the specimens with fewer links buckling easier.


This chapter presented the observations and results from ten tests performed on PEC

members and CFT members. The partially encased members included basic I sections

with improved detailing – transverse links to delay the onset of local buckling. The

specimens were tested under cyclically increasing lateral displacement, with or

without axial load. The increase of the level of axial load causes a direct reduction in

the member ductility. The adoption of new links enhanced the energy dissipation.

Moreover, the early fracture of the flange was prevented by the new transverse links.

Although the local buckling of CFT members occurred earlier than that of PEC

members, the occurrence of fracture of CFT members was later than that of PEC

members. All the test results will be used in Chapter 5 for verification of the finite

element models followed by further assessment.

70

-1.4 -1.2 -1.0 -0.8 -0.6 -0.4 -0.2 0.0 0.2-150

-100

-50

0

50

100

150

Dis

plac

emen

t (m

m)

Strain (%)G33 -0.25 -0.20 -0.15 -0.10 -0.05 0.00 0.05 0.10

-150

-100

-50

0

50

100

150

Dis

plac

emen

t (m

m)

Strain (%)G34

-0.30 -0.25 -0.20 -0.15 -0.10 -0.05 0.00 0.05-150

-100

-50

0

50

100

150

Dis

plac

emen

t (m

m)

Strain (%)G35

-1.0 -0.8 -0.6 -0.4 -0.2 0.0 0.2 0.4 0.6 0.8-150

-100

-50

0

50

100

150

Dis

plac

emen

t (m

m)

Strain (%)G36

Figure 4.24 Displacement versus strain for transverse links: IC2

-0.5 -0.4 -0.3 -0.2 -0.1 0.0 0.1 0.2 0.3 0.4 0.5-150

-100

-50

0

50

100

150

Dis

plac

emen

t (m

m)

Strain (%)G33 -0.10 -0.05 0.00 0.05 0.10

-150

-100

-50

0

50

100

150

Dis

plac

emen

t (m

m)

Strain (%)G34

-0.5 -0.4 -0.3 -0.2 -0.1 0.0 0.1-150

-100

-50

0

50

100

150

Dis

plac

emen

t (m

m)

Strain (%)G35

-0.10 -0.05 0.00 0.05 0.10-150

-100

-50

0

50

100

150

Dis

pla

cem

en

t (m

m)

Strain (%)G36


71

-0.15 -0.10 -0.05 0.00 0.05-150

-100

-50

0

50

100

150

Dis

plac

emen

t (m

m)

Strain (%)G33 -0.30 -0.25 -0.20 -0.15 -0.10 -0.05 0.00 0.05 0.10

-150

-100

-50

0

50

100

150

Dis

plac

emen

t (m

m)

Strain (%)G34

-0.25 -0.20 -0.15 -0.10 -0.05 0.00 0.05-150

-100

-50

0

50

100

150

Dis

plac

emen

t (m

m)

Strain (%)G35

-0.25 -0.20 -0.15 -0.10 -0.05 0.00 0.05-150

-100

-50

0

50

100

150

Dis

pla

cem

ent (

mm

)

Strain (%)G36


-0.16 -0.12 -0.08 -0.04 0.00 0.04-150

-100

-50

0

50

100

150

Dis

plac

emen

t (m

m)

Strain (%)G37 -0.16 -0.12 -0.08 -0.04 0.00 0.04

-150

-100

-50

0

50

100

150

Dis

plac

emen

t (m

m)

Strain (%)G38

-0.20 -0.15 -0.10 -0.05 0.00 0.05 0.10-150

-100

-50

0

50

100

150

Dis

plac

emen

t (m

m)

Strain (%)G39

-0.25 -0.20 -0.15 -0.10 -0.05 0.00 0.05-150

-100

-50

0

50

100

150

Dis

plac

emen

t (m

m)

Strain (%)G40


72

-4.0 -3.5 -3.0 -2.5 -2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0-150

-100

-50

0

50

100

150

Dis

pla

cem

en

t (m

m)

Strain (%)G33 -0.8 -0.6 -0.4 -0.2 0.0 0.2 0.4

-150

-100

-50

0

50

100

150

Dis

plac

eme

nt (

mm

)

Strain (%)G34

-3.0 -2.5 -2.0 -1.5 -1.0 -0.5 0.0 0.5-150

-100

-50

0

50

100

150

Dis

pla

cem

en

t (m

m)

Strain (%)G35 -0.20 -0.15 -0.10 -0.05 0.00 0.05

-150

-100

-50

0

50

100

150

Dis

pla

cem

en

t (m

m)

Strain (%)G36


-1.2 -1.0 -0.8 -0.6 -0.4 -0.2 0.0 0.2 0.4-150

-100

-50

0

50

100

150

Dis

plac

emen

t (m

m)

Strain (%)G33

-0.35 -0.30 -0.25 -0.20 -0.15 -0.10 -0.05 0.00 0.05-150

-100

-50

0

50

100

150

Dis

plac

emen

t (m

m)

Strain (%)G34

-0.6 -0.5 -0.4 -0.3 -0.2 -0.1 0.0 0.1-150

-100

-50

0

50

100

150

Dis

plac

emen

t (m

m)

Strain (%)G35

-0.5 -0.4 -0.3 -0.2 -0.1 0.0 0.1 0.2 0.3 0.4 0.5-150

-100

-50

0

50

100

150

Dis

pla

cem

en

t (m

m)

Strain (%)G36 Figure 4.29 Displacement versus strain for transverse links: IC7

73

Chapter 5. Numerical Simulation

5.1 Introduction

The experimental results described in the previous chapter presented a fundamental

insight into the inelastic behaviour of composite members. These tests provided direct

information on the relative influence of a number of parameters and improved

transverse links configurations. However, it should be noted that despite the

indispensable role played by testing in understanding the nonlinear behaviour of

structural members, the cost and time associated with experimental work imposes

severe constraints on the scope and extent of such studies. Therefore, there is a need

for employing nonlinear analysis techniques for complementing and extending the

results of experimental investigations. Appropriate analytical models can be adopted

for achieving better understanding of complex nonlinear structural behaviour.

Reliable analytical methods could also provide detailed information through

sensitivity and parametric studies, which could be used for conducting design-related

assessments.

This chapter describes the numerical studies carried out with the purpose of

simulating the behaviour observed during the cyclic tests on composite members

presented in previous chapters. The purpose of this simulation is to validate and

calibrate the numerical models as well as to provide more detailed insight into the

nonlinear inelastic behaviour of composite members. The finite element program

ABAQUS [34] is employed herein for the nonlinear studies. After giving a brief

description of the program and material models, the numerical simulations are

presented and the effect of transverse links is discussed.

74

5.2 Development of FE models

5.2.1 General

The general purpose finite element program ABAQUS [34] was used herein in order

to examine issues related to local buckling in PEC and CFT members. The

ABAQUS/Dynamic nonlinear solution procedure was utilised here.

Models representing PEC members with conventional details as well as those

incorporating the additional welded bars were constructed. The basic model is made

up of five parts: (1) steel profile, (2) confined concrete, (3) unconfined concrete, (4)

end plates and (5) transverse links. The basic model representing CFT members

consists of three parts: (1) steel profile, (2) confined concrete and (3) end plates. All

the models were constructed using the same loading arrangement, boundary

conditions and geometry to maintain consistency with the experimental results.

5.2.2 Element type and mesh size

The flanges and webs of the steel sections were modelled using four node reduced

integration shell elements (S4R) with five through-thickness Gauss integration points.

The confined concrete and unconfined concrete were modelled using eight-node

reduced integrated linear brick elements (C3D8R). The end and top plates were

simulated using rigid body idealizations whereas the transverse links were represented

by 2-node linear beam elements (B31).

Various interactions and constraints were used to establish a full composite action. A

combination of friction and normal contact based on surface-to-surface interaction

was used for the interface between steel and concrete. A tie constraint was used for

the steel web-concrete and steel flange-link interface while the steel section was tied

to both of the end plates. Varying mesh densities were employed in different areas in

the models following a mesh sensitivity study. Refined meshes on steel were used

only in areas where local buckling was expected. To this end, a fine mesh at the end

75

of the member was required to capture the location and shape of local buckling

accurately. The studies were performed on CFT members. The mesh sensitivity study

includes three levels of refinement for the steel. The mesh size of concrete was kept

the same for all the specimens. The component of steel was refined gradually as

follows: (1) 50mm × 50mm global mesh, (2) 30mm × 30mm refined bottom zone, and

(3) 15mm × 15mm refined bottom zone. The load versus displacement response for

CFT members with different levels of refinement is presented in Figure 5.1. It is

shown that the initial member stiffness and yield point between different mesh sizes

remain the same. The displacement and load curves show a slight drop in member

capacity as the mesh is refined. It has also been found that a coarse mesh is stiffer and

therefore was less prone to local buckling than a finer mesh. For all the specimens

studied here, the mesh size of 15mm × 15mm was selected in the bottom zone.

0 50 100 150 200 250 3000

20

40

60

80

100

120

140

Load

(kN

)

Displacement (mm)

15x15 30x30 50x50

Figure 5.1 Mesh sensitivity study for composite members

5.2.3 Constitutive material relationships

The ABAQUS models developed herein used several material representations for the

steel and concrete constituents (described in Chapter 3 with parameters obtained

directly from coupon tests). The combined hardening model in ABAQUS was

adopted for steel in all FE models. The concrete behaviour, including the unconfined

76

concrete and confined concrete, was modelled using the concrete damage plasticity

model as shown in Figure 5.2 and Figure 5.3, respectively. The unconfined concrete

and confined concrete models adopted here were described in Chapter 2.

c

cu

c0

cc0 cu

(a) Compression response

E

t

t0

ct t

E

(b) Tensile response

Figure 5.2 Concrete damage plasticity material model for unconfined concrete

c

cu

c0

cc0 cu

(a) Compression response

E

c0

t

t0

ct t

E

(b) Tensile response

Figure 5.3 Concrete damage plasticity material model for confined concrete

5.2.4 Boundary conditions and displacement history

Boundary conditions were applied to the numerical models to represent the fixed end

conditions of the test specimens. The bottom plate was modelled as a rigid object, and

the specimen was tied to the bottom plate. All degrees of freedom of nodes at the

bottom end of the members were restrained. The out-of-plane displacements at top

plate of the members were also restricted. The applied axial load and lateral

displacement history followed the experimental steps.

The explicit dynamic solution strategy was selected to simulate the behaviour of

composite members. In the case of PEC members, as well as in other complex

77

problems which exhibit highly nonlinear behaviour, convergence may not be possible

using an implicit strategy. The explicit solution method was firstly developed with the

purpose to solve the dynamic problems in which inertia plays an important role in the

solution. Research also found that it also could be applied to simulate quasi-static

problems [43, 64].

In order to evaluate whether the numerical models are producing a quasi-static

response, the energy history was investigated. According to the research from Begum

[43], the external energy should be nearly equal to the internal energy of the whole

system, while the kinematic energy remains small in a quasi-static system. It is shown

in Figure 5.4 that these criteria were observed to be satisfied in the energy history of a

PEC members.

0 20 40 60 80 100 120 140 1600.00E+000

5.00E+007

1.00E+008

1.50E+008

2.00E+008

2.50E+008

En

erg

y (J

)

Time (second)

Kinetic energy

External work energy

Internal energy

Figure 5.4 Energy history of the numerical analysis of PEC member

5.3 Validation

5.3.1 Load-displacement response

In this section, the finite element model predictions are verified against the cyclic

lateral loading tests. The hysteresis curves from finite element simulations are shown

in Figures 5.5 to 5.14. The overall load-displacement relationships for Specimens IC1,

78

IC2 and IC3, subjected to axial load of 125 kN are presented in Figures 5.5, 5.6 and

5.7, respectively.

It can be seen from Figure 5.5 that for Specimen IC1 there is very good agreement

between the experimental results and finite element results in terms of initial stiffness

and yield point. The capacity was slightly overestimated by the ABAQUS

representation. In the case of Specimen IC2, its experimental capacity was almost the

same as that of numerical result.

On the other hand, it is clear from Figure 5.7 that for Specimen IC3, the numerical

results are similar to those obtained from the experiment. After concrete cracking, the

numerical results are slightly higher than those obtained from the experimental results.

It seems that the cumulative damage due to the cyclic loads has not been reflected in

the results from finite element models.

-150 -100 -50 0 50 100 150-100

-80

-60

-40

-20

0

20

40

60

80

100

Lo

ad

(kN

)

Displacement (mm)

Experiment FE

IC1

Figure 5.5 Comparison of hysteretic curves for IC1 from FE simulation and

experiment

79

-150 -100 -50 0 50 100 150-100

-80

-60

-40

-20

0

20

40

60

80

100

Lo

ad

(kN

)

Displacement (mm)

Experiment FE

IC2

Figure 5.6 Comparison of hysteretic curves for IC2 from FE simulation and experiment

-150 -100 -50 0 50 100 150-100

-80

-60

-40

-20

0

20

40

60

80

100

Lo

ad

(kN

)

Displacement (mm)

Experiment FE

IC3


The load-displacement responses for IC4, IC5, IC6 and IC7, incorporating improved

transverse links, are presented in Figures 5.8, 5.9, 5.10 and 5.11, respectively. In

terms of initial stiffness, very good agreement was also found between the

experimental results and the analysis in these four cases. By observing the

comparative plots of IC4 and IC6, it is clear that the results obtained from ABAQUS

80

are very similar to those from the experiments over the whole load-displacement

response.

-150 -100 -50 0 50 100 150-100

-80

-60

-40

-20

0

20

40

60

80

100

Load

(kN

)

Displacement (mm)

Experiment FE

IC4


-150 -100 -50 0 50 100 150-100

-80

-60

-40

-20

0

20

40

60

80

100

Load

(kN

)

Displacement (mm)

Experiment Test

IC5


81

-150 -100 -50 0 50 100 150-100

-75

-50

-25

0

25

50

75

100

Lo

ad

(kN

)

Displacement (mm)

Experiment FE

IC6


experiment

-150 -100 -50 0 50 100 150-100

-75

-50

-25

0

25

50

75

100

Lo

ad

(kN

)

Displacement (mm)

Experiment FE

IC7


experiment

82

Hysteresis curves from selected finite element simulations and corresponding tests on

SY0, SY1 and SY2 are shown in Figures 5.12, 5.13 and 5.14. The comparison shows

that the FE models are capable of simulating the hysteretic behaviour of CFT

members well.

-150 -100 -50 0 50 100 150-150

-100

-50

0

50

100

150

Lo

ad

(kN

)

Displacement (mm)

Experiment FE

SY0

Figure 5.12 Comparison of hysteretic curves for SY0 from FE simulation and

experiment

-150 -100 -50 0 50 100 150-150

-100

-50

0

50

100

150

Lo

ad

(kN

)

Displacement (mm)

Experiment FE

SY1

Figure 5.13 Comparison of hysteretic curves for SY1 from FE simulation and

experiment

83

-150 -100 -50 0 50 100 150-150

-100

-50

0

50

100

150

Lo

ad

(kN

)

Displacement (mm)

Experiment FE

SY2

Figure 5.14 Comparison of hysteretic curves for SY2 from FE simulation and experiment

It is clear from the above figures that the results obtained from ABAQUS closely

represent the experimental curves. However, within the final cycles, the difference

between the experiment and simulation was larger. One possible explanation for the

difference between tests and simulations is the choice of material models in ABAQUS.

The fracture of the steel flanges and the effect of concrete confinement observed

during the tests were not incorporated within the present numerical models.

5.3.2 Forces in PEC transverse links

Additional transverse welded links can help to delay buckling of the steel flanges thus

enhancing the member ductility. Therefore, it is necessary to have some insight into

the forces that develop in these links. Figure 5.15 depicts the forces developed in the

transverse links for IC2 as observed from the FE representation observed above. The

location of the three links is also shown in Figure 5.15. The peak forces developed in

the three links are 17.5 kN, 27 kN and 27 kN. It can be appreciated from Figure 5.15

that Link 2 and Link 3 have reached the yield load. Additionally, local buckling of the

flange was visible between the links. In the case of Specimen IC3, Link 3 has reached

the yield load at an axial deformation of 1.3 mm as shown in Figure 5.17. Link 1 and

Link 2 were still in the elastic stage.

84

The same study was carried out for IC4, IC5, IC6 and IC7. The corresponding plots

and views of the models are shown in Figure 5.19 to Figure 5.26. For Specimens IC4,

IC5, IC6 and IC7, all the link forces were above yield load. Yielding of the link

occurred relatively early at an axial deformation of around 0.6 mm for these four

specimen. The formation of the buckle between the links only happened in Specimens

IC6 and IC7 are shown in Figure 5.24 and Figure 5.26. Despite yielding of the links,

local buckling was largely limited to the distance between the links.

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.00

5

10

15

20

25

30

Axi

al l

oa

d (

kN)

Axial deformation (mm)

Link 1 Link 2 Link 3

Figure 5.15 Axial loads in selected links for IC2

Figure 5.16 Location of links for IC2

Link 1

Link 3 Link 2

85

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.00

5

10

15

20

25

30

Axi

al lo

ad (

kN)





Link 1

Link 3Link 2

86

0 1 2 3 4 5 6 70

5

10

15

20

25

30

Axi

al lo

ad (

kN)





Link 1

Link 3Link 2

87

0 1 2 3 4 5 6 7 8 9 100

5

10

15

20

25

30

Axi

al l

oa

d (

kN)





Link 1

Link 3Link 2

88

0 1 2 3 4 5 6 7 8 90

5

10

15

20

25

30

Axi

al lo

ad (

kN)





Link 3

Link 1

Link 2

89

0 1 2 3 4 5 6 7 8 9 10 11 120

5

10

15

20

25

30

Axi

al l

oa

d (

kN)






This chapter has presented finite element models constructed in ABAQUS as applied

to study the cyclic behaviour of seven PEC and three CFT members. All of the

proposed models were verified against experimental results. Three-dimensional

Link 1 Link 2

Link 3

90

simulations in ABAQUS were performed in order to examine the local flange

buckling in PEC members and CFT members. It was demonstrated that the proposed

models are able to capture the occurrence of local buckling and the influence of axial

loading. The three dimensional analyses also provide useful insights into the forces

developing within additional transverse links.

91

Chapter 6. Sensitivity Studies and Design

Implications

6.1 Introduction

As discussed in previous chapters, the performance of composite members depends

on various factors including material properties, local slenderness, axial load levels

and section geometry. Chapter 2 reviewed a number of experimental studies carried

out in order to examine the cyclic inelastic behaviour of composite members [65-71].

Although these experimental studies provided direct information on the inelastic

behaviour of composite members, it is prohibitive to investigate a large variety of

member configurations solely by means of experimental methods. To this end,

nonlinear analysis offers a powerful tool for detailed studies and evaluations. This

chapter focuses on examining some key parameters required for quantifying the

behaviour of composite members. An assessment of effective stiffness, moment

capacity and ductility of a member was required. Particular emphasis is needed to

determine the parameters which would enable a reliable representation of the inelastic

response.

6.2 Stiffness considerations

An estimate of the stiffness of composite members is necessary in seismic design. The

stiffness of experimental results is compared with the elastic stiffness applying both

an uncracked and a cracked concrete section [72].

Figure 6.1 depicts the secant stiffness of all the experimental specimens. The values

of uncracked and cracked stiffness of the members are also indicated in the figures. In

calculating this stiffness, the modulus of elasticity of steel and concrete were assumed

as 200000 N/mm2 and 30000 N/mm2, respectively. In the case of cracked section,

twenty percent of the concrete stiffness was considered to contribute to the total

stiffness. The stiffness of all models drops below both the uncracked stiffness and

cracked stiffness at early stages of loading. When ductility ratio was equal to one, the

92

PEC members exhibit a secant stiffness which was slightly lower than the cracked

stiffness. So it was concluded that the cracked stiffness could represent the stiffness of

PEC members at the yield level. On the other hand, for CFT members, the cracked

stiffness was still larger than the member stiffness even the displacement of

specimens was larger than the yield displacement. It was suggested that the adoption

of cracked stiffness for CFT members overestimated the stiffness of CFT members at

the yield level.

0 1 2 3 4 5 60.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

Cracked Stiffness

Stif

fne

ss (

KN

/mm

)

IC1 IC2 IC3

Uncracked Stiffness

(a)

0 1 2 3 4 5 60.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

Cracked Stiffness

Stif

fnes

s (K

N/m

m)

IC4 IC5 IC6 IC7

Uncracked Stiffness

(b)

Figure 6.1 Experimental secant stiffness of PEC member (Cont’d)

93

0 1 2 3 4 5 60

1

2

3

4

5

6

7

Stif

fnes

s (K

N/m

m)

SY0 SY1 SY2

Uncracked Stiffness

Cracked Stiffness

(c)

Figure 6.1 Experimental secant stiffness of all the specimens

6.3 Moment capacity

In this section, the influence of number of links and levels of axial load on the

ultimate moment is studied.

Firstly, Figure 6.2 depicted the moment-rotation curves of PEC members with

different transverse links. Three different sections, UC 152×23, HEA 200 and HEA

240, were employed. The axial loads used here were 30% of their nominal plastic

loads. It was shown that the stiffness of members with different links was almost the

same.

It has been found previously that the application of links could marginally improve

the maximum moment [30, 31]. The moment of specimen with more transverse links

was a little higher than that of specimen with fewer transverse links. It has also been

found that PEC members without links exhibit more pronounced degradation than

their counterparts employing links. These advantages are related to the ability of

transverse links to prevent local buckling in the flanges.

94

0.00 0.03 0.06 0.09 0.12 0.150

50

100

150

200

Mo

men

t (k

Nm

)

Rotation (mrad)

d = 40 mm d = 60 mm d = 0 mm

(a) UC 152x23

Mmax,Rd

= 127.1 kNm

0.00 0.03 0.06 0.09 0.12 0.150

50

100

150

200

250

300

350M

max,Rd = 302.6 kNm

Mo

me

nt (

kNm

)

Rotation (mrad)

d = 53 mm d = 80 mm d = 0 mm

(b) HEA200

Figure 6.2 Moment-displacement response for PEC members with different link

spacing

95

0.00 0.03 0.06 0.09 0.12 0.150

100

200

300

400

500

600

Mmax,Rd

= 507.3 kNm

Mo

me

nt

(kN

m)

Rotation (mrad)

d = 64 mm d = 96 mm d = 0 mm

(c) HEA 240

Figure 6.2 Moment-displacement response for PEC members with different link

spacing

The influence of the level of axial load on composite sections was investigated in

Figures 6.3 and 6.4. For PEC members, UC 152×23 and HEA 200 sections were

employed, while SHS 180×6.3, SHS 250×8 and SHS 300×8 were chosen for CFT

members. The distance between two links of UC 152×23 and HEA 200 was 40 mm

and 53 mm, respectively. The axial load ratios (P/Pu) adopted here were 0, 10% and

30%. Figure 6.3 and Figure 6.4 show the monotonic moment-rotation curves for PEC

members and CFT members, respectively. Due to the presence of axial load, an

important consideration is related to the influence of the second order effect. The

second order moment could be viewed as part of the total moments presented in

Figure 6.3 and Figure 6.4. In the presence of axial load and with increasing lateral

displacement, the maximum moment of composite members with increased axial load

was higher.

96

0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.350

50

100

150

200

Mo

me

nt

(kN

m)

Rotation (mrad)

n =0 n =10% n =30%

(a) UC 152x23

Mmax.Rd

= 127.1 kNm

0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.350

50

100

150

200

250

300

350

Mo

men

t (k

Nm

)

Rotation (mrad)

n =0 n =10% n =30%

(b) HEA200

Mmax,Rd

= 302.6 kNm

Figure 6.3 Moment-displacement response for PEC members with different axial load

97

0.00 0.03 0.06 0.09 0.12 0.150

50

100

150

200

250

Mo

men

t (kN

m)

Rotation (mrad)

n = 0 n = 10% n = 30%

(a) SHS 180x6.3

Mmax,Rd

= 202.5 kNm

0.00 0.03 0.06 0.09 0.12 0.150

100

200

300

400

500

600M

max,Rd = 518.7 kNm

Mo

men

t (kN

m)

Rotation (mrad)

n = 0 n = 10% n = 30%

(b) SHS 250x8

Figure 6.4 Moment-displacement response for CFT members (Cont’d)

98

0.00 0.03 0.06 0.09 0.12 0.150

100

200

300

400

500

600

700

800

900

Mmax,Rd

= 760.9 kNm

Mo

me

nt (

kNm

)

Rotation (mrad)

n = 0 n = 10% n = 30%

(c) SHS 300x8

Figure 6.4 Moment-displacement response for CFT members

Eurocode 4 [73] considers the full plastic moment (Mmax,Rd) based on the steel section.

The confined/unconfined strength of concrete was also depicted in the above figures.

It was found that the predictions are generally similar to the numerical results within

the practical range of member sizes and material properties.

6.4 Ductility considerations

6.4.1 Ductility of PEC members

It is necessary to consider limiting criteria for ductility for the purpose of seismic

assessment and design. From the investigation on the tests and previous numerical

simulations of PEC members, the onset of local buckling was typically followed by a

reduction in load capacity, particularly in the presence of larger axial loads. Therefore,

it seems plausible to consider local buckling as a possible limiting criterion for PEC

members. On the other hand, in the case of CFT members, it has been found that local

buckling would be a more conservative limiting criterion.

In the inelastic range, local flange or tube buckling could be assessed in terms of the

critical strain corresponding to its onset in the inelastic range. A reasonable treatment

of this complex problem can be obtained by combining fundamental plate buckling

99

theories with experimental results [33]. It has also been suggested that the relationship

between critical buckling strain (εcr) and yield strain (εy) can be expressed as [33]:

22

22

)1(12 c

tEk

y

s

y

cr

6.1

Where ν is the Poisson’s ratio, E is the modulus of elasticity, σy is the yield stress, t is

the thickness of flange or square box, c is the flange outstand or box width, and k is

the buckling coefficient. The value of k is a function of plate geometry and boundary

conditions. The variation in k with the aspect ratio (a/b) for plates with different edge

conditions is shown in Figure 6.5 [74].

Figure 6.5 Buckling coefficient versus aspect ratio [74]

Equation 6.1 could also be rearranged and presented in terms of the commonly used

plate slenderness parameter defined as:

cr

y

s

yp Ekt

c

2

2 )1(12 6.2

100

Another suggested relationship between εcr/εy and λp which was based on

experimental investigations on the local buckling of the flange can be expressed as

[27]:

15.01

1

y

cr

p

6.3

The above two equations between εcr/εy and λp are shown in Figures 6.6 and 6.7,

respectively. The results from the experimental specimens and numerical assessment

are depicted in Figure 6.6 and 6.7 respectively, according to the definition of

Eurocode 4 [73]. The details of steel profiles used in finite element model, including

PEC members and CFT members are shown in Table 6.1 and Table 6.2.

Figure 6.6 depicts the influence of flange slenderness on normalized critical strain of

PEC members. Only the experimental results from IC1, IC6 and IC7 were presented

in figures because the other specimens failed without local buckling due to stress

concentration around the holes employed for placing the transverse bars. It has been

found in Chapter 4 that the strain gauges location coincided with the buckled flange or

box. It is evident from Figure 6.6 that Equation 6.3 provides a closer prediction of the

critical buckling strain obtained from both the experiments and finite element

estimations in the case of PEC members while Equation 6.2 seems to be conservative.

Table 6.1 Details of steel profiles of PEC members used in Figure 6.6

No. 1 2 3 4 5 6 7 8

Configuration

of members HEA240 HEA200 HEA240 HEA200 450×450 450×450 450×450 450×450

Slenderness of

flange 9.7 9.7 9.7 9.7 23.2 23.2 23.3 35.4

Details of

links 8@96 8@80 No links No links 8@225 [email protected] 8@450 8@450

101

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.00

5

10

15

20

25

30 class 3class 2

p

cr/

y

Eq 6.2 Eq 6.3

class 1

1

2IC6

3IC7

4 IC1

5 6 78

Local buckling

Figure 6.6 Influence of flange slenderness on normalized critical strain for PEC members

As discussed in previous chapters, the additional straight bars welded to the flanges

within the potential plastic hinge zone could delay local buckling. It could also be

observed from Figure 6.6 that the ductility of PEC members with links could be

increased. A simplified approach to consider the effect of the additional bars could be

undertaken by reconsidering Curve D in Figure 6.5. The aspect ratio ‘a/b’ would

represent the ratio between the length of the local buckling and the outstand width.

The value for ‘a’ and ‘b’ obtained in IC1 was about 140 mm and 75 mm, respectively.

In Figure 6.5, the buckling coefficient k corresponding to a/b equalling to 1.9 is about

1.3. The additional bars were effective in limiting the length of the buckle to the

spacing between the links. This means that the additional bars can be considered as an

approach of reducing the ratio ‘a/b’ by limiting the value of ‘a’ to the distance

between the links which would lead to higher values for the buckling coefficient ‘k’.

In the experiments, the spacing of the welded bars was either 40 mm or 60 mm.

Hence, ratio ‘a/b’ was 0.53 or 0.8, respectively. Compared to conventional specimen,

the enhancement in ductility was at least 361% and 160% for PEC members where

the aspect ratio was equal to 0.53 and 0.8, respectively, if no premature weld and

transverse bar failure happened. Based on the above discussions, significant benefit in

102

ductility would occur if a/b is smaller than 1.0. As discussed in Chapter 4, premature

weld or link failure limited the effectiveness of the additional bars in some tests,

especially when the distance between two links was small, being equal to 40 mm. On

the other hand, for IC2 and IC3, it was evident that the transverse bars were not fully

effective because the flange around bars fractured earlier. However, the use of 8 mm

by 6 mm transverse plate with an improved welding procedure provided a

considerable improvement in performance.

6.4.2 Ductility of CFT members

Table 6.2 lists the details of CFT members which are depicted in Figure 6.7. Previous

studies have suggested that a buckling coefficient k of 10.3 can be employed to

determine the slenderness of column cross-sections [75]. In Figure 6.7, the grey

squares gave the critical strain corresponding to local buckling, while the red squares

represented the critical strain according to flange fracture. Figure 6.7 also presents the

results related to the cross-section classification of Eurocode 3 [61]. In the case of

CFT members, Equation 6.2 was still over-conservative for determining the buckling

strain. It was suggested that Equation 6.3 should be applied to determine the buckling

strain of CFT members. Furthermore, it was also noted from Figure 6.7 that in the

case of SY0, SY1 and SY2, members failed in thirteen cycles, sixteen cycles and

thirteen cycles, respectively, since local buckling occurred. Hence in the case of CFT

members, it was conservative to consider local buckling as the limiting criterion.

Table 6.2 Details of steel profiles of CFT members used in Figure 6.7

No. 1 2 3 4 5 6 7 8

Configuration

of members

(mm×mm)

180×6.3

180×12.5

180×16

250×8

250×16

300×8

300×12

300×20

103

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.005

1015202530354045505560

SY2SY1

SY0

SY0

SY2

class 3class 2

cr/

y

p

Eq 6.2 Eq 6.3

class 13

82

5

7

6

4

1

SY1

local buckling

fracture

Figure 6.7 Influence of flange slenderness on normalized critical strain for CFT members


The experimental and numerical studies offered an assessment of key response

parameters and design consideration. In terms of the stiffness of PEC members with

lower axial loads, the estimated experimental value was largely in agreement with the

assumption based on 20% of the concrete contribution. In terms of local buckling of

PEC members, the critical strain could be predicted from simple equations dependent

on the normalised plate slenderness parameters. The enhancement of ductility by

delaying local buckling through the provision of additional links could be captured by

a corresponding enhancement in the buckling coefficient. However, the ductility of

CFT members based on the local buckling of the steel tube was over-conservative.

104

Chapter 7. Conclusions and Suggestions for Future

Work

7.1 Conclusions

The inelastic behaviour of composite steel/concrete members subjected to cyclic

loading conditions was investigated. The research included cyclic testing on seven

PEC members and three CFT members, detailed numerical modelling, as well as

simplified analytical assessments. This thesis aims to represent a contribution towards

providing necessary information on the inelastic behaviour of PEC members and CFT

members. This chapter provides a brief summary of the research and gives the main

results from the work.

Cyclic tests were firstly performed on seven PEC members. PEC members with one

cross-sectional size, utilising Grade 355 steel, and axial load levels of 10% and 20%

of the corresponding normal strength were employed in the experimental programme.

In order to enhance the ductility of the members, PEC members incorporating special

detailing features were utilised. Two PEC members used round bars in the possible

local buckling area, and another four PEC members adopted I-section links. The

required experimental arrangement, including lateral cyclic displacements and axial

loading was applied.

The PEC members with close transverse links were easy to fracture due to the stress

concentration on the welding area. The specimens were tested under cyclically

increasing lateral displacement, with or without axial load. The increase of the level

of axial load caused a direct reduction in the member ductility. The adoption of new

links enhanced the energy dissipation. Moreover, the early fracture of the flange was

prevented by the new transverse links.

Similarly, CFT members with cross-sectional size SHS 180 tubes and Grade 355 were

included in the experimental programme. The axial load levels ranged from 0 to 20%

of the corresponding nominal strength. The results from the tests gave a direct

105

assessment of the influence of axial loading and improved detailing on the behaviour.

Furthermore, the experimental results provided essential data for the validation and

calibration of numerical models. Although the local buckling of CFT members

occurred earlier than that of PEC members, the occurrence of fracture of CFT

members was later than that of PEC members. The experimental results enabled a

direct assessment of the influence of axial loading and improved detailing on the

behaviour. The results also provided essential data for the validation of numerical

models.

Numerical simulations of the cyclic tests were performed using finite element

program ABAQUS. The non-linear combined isotropic/kinematic hardening model

was used in ABAQUS to represent the steel material. Furthermore, the concrete

damage plasticity model was employed to simulate both the confined concrete and

unconfined concrete. It was found that the application of these two models was able to

capture the key observed behavioural features. Numerical simulations of the cyclic

tests were performed using the finite element programs ABAQUS/Dynamic. All of

the proposed models were verified against experimental results. Three-dimensional

simulations in ABAQUS were performed in order to examine the local flange

buckling in PEC members and CFT members. It was demonstrated that the proposed

models were able to capture the occurrence of local buckling, the influence of axial

loading and detailing. The three dimensional analyses also provided useful insights

into the forces developing within additional transverse links.

The experimental and numerical studies presented an important assessment on

parameters and design consideration. In terms of stiffness, it was found that the

assumption based on 20% of the concrete contribution to the PEC stiffness lead to

largely good agreement with experimental values for PEC members. Eurocode 4

considered the full plastic distribution based on the steel section and the unconfined

strength of concrete. The predictions of moment capacity were appropriate for normal

design situations. The difference between Mmax,Rd and the maximum moment of each

specimen was in the range from 20% to 30%.

106

The critical strain predicted from simple equations dependent on the normalised plate

slenderness parameter could be used to evaluate local buckling in the case of PEC

members. The enhancement of ductility by delaying local buckling through the

application of additional welded links was shown to be captured by an increase in the

buckling coefficient. In the case of CFT members, specimen failed in thirteen cycles,

sixteen cycles and thirteen cycles, respectively, since local buckling occurred. Hence

in the case of CFT members, it was conservative to consider local buckling as the

limiting criterion.

7.2 Suggestions for future work

The results from this research highlighted a number of topics which need additional

exploration and investigation. The final section identified potential areas for further

work.

The experimental and numerical studies in this research focused on investigating the

inelastic behaviour of PEC members and CFT members. Particular attention was

given to PEC members due to the increased application in worldwide practice. In

order to enhance the ductility of PEC members, two transverse link alternatives were

examined. Since the behaviour was mainly determined by the plastic hinge zone, the

findings were able to be used in other similar members with different geometry and

boundary conditions. In addition, there is still a need to validate the application of

new transverse links in other type of composite members. Furthermore, the research

here reported concentrated on the behaviour of PEC members subjected to cyclic

loads along their major axis. It is necessary to study the behaviour of PEC members

under the similar cyclic loads in the minor axial direction.

Finite element program ABAQUS/Dynamic was used to simulate the hysteretic

performance of PEC and CFT members. The application of this method could be

extended to other structural element or other cyclic loading programs. The detailed

three-dimensional analysis provided useful insight into the local buckling behaviour

and forces developing in additional links. The results involve complex interactions

107

that would provide useful information for the future work. On the other hand, the

fracture of the steel profile could not be simulated in the analysis here, and appears to

be an important issue for future study.

This thesis provided information on the response of composite members under cyclic

loads. Methods for estimating the inelastic demands on critical members were based

on the limited loading condition. It is necessary to expand the research to the fields of

various extreme loading conditions, such as impact, blast or seismic scenarios.

108

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113

Appendix A Supplementary Experimental Results

for PEC members

114

-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6-150

-100

-50

0

50

100

150

Dis

pla

cem

en

t (m

m)

Strain (%)G17

-6 -5 -4 -3 -2 -1 0 1-150

-100

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0

50

100

150

Dis

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cem

ent

(mm

)

Strain (%)G18

-6 -5 -4 -3 -2 -1 0 1-150

-100

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0

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100

150

Dis

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cem

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(mm

)

Strain (%)G19

-4 -3 -2 -1 0 1 2-150

-100

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0

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Dis

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(mm

)

Strain (%)G20

-4 -3 -2 -1 0 1 2-150

-100

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Dis

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(mm

)

Strain (%)G21

-3 -2 -1 0 1 2 3 4 5-150

-100

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0

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150

Dis

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em

ent

(m

m)

Strain (%)G22

-5 -4 -3 -2 -1 0 1-150

-100

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0

50

100

150

Dis

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ent

(mm

)

Strain (%)G23

-6 -5 -4 -3 -2 -1 0 1 2-150

-100

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150

Dis

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t (m

m)

Strain (%)G24

Figure A. 1 Strain-Displacement response for IC1 (Cont’d)

115

-3 -2 -1 0 1 2 3-150

-100

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Dis

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-3 -2 -1 0 1 2-150

-100

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Dis

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Strain (%)G26

-4 -3 -2 -1 0 1 2-150

-100

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Dis

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-4 -3 -2 -1 0 1 2-150

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Dis

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mm

)

Strain (%)G28

-7 -6 -5 -4 -3 -2 -1 0 1 2 3-150

-100

-50

0

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Dis

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Strain (%)G29

-3 -2 -1 0 1 2 3 4 5 6-150

-100

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Dis

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Strain (%)G30

-7 -6 -5 -4 -3 -2 -1 0 1 2-150

-100

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0

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Dis

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Strain (%)G31

-6 -5 -4 -3 -2 -1 0 1 2 3 4 5-150

-100

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Dis

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(mm

)

Strain (%)G32

Figure A. 1 Strain-Displacement response for IC1

116

-1.5 -1.0 -0.5 0.0 0.5 1.0-150

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Dis

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Strain (%)G17

-2.5 -2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5-150

-100

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0

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150

Dis

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Strain (%)G18

-4 -3 -2 -1 0 1 2-150

-100

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0

50

100

150

Dis

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t (m

m)

Strain (%)G19

-2.5 -2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5-150

-100

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0

50

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Dis

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ent

(mm

)

Strain (%)G20

-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2-150

-100

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0

50

100

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Dis

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t (m

m)

Strain (%)G21

-1.5 -1.0 -0.5 0.0 0.5 1.0-150

-100

-50

0

50

100

150

Dis

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cem

en

t (m

m)

Strain (%)G22

-2.5 -2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0-150

-100

-50

0

50

100

150

Dis

pla

cem

ent

(mm

)

Strain (%)G23

-3.0 -2.5 -2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0-150

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Dis

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(m

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Strain (%)G24


117

-2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0-150

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t (m

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Strain (%)G25

-2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5-150

-100

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0

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150

Dis

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t (m

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Strain (%)G26

-7 -6 -5 -4 -3 -2 -1 0 1 2-150

-100

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0

50

100

150

Strain (%)

Dis

pla

cem

ent

(mm

)

G27

-2.5 -2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5-150

-100

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0

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150

Dis

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(mm

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Strain (%)G28

-20 -15 -10 -5 0 5-150

-100

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50

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150

Dis

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em

ent

(mm

)

Strain (%)G29

-1.0 -0.8 -0.6 -0.4 -0.2 0.0 0.2 0.4 0.6 0.8 1.0 1.2-150

-100

-50

0

50

100

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Dis

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em

ent

(mm

)

Strain (%)G30

-1.5 -1.0 -0.5 0.0 0.5 1.0 1.5-150

-100

-50

0

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Dis

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em

ent

(m

m)

Strain (%)G31

-1.5 -1.0 -0.5 0.0 0.5 1.0 1.5-150

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118

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Strain (%)G17

-1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0-150

-100

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0

50

100

150

Dis

pla

cem

en

t (m

m)

Strain (%)G18

-8 -7 -6 -5 -4 -3 -2 -1 0 1-150

-100

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0

50

100

150

Dis

plac

em

ent

(m

m)

Strain (%)G19

-1.5 -1.0 -0.5 0.0 0.5 1.0 1.5-150

-100

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Dis

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(m

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Strain (%)G20

-7 -6 -5 -4 -3 -2 -1 0 1-150

-100

-50

0

50

100

150

Dis

plac

em

ent

(m

m)

Strain (%)G21

-1.5 -1.0 -0.5 0.0 0.5 1.0-150

-100

-50

0

50

100

150

Dis

pla

cem

en

t (m

m)

Strain (%)G22

-2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5-150

-100

-50

0

50

100

150

Dis

pla

cem

ent (

mm

)

Strain (%)G23

-2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5-150

-100

-50

0

50

100

150

Dis

pla

cem

ent

(m

m)

Strain (%)G24


119

-2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5-150

-100

-50

0

50

100

150

Dis

plac

emen

t (m

m)

Strain (%)G25

-2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0 2.5-150

-100

-50

0

50

100

150

Dis

pla

cem

en

t (m

m)

Strain (%)G26

-4 -3 -2 -1 0 1 2-150

-100

-50

0

50

100

150

Dis

pla

cem

en

t (m

m)

Strain (%)G27

-1.0 -0.5 0.0 0.5 1.0 1.5 2.0 2.5-150

-100

-50

0

50

100

150

Dis

plac

emen

t (m

m)

Strain (%)G28

-4 -3 -2 -1 0 1 2-150

-100

-50

0

50

100

150

Dis

pla

cem

en

t (m

m)

Strain (%)G29

-2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5-150

-100

-50

0

50

100

150

Dis

pla

cem

en

t (m

m)

Strain (%)G30

-2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0-150

-100

-50

0

50

100

150

Dis

pla

cem

en

t (m

m)

Strain (%)G31

-0.8 -0.6 -0.4 -0.2 0.0 0.2 0.4 0.6 0.8 1.0 1.2-150

-100

-50

0

50

100

150

Dis

pla

cem

en

t (m

m)

Strain (%)G32


120

-3.5 -3.0 -2.5 -2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5-150

-100

-50

0

50

100

150

Dis

pla

cem

ent

(mm

)

Strain (%)G17

-3.0 -2.5 -2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5-150

-100

-50

0

50

100

150

Dis

pla

cem

ent

(mm

)

Strain (%)G18

-2.5 -2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5-150

-100

-50

0

50

100

150

Dis

pla

cem

ent

(mm

)

Strain (%)G19

-3.5 -3.0 -2.5 -2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0-150

-100

-50

0

50

100

150

Dis

plac

em

ent

(m

m)

Strain (%)G20

-4 -3 -2 -1 0 1 2-150

-100

-50

0

50

100

150

Dis

pla

cem

en

t (m

m)

Strain (%)G21

-5 -4 -3 -2 -1 0 1-150

-100

-50

0

50

100

150

Dis

plac

em

ent

(m

m)

Strain (%)G22

-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1-150

-100

-50

0

50

100

150

Dis

pla

cem

en

t (m

m)

Strain (%)G23

-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1-150

-100

-50

0

50

100

150

Dis

pla

cem

ent

(m

m)

Strain (%)G24


121

-2.5 -2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5-150

-100

-50

0

50

100

150

Dis

pla

cem

ent (

mm

)

Strain (%)G25

-2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0-150

-100

-50

0

50

100

150

Dis

pla

cem

ent

(mm

)

Strain (%)G26

-1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5-150

-100

-50

0

50

100

150

Dis

pla

cem

en

t (m

m)

Strain (%)G27

-2.5 -2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0-150

-100

-50

0

50

100

150

Dis

pla

cem

ent (

mm

)

Strain (%)G28

-6 -5 -4 -3 -2 -1 0 1 2-150

-100

-50

0

50

100

150

Dis

plac

em

ent

(m

m)

Strain (%)G29

-5 -4 -3 -2 -1 0 1-150

-100

-50

0

50

100

150

Dis

pla

cem

en

t (m

m)

Strain (%)G30

-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2-150

-100

-50

0

50

100

150

Dis

pla

cem

en

t (m

m)

Strain (%)G31

-2.5 -2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0-150

-100

-50

0

50

100

150

Dis

pla

cem

ent (

mm

)

Strain (%)G32


122

-1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0 2.5-150

-100

-50

0

50

100

150

Dis

pla

cem

en

t (m

m)

Strain (%)G17

-1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0 2.5-150

-100

-50

0

50

100

150

Dis

pla

cem

ent (

mm

)

Strain (%)G18

-2 -1 0 1 2 3 4 5-150

-100

-50

0

50

100

150

Dis

pla

cem

ent

(mm

)

Strain (%)G19

-4 -3 -2 -1 0 1 2-150

-100

-50

0

50

100

150

Dis

pla

cem

ent (

mm

)

Strain (%)G20

-4 -3 -2 -1 0 1 2-150

-100

-50

0

50

100

150

Dis

plac

em

ent

(m

m)

Strain (%)G21

-1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0-150

-100

-50

0

50

100

150

Dis

plac

emen

t (m

m)

Strain (%)G22

-1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0 2.5-150

-100

-50

0

50

100

150

Dis

pla

cem

ent

(mm

)

Strain (%)G23

-2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0 2.5-150

-100

-50

0

50

100

150

Dis

pla

cem

ent

(mm

)

Strain (%)G24


123

-2.5 -2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0-150

-100

-50

0

50

100

150

Dis

pla

cem

ent (

mm

)

Strain (%)G25

-12 -10 -8 -6 -4 -2 0 2-150

-100

-50

0

50

100

150

Dis

pla

cem

ent (

mm

)

Strain (%)G26

-8 -7 -6 -5 -4 -3 -2 -1 0 1-150

-100

-50

0

50

100

150

Dis

pla

cem

en

t (m

m)

Strain (%)G27

-2.5 -2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5-150

-100

-50

0

50

100

150

Dis

pla

cem

en

t (m

m)

Strain (%)G28

-2.5 -2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5-150

-100

-50

0

50

100

150

Dis

pla

cem

en

t (m

m)

Strain (%)G29

-3.5 -3.0 -2.5 -2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5-150

-100

-50

0

50

100

150

Dis

plac

emen

t (m

m)

Strain (%)G30

-7 -6 -5 -4 -3 -2 -1 0 1 2-150

-100

-50

0

50

100

150

Dis

pla

cem

en

t (m

m)

Strain (%)G31

-6 -5 -4 -3 -2 -1 0 1-150

-100

-50

0

50

100

150

Dis

pla

cem

en

t (m

m)

Strain (%)G32


124

-4.0 -3.5 -3.0 -2.5 -2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0-150

-100

-50

0

50

100

150

Dis

pla

cem

en

t (m

m)

Strain (%)G17

-8 -7 -6 -5 -4 -3 -2 -1 0 1-150

-100

-50

0

50

100

150

Dis

pla

cem

ent (

mm

)

Strain (%)G18

-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2-150

-100

-50

0

50

100

150

Dis

pla

cem

ent

(mm

)

Strain (%)G19

-2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0-150

-100

-50

0

50

100

150

Dis

pla

cem

en

t (m

m)

Strain (%)G20

-4 -3 -2 -1 0 1 2-150

-100

-50

0

50

100

150

Dis

pla

cem

en

t (m

m)

Strain (%)G21

-2.5 -2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5-150

-100

-50

0

50

100

150

Dis

pla

cem

en

t (m

m)

Strain (%)G22

-5 -4 -3 -2 -1 0 1-150

-100

-50

0

50

100

150

Dis

pla

cem

en

t (m

m)

Strain (%)G23

-8 -7 -6 -5 -4 -3 -2 -1 0 1 2-150

-100

-50

0

50

100

150

Dis

pla

cem

ent (

mm

)

Strain (%)G24


125

-5 -4 -3 -2 -1 0 1-150

-100

-50

0

50

100

150

Dis

pla

cem

en

t (m

m)

Strain (%)G25

-8 -7 -6 -5 -4 -3 -2 -1 0 1 2-150

-100

-50

0

50

100

150

Dis

pla

cem

en

t (m

m)

Strain (%)G26

-6 -5 -4 -3 -2 -1 0 1 2-150

-100

-50

0

50

100

150

Dis

pla

cem

ent

(mm

)

Strain (%)G27

-2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0-150

-100

-50

0

50

100

150

Dis

pla

cem

ent

(mm

)

Strain (%)G28

-4 -3 -2 -1 0 1 2-150

-100

-50

0

50

100

150

Dis

pla

cem

en

t (m

m)

Strain (%)G29

-4 -3 -2 -1 0 1-150

-100

-50

0

50

100

150

Dis

pla

cem

en

t (m

m)

Strain (%)G30

-6 -5 -4 -3 -2 -1 0 1-150

-100

-50

0

50

100

150

Dis

plac

em

ent

(mm

)

Strain (%)G31

-8 -7 -6 -5 -4 -3 -2 -1 0 1 2-150

-100

-50

0

50

100

150

Dis

pla

cem

ent

(mm

)

Strain (%)G32


126

-2.5 -2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0-150

-100

-50

0

50

100

150

Dis

pla

cem

en

t (m

m)

Strain (%)G17

-5 -4 -3 -2 -1 0 1-150

-100

-50

0

50

100

150

Dis

pla

cem

ent

(mm

)

Strain (%)G18

-20 -15 -10 -5 0 5-150

-100

-50

0

50

100

150

Dis

plac

emen

t (m

m)

Strain (%)G19

-3.5 -3.0 -2.5 -2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0-150

-100

-50

0

50

100

150

Dis

pla

cem

ent

(mm

)

Strain (%)G20

-10 -8 -6 -4 -2 0 2-150

-100

-50

0

50

100

150

Dis

pla

cem

en

t (m

m)

Strain (%)G21

-3.0 -2.5 -2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0-150

-100

-50

0

50

100

150

Dis

pla

cem

ent

(m

m)

Strain (%)G22

-5 -4 -3 -2 -1 0 1-150

-100

-50

0

50

100

150

Dis

pla

cem

en

t (m

m)

Strain (%)G23

-8 -7 -6 -5 -4 -3 -2 -1 0 1 2-150

-100

-50

0

50

100

150

Dis

pla

cem

ent (

mm

)

Strain (%)G24


127

-2.5 -2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5-150

-100

-50

0

50

100

150

Dis

pla

cem

en

t (m

m)

Strain (%)G25

-5 -4 -3 -2 -1 0 1-150

-100

-50

0

50

100

150

Dis

pla

cem

ent (

mm

)

Strain (%)G26

-7 -6 -5 -4 -3 -2 -1 0 1-150

-100

-50

0

50

100

150

Dis

pla

cem

en

t (m

m)

Strain (%)G27

-2.5 -2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0-150

-100

-50

0

50

100

150

Dis

pla

cem

ent

(mm

)

Strain (%)G28

-7 -6 -5 -4 -3 -2 -1 0 1-150

-100

-50

0

50

100

150

Dis

pla

cem

en

t (m

m)

Strain (%)G29

-2.5 -2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0-150

-100

-50

0

50

100

150

Dis

pla

cem

en

t (m

m)

Strain (%)G30

-4 -3 -2 -1 0 1-150

-100

-50

0

50

100

150

Dis

pla

cem

ent

(mm

)

Strain (%)G31

-20 -15 -10 -5 0 5-150

-100

-50

0

50

100

150

Dis

pla

cem

ent

(mm

)

Strain (%)G32


128

Appendix B Supplementary Experimental Results

for CFT members

129

-3.0 -2.5 -2.0 -1.5 -1.0 -0.5 0.0 0.5-150

-100

-50

0

50

100

150

Dis

pla

cem

ent

(mm

)

Strain (%)G17

-6 -4 -2 0 2 4 6 8 10-150

-100

-50

0

50

100

150

Dis

pla

cem

ent

(mm

)

Strain (%)G18

-5 -4 -3 -2 -1 0 1-150

-100

-50

0

50

100

150

Dis

pla

cem

ent

(mm

)

Strain (%)G19

-20 -15 -10 -5 0 5-150

-100

-50

0

50

100

150

Dis

pla

cem

en

t (m

m)

Strain (%)G20

-5 -4 -3 -2 -1 0 1-150

-100

-50

0

50

100

150

Dis

pla

cem

en

t (m

m)

Strain (%)G21

-5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8-150

-100

-50

0

50

100

150

Dis

pla

cem

en

t (m

m)

Strain (%)G22

-5 -4 -3 -2 -1 0 1-150

-100

-50

0

50

100

150

Dis

pla

cem

en

t (m

m)

Strain (%)G25

-6 -4 -2 0 2 4 6 8 10 12-150

-100

-50

0

50

100

150

Dis

pla

cem

en

t (m

m)

Strain (%)G26

Figure B. 1 Strain-Displacement response for SY0 (Cont’d)

130

-5 -4 -3 -2 -1 0 1-150

-100

-50

0

50

100

150

Dis

pla

cem

en

t (m

m)

Strain (%)G27

-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2-150

-100

-50

0

50

100

150

Dis

pla

cem

en

t (m

m)

Strain (%)G28

Figure B. 1 Strain-Displacement response for SY0

131

-6 -5 -4 -3 -2 -1 0 1-150

-100

-50

0

50

100

150

Dis

pla

cem

en

t (m

m)

Strain (%)G17

-15 -10 -5 0 5 10-150

-100

-50

0

50

100

150

Dis

pla

cem

en

t (m

m)

Strain (%)G18

-5 -4 -3 -2 -1 0 1 2 3-150

-100

-50

0

50

100

150

Dis

pla

cem

ent (

mm

)

Strain (%)G19

-12 -10 -8 -6 -4 -2 0 2-150

-100

-50

0

50

100

150

Dis

pla

cem

ent

(m

m)

Strain (%)G20

-2 -1 0 1 2 3 4-150

-100

-50

0

50

100

150

Dis

plac

em

ent

(m

m)

Strain (%)G21

-5 -4 -3 -2 -1 0 1-150

-100

-50

0

50

100

150

Dis

pla

cem

ent

(mm

)

Strain (%)G22

-5 -4 -3 -2 -1 0 1-150

-100

-50

0

50

100

150

Dis

pla

cem

en

t (m

m)

Strain (%)G25

-4 -2 0 2 4 6 8 10 12-150

-100

-50

0

50

100

150

Dis

pla

cem

en

t (m

m)

Strain (%)G26

Figure B. 2 Strain-Displacement response for SY1 (Cont’d)

132

-5 -4 -3 -2 -1 0 1 2-150

-100

-50

0

50

100

150

Dis

pla

cem

ent

(mm

)

Strain (%)G27

-8 -6 -4 -2 0 2 4-150

-100

-50

0

50

100

150

Dis

pla

cem

ent (

mm

)

Strain (%)G28


133

-3.0 -2.5 -2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0-150

-100

-50

0

50

100

150

Dis

pla

cem

en

t (m

m)

Strain (%)G17

-4 -2 0 2 4 6 8-150

-100

-50

0

50

100

150

Dis

plac

emen

t (m

m)

Strain (%)G18

-3 -2 -1 0 1 2 3-150

-100

-50

0

50

100

150

Dis

plac

emen

t (m

m)

Strain (%)G19

-20 -15 -10 -5 0 5-150

-100

-50

0

50

100

150

Dis

pla

cem

en

t (m

m)

Strain (%)G20

-4 -3 -2 -1 0 1 2-150

-100

-50

0

50

100

150

Dis

pla

cem

en

t (m

m)

Strain (%)G21

-15 -10 -5 0 5 10-150

-100

-50

0

50

100

150

Dis

pla

cem

en

t (m

m)

Strain (%)G22

-1 0 1 2 3 4 5-150

-100

-50

0

50

100

150

Dis

pla

cem

en

t (m

m)

Strain (%)G23

-12 -10 -8 -6 -4 -2 0 2-150

-100

-50

0

50

100

150

Dis

pla

cem

ent (

mm

)

Strain (%)G24 Figure B. 3 Strain-Displacement response for SY2 (Cont’d)

134

-0.5 0.0 0.5 1.0 1.5 2.0 2.5-150

-100

-50

0

50

100

150

Dis

pla

cem

en

t (m

m)

Strain (%)G25

-12 -10 -8 -6 -4 -2 0 2-150

-100

-50

0

50

100

150

Dis

plac

emen

t (m

m)

Strain (%)G26

-4 -3 -2 -1 0 1-150

-100

-50

0

50

100

150

Dis

pla

cem

ent (

mm

)

Strain (%)G27

-4 -2 0 2 4 6 8-150

-100

-50

0

50

100

150

Dis

plac

emen

t (m

m)

Strain (%)G28


Documents

INELASTIC PERFORMANCE OF STEEL/CONCRETE COMPOSITE … · This thesis deals with the behaviour of Partially Encased Composite (PEC) and Concrete Filled Tubes (CFT) subject to cyclic