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Kabir, Md, Fawzia, Sabrina, Chan, Tommy, Gamage, J.C.P.H., & Bai, J.(2016)Experimental and numerical investigation of the behaviour of CFRPstrengthened CHS beams subjected to bending.Engineering Structures, 113, pp. 160-173.

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https://doi.org/10.1016/j.engstruct.2016.01.047

1

Experimental and Numerical Investigation of the Behaviour of CFRP Strengthened CHS Beams Subjected

to Bending M. H. Kabir a,, S. Fawzia a*, T.H.T. Chan a, J.C.P.H. Gamage b, J.B. Bai c

a School of Civil Engineering and Built Environment, Faculty of Science and Engineering, Queensland

University of Technology, 2 George Street, Brisbane, QLD 4000, Australia, Email: sabrina.fawzia@qut.edu.au b Department of Civil Engineering, University of Moratuwa, Sri Lanka.

c Laboratory MSS/MAT, CNRS UMR 8579, Ecole Centrale Paris, 92295 Chatenay Malabry, France

Abstract

This paper presents the results of an experimental and numerical program to investigate the

circular hollow section (CHS) beams, strengthened using Carbon Fibre Reinforced Polymer

(CFRP) sheets. The circular hollow shaped steel beams bonded with different CFRP layer

orientations were tested under four-point bending. The mid-span deflection, service load and

failure load were recorded. The LHL (where L, first inner longitudinal layer, H, second hoop

layer and L, third outer longitudinal layer) and LLH (where L, first inner longitudinal layer,

L, second longitudinal layer and H, third outer hoop layer) layer oriented strengthened beams

perform slightly better than HHL (where H, first inner hoop layer, H, second hoop layer and

L, third outer longitudinal layer) layer oriented strengthened beams. The LHL and LLH layer

oriented treated beams showed very similar structural behaviour. Numerical analyses were

then conducted on the CFRP strengthened steel CHS beams. The validity of the models has

been assessed by comparing the failure loads and mid-span deflections. The effects of various

parameters such as bond length, section types, tensile modulus of CFRP, adhesive layer

thickness and adhesive types have been studied.

Keywords: CHS; CFRP; strengthened; layer orientation; numerical investigation; bending

Nomenclature

ARK630 araldite K630

BL bond length

COV coefficient of variance

df orthotropic ply damage parameter in fibre direction

dm orthotropic ply damage parameter transverse to fibre direction

2

ds orthotropic ply damage parameter in shear direction

Ea elastic modulus of adhesive

Ei elastic modulus of fibres in i direction

Exp experiment

FE finite element

G with GFRP

Ga shear modulus of the adhesive

Gcmax maximum fracture energy

Gn fracture energy in normal direction

Gs, Gt fracture energy in shear directions

Gij shear modulus

GT1C or GC

1C mode I Fracture energy in fibre direction

GT2C or GC

2C mode II Fracture energy in transverse direction

ID identification

Knn elastic stiffness of the adhesive in normal direction

Kss, Ktt elastic stiffness of the adhesive in shear directions

LCFRP length of bonded CFRP

Le effective span

MBr MBrace saturant

Nuij poisson’s ratio

OD outer diameter

PFE ultimate load determined from FE analysis

PL point load

Ps(cs) service load of the strengthened beams

Ps(s) service load of the unstrengthened beams

Pu(cs) ultimate load of the strengthened beams

Pu(s) ultimate load of the unstrengthened beams

Pult ultimate load from experimental test

SKD330 sikadur 330

SL or ST ultimate in-plane strength shear directions respectively

t thickness

tn nominal stress normal mode only

ts, tt nominal stresses shear directions

tn0 peak value of nominal stress in normal direction

3

ts0, tt0 peak values of nominal stress in shear directions

T0 thickness of the adhesive

Ui linear displacement in i direction

US unstrengthened

URi rotation in i direction

XT or XC ultimate in-plane strength in fibre direction

YT or YC ultimate in-plane strength in transverse direction

δn normal separation

δs, δt separation in shear directions

εn strain in normal direction

εs, εt strain in shear directions

εn0 peak nominal strain in normal direction

εs0, εs

0 peak nominal strain in shear directions

1. Introduction

In some especial cases such as compression, torsion and bending in all directions, aesthetic

demand, corrosion resistance due to absent of sharp edge and fire protection capability by

pouring water inside the tube, the tubular shape hollow members perform better than other

open sections [1]. Therefore, the application of such members has been increasing

dramatically for building various onshore and offshore structures. In offshore structures,

circular hollow section is mainly used to form jacket structures which sometimes subjects to

bending due to wave force [2]. A large number of such structures are sometimes found

structurally inadequate due to design errors, loss of material properties, exposure to severe

environments, or increase in service loads. This degradation phenomenon draws a great

attention to the engineers for strengthening or rehabilitation of metallic structures.

There are many advantages of using CFRP materials for strengthening and rehabilitating of

bridges and structures. The high durability and fatigue endurance, superior strength-to-weight

ratio, costs saving through labour savings, flexibility to form all kind of shapes of these

materials enable them to compete easily with other traditional strengthening materials in this

field [3-5]. After having the initial success of using CFRP to concrete structures [6-8], the use

of CFRP composites for strengthening and rehabilitating work has been prolonged to timber

and masonry and more recently also metallic structures. Several field applications of

composites materials have been reported in [9, 10], where mostly steel bridges have been

4

strengthened using adhesively bonded CFRP composites. A satisfactory number of

experimental works have been conducted to strengthened open and close steel sections using

various numbers and orientations of CFRP layers [2, 11-25]. Their results have shown that the

combination of two materials, CFRP and steel, has found to increase strength, stiffness,

ductility and structural performance of strengthened systems. Some of the studies also have

shown that the number and the orientation of CFRP layers affect the strength of the sections

primarily when they are subjected to compression and bending. From the durability point

view, the current study has used LHL layers orientation (where L is the longitudinal layer and

H is the hoop layer) of CFRP to strengthened CHS member and tested under bending. The

reasons of selecting LHL layers and treating the surface with primer have been clearly

mentioned in one of the authors’ published works [26]. The experimental works are

considered to be satisfactory, and yet, not many numerical studies have been done yet for

adhesively bonded CFRP structures to simulate the real experimental works. Considering time

and cost of the experimental testing, finite element (FE) techniques offer the opportunity to

develop a numerical model, which would accurately predict the failure or damage mechanism

of the structures in a relatively short time. The complicated composite behaviour of the

structures has been simulated by several researchers under bending, tension and impact

loadings [10, 13, 27-33]. Their studies dealt with mainly hollow columns, H and I shape steel

beams, double strap joints and orthotropic damage models. Various techniques of material

models were deployed. It was reported that the damage mechanism mainly depends on the

model of composites and adhesives. According to aforementioned literatures, continuum shell

for CFRP composites and cohesive model for adhesive are able to predict real damage of the

structures with delamination of CFRP. There are no research has been found yet to present the

numerical model of CFRP strengthened circular hollow steel members under bending. It is

common that the strength capacity varies from section to section for circular steel hollow

members. Hence, it is very urgent to do more numerical models for different types of section

to minimise cost and time and to guide the engineers. To overcome this gap in knowledge,

this paper aims to investigate the numerical simulations with various types of parameters of

CFRP strengthened circular hollow section members under bending. The results from

numerical simulations have been validated with experimental findings.

5

2. Experimental Investigation

2.1. Material properties

The modulus of elasticity, tensile strength and tensile strain of steel, CFRP and GFRP were

determined experimentally by coupon test. The material properties for these three materials

are listed in Table 1.

2.2. Test specimens

The test specimens including total of ten steel tubes with circular cross-sections of 101.6 mm

outer diameter and 4.0 mm thickness were cut into required size. The length of the circular

member was chosen 1300 mm and the effective span was considered 1200 mm for a four-

point bending test. Fig. 1 shows the schematic diagram of the test set-up with all dimensions

being in mm.

2.3. Specimen preparation

It is very important to have a properly prepared surface of the steel substrate for the success of

steel/CFRP strengthening system. Solvent cleaning, grit blasting, sand blasting and surface

grinding are the most common methods to prepare steel surface [12, 23, 34-38]. Among these,

grit or sand blasting method has been proven to be most effective method to get uniform high

energy surface [12, 23, 34, 36, 38]. A uniform high energy surface indicates that the energy

exerted by the surface will be almost similar on the whole area to be bonded with CFRP

patch. When a substrate, steel tube in this study, has a high surface energy, it tends to attract

other material (adhesive and CFRP) significantly. As a result, a perfect bond between

substrate and CFRP patch is achieved. The surface preparation generally involves cleaning,

followed by removal of weak layers and then re-cleaning [39, 40]. The current study was

involved a large amount of surface to be prepared. Therefore, the relatively cheap and locally

available sand blasting method was deployed. The garnet abrasive system (grit no. 30/60) was

used for sandblasting. The grit size varies from 600 to 250 micron which results the average

size of the grit 0.425 mm and it was between the range used by Teng et al [23]. Then the sand

blasted surface was cleaned by washing with acetone to remove the weak layer, deposited

dust particles and grease [41]. At this stage, two strain gauges were attached to specially

cleaned surface on top and bottom of steel beam at mid-length where the maximum bending

moment occurred to record the compressive and tensile strains.

The acetone cleaned surface of the eight specimens was then treated with adhesion promoter

prior to applying epoxy adhesive and allowing it to dry for approximately 1 hour. Then the

6

two part impregnated epoxy adhesive was mixed according to manufacturer guidelines [42]

and applied on primed steel surface during its pot life. The CFRP sheet was cut into the

required dimensions oriented longitudinally, horizontally and longitudinally to the length of

the beam was directly applied on top of the adhesive layer. For two identical specimens (S3A-

1), an additional Glass Fibre Reinforced Polymer (GFRP) layer oriented longitudinally was

embedded in adhesive before applying CFRP sheet. The embedded GFRP layer acts as a

barrier to protect galvanic corrosion when exposed to wet environment. A rib roller was run

immediately to press the fabric along the fibre direction against the substrate until visual signs

of adhesive were observed bleeding through the fabrics. It helps the fabrics to form a plate

after getting desired shape. The whole procedure was done on the wet surface which implies

the top surface of the lower layer remained still sticky. To achieve a uniform and high quality

bond, masking tape was wrapped around the circumference of the CFRP wrapped area and

kept for a period of at least 24 hours (Fig. 2a). Then the masking tape was removed and the

finished specimens (Fig. 2b) were cured for about two weeks under ambient temperature to

ensure full curing.

2.4. Test set-up and instrumentation

A 230 kN controlled MTS actuator was used to do the tests of the CHS beams. All the tests

were performed under four-point bending with simply supported condition. Fig. 3 shows the

test set-up with apparatus. The load was applied as a displacement control ‘static compression

load’ at a constant rate and was continued up to failure of each specimen. Two string pots

were placed at the centre of the beams to measure the average mid-span deflection of the

specimens. Two additional LVDTs were mounted on top of the supports to measure support

displacement. The actual deflection of the beams was determined by deducting support

displacement from mid-span displacement.

3. Experimental Results

Two specimens were tested for each group and the difference of service and ultimate load

between them was very close. The service load was taken at deflection Le/250 in accordance

with AS 3600 [43] for all members not supporting articulated brittle partitions and failure

loads for all the beams. The ultimate load was considered as the maximum load taken by the

beams during four-point bending test. Since the differences of service and ultimate loads

between two identical specimens were very marginal, the worst case scenario for both loads

has been discussed for each group in the results section as well in the finite element section.

7

3.1. Failure modes of the tested beams

Fig. 4 shows the failure modes of the tested unstrengthened and strengthened beams with

various layers orientation. Typical ductile modes of failure were displayed by all the

specimens during testing. It can be seen that (Fig. 4) the failure occurred to both LHL and

LLH layer oriented beams due to local buckling of the tubular hollow section in the

compression zone near the loading points where the crushing of fibre layers was found as

well. Though the failure occurred to both beams due to local buckling of the section near the

loading points in the compression zone, the load-strain (tensile strain of steel section at mid

length of beam) curves (see Fig. 5) show that the full capacity of the section was utilized

during failure. It was also noticed that a minor debonding occurred at tension face of both

ends. It may happen due to high stress concentrations at ends. The CFRP composites in

tension face remained intact. However, the failure modes for the strengthened beams with

HHL layers orientation were totally different and it failed due to complete rupturing of CFRP

at middle of tension face and yielding of steel at middle of tension face as well. The fibres at

compression face also crushed and steel also yielded. No end de-bonding was found for HHL

layers oriented beams until failure. This change of failure mode is interesting. However, it can

be said that this different failure mode may happen due to replacing one longitudinal layer by

one hoop layer of CFRP composites.

3.2. Failure load

Table 2 shows the service and failure loads for all the beams. The corresponding ratios of

service and ultimate loads of the strengthened specimens Ps(cs) and Pu

(cs) relative to

unstrengthened steel beam Ps(s) and Pu

(s) tested under bending are also shown (Table 2). It can

be seen that the ratios of service and ultimate loads for LHL layers oriented strengthened

beams is higher than that of HHL layers oriented beams.

The three layers of CFRP configuration with various layer orientation helps to increase the

ultimate strength through the effective use of the longitudinal fibre strength and restraining

action of hoop-oriented fibres as shown in Fig. 6. The strengthened techniques (LHL, HHL

and LLH) adopted in the current study for compact section were able to increase ultimate load

to maximum of 33.0%, 37.0%, 30.0% and 33.0% for LHL, LHL (embedded GFRP), HHL and

LLH respectively in oriented beams compared to the unstrengthened beam. Similarly, the

load resistance at service has increased about 45.0%, 53.0%, 42.0% and 50.0% for LHL, LHL

(embedded GFRP), HHL and LLH respectively. It is interesting to see that the GFRP

8

embedded LHL layer oriented beam shows higher ultimate and service load than the LHL

layer oriented beam without embedded GFRP. It may have happened due to additional

sectional properties contributed by the embedded GFRP layer. However, a previous study

conducted by Haedir et al. [17], shows maximum strength gain at ultimate state is about 3%

for compact tubular section (OD = 33.81 mm, t = 2.70 mm similar CFRP used in the current

study) strengthened using HHL combination of CFRP and tested under four-point bending. In

another study [2], the maximum increment of ultimate load was 27% for strengthened

compact tubular hollow steel member (OD =168.5, t = 4.9 mm and CFRP used is Tyfo with

average tensile strength of 500 MPa and tensile modulus of 62500 MPa respectively, where in

the combination of CFRP were used as LLH and tested under four-point bending condition.

Therefore, strength increment for strengthened beam without embed GFRP was found 6%

more than the previous study. This higher strength capacity may have appeared due to bond

enhancement which may be contributed by pre-treated surface and uniform pressure exerted

by wrapped masking tape during initial curing stage.

The beams S5B-1 and S6B-2 which had LHL and LLH fibres orientation were slight stronger

than the beam S6B-1 with HHL layers of CFRP composites. It may have appeared due

presence of less number of longitudinal layer in HHL layers oriented beam. It is interesting to

see that both beams S5B-1 and S6B-2 perform similar way in term of load enhancement.

Finally the GFRP embedded LHL layers oriented beam performed better than all other beams

with the highest strength gain.

3.3. Mid-span deflection

The load-deflection responses of unstrengthened and strengthened beams with various fibres

layer orientations are shown in Fig. 7. It can be seen that all the strengthened beams with

various layer orientations display higher stiffness than that of unstrengthened beam B2

starting from around 40 kN load until the end of the test. This stiffness increment is the good

agreement with that measured experimentally by Seica and Packer [2] for CFRP strengthened

HHL fibres oriented compact tubular members tested under bending.

It is observed that (Fig. 7) the strengthened beams with various fibre layer orientations display

similar deflection trend and linear-elastic behaviour until around 78 kN load is attained and

then the deflection trend alternates to inelastic behaviour. The identical deflecting trend is

further continued up to 100 kN load for LHL and LLH layer oriented beams S5B-1, S3A-1

and S6B-2. It is noted that the beams S5B-1, S3A-1 and S6B-2 show stiffer behaviour than

9

beam S6B-1 in the plastic zone until the first sudden drops of stiffness where the sudden

debonding or rupture of CFRP composites occurs. However, the first sudden drop of stiffness

for beam S6B-1 delays and then it shows higher deflection than LHL and LLH layers oriented

beams. The LHL and LLH layers oriented beams S5B-1 and S6B-2 without embedded GFRP

show negligible difference in stiffness after a final noticeable drop of stiffness till to the

recorded values of deflection. In addition, the LHL layers oriented beam S3A-1 with

embedded GFRP shows a slight stiffer behaviour in elastic zone and this variation becomes

more evident at higher load in higher deflection. This may have happened due to additional

strength provided by embedded GFRP.

4. Finite element model

Finite element (FE) models were developed using the commercially available finite element

package ABAQUS version 6.12-2. The models were with the same configurations of the

tested beams as given in Fig. 8, where U is the linear displacement, and UR denotes the

rotation. Firstly, the FE models were validated by experimental results and later the effects of

different parameters such as the bond length, section variation, CFRP modulus of elasticity,

adhesive thickness, types of adhesives and loading conditions were studied. The Newton-

Raphson incremental iterative solution method was used to determine the response of the

beams.

4.1. Element types and mesh density

Various types of elements are available in the finite element package, ABAQUS software.

Four materials including steel, adhesive, CFRP and GFRP patches are modelled as four

different part instances. Three different types of elements are used to designate these part

instances since CFRP and GFRP patches are considered as similar type of element

(continuum shell). The steel tube component is modelled using 8-node 3-D solid element

(C3D8H), hybrid with constant pressure while the adhesive layers between the fibre layers are

modelled using the eight-node three-dimensional cohesive elements COHD8 that are useful in

modelling adhesives, bonded interfaces, gaskets and rock fracture [44]. The CFRP and GFRP

patches are meshed with an 8-node quadrilateral in-plane general-purpose continuum shell,

reduced integration with hourglass control, finite membrane strains (SC8R). This type of

element is capable of predicting CFRP failure [32, 45]. In addition, the continuum shell

element allow a full three dimensional model and they are more attractive in computation than

the standard brick elements because of capturing through-the-thickness shear stress without

using one element per layer [45, 46]. Finally, the three dimensional thick shell geometry leads

10

to improve accuracy in resolving contact problems. The computational time was reduced by

introducing 10 mm mesh for steel tube, 4 mm mesh for adhesive layers and 10 mm mesh for

CFRP and GFRP respectively. The connections between steel surface and adhesive surface

and between adhesive surface and CFRP composite surface are achieved by tie constraints.

Steel tube and CFRP composite are considered as master surface and adhesive is considered

as slave surface for tying purpose.

4.2. Steel tube model

The steel tube is modelled as a classical elastic-plastic metal with isotropic hardening. The

experimental stress-strain curve of the steel was adopted in FE model to represent the material

behaviour.

4.3. Adhesive model

It is very important to model adhesive layers appropriately between steel and CFRP patch or

between CFRP patch itself to capture the delamination of bond laminate. The cohesive zone

model (CZM) approach adopted to model the constitutive behaviour of adhesive layers. The

cohesive elements are more realistic and practical to model the behaviour of adhesive joints,

interfaces in composites and any situation where the integrity and strength of interfaces may

be of interest [44]. Cohesive elements are also capable of simulating damage and

delamination in composites [31, 32, 47]. Hence, in this study, the adhesive layers are

modelled as cohesive elements with fracture mechanics constitutive definitions. A triangular

traction-separation cohesive law with linear softening is used to characterize the material

behaviour of the adhesive because of having very thin layers of adhesive in composites. In

this case the macroscopic material properties are not relevant directly and it obvious to derive

concepts from fracture mechanics [44]. The mixed mode cohesive law considers all the three

components of stresses, which are one normal component and two shear component. These

components are denoted by tn, ts and tt respectively, while the corresponding separations are

presented by δn , δs and δt respectively.

It is assumed that the cohesive elements behave linear-elastically until the initiation of

damage [48, 49]. The elastic behaviour can be written as

(1)

=

t

s

n

tt

ss

nn

t

s

n

KK

K

ttt

δδδ

000000

11

It can be said that Knn will be equal to the initial slope of the bond-separation model for mode

I loading and can be expressed by

(2)

where Ea is the elastic modulus of adhesive determined by coupon test and To is the original

thickness of the adhesive layer.

Kss and Ktt are assumed to be the same, and should be equal to the initial slope for mode II

loading [48] and they can be written as

(3)

where Ga is the shear modulus of the adhesive. Due to absence of experimental data, a simple

relation may be used for the initial approximation of shear modulus. Although this relation is

developed for homogeneous isotropic materials. The relation can be expressed as

(4)

where ν is the Poisson’s ratio of adhesive.

The initial stiffness parameters, Knn, Kss, and Ktt can not be measured directly through the

experiment; however the eqs. 3 and 4 also give a reasonable initial approximation for K.

Therefore, in order to find a reasonable estimation of K, various numerical simulations with

different K values need to be compared to the experimental results [47]. The stiffness of the

cohesive elements should be large enough to provide reasonable stiffness but also not so large

to cause oscillations in interfacial traction of the element. In the current study reasonable

approximations are made for undetermined properties of materials to match the results with

experimental results and these values were constant for all specimens. These approximations

are made for stiffness parameters (Knn, Kss, and Ktt) and fracture energies (Gn, Gs and Gt) of

adhesives as shown in Table 3.

The cohesive elements are able to represent the failure of adhesive include crack initiation and

propagation. The damage criteria has been clearly presented by Teng et al. [50]. There are

four built-in failure criteria for damage initiation under traction separation law in ABAQUS

library. These are maximum nominal stress criterion, maximum nominal strain criterion,

0TEK a

nn =

65.0

0

3

==

TGKK a

ttss

( )ν+=12EaGa

12

quadratic nominal stress criterion and quadratic nominal strain criterion. The first two criteria

assume that the adhesive damage initiate when the maximum nominal stress or strain reaches

the maximum capacity of the adhesive. These criteria can be represented as

(5)

(6)

The last two criteria consider the combination effect of stresses and strains and it is assumed

that the damage initiate when a quadratic interaction function involving the nominal stresses

or strain ratios reaches a value of one. These criteria can be represented as

(7)

(8)

It has been reported that under mixed-mode loading, the adhesively bonded joints are

subjected to complex state of stress (normal stress and shear stress) and these stresses

contribute to adhesive failure [50, 51]. Therefore, the current study considers the mixed mode

failure criteria which is the quadratic traction damage criterion (QUADS) as shown in eq. 7

for both mode I and mode II loading. To define this QUADS damage criterion in ABAQUS,

nominal stress (tn) in normal mode only, nominal stress (ts) in first shear direction and

nominal stress (tt) in second shear direction are required as input values. In the current study,

nominal stress in normal mode and shear directions are considered similar. The other three

parameters, 0nt

0st and 0

tt are the peak values of the nominal stress in normal, first and second

shear directions of adhesive layer which are generated by ABAQUS during running of the FE

model. Nominal strain values can be found from coupon test.

4.4. CFRP model

In adhesively-bonded composite materials, the failure generally occurs either in the patching

materials or the bonding materials, or both. The ABAQUS software is able to capture the

damage and failure of the fibre reinforced polymer composites by using the available

materials model in it as discussed in sub-section 4.1. By implementing this material model in

ABAQUS, the damage initiation and propagation of an elastic-brittle material with an

12

0

2

0

2

0 =

+

+

t

t

s

s

n

n

tt

tt

tt

12

0

2

0

2

0 =

+

+

t

t

s

s

n

n

εε

εε

εε

1,,max 000 =

t

t

s

s

n

n

tt

tt

tt

1,,max 000 =

t

t

s

s

n

n

εε

εε

εε

13

isotropic behaviour such as unidirectional normal modulus carbon fibre reinforced polymer

(CFPR) fabrics can be achieved [52]. The material model for CFRP fabrics depends on

continuum damage mechanism and in-built Hashin damage criteria in ABAQUS [44]. In

Hashin damage model, the plasticity of the CFRP is always neglected and damage is detected

and characterised based on material stiffness reduction. The damage of the CFRP layer

initiates due to four main failure criteria, namely: fibre rupture in tension, fibre bucking in

compression, matrix cracking under transverse tension and shearing, and matrix crushing

under transverse compression [47]. Damage propagates when the fracture energy (damage

variable) in any of the four mentioned criteria reaches its maximum value (Gcmax) which can

be specified as an input parameter as longitudinal tensile and compressive fracture energy,

transverse tensile and compressive fracture energy in ABAQUS. Once damage initiates, three

non-negative in-ply parameters, df, dm and ds reduce the ply stiffness numerically in fibre,

transverse and shear direction respectively, until the final failure point is reached [47]. Hence,

to provide a more accurate validation of the numerical model with experimental results, the

CFRP composite damage is considered in the current study. The parameters used in

ABAQUS to facilitate Hashin damage criteria are longitudinal tensile and compressive

strength which represent ultimate tensile and compressive strength (XT and XC) of CFRP in

fibre direction, transverse tensile and compressive strength which represent ultimate tensile

and compressive strength (YT and YC) of CFRP in transverse direction.

5. Material properties in FE analysis

The tensile strength, strain and modulus of elasticity for steel, CFRP and adhesive are taken

form experimental data. The steel tubes had an average yield stress of 327 MPa, an ultimate

strength of 383 MPa and the modulus of elasticity was about 214 GPa confirmed by coupon

test. The properties for all the other elements used in FE model are listed in Tables 3 to 6. The

tensile tests of the CFRP composites patch were performed and peak failure strength and

tensile modulus were directly input to the FE model. The compressive strength of CFRP patch

was considered a 20% of the average tensile strength. For the interlaminar damage model, the

fracture energies associated with the various damage mechanism and all other properties used

in FE were initially approximated for numerical computations [27, 31, 45, 47, 53]. To

determine the undetermined damage properties of adhesive and CFRP at structural level, the

numerical models were run several times until the best validation were achieved.

14

6. Validation of the numerical model

The numerical simulation has been carried out based on the above FE model and the results

obtained from numerical analysis were standardized against the corresponding experimental

data. The ultimate load, load-deflection curves and failure mode of the unstrengthened and

composite beams having various layers orientation executed by FE models are compared with

the experimental results.

6.1. Ultimate load

A clear comparison of the experimentally measured ultimate load and those executed from FE

analyses for unstrengthened and strengthened control beams can be seen in Table 7. It can be

seen that the (PFE/Pult) ratios of ultimate load determined from FE analyses and experimental

tests varies from 0.97 to 1.03 which are very close to unity. Moreover, the COV of ultimate

load are very minimal and it varies from 0.002 to 0.022. Thus, it can be said that the

numerical models have been validated reasonably by showing very close values of ultimate

loads to that of the experimental values.

6.2. Mid-span deflection

Figs. 9-11 show the comparison between load vs deflection measured experimentally and

numerically for the unstrengthened and strengthened beams. It can be seen that the numerical

results and experimental data match very well until failure of the beams. Nonetheless, the load

drops are observed experimentally in Figs. 10 and 11 which are common for CFRP

strengthened steel structures [2, 54]. The current FE model developed using ABAQUS

software is not able to show this sudden drop of load which agrees with the model presented

by Teng et al. [50]. This sudden drop may have happened due to fracture of CFRP composite

which has not been depicted in the current model.

6.3. Failure mode

The failure modes of FE analyses models are found similar with the tested unstrengthened

beams and strengthened beams with LHL and LLH layer orientation of CFRP as shown in

Fig. 12. However, the failure mode of HHL layer oriented strengthened beam monitored

experimentally is slightly different from failure mode predicted experimentally. This is

because the experiment was done by deflection control of the MTS actuator and the test was

continued up to the end level of actuator. For HHL layer oriented beam, the failure mode was

captured at the end of test but the failure occurred at earlier stage of loading. Therefore, the

15

excessive bending can be seen in Fig. 12 for HHL layer oriented tested beam. Although, this

layer combination is not considered for later parametric study in this paper.

7. Parametric study

It is common that some strengthening parameters such as bond length, type of tubular section,

CFRP modulus of elasticity, adhesive thickness and adhesive type may have effects on the

strength of the strengthened beams. To understand the effects of these parameters, a range of

parametric study has been conducted using the corresponding validated FE models. The

parametric study is performed for LHL layer oriented strengthened beam only. The LHL layer

combination performs slightly better than HHL layer combination in terms of strength and

stiffness. The LHL and LLH layer combination show very similar structural behaviour. In

structural application under bending, both LHL and LLH layer combination can be used.

However from theoretical point of view, under tension the outer L is stronger than outer H

layer and hence H layer may elongate more than L layer. At this situation, the H layer may

allow more moisture infiltration especially when it goes in wet environment. In the case of FE

analysis, it can be seen that (see Table 7) the LHL layer oriented strengthened beam shows

higher ultimate load than other layer oriented beams, although the difference is not

significant. Therefore, the LHL layer combination is proposed in the current study for

considering durability in wet environment.

7.1. Bond length

Based on the test set-up (Fig. 8), the bond length is considered from loading points to the

supports points. This is one of the most important strengthening parameters that could be

much more easily changed in civil engineering practise and could affect the cost of the

project. The main objective of this section is to find the structurally sound but cost effective

bond length and this bond length will be continued for further parametric studies. The effects

of bond length are shown in Figs. 13 to 15 and Table 8.

It can be seen that (Fig. 13) as the bond length increases the strengthened beam become stiffer

and the degree of stiffness is more prominent in plastic zone and is less prominent in elastic

zone. It can also been seen that (Fig. 14) the debonding effect is becoming more evident with

decreasing of bond length. It means that the stress intensity decreases near the debonding area

with the increase of bond length as can be seen in Fig 15.

16

The loads of the beams at failure for different bond lengths are shown in Table 8. It can be

seen that the bond failure load increases with the increase of bond length and reaches to

maximum at 300 mm bond length. In addition, as the bond length increases from 100 to 300

mm, it is found that the relative load increment is minimal when the bond length approaches

to maximum length. Based on these observations from FE results, it can be concluded that the

increase in bond length is one of the most effective measures to enhance bond failure

resistance capacity of CFRP strengthened steel circular hollow beams. This parametric study

has been conducted to find out the cost effective bond length with reasonable strength

increment. Therefore, 200 mm bond length is selected as cost effective bond length with

reasonable strength increment based on the available dimension of CFRP, although the

effective bond length can be considered as 250 mm as shown in Fig. 13.

7.2. Section types

In this section ten different sections with various diameter-thickness ratios available in

Australia are studied using FE results for LHL layers oriented strengthened beams without

embedded GFRP. The effects of welded end plate are also discussed.

Fig. 16 shows the effect of welded plate at end on failure mode of the strengthened beams

having two different section properties. In case of the larger section (OD =165.0, t = 5.4 mm),

the strengthened beam without welded plate fails by local buckling of the wall at the supports,

while the beams with welded plate at end fails by local buckling of the tube wall near or

below the loading points which is similar to experimental failure mode for LHL layers

oriented beam as shown in Fig. 4. On the other hand, failure modes are similar for beams

having smaller section (OD =101.6, t = 4.0 mm) with and without welded plate at end.

Therefore, it can be said that for smaller section welded end plate is not mandatory whereas

welded end plate is mandatory for larger section to overcome local buckling at support.

It is interesting to see that (Table 9) the strength increment for different sections compared to

corresponding unstrengthened sections is not equal although the wrapping scheme and the

material properties are similar. It varies from 3.35% to 28.80% for strengthened beams

without out welded plate at ends. It can be seen that the strength increment is not significant

(3.25% and 4.26%) for sections with higher diameter and without welded plate at ends. It may

happen due to complete collapse of the tube section at supports before utilizing the full

contribution of CFRP as shown in Fig. 16a. In the case of strengthened beams with welded

plate at ends, the strength increment varies from 7.08% to 28.13%. Therefore, from these

17

observations, it can be concluded that the percentage of strength increment for a particular

section cannot be used for other sections having different outer diameter and thickness.

Hence, the proposed FE model is capable of predicting strength increment for different

sections strengthened using LHL layers oriented CFRP composites when the material

properties are known.

Table 9 also shows the variation of strength increment for strengthened beams with and

without welded plate at ends. It can be seen that this variation is significant for cross-sections

having diameter ranges from 165.0 mm to 140.0 mm. However, for the cross-sections having

diameter ranges from 114.0 mm to 90.0 mm show negligible difference in strength increment.

Hence, it can be said that the effect of welded end plate is negligible for cross-sections with

smaller sections available in the market. The circular hollow section (OD =101.6, t = 4.0 mm)

with and without welded plate at ends used in the current study shows almost the same

strength increment. Therefore, to minimise cost and time, the experiment was conducted for

the sections without welded plates.

7.3. Tensile modulus of CFRP composites

One of the important parameters is the tensile modulus of the CFRP composites. The material

technology has been improving rapidly and the elastic modulus of composite material could

be increased dramatically in the coming years. Therefore, three different tensile moduli up to

552 GPa have been investigated numerically. Fig. 17 shows the effect of CFRP modulus on

stiffness of the strengthened beams. The tensile moduli are considered 150, 210 and 552 GPa

respectively. It can be seen that the stiffness and ultimate load increase as the modulus of the

CFRP composites increase.

7.4. Adhesive layer thickness

Fig. 18 illustrates the effect of adhesive layer thickness on stiffness and ultimate load of the

strengthened beams for three different thicknesses of adhesives. The MBrace saturant

adhesive is used in this study with similar properties for different thickness of adhesive. The

strengthened beams are analysed numerically by introducing 0.20, 0.35 and 0.50 mm thick

adhesive layers respectively. It can be seen that the strengthened beam with higher adhesive

thickness shows higher stiffness and ultimate load. This increase in stiffness and ultimate load

for various thicknesses of adhesive layers is agreed with that measured numerically by Luo et

al. [55] for bonded steel-concrete composite beams, although the influence of adhesive layer

18

thickness was relatively small. It may happen due to higher sectional properties such as cross-

sectional area and moment of inertia contributed by the thicker layers of adhesive.

7.5. Types of adhesive

Another parameter of interest is types of adhesive. Various types of adhesive are available in

the market, however depending on the availability of material properties for FE analysis, three

types of adhesives are chosen in this study. The load-midspan deflection response for

different types of adhesive is shown in Fig. 19. It can be seen that the araldite K630 shows

higher stiffness than MBrace saturant and Sikadur 330. Sikadur 330 shows intermediate level

of stiffness. It may appear due to higher elastic modulus which leads to higher stiffness

parameters of adhesive as FE input.

8. Conclusions

In this paper, the structural behaviour of CFRP strengthened tubular steel members for

various layers orientations have been investigated experimentally first. The presented

experimental results of CFRP strengthened circular hollow steel beams are very promising. A

full three-dimensional finite element model has been developed in the numerical analysis of

both unstrengthened and strengthened beams. A range of parametric studies have also been

conducted. From the study conducted, the following conclusions can be drawn:

• Two different types of failure modes were observed for strengthened beams depending on

layer orientations. The LHL and LLH layers oriented beams failed by showing local

buckling of the tube wall near the loading points. However, the HHL layers oriented beams

failed by complete rupturing of CFRP and yielding of steel at tension face.

• The effects of CFRP fabrics on service and ultimate loads were remarkable. In particular

the maximum load resistance at service and failure were found about 53.0% and 37.0%

respectively. The effect of layer orientation on failure load was not significant and LHL and

LLH layers oriented treated beams performed slightly better than HHL layers oriented

treated beam.

• The effect of bonded CFRP fabrics on elastic stiffness of the beams was negligible at lower

level of load (until about 36 kN load). While at higher load, a significant increase in plastic

and elastic stiffness was observed for all the strengthened beams compared to

unstrengthened beam. The LHL and LLH layers oriented strengthened beams without

embedded GFRP showed very similar elastic and plastic stiffness until failure while LHL

layers oriented beam with embedded GFRP showed slight higher stiffness. The HHL layers

19

oriented beam showed more ductility and significant decrease in plastic stiffness until the

failure of LHL and LLH layers oriented beams.

• The proposed finite element model produces estimation of the ultimate load, midspan load-

deflection curves and failure mode for unstrengthened beam and strengthened beams with

various layers orientation of CFRP in good agreement with the experimental results.

• Parametric study shows that the proposed 200 mm bond length is reasonable in terms of

cost and strength. The section dimensions such as outer diameter and thickness play an

important role on strength increment of CFRP strengthened CHS steel beams. It is

suggested to use welded steel plate at the end for larger section of CHS beams. The section

chosen in this study was perfect in terms of strength increment. The CFRP with higher

tensile modulus and adhesive with higher thickness, perform better under bending by

increasing stiffness and ultimate load. Similarly the adhesive with high tensile modulus and

high stiffness parameters (K) performed better in terms of ultimate load and stiffness.

• The analysis, design and prediction of moment-curvature behaviour of CFRP strengthened

CHS beams are being conducted by the authors. The results will be compared in future

study with those reported in the literature on the same topic [56-58].

Acknowledgement

The authors would like to thank, Queensland University of Technology (QUT) for providing

support to carry out the work reported in this paper. The authors also wish to thank the high

performance computer facility and IT staff in Science and Engineering Faculty at QUT for

their assistance in carrying out this research.

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23

Figure Caption:

Fig. 1. Schematic diagram of test set-up (all dimension are in mm) [24, 26]

Fig. 2. Curing (a) with, (b) without masking tape at ambient condition

Fig. 3. Experimental set-up

Fig. 4. Failure mode of the tested beams

Fig. 5. Experimental and numerical load-strain curves of LHL layer oriented beam (Typical)

Fig. 6. Ultimate load for unstrengthened and strengthened beams

Fig. 7. Experimental load-displacement response for unstrengthened and strengthened beams

Fig. 8. Geometry for the composite beam for FE model

Fig. 9. Numerical and experimental load-displacement response for unstrengthened beam

Fig. 10. Numerical and experimental load-displacement response of LHL layer oriented strengthened beams (a) without, (b) with embedded GFRP

Fig. 11. Numerical and experimental load-displacement response of (a) HHL and (b) LLH layer oriented strengthened beams

Fig. 12. Comparison of failure modes between test and FE analysis

Fig. 13. Numerical load-displacement response of LHL layer oriented strengthened beams for various bond lengths

Fig. 14. Debond of CFRP at bottom ends from FE model

Fig. 15. Stress variation in the 1st layer of adhesive between loading point and end, (a) BL =100 mm, (b) BL= 200 mm, (c) BL=250 mm (d) BL=300 mm

Fig.16. Failure mode of beams determined numerically having different cross-section without and with welded end plate

Fig.17. Numerical load-displacement response of LHL layer oriented beam for various modulus of elasticity of CFRP

Fig. 18. Numerical load-displacement response of LHL layer oriented beam for various adhesive thickness

Fig. 19. Numerical load-displacement response of LHL layer oriented beam for various types of adhesives

24

Fig. 1.

(a) (b)

Fig. 2.

Fig. 3.

25

Fig. 4.

Fig. 5.

0.000 0.002 0.004 0.006 0.008 0.010 0.012 0.014 0.016 0.0180

20

40

60

80

100

120

Load

(kN)

Strain (mm/mm)

S6B-2_Exp_LLH S6B-2_FE_LLH

26

Fig. 6.

Fig. 7.

Fig. 8.

0 10 20 30 40 500

20

40

60

80

100

120

Load

(kN)

Deflection (mm)

B2_US S5B-1_LHL S3A-1_LHL_G S6B-1_HHL S6B-2_LLH

27

Fig. 9.

(a) (b)

Fig. 10.

(a) (b)

Fig. 11.

0 10 20 30 40 500

20

40

60

80

100

120

Load

(kN)

Deflection (mm)

B2-Exp B2-FE

0 10 20 30 40 500

20

40

60

80

100

120

Load

(kN)

Deflection (mm)

S5B-1-Exp_LHL S5B-1-FE_LHL

0 10 20 30 40 500

20

40

60

80

100

120Lo

ad (k

N)

Deflection (mm)

S3A-1-Exp-G_LHL S3A-1-FE-G_LHL

0 10 20 30 40 500

20

40

60

80

100

120

Load

(kN)

Deflection (mm)

S6B-1_Exp_HHL S6B-1_FE_HHL

0 10 20 30 40 500

20

40

60

80

100

120

Load

(kN)

Deflection (mm)

S6B-2_Exp_LLH S6B-2_FE_LLH

28

Test: Unstrengthened FE: Unstrengthened

Test: Strengthened (LHL and LLH) FE: Strengthened (LHL and LLH)

Test: Strengthened (HHL) FE: Strengthened (HHL)

Fig. 12.

Fig. 13.

Debond at BL =100mm Debond at BL =200mm Debond at BL =250mm Debond at BL =300mm

(a) (b) (c) (d)

Fig. 14.

0 10 20 30 40 500

20

40

60

80

100

120

Load

(kN)

Deflection (mm)

S5B-1-FE-BL-100 S5B-1-FE-BL-200 S5B-1-FE-BL-250 S5B-1-FE-BL-300

29

Fig. 15.

(a) OD=165.0, t=5.4 mm, without welded plate (b) OD=165.0, t=5.4 mm, with welded plate

(c) OD=101.60, t=4 mm, without welded plate (d) OD=101.60, t=4 mm, with welded plate

Fig. 16.

30

Fig. 17.

Fig. 18.

Fig. 19.

0 10 20 30 40 500

20

40

60

80

100

120

Load

(kN)

Deflection (mm)

S5B-1-FE_E=1.50xE11 S5B-1-FE_E=2.10xE11 S5B-1-FE_E=5.52xE11

0 10 20 30 40 500

20

40

60

80

100

120

Load

(kN)

Deflection (mm)

S5B-1-FE_To=0.20 mm S5B-1-FE_To=0.35 mm S5B-1-FE_To=0.50 mm

0 10 20 30 40 500

20

40

60

80

100

120

Load

(kN)

Deflection (mm)

S5B-1-FE-MBr S5B-1-FE-ARK630 S5B-1-FE-SKD330

31

List of Tables:

Table 1 Material properties of steel, CFRP and GFRP Steel tube CFRP GFRP

Elastic modulus (GPa) 214 205 55 Tensile strength (MPa) 327 2760 1065 Yield stress (MPa) 383 - - Tensile strain (mm/mm) 0.029 0.014 0.019

Table 2 Test details, beam resistance at service and failure and failure mode of the tested beams

Beam ID

No of beam

Wrapp -ing

Scheme

Service load at Le/250 (kN)

Ps(cs) /

Ps(s)

Ultimate load (kN)

Pu(cs) /

Pu(s) Failure mode

B2_US 2 - 44.10 50.30

- 76.75 78.40

- A

S5B-1 2 LHL 64.00 66.00

1.45 101.70 102.00

1.33 B

S3A-1 2 LHL 67.32 72.50

1.53 104.90 106.70

1.37 B

S6B-1 2 HHL 62.50 62.80

1.42 100.32 99.65

1.30 C

S6B-2 2 LLH 66.00 69.00

1.50 102.00 104.00

1.33 B

A for Ductile failure, B for Local buckling of wall, crushing of CFRP and debonding at ends, C for Rupture of CFRP & yielding of steel at bottom, no debonding at ends.

Table 3 Material properties of adhesives

Parameters

Adhesive types Mbrace Saturant

Araldite K630 Sikadur 330 [44]

Value Value value Ea (Pa) 2.86 x 109 6.5 x 109 4.82 x 109 tn (Pa) 46 x 106 33 x 106 31.28 x 106 ts (Pa) 46 x 106 33 x 106 31.28 x 106 tt (Pa) 46 x 106 33 x 106 31.28 x 106 Knn (N/mm3) 2.8 x 1013 6.07 x 1013 4.72 x 1013 Kss (N/mm3) 1.4 x 1013 3.03 x 1013 2.36 x 013 Ktt (N/mm3) 1.4 x 1013 3.03 x 1013 2.36 x 1013 Gn (N/m) 1000 1000 1000 Gs (N/m) 1250 1250 1250 Gt (N/m) 1250 1250 1250

32

Table 4 Orthotropic elastic properties of the fibre-reinforced epoxy Fibre types E1 (Pa) E2 (Pa) G12 (Pa) G13 (Pa) G23 (Pa) Nu12 CFRP 205 x 109 25 x 109 1 1 3.0 x 109 0.33 GFRP 55 x 109 1 1 1 6.7 x 109 0.33

Table 5 Orthotropic damage initiation properties of fibre-reinforced epoxy Fibre types XT (Pa) XC (Pa) YT (Pa) YC (Pa) SL (Pa) ST (Pa) CFRP 2760 x 106 552 x 106 1 1 50 x 106 1 GFRP 1065 x 106 213 x 106 1 1 50 x 106 1

Table 6 In-plane fracture energies for fibre-reinforced epoxy Fibre types GT

1C (N/m) GC1C (N/m) GT

2C (N/m) GC2C (N/m)

CFRP 91600 79900 1 1 GFRP 58000 50600 1 1

Table 7 Comparison of ultimate load between experimental and finite element analysis results

Beam ID

Experiment Finite element analysis

PFE /Pult COV Pult (kN) PFE (kN) B2 76.75 79.20 1.03 0.022 S5B-1 101.70 102.00 1.00 0.002 S3A-1 104.90 101.78 0.97 0.021 S6B-1 99.65 98.60 0.99 0.007 S6B-2 102.00 99.00 0.97 0.021

Table 8 Ultimate load at different bond length

Bond

Length(mm)

Ultimate

load

(FE)

Relative

increment of

ultimate load

(kN)

Relative

increment

of bond

length

(mm)

BL =100 93.09 0.00 0

BL =200 102.00 8.91 100

BL =250 106.88 4.88 50

BL =300 107.50 0.62 50

33

Table 9 Numerically determined ultimate load of unstrengthened and strengthened beams for various sections

Thickness (mm)

Ultimate Load (kN) Load increment

Outer Diameter

(mm)

Unstrengthened Strengthened

DS/t

Without welded plate

Welded plate at

end

Without welded plate at

end

Welded plate at

end

Without welded plate at

end

Welded plate at

end

165.0 5.4 30.6 219.50 265.70 228.85 284.50 4.26% 7.08%

165.0 5.0 33.0 203.00 247.00 209.80 271.80 3.35% 10.04%

140.0 5.4 25.9 202.00 202.00 230.00 235.90 13.86% 16.78%

140.0 5.0 28.0 187.60 187.50 216.00 221.60 15.14% 18.19%

114.0 5.4 21.1 134.88 134.66 161.85 162.50 20.00% 20.67%

114.0 4.5 25.3 113.90 113.90 139.00 139.60 22.04% 22.56%

101.6 5.0 20.3 98.84 98.68 120.50 120.55 21.91% 22.16%

101.6 4.0 25.4 79.20 81.12 102.00 103.00 28.80% 26.97%

90.0 6.0 15.0 93.00 93.00 111.55 112.00 19.95% 20.43%

90.0 4.0 22.5 64.00 64.00 82.40 82.00 28.75% 28.13%