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Axial Load-Bending Moment Diagrams of Carbon-FRP Wrapped Hollow Core Reinforced Concrete Columns

Veysel Yazici1, Muhammad N.S. Hadi2

Abstract: Hollow core reinforced concrete columns are generally preferred in use to decrease

the cost and weight/stiffnesss ratio of members such as bridge columns and piles. With a

simplified stress state assumption, strengthening a hollow core reinforced concrete column with

FRP wrapping provides a biaxial confinement to the concrete which leads to a need of defining

the effect of FRP wrapping on the strength and ductility of the hollow core reinforced concrete

columns. In this study, two groups of four hollow core reinforced concrete columns (205 mm

outer diameter, 56 mm hollow core diameter, and 925 mm height) were tested under concentric,

eccentric (25 mm and 50 mm eccentricity) and bending loads to observe the effect of Carbon-

FRP (CFRP) wrapping. All the columns had internal steel reinforcement. Half of the columns

had three layers of circumferential CFRP wrapping, whereas the other half had no external

confinement. Axial load-bending moment (P-M) diagrams of each group were drawn using the

obtained experimental results for both groups. It was observed that, CFRP wrapped columns had

higher load and moment carrying capacities than the other group. An analytical model is

proposed for drawing the P-M diagram of CFRP wrapped hollow core reinforced concrete

columns.

CE Database subject headings: FRP; Column strengthening; Hollow sections; Eccentric Loads;

Axial load-Bending moment diagram

1 Phd Candidate, School of Civil, Mining and Environmental Engineering, University of Wollongong, Wollongong

NSW 2522 Australia. E-mail: vy210@uow.edu.au

2 Associate Professor in Structural Engineering, School of Civil, Mining and Environmental Engineering, University

of Wollongong, Wollongong NSW 2522 Australia (corresponding author). E-mail: mhadi@uow.edu.au

ManuscriptClick here to download Manuscript: paper_asce_hadi.doc

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Introduction

Hollow columns have been preferred to solid columns to reduce the cost of the structures, and to

decrease the self weight of the structures where it is technically necessary. In spite of their

widespread use, even modern design codes do not address any specific problems related to

hollow section columns (Lignola et al. 2007, Sheikh et al. 2007). In practice, hollow columns are

commonly constructed as bridge columns and piles.

It is a well known fact that the infrastructure of a country needs to be maintained either by

demolishing the insufficient structures and building new ones, or by rehabilitating the old ones

with appropriate techniques to meet the current requirements. Thus, it is highly possible that

hollow core reinforced columns will also be needed to be strengthened where necessary.

The use of Fiber Reinforced Polymer (FRP) sheets to strengthen RC columns under axial loads

has been a popular subject for the last decade or so. Its resistance to corrosion, excellent

durability to harsh environmental conditions, high strength to weight ratio, ease of installation to

existing structures, and being electromagnetically inert make this new material more suitable to

use when compared to steel (ISIS Canada 2001). Studies conducted by Nanni and Bradford

(1995), Mirmiran and Shahawy (1997), Fam and Rizkalla (2001), Li and Hadi (2003), Hadi

(2005 a,b,c), Mathys at al. (2005) have shown that ductility and strength of concrete columns are

substantially improved by wrapping FRP sheets around the columns.

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Many studies have shown that FRP confinement alters the stress-strain relationship of concrete

in a different way than steel confinement (Teng et al. 2002, Samaan et al. 1998, Spoelstra and

Monti 1999, Toutanji 1999). The difference in the behavior of steel and FRP confined concrete is

due to the difference in the behaviour of steel and FRP (Figure 1). Steel is an elasto-plastic

material, that is, up to the yield load, it undergoes elastic deformation which can be recovered if

the load is removed. After the yield load, steel undergoes large deformations even if the load is

kept constant (regardless of the load increase). Thus, after the yield load, it is assumed that steel

confinement provides a constant confining stress resulting in a simplicity of stress calculations.

Unlike steel, FRP exhibits a linear deformation under tensile loading until failure. Thus, the

confinement it provides to the concrete is highly dependant on the stress level of FRP. There are

a number of equations that model the behaviour of steel confined concrete. Most of them seem to

be based on Richart et al. (1928). A number of studies, for example, Teng et al. (2002), Samaan

et al. (1998), Spoelstra and Monti (1999), Toutanji (1999) have proven that all previously

defined models for conventionally steel confined concrete need to be re-defined for FRP

confined concrete.

This paper presents the effects of FRP wrapping on axial load-bending moment (P-M) diagrams

of hollow core circular reinforced concrete columns, and results of an analytical and

experimental study conducted to draw P-M diagrams of circumferentially FRP wrapped hollow

core circular reinforced concrete columns. All columns were tested to failure by applying

concentric, eccentric, and pure bending loads. The analytical approach gave close enough results

to the test results, proving the load carrying capacities of FRP wrapped hollow core circular

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reinforced concrete columns under concentric, eccentric and pure bending loads can be

sufficiently predicted.

Theoretical Considerations

Background

Although the only apparent difference from an FRP wrapped solid column seems to be the

hollow portion in the center, confinement mechanism of an FRP wrapped hollow core column

under an axial load is quite different.

In fact, confinement stresses in hollow columns due to FRP wrapping are quite complex and

non-uniform (Lignola et al. 2008). The helical steel reinforcement is assumed to have no

confinement effect on the concrete. A constant average confining stress was assumed to develope

within the column under compressive loads due to FRP confinement only. According to this

simplified assumption, FRP wrapping at the outside face of a circular hollow core column

restrains the growth of the tube diameter as shown in Figure 2(a,b) and an average confinement

stress, fl, can be found by the following force equilibrium equation written for Section A-A:

w

tfftfwf frpfrp

lrpffrpl 22 (1)

Where w= thickness of the wall, ffrp= tensile strength of FRP in the hoop direction, fl= lateral

confining pressure, tfrp= total thickness of FRP.

The FRP applies a radial pressure to the outside face of the wall of the tube, which in turn causes

a circumferential compression stress fl in the curved tubular wall (Figure 2(c)). The

circumferential compression stress fl puts a concrete element cut out of the curved wall into

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biaxial compression, with the primary stress σ1 arising from the axial load. In contrast to the

situation in a solid confined concrete section, there is no compressive confining stress acting on

the inside face of the curved wall in the radial direction (Zahn et al. 1990). Thus, according to

this constant average confinement stress assumption, any concrete element inside the column is

under biaxial state of stress as shown in Figure 3. Although biaxial state of stress for FRP

confined hollow columns may seem a simplistic assumption, it may be used to estimate the

capacity of hollow columns for a start. In fact, similar assumptions, such as constant confinement

stress, were made to determine the capacity of solid columns confined with FRP.

Although the concrete is assumed to be under biaxial confinement, its compressive strength and

deformation capability is increased. Since the FRP confined concrete stress-strain models

describe the behaviour of concrete under triaxial stress condition such as in the case of solid

columns, they are not suitable to use for biaxially confined concrete, as in the case of hollow

core columns.

To determine improved compressive strength as a result of FRP wrapping, fcc, a simplified

interaction diagram presented by Mander et al. (1988) that related fcc to the two orthogonal

stresses (fl) confining the concrete laterally was used in this study. This interaction diagram was

originally derived from the work of William and Warnke (1975).

The average confinement stress, fl can be calculated using Equation 1. Unconfined compressive

strength of concrete (fco) is determined by compression tests on the concrete. Using the curve for

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biaxial state of stress on the simplified interaction diagram presented by Mander et al. (1988), the

fcc/fco value corresponding to fl/fco value can be read and fcc can be calculated.

In the same study, Mander et al. (1988) determined a general equation for the crushing strain of

concrete, εcc, under confinement.

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co

cccocc f

fR (2)

where εco is the strain of unconfined concrete corresponding to the maximum stress. The

constant, R, was determined to be 5.0 by Mander et al. (1988) for concrete in triaxial

compression such as solid columns. Darwin and Pecknold (1977) determined an average value

3.25 for R after testing concrete panels under biaxial compression. Thus, a value of R=3.25 was

used in this study. A smaller R value gives a smaller crushing strain which implies that the stress

within the concrete reaches its maximum value, fcc, with a less deformation of concrete.

A continuous stress-strain model proposed by Mander et al. (1988) was used to express the

compressive stress in the concrete. The model is based on an equation proposed by Popovics

(1973).

rcc

c xr

rxff

1

'

(3)

where

cc

x

(4)

secEE

Er

C

C

(5)

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cc

ccfE

'

sec (6)

where εc= compressive strain of concrete corresponding to axial stress fc; fcc=peak compressive

stress found from simplified interaction diagram; fco=compressive strength of unconfined

concrete. The value of εcc can be calculated by Equation 2. Ec is the modulus of elasticity for

unconfined concrete which was calculated using the equations given by AS3600 (2001) for this

particular study.

MPafEMPaffor cocco )043.0(40 '5.1' (7)

MPafEMPaffor cocco )12.0024.0(40 '5.1' (8)

where ρ= density of concrete in kg/m3 ( taken as 2400 kg/m3 in this study).

It is important to note that, the stress-strain model proposed above can also be used for

unconfined concrete just by substituting fco in place of fcc and co in place of co into Equations 2-

6, which implies that there is no confinement provided by an external FRP wrapping, and thus no

increase in the ultimate strength of the concrete. The model proposed by Mander et al. (1988)

then gives a stress-strain model for unconfined concrete under compression up to the crushing

strain (ε=0.003).

Theoretical P-M Diagrams of FRP wrapped hollow core columns

A P-M diagram is a continuous curve used to determine the axial load and bending moment

carrying capacity of a given reinforced concrete column cross section and materials. A point on

this curve may represent a concentric loading, an eccentric loading, or a pure bending load.

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To draw a P-M diagram for an FRP wrapped hollow core reinforced concrete column, the

biaxially confined concrete model defined in the section above was utilized. This direct use of

stress-strain curves for uniformly confined concrete to eccentrically loaded columns implies the

assumption of a non-uniform confining pressure in an eccentrically loaded column which varies

from zero at the neutral axis position to a maximum value at the extreme compression fibre of

concrete as shown in Figure 4 (Teng et al. 2002).

The axial load capacity under concentric loading is given by

syccco AfAfN ' (9)

Where Ac= gross cross-sectional area of hollow column (mm2); fy= yield strength of longitudinal

steel reinforcement (MPa); As= total cross-sectional area of longitudinal steel reinforcement

(mm2); fcc= peak compressive stress (MPa) after FRP wrapping found from simplified interaction

diagram given by Mander et al. (1988).

For calculation of axial load capacities and moment capacities under eccentric loads and pure

bending, the cross-section of the column is assumed to be consisting of parallel finite strips with

small thicknesses for the ease of calculation (Figure 5), where b= total width of the strip (the

length on the hollow part is excluded where it intersects the hollow core), Δx= height of the strip,

k= depth of the centroid of the strip from the outermost concrete fibre. The heigth of the strips

(Δx) must be taken large enough to shorten the calculations and small enough to be close to

reflect the actual shape of the cross section. A value of 5 mm was taken as the heigth of

horizontal strips in this study

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With the basic assumption that plane sections remain plane after bending, the strain in the centre

of each strip can be estimated and the corresponding stress is calculated according to the

biaxially confined concrete stress-strain model defined. For tensile strains in the concrete, the

stress will be assumed as zero since the concrete is generally assumed to have no tensile strength

in the calculations. Summation of the forces acting on the strips and the steel reinforcement adds

up to the axial load carrying capacity, and summation of the moments with respect to the

centerline of the section add up to the moment carrying capacity of the section under a given

eccentricity.

Experimental Program

The experimental part of this study involved testing two groups of four hollow core circular

reinforced concrete columns under different eccentricities and pure bending. All the columns had

a height of 925 mm. The cross section of the columns had an outer diameter of 205 mm and a

hollow part with an inner diameter of 56 mm, leaving a wall thickness (w) of 74.5 mm. The

concrete used to cast the columns had a 28 day compressive strength of 60 MPa. Longitudinal

steel reinforcement consisted of evenly distributed six N12 (12 mm diameter deformed bar) bars

which were tested to have 550 MPa tensile strength and tied inside a helical steel reinforcement.

The helical reinforcement was an R10 (10 mm diameter plain bar) helix with a 50 mm pitch

which were tested to have 300 MPa tensile strength. The steel reinforcement was placed into the

column moulds with 20 mm clearance to the outer moulds (Figure 6).

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A PVC pipe having an inner diameter of 205 mm was used as the outer mould, and a 56 mm

outer diameter PVC pipe was used to form the hollow part. After setting of the concrete, the

outer moulds were removed using the previously cut joints on the PVC pipe, and the inner PVC

pipes were pulled out by means of a hydraulic jack.

In total eight specimens (subdivided into two groups denoted here as C for externally unconfined

and L for externally confined in the hoop direction by wrapping with 3 layers of lateral FRP

sheets) were cast and tested. All specimens were internally reinforced with the same amount of

steel reinforcement. The first group of four RC columns were without external confinement,

whereas the second group of four columns had three layers of CFRP sheets wrapped

circumferentially around the columns applying a wet lay-up process with epoxy resin. The CFRP

was tested according to ASTM 3039 (2006) standard in order to determine its tensile strength.

The CFRP specimens were made of three unidirectional layers of CFRP and epoxy was used to

adhere the three layers. The test revealed that the tensile strength of the three layered CFRP was

920 MPa with a corresponding maximum strain of 0.02.

One specimen from each group (Specimens C0 and L0) was tested to failure under concentric

loading, the next two specimens were tested under 25 mm (C25 and L25) and 50 mm (C50 and

L50) eccentric loading. The final specimen of each group (CB and LB) was tested under pure

bending. Table 1 shows a summary of the specimens and testing conditions for each specimen.

Compared to the column diameter (D=205 mm), 25 mm eccentricity can be assumed as a

relatively small eccentricity (e/D=0.1212). However, 50 mm eccentricity can be assumed as a

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relatively large eccentricity (e/D=0.244). It was aimed to test the hollow columns under both

small and relatively large eccentricities. Eccentric loadings were applied to the columns by

means of especially designed and manufactured loading heads (Figure 7).

Pure bending was applied to specimens (in fact beams) CB and LB by means of a four point

loading apparatus. The method of loading and moment distribution for the Specimens CB and

LB is shown in Figure 8.

Load, P, applied to the columns was measured by the internal load cell of the loading machine.

For the axially loaded specimens, the axial deformations (Δ) of the columns were monitored by

an LVDT attached to the moving (lower) plate of the loading device. Lateral deformations of the

specimens (δ) (Figure 9) were monitored at the mid height of columns using a laser displacement

sensor.

All specimens were tested at the laboratories of the School of Civil, Mining and Environmental

Engineering at the University of Wollongong. A 500 tonne Denison compression machine was

used to test the column and beam specimens.

Experimental Results

All specimens were tested to failure. Table 2 shows a summary of testing the specimens. For 25

mm and 50 mm eccentrically loaded columns, bending moment capacities are calculated by

multiplying the maximum load capacity (Pmax) and the eccentricity. Bending moment capacities

including the secondary moments (MII) were also calculated as follows:

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)(max ePM II(10)

Where Pmax = max axial load, e=eccentricity, and δ=lateral deflection at maximum load.

For specimens CB and LB, the moment capacity was calculated using the equation:

)(2

aP

M (11)

Where P is the maximum load applied to a specimen with four point apparatus, and the constant

a is the length of the shear span which is the distance between an outer loading point to the

closer inner loading point (a= 280 mm, s=270 mm in this study, see Figure 8).

Results And Discussion

Test results show that (Table 2), CFRP wrapping of hollow columns is more effective on the

axial load carrying capacity, Pmax, when the loading is concentric. Compared to the unwrapped

specimen C0, there was 50.91% increase in the axial load carrying capacity of the FRP wrapped

specimen, and 178.67% increase in the axial deflection corresponding to the maximum load (Δ).

For specimens tested under 25 mm eccentricity, L25 had a 5.03% larger axial load carrying

capacity, Pmax, than C25. The corresponding axial deformations for both specimens were similar

(2.13% greater for L25), whereas the lateral deformation capacity was 83.21% greater for L25.

For specimens tested under 50 mm eccentricity, L50 had a 22.23% larger axial load carrying

capacity than specimen C50. For the same eccentricity, axial and lateral deformation capacity

increases were much more substantial for L50, which were 105.02% and 133.71%, respectively.

Beam specimens (CB and LB) were tested under pure bending conditions. Flexural load carrying

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capacity and the corresponding maximum deformation of LB were larger than CB by 58.16%

and 28.35%, respectively.

In deformation aspect, eccentrically loaded CFRP wrapped columns behaved like slender

columns in which the effect of secondary moments are considerable due to large lateral

deformations. In internally steel reinforced columns, axial load carrying capacities decrease as

the secondary moments increase. In CFRP wrapped columns P-M diagrams were modified so as

to increase both the axial load capacities and bending moment capacities at the same time.

As experimental P-M diagrams of FRP wrapped columns are different than that of the columns

having only internal steel reinforcement, the stress-strain model described in the Background

section above was used to predict the P-M diagram of both columns without external FRP

wrapping and CFRP wrapped hollow core reinforced concrete columns. The capacities under

different loading conditions were calculated using the approach described in the Theoretical P-M

Diagrams of FRP wrapped hollow core columns section above. The calculated P-M diagram and

experimental results for the specimens without external CFRP wrapping and CFRP wrapped

specimens are shown in Figure 10 and Figure 11, respectively.

When the theoretical and experimental values for the axial load (P) carrying capacity of the

specimens under concentric and eccentric loads are compared, it can be seen that the proposed

model gave closer predictions for FRP wrapped sample columns under eccentric loads (see Table

3). However, the scatter between the experimental and the theoretical value for pure bending

capacity is higher for LB (40%) (see Table 4).

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For the specimens without CFRP wrapping, secondary moments were much smaller than CFRP

wrapped specimens, which reveals that CFRP wrapping significantly increased the lateral

deformation capacity of specimens under compressive loads. The axial load carrying capacities

and corresponding axial deformations were significantly increased for CFRP wrapped columns

(see Table 2).

The scatter between the experimental results and the predicted capacities imply that the assumed

biaxial state of stress is only a simplified approach and the actual confining stresses are more

complex. It can also be said that the differences may have arisen from the insufficiency of

proposed model to quantify the increase in strength and strain capacity of confined concrete

under given loading conditions.

Conclusions

A total of eight hollow core reinforced columns were tested. Strength improvement for CFRP

wrapped column under concentric load was higher than eccentrically loaded CFRP wrapped

columns. Lateral deformation capacities under eccentric loads were substantially increased after

CFRP wrapping. The results may be interpreted that, the CFRP wrapping of hollow core

reinforced concrete columns provides a better ductility under eccentric loads. Nevertheless, the

effect of secondary moments becomes more important after CFRP wrapping.

Based on the experimental results it can be concluded that although the concrete was under a

state of two dimensional stress, CFRP wrapping proved to increase both the strength and the

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ductility (by increasing axial and lateral deformation capacities) of the tested column specimens.

In addition the developed theoreticall model yielded results that are comparable to the

experimental results however the scatter between the test results and predicted capacities are

quite large for some columns. The study is believed to give an insigth on the behaviour of FRP

wrapped hollow core reinforced concrete columns under various loading conditions.

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Nomenclature

The following symbols are used in this paper:

Ac = gross cross-sectional area of hollow column;

As = total cross-sectional area of longitudinal steel reinforcement;

e = eccentricity;

Ec = modulus of elasticity for unconfined concrete;

fcc = improved compressive strength as a result of FRP wrapping;

ffrp = tensile strength of FRP in the hoop direction;

fy = yield strength of longitudinal steel reinforcement;

w = thickness of the hollow column wall;

fl = lateral confining pressure;

MI = Bending moment capacity excluding secondary moments;

MII = Bending moment capacity including secondary moments;

Pmax = max axial load applied to column;

tfrp = total thickness of FRP;

δ = lateral deflection at maximum load;

εc = strain of concrete;

εcc = crushing strain of concrete;

εco = strain of unconfined concrete corresponding to the maximum stress; and

ρ = density of concrete, taken as 2400 kg/m3.

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William, K.J., and Warnke, E.P. (1975), “Constitutive Model for the Triaxial Behaviour of Concrete”, IABSE Proceedings, International Association for Bridge and Structural Engineering, Zurich.

Zahn, F.A., Park, R., and Priestley, M.J.N. (1990), “Flexural Strength and Ductility of Circular Hollow Reinforced Concrete Columns without Confinement on Inside Face”, ACI Structural Journal, 87(2), 156-166.

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List of Tables

Table 1. Testing matrix on column specimens

Specimen External ConfinementLoading eccentricity

(mm)C0 No 0

C25 No 25C50 No 50CB No -L0 3 layers of CFRP 0

L25 3 layers of CFRP 25L50 3 layers of CFRP 50LB 3 layers of CFRP -

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Table 2. Summary of column testing results

SpecimenMax. Load, (kN)

Axial Deflection

at max.load,Δ, (mm)

Lateral Deflection at max. load, δ, (mm)

Max. axial Load,Pmax (kN)

MI=Pmaxe(kNm)

MII=Pmax(e+δ)(kNm)

C0 2145.4 4.50 0 2145.4 0 0C25 1699.5 7.03 4.17 1699.5 42.49 49.52C50 915.7 4.38 5.34 915.7 45.78 50.67CBa 207.2 - 7.62 b 0 29.01 29.01L0 3237.7 12.54 0 3237.7 0 0

L25 1785.0 7.18 7.64 1785.0 44.63 58.26L50 1119.3 8.98 12.48 1119.3 55.97 69.93LBa 327.7 - 9.78 b 0 45.88 45.88

a Specimens CB and LB were loaded flexurally. b Lateral deflections for CB and LB are in the direction of loading, thus they do not create secondary moments.

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Table 3. Comparison of Experimental and Theoretical Results for concentrically and eccentrically loaded column samples.

SpecimenExperimental

Maximum Axial Load (kN)

Theoretical Maximum Axial Load (kN)

Difference (%)

C0 2145.4 2205.8 -2.81C25 1699.5 1251.6 26.4C50 915.7 810.3 11.5L0 3237.7 2828.2 12.6

L25 1785.0 1821.8 -2.1L50 1119.3 1194.5 -6.7

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Table 4. Comparison of Experimental and Theoretical Results for column samples tested under pure bending.

Specimen

Experimental Maximum Bending

Moment (kNm)

Theoretical Maximum Bending Moment

(kNm)Difference (%)

CBa 29.0 24.9 14.1LBa 45.9 27.7 40.0

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List of Figures

Figure 1. Stress-strain relationship for unconfined, steel confined and FRP-confined concrete.

Figure 2 . Stresses in the wall of circular hollow core column.

Figure 3. Concrete element under biaxial compression.

Figure 4 . Stress-strain distribution for FRP wrapped hollow core reinforced concrete column.

Figure 5. Division of cross section into parallel strips.

Figure 6. Geometry of hollow core circular columns.

Figure 7. Loading heads for eccentric loading.

Figure 8. (a)Four point loading apparatus, (b) bending moment diagram.

Figure 9. Axial (Δ) and lateral (δ) deformations of column under the load applied with an eccentricity (e).

Figure 10. Calculated P-M diagram and Experimentally drawn P-M diagrams of hollow core columns without external CFRP wrapping.

Figure 11. Calculated P-M diagram and experimental P-M diagrams of CFRP wrapped hollow core columns.

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