nonlinea rbehavior of frp-reinforced concrete-filled double-skin

7/24/2019 Nonlinea Rbehavior of FRP-reinforced Concrete-filled Double-skin

1/19

Nonlinear behavior of FRP-reinforced concrete-lled double-skin

tubular columns using nite element analysis

Sayed Behzad Talaeitaba a, Minoo Halabian a, Mohammad Ebrahim Torki b,n

a Faculty of Engineering, Azad University of Science and Research, Isfahan, Iranb Department of Aerospace Engineering, Texas A&M University, College Station, TX 77843, USA

a r t i c l e i n f o

Article history:

Received 11 January 2015Received in revised form

26 June 2015

Accepted 24 July 2015

Keywords:

Hybrid columns

CFDST columns

FRP bers

Hollow section ratio

Nonlinear behavior of reinforced concrete

a b s t r a c t

The literature lacks exhaustive study on CFDST hybrid columns circumscribed by FRP layers. Extended

FEM analysis was carried out on 70 real-scale models with varying parameters including the material andnumber of FRP layers, concrete strength, length-to-diameter ratio (specic length), and hollow section

ratio. Carbon bers proved stronger than glass bers, leading to higher ultimate stress associated with

lower strain. Specimens with high specic lengths suffered from steel premature buckling, thus stiffened

with steel plates. Specimens with various hollow section ratios were nally compared, showing an in-

crease range of 70% between the maximum (0.75) and minimum (0.25) ratios.

& 2015 Elsevier Ltd. All rights reserved.

1. Introduction

Thanks to the established intrinsic synergy between steel and

concrete, hybrid columns have received growing applications

through the past decades. The virtues of hybrid columns are

manifold. They include construction convenience (e.g. applicability

as a duct for plumbing) and signicant mechanical enhancement

of structural elements in comparison to ordinary reinforced or

even purely steel members. Amongst the enhanced mechanical

properties is increased connement and shear strength underlying

further efciency in the structural element. That is, the conning

effect is applied on concrete at best when the hybrid column is

circular [1]. With regards to the relative placement of steel and

concrete, hybrid columns can take the form of a concrete-lled

steel tube (CFST), a concrete-lled FRP tube (CFFT), a steel section

encased in a concrete section, a steel-reinforced concrete section

(SRC), a double steel tubular column, or a concrete-

lled doubleskin tubular column (CFDST)[2] .

Research work about hybrid concrete columns is plentiful in

the literature. The seminal idea of using double tubular steel col-

umns was rstly proposed by Khalil and Illouli[3] to be consisting

of two steel layers embedding a concrete layer in between. Others

investigated various properties of similar tubular columns in-

cluding Wei et al. [4], Han et al. [5], Zhao and Grzebieta [6], and

Tao et al.[7]. Along with their virtues, these columns were proven

to have certain shortcomings stemming from placing steel at the

outer layer, which would entail protection against re and corro-

sion. Thus, researchers were lead through further strengthening

tubular columns with FRP strips, which was rstly brought up by

Fam and Rizkalla[8]. They set forth both the inner and outer layers

to be made of FRP layers, as shown in Fig. 1. This would trigger

certain issues concerning the connectivity problem between the

column and a beam in absence of steel and the inability of FRP

layers to bear structural loads. Later on, other researchers in-

troduced the idea of hybrid columns into CFDST and investigated

the load bearing properties of this type of column. Later on, Yu

et al. [9] carried out FEM calculations, in agreement to the corre-

sponding experimental outcomes, on the exural behavior of

columns with a steel inner layer and an FRP outer layer embracing

concrete in between. Owing to the conning effect of concrete,

buckling of the steel tube will be remarkably delayed or even to-tally dispensed with. However, tearing in the FRP layer will give

rise to premature fracture, and that is where the thickness of the

steel inner layer will take effect [10].

Hu et al.[1] proposed and veried proper material constitutive

models for concrete-lled tubes (CFT) using ABAQUS in agreement

to experimental data. Circular tubes proved to provide the best

conning effect when the width-to-thickness ratio was small.

Square CFT columns, however, did not provide a large conning

effect, esp. when the width-to-thickness ratio was large. Later on,

Hu and Su [11] established empirical equations to predict the

lateral conning pressure exerted on the concrete core.

Contents lists available atScienceDirect

journal homepage: www.elsevier.com/locate/tws

Thin-Walled Structures

http://dx.doi.org/10.1016/j.tws.2015.07.018

0263-8231/&2015 Elsevier Ltd. All rights reserved.

n Corresponding author.

E-mail addresses: [email protected](S.B. Talaeitaba), [email protected],

[email protected] (M. Ebrahim Torki).

Thin-Walled Structures 95 (2015) 389407
http://localhost/var/www/apps/conversion/tmp/scratch_4/http://www.elsevier.com/locate/twshttp://dx.doi.org/10.1016/j.tws.2015.07.018mailto:[email protected]:[email protected]:[email protected]://dx.doi.org/10.1016/j.tws.2015.07.018http://dx.doi.org/10.1016/j.tws.2015.07.018http://dx.doi.org/10.1016/j.tws.2015.07.018http://dx.doi.org/10.1016/j.tws.2015.07.018mailto:[email protected]:[email protected]:[email protected]://crossmark.crossref.org/dialog/?doi=10.1016/j.tws.2015.07.018&domain=pdfhttp://crossmark.crossref.org/dialog/?doi=10.1016/j.tws.2015.07.018&domain=pdfhttp://crossmark.crossref.org/dialog/?doi=10.1016/j.tws.2015.07.018&domain=pdfhttp://dx.doi.org/10.1016/j.tws.2015.07.018http://dx.doi.org/10.1016/j.tws.2015.07.018http://dx.doi.org/10.1016/j.tws.2015.07.018http://www.elsevier.com/locate/twshttp://localhost/var/www/apps/conversion/tmp/scratch_4/


2/19

Tao et al. [7] investigated the behavior of concrete-lled stub

columns and beam-columns by centering in the diameter-to-

thickness and hollow section ratios for stub columns as well as

slenderness ratio and load eccentricity for beam-columns. They

developed a theoretical model using a unied theory by introdu-

cing a connement factor to describe the composite action be-

tween the outer steel tube and the inner concrete layer. Tao and

Han[12] expanded their studies by evaluating the failure modes

and load vs deformation behavior of test specimens in comparison

with those of ordinarily concrete-lled steel tubular columns and

empty double skin tubes.

More recently, Huang et al. [13] executed nite element ana-

lysis for the compressive behavior of concrete-lled stub columns

with square and circular cross sections. They presented their re-

sults in terms of average stress vs longitudinal strain, stress dis-

tributions in the concrete layer, interaction between concrete and

steel tubes, and the effect of hollow section ratio. Han et al. [14]

modeled the behavior of CFDST columns under long-term sus-

tained loading conditions. They generated a simplied formula for

calculating the ultimate strength of these columns subjected to

long-term sustained loading in accordance to performed long-

term service and ultimate strength tests. Li et al. [15]discussed the

behavior of CFDST columns subjected to axial preloads either on

the outer tube alone or on both tubes using FE analysis. They

predicted the inuences of the preload ratio, slenderness ratio,

hollow section ratio and concrete strength on the axial strength.

The compressive strength of CFDST stub columns with external

carbon or stainless steel tubes was calculated by Hassanein and

Kharoob[16, 17]over a complete range of the diameter-to-thick-

ness ratio. Wang and Li[18]used ANSYS to analyze the mechanical

behavior of CFDST columns from loading to failure, with the hol-

low section ratio being the main varying parameter.

Investigation through the literature reects the need in a more

exhaustive insight through the effects due to geometric properties

of the constituting elements of CFDSTcolumns on the strength and

stability of these columns. More consequentially, similar effects in

presence of FRP strips as a third constituent are still far from es-

tablished. The present research investigates the nonlinear

Fig. 1. Schematic outline of a circular or square prismatic CFDST column consisting of steel and FRP layers.

Table 1

Geometric properties of validating specimens[19].

Type Dim. (mm) No. of

FRP

layers

Di (mm) Hollow

section

ratio ()

ti (mm) Concrete com-

pressive

strength (fc )

C37-A2 152305 2 42 0.28(A) 2.3 36.7

C47-B2 152305 2 76 0.5(B) 3.5 46.7

C37-C2 152

305 2 88 0.58(C) 2.1 36.9

Table 2

Mechanical properties of FRP layers[19].

Efrp (MPa) to (mm) fu h,rup

80100 0.17 0.031 0.018

Table 3

Mechanical properties of steel tie plates.

Steel tube dia-

meter (mm)

Steel tube thick-

ness (mm)

Esteel(MPa) Fysteel(MPa)

Fusteel(MPa)

steel

76 3.3 198700 406.2 475.5 0.3

Fig. 2. Experimental set-up of the hybrid column: (a) prior to and (b) after compressive loading [9].

S.B. Talaeitaba et al. / Thin-Walled Structures 95 (2015) 389407390


3/19

compressive behavior of CFDST columns determined from non-

linear FEM calculations executed on 70 models made in ABAQUS.

The FEM models as such are made on the basis of the idea pri-

marily put forward by Teng [19]. The stressstrain curves plotted

compare favorably with the experimental results produced by

Teng[19]. Then, the models are extended as to measure the effects

of geometric parameters in presence of an FRP layer generating the

outer layer on the load bearing capacity, strain to failure, and

buckling load. The so-called geometric parameters include the

column height, diameter, and hollow section ratio, dened as the

Fig. 3. FEM model of the hybrid column: (a) prior to and (b) after compressive loading.

Axial strain

Axialstress(MPa)

0 0.005 0.01 0.015 0.020

10

20

30

40

50

60

Experimental

FEM (Yu et al)

FEM (present)

Specimen C37-A2

Axial strain

Axialstress(MPa)

0 0.005 0.01 0.015 0.020

10

20

30

40

50

60

Experimental

FEM (Yu et al)

FEM (present)

Specimen C47-B2a b

c

Axial strain

Axialstress(MPa)

0 0.005 0.01 0.015 0.020

10

20

30

40

50

60

Experimental

FEM (Yu et al)

FEM (present)

Specimen C37-C2

Fig. 4. Plots showing compressive stress vs axial strain, as compared with experimental data and FEM calculations in Ref. [19], for (a) the C37-A2 specimen, (b) the C47-B2

specimen, and (c) the C37-C2 specimen. A very nice agreement between all data sets could be observed in all curves.

S.B. Talaeitaba et al. / Thin-Walled Structures 95 (2015) 389407 391


4/19

external-to-internal diameter ratio. Aside from geometry, the ef-

fects due to material were assessed. In this regard, concrete com-

pressive strength as well as FRP material (either carbon or glass)

and number of FRP layers will be noticed in the passing.

2. FEM modeling

In order to ensure maximal accordance with reality, SOLID

(brick) elements were used representing concrete, and steel as

well as FRP layers were modeled using SHELL elements.

To be more specic, due to the essence of 3D modeling, C3D8R

(8-node solid elements) elements were utilized to represent con-

crete. The mechanical properties of concrete should be dened

over a complete elasticplastic range. In the elastic range, knownto be up to a compressive stress equal to f0.5 c , the elasticity

modulus and the Poisson's ratio are specied. The nonlinear be-

havior of concrete used in the present work stems from the

Hognestad stressstrain model[2]. The elasticity modulus can be

obtained from Eq.(1) [20].

E f4700 1c c= ( )

where f c is the specic strength of concrete in MPa. The concrete

damaged plasticitymodel has been applied to dene the plasticity

parameters of concrete. In the meantime, on account of better

agreement between numerical outcomes and experimental data,

sensitivity analysis was performed on the dilation angle and

viscosity to reach maximum concordance with experiment in theallowable ranges recommended by the software. The dilation

Table 4

Mechanical properties of GFRP strips.

Type Efrp (MPa) to(mm) fu h,rup

GFRP 80,100 0.17 0.031 0.018

CFRP 230,000 0.17 0.017 0.0102

Table 5

Mechanical properties of inner-layer steel tubes.

Esteel (MPa) Fysteel(MPa) Fusteel(MPa) steel

198,700 240 60 0.3

Table 6

Geometric properties of main specimens for the effects of the material and the number of FRP layers.

No. of specimen Type Do(mm) H (mm) No. of FRP layers Di (mm) Hollow section ratio () ti (mm) Concrete compressive strength (f c )

1 C47-15-30-B2-G 152 305 2 76 0.5(B) 3.5 46.7

2 C47-15-30-B4-G 152 305 4 76 0.5(B) 3.5 46.7

3 C47-15-30-B6-G 152 305 6 76 0.5(B) 3.5 46.7

4 C47-15-30-B2-C 152 305 2 76 0.5(B) 3.5 46.7

5 C47-15-30-B4-C 152 305 4 76 0.5(B) 3.5 46.7

6 C47-15-30-B6-C 152 305 6 76 0.5(B) 3.5 46.7

Table 7Geometric properties of main specimens for the effect of concrete compressive strength.

No. of specimen Type Do (mm) H (mm) No. of FRP layers Di (mm) Hollow section ratio () ti (mm) Concrete compressive strength (f c )

7 C30-15-30-B2-G 152 305 2 76 0.5(B) 3.5 30

8 C40-15-30-B2-G 152 305 2 76 0.5(B) 3.5 40

9 C50-15-30-B2-G 152 305 2 76 0.5(B) 3.5 50

10 C60-15-30-B2-G 152 305 2 76 0.5(B) 3.5 60

Axial strain

Axialstress(MPa)

0 0.005 0.01 0.015 0.020

20

40

60

80

100

120

140

160

C47-15-30-B2-C

C47-15-30-B4-C

C47-15-30-B6-C

Axial strain

Axialstress(MPa)

0 0.005 0.01 0.015 0.020

20

40

60

80

100

120

140

160

C47-15-30-B2-G

C47-15-30-B4-G

C47-15-30-B6-G

a b

Fig. 5. Stressstrain behavior of specimens with differing FRP layers.



5/19

angle and viscosity turn out to be 30 and 5104 at best,

respectively.

On the other hand, steel and FRP have been represented with

S4R shell elements. The elasticity modulus and Poisson's ratio of

steel are considered to be 2105 MPa and 0.3, respectively. FRP is

dened as a laminated composite by determining the elasticity

and shear moduli as well as Poissons ratios along and perpendi-

cular to the bers' direction. Bearing in mind that rening the FRP

Axial strain

Axialstress(

MPa)

0 0.005 0.01 0.015 0.020

20

40

60

80

100

120

140

160

C47-15-30-B2-G

C47-15-30-B2-C

Hognestad

Fig. 6. Stressstrain behavior of specimens with differing FRP material.

Axial strain

Axialstress(MPa)

0 0.005 0.01 0.015 0.020

20

40

60

80

100

120

140

160

C40-15-30-B2-G

Hognestad

f = 40 MPac/

Axial strain

Axialstress(MPa)

0 0.005 0.01 0.015 0.020

20

40

60

80

100

120

140

160

C30-15-30-B2-G

Hognestad

f = 30 MPac/

Axial strain

Axials

tress(MPa)

0 0.005 0.01 0.015 0.020

20

40

60

80

100

120

140

160

C60-15-30-B2-G

Hognestad

f = 60 MPac/

Axial strain

Axials

tress(MPa)

0 0.005 0.01 0.015 0.020

20

40

60

80

100

120

140

160

C50-15-30-B2-G

Hognestad

f = 50 MPac/

a b

dc

Fig. 7. Concrete stressstrain curves in C30-15-30-B2-G for: (a) f 30 MPac = , (b) f 40 MPac = , (c) f 50 MPac = , and (d)f 60 MPac = .



6/19

mesh size better enhances the results' precision, the optimum

mesh size in this zone has been obtained to be 10 mm to com-

promise between the highest accuracy and the lowest time of

analysis. Furthermore, steel stiffening plates have been utilized in

the supporting and loading zones, and they have been representedwith R3D4 four-node solid elements. It is inevitable that the plate

height be taken as such to induce minimum stress concentration

and to be ineffective on the overall specimen's stiffness. To this

end, two plates with 20 mm thickness and with a high elasticity

modulus have been placed at the two column ends. In order to

dene the support constraints, the lower plate center is restrained

against all directions while the upper plate, bearing the com-

pressive load, is allowed to move only along the loading direction

(y)[19].

Finally, a surface-to-surface type contact has been assigned to

the connection between steel and concrete in the interest of a

unitary behavior in steel and concrete. In this respect, the concrete

surface around steel is considered as the master surface and steel

itself is the slave surface. Along with this assumption, the

deformation in steel will be attributed mainly to the deformation

of the concrete layer around it. To be more specic, the radial

contact type has been chosen as hard contactwhereas a friction

factor has been dened in the tangential direction. Of course, this

friction factor would never impact the peripheral sliding betweensteel and concrete, and, more generally, would not majorly affect

the overall behavior of the column [19]. Analysis attests that a

value of 0.1 for friction factor would make the deformation of the

slave layer totally dependent upon the master surface. Moreover,

to model the true interaction between them, a mesh-tieconstraint

has been imposed between concrete and the surrounding FRP

layer by tying between one node from FRP and one from the outer

surface of concrete[19].

3. Validation of FEM models

To issue further credit to the outcomes from analyses, the re-

sults ought to be specied for comparison in accordance with

Fig. 8. Representative cross sections with each hollow section ratio: (a) 0.25 = , (b) 0.5 = , and (c) 0.75 = .



7/19

existing experimental and FEM data. To this end, the experimental

results obtained by Teng et al. [19] and their FEM counterparts

calculated by Yu et al. [9] (made with a similar procedure as dis-

cussed herein) are considered for validation. Table 1 includes the

geometric properties of the specimens at hand. Each specimen is

named after its cross section type (C standing for Circular), cy-

lindrical compressive strength (e.g. 37 for 37 MPa), hollow section

ratio, dened as the ratio between the internal and external dia-

meters (A,B, andCshowing 0.28, 0.5, and 0.58, respectively), and

the number of FRP layers (2 showing two layers). The void size

represents the internal tube diameter, which can be determined

from the hollow section ratio multiplied by the overall diameter.FRP strips are of a laminated type and have been modeled as an-

nular ties (hoops), all the same as in Teng's experiments. Hence,

the FRP ties will mainly evince as conning agents operating

against the so-called hoop stresses in columns under pure

compression.

The mechanical properties of FRP layers have been collected in

Table 2, where Efrpis the elasticity modulus, to is the layer thick-

ness,h,rupis the rupture hoop strain (known to be always smallerthan the direct ultimate strain ofbers,fu). Finally, the mechan-ical properties of steel tie plates (placed at the column ends to

provide support constraints) are dened inTable 3.

The experimental and FEM specimens, prior to and after

loading, are shown inFigs. 2and 3.

Plots representing the evolution of the ultimate concrete stress

vs axial strain are depicted in Fig. 4. It might be appealing to the

reader that the compressive axial stress is read as a reaction force

at the node at which an axial displacement restraint is imposed

placed at the center of the top tie plate along the loading di-

rection divided by the net cross section area of the specimen,

dened as the area undergoing the compressive load. Moreover,

the total axial strain is determined from the total displacement at

the opposite steel plate divided by the overall specimen length.

This strain would equal that for the middle of the height. The

curves, as shown ifFig. 4, are in appropriate agreement with ex-

perimental data and the FEM counterparts from Ref. [19].

Experimental observations in this test attest that failure of thespecimens takes place in the form of tearing in FRP strips due to

increasing hoop stress. Afterwards, concrete will crush, and ulti-

mately the column will lose overall stability due to buckling in the

steel tube [19]. Tearing FRP strips would invariably occur at the

middle of the column height. The TsaiWu yield criterion with the

maximum-strain phenomenon has been taken into account in the

tearing of FRP strips in contact with concrete[21]. Throughout the

present study, all curves corresponding to FRP-reinforced speci-

mens are prescribed to end at the FRP tearing instant.

4. Parametric study

In the foregoing section, the effects of material and the number

of FRP layers as well as the inuence of compressive strength were

Axial strain

Axialstress(MPa)

0 0.01 0.02 0.03 0.04 0.050

20

40

60

80

100

120

140

160

C47-50-100-A2-C

C47-50-200-A2-C

C47-50-300-A2-C

Axial strain

Axialstress(MPa)

0 0.01 0.02 0.03 0.04 0.050

20

40

60

80

100

120

140

160

C47-40-100-A2-C

C47-40-200-A2-C

C47-40-300-A2-C

Axial strain

Axialstress(MPa)

0 0.01 0.02 0.03 0.04 0.050

20

40

60

80

100

120

140

160

C47-60-100-A2-C

C47-60-200-A2-C

C47-60-300-A2-C

a b

c

Fig. 9. Stressstrain curves for specimens: (a) C47-40-100-A2-C, C47-40-200-A2-C, and C47-40-300-A2-C; (b) C47-50-100-A2-C, C47-50-200-A2-C, and C47-50-300-A2-C;

(c) C47-60-100-A2-C, C47-60-200-A2-C, and C47-60-300-A2-C. The given specic lengths have been dened, in fact, to have a proper comparator intrinsic to the column.



8/19

evaluated on 6 and 4 specimens, respectively. In what follows, the

specimens have the same dimensions as those in Ref. [19]. Unlike

validation specimens, however, each specimen is named with

7 parameters here. For instance, C47-15-30-B2-G has a Circular

cross section, a 47 MPa compressive strength, a 15 cm diameter, a

30 cm height, a B hollow section ratio (as dened in Section 3),

and 2 FRP layers made of Glass bers. All FRP materials used

constitute either glass (G) or carbon (C) bers.Table 4shows the

mechanical properties of FRP strips, all of which have been dened

in Section 3. The steel tubes placed at the inner layer have the

properties as shown in Table 5.

The complete collection of specimens' properties for the

Time (analysis stage)

Axialstress(MPa)

0 0.05 0.1 0.15 0.2 0.25 0.3-300

-250

-200

-150

-100

-50

0

Right (-)

Left (+)

C47-40-100-A2-C


Axialstress(MPa)

0 0.05 0.1 0.15 0.2 0.25 0.3-300

-250

-200

-150

-100

-50

0

Right (-)

Left (+)

C47-40-100-A2-C


Axialstress(MPa)

0 0.05 0.1 0.15 0.2 0.25 0.3-300

-250

-200

-150

-100

-50

0

Right (-)

Left (+)

C47-40-300-A2-C

a b

c

e f

d

Fig. 10. Stress vs time curves and their corresponding deformed states belonging to specimens: (a,b) C47-40-100-A2-C, (c,d) C47-40-200-A2-C, and (e,f) C47-40-300-A2-C

specimens. One could easily observe the bifurcation phenomenon in (e) after 0.1 s from the loading outset.



9/19

investigation of the effects of FRP layers and compressive strength

are included inTables 6and 7, respectively. The parameters havebeen dened in advance. The name of each specimen is expressed

in the second column.

4.1. Investigating the effects due to the material and number of FRP

layers

Specimens respective of the FRP material are sufxed byG and

C, signifying GFRP and CFRP, respectively. FRP layers have been

provided in 2, 4, and 6 layers.Figs. 5and6demonstrate the effects

of FRP layers and material on the stressstrain behavior of speci-

mens. It can be observed in Fig. 5 that the ultimate compressive

stress in concrete increases by 45% when the number of FRP layers

changes from 2 to 6. Moreover, the stress

strain curve of CFDST

columns consists of two zones. The rst zone takes after that of

plain concrete, where steel and FRP are not yet signicantly in-volved in resisting the load. The secondary zone, however, is when

the stiffness of the material is, for the most part, dictated by the

reinforcing elements, including steel and FRP layers. Thus, the

number of FRP layers should have a remarkable inuence in the

slope of the secondary zone. Furthermore,Fig. 6, pertaining to two

specimens with dissimilar FRP layers, reveals that carbon bers

would have a greater effect on the ultimate compressive stress in

concrete, i.e. by 13%. By way of contrast, glass bers, due to their

lower rigidity, endure larger strains in comparison to carbon -

bers. Thus, using carbon bers would decrease the strain to failure,

and the material toughness would decline accordingly. The dashed

curves represent the Hognestad unconned specimens. The con-

ned specimen, as demonstrated in Fig. 6, exhibits a 460 percent

Axial strain

Axialstress(

MPa)

0 0.01 0.02 0.03 0.04 0.050

20

40

60

80

100

C47-40-300-A2-C

(0.003 , 45.328)

Fig.11. Stressstrain curve for the C47-40-300-A2-C specimen, showing an abrupt drop at the circled zone due to damage initiation. Further discussion will be given in the

following for this damage. It can be observed that the curve would continue, more or less, smoothly after this point.

Hoop stress (MPa)

Axial

stress(MPa)

0 1000 2000 3000 4000-300

-250

-200

-150

-100

-50

0

C47-40-300-A2-CTsai-Wu

(2734.49 , -69.60)

Fig.12. Compressive axial stress vs tensile hoop stress for a composite element having an intersection with the TsaiWu failure curverepresentative of tearing in FRPfor

the D47-40-300-A2-C specimen.



10/19

Fig.13. Contours showing: (a) hoop strain (mm/mm) and (b) hoop stress ( N/mm MPa2 ) for the C47-40-300-A2-C specimen. The color legend beside (a) shows the region

where the hoop strain has exceeded or is still below the FRP tearing limit.

Axial strain

Axialstress(MPa)

0 0.005 0.01 0.015 0.02 0.0250

25

50

75

100

C47-40-300-A2-CConcrete

Axial strain

Axialstress(MPa)

0 0.01 0.02 0.03 0.040

100

200

300

400

C47-40-300-A2-CSteel

Axial strain

Axialstress(MPa)

0 0.005 0.01 0.015 0.020

1000

2000

3000

4000

5000

C47-40-300-A2-C

FRP

a b

c

Fig. 14. Stressstrain curve in the C47-40-300-A2-C specimen belonging to: (a) steel, (b) concrete, and (c) FRP, demonstrating the differences existing in mechanical

behaviors as well as stress and strain ranges. The plots have been generated only for the ascending region.



11/19

increase in the strain to failure in comparison with that in its

unconned counterpart.

4.2. Investigating the effect of concrete compressive strength

The effect of concrete compressive strength was measured by

changing from 30 to 60 MPa in specimens with constantly 2 FRP

layers, as depicted inFig. 7. A deeper insight into this effect entails

that each stressstrain curve be compared with its counterpart for

plain concrete (without any steel reinforcing bars), basically

known as the Hognestad curve[2]. Then,Fig. 7shows the increaseextent in concrete axial (compressive) stress and strain as nor-

malized with respect to the Hognestad ultimate stress and strain,

i.e. f c and hog , respectively. It can be deduced that increasing

f c limits the increase level in ultimate compressive stress whereas

the ultimate strain increases by the same percentage since, by all

means, it is majorly affected by the FRP material rather than the

concrete compressive strength. Stated another way, increasing the

concrete compressive strength would downgrade the effect of

applying the CFDST technique on the overall strength and stability.

5. New models

In order to have more condence in the application of CFDST in

structures, the specimens had better be made in dimensions close

to reality. This is suggestive of more profound study into the effect

of column geometry within a wider range of parameters. To this

challenge, 54 specimens were made with various heights, dia-

meters, and 3 different hollow section ratios. The cross section of a

representative column with each hollow section ratio is shown in

Fig. 8, and the geometric properties of all specimens are com-

pletely enlisted inAppendix A.

5.1. Investigating the effect of column height

The effect of height is being evaluated according to 18 classes of

specimens, each class entitled to identical geometric properties

but 3 different heights. To this effect, the stressstrain curves have

been plotted up to the last load step. In accordance with Shanley's

buckling theory, the convex lines in a column deformed from its

straight state will undergo compressive exural stress while the

concave ones feel tensile exural stress. Thus, bending in the

column is triggered by the so-called buckling effect (Fig. 9). In this

respect, for each specimen, the stress vs time curve was inspected

for two points on the same altitude but one belonging to the

convex zone and the other to the concave zone. As long as the two

curves are concurrent, the column remains stable. All the same,

buckling occurs at the onset of separation between the two curves,

a phenomenon known as bifurcation. A representative bifurcation

Axial strain

Axialstre

ss(MPa)

0 0.005 0.01 0.015 0.020

20

40

60

80

C47-40-300-B2-C

C47-50-300-B2-C

C47-60-300-B2-C

Axial strain

Axialstre

ss(MPa)

0 0.005 0.01 0.015 0.020

20

40

60

80

C47-40-300-A2-C

C47-50-300-A2-C

C47-60-300-A2-C

Axial strain

Axialstress(MPa)

0 0.005 0.01 0.015 0.020

20

40

60

80

C47-40-300-C2-C

C47-50-300-C2-C

C47-60-300-C2-C

a b

c

Fig. 15. Axial load vs strain plots for specimens, with constant ratio, made with 300 mm diameters: (a) C47-40-300-A2-C, C47-50-300-A2-C, and C47-60-300-C; (b) C47-40-300-B2-C, C47-50-300-B2-C, and C47-60-300-B2-C; (c) C47-40-300-C2-C, C47-50-300-C2-C, and C47-60-300-C2-C. The abrupt drops occurring shortly after the yield

point indicate premature buckling in the specimen.



12/19

Hoop stress (MPa)

Axialstre

ss(MPa)

0 1000 2000 3000 4000-300

-250

-200

-150

-100

-50

0

C47-30-300-B2-G

Tsai-Wu

Hoop stress (MPa)

Axialstre

ss(MPa)

0 1000 2000 3000 4000-300

-250

-200

-150

-100

-50

0

C47-30-300-A2-G

Tsai-Wu

Hoop stress (MPa)

Axialstress(MPa)

0 1000 2000 3000 4000-300

-250

-200

-150

-100

-50

0

C47-30-300-C2-G

Tsai-Wu

a b

c

Fig. 16. Axial vs hoop stress for composite elements in the unstiffened specimens with 300 mm diameters (made with GFR), in conjunction with the Tsai

Wu failure curvefor: (a) D47-30-300-A2-G, (b) D47-30-300-B2-G, and (c) D47-30-300-C2-G specimens.

Fig. 17. Cross section of specimens strengthened with steel plates, all with a 300 mm outer diameter but different inner diameters.

Table 8

Properties of specimens strengthened with steel plates as compared with their counterparts without stiffeners.

No. of specimen Type Do (mm) H (mm) No. of FRP layers Di (mm) Hollow section ratio () ti (mm) Concrete compressive strength (f c )

65 C47-30-300-A2-G 300 3000 2 75 0.25 4 46.7

66 C47-30-300-A2-G-S 300 3000 2 75 0.25 4 46.7

67 C47-30-300-B2-G 300 3000 2 150 0 .5 5.6 46.7

68 C47-30-300-B2-G-S 300 3000 2 150 0.5 5.6 46.7

69 C47-30-300-C2-G 300 3000 2 225 0.75 6.3 46.7

70 C47-30-300-C2-G-S 300 3000 2 225 0.75 6.3 46.7



13/19

Displacement (mm)

Axiallo

ad(kN)

0 5 10 15 20 25 300

1000

2000

3000

4000

5000

C47-30-300-B2-G

C47-30-300-B2-G-S

Displacement (mm)

Axiallo

ad(kN)

0 5 10 15 20 25 300

1000

2000

3000

4000

5000

C47-30-300-A2-G

C47-30-300-A2-G-S

Displacement (mm)

Axialload(kN)

0 5 10 15 20 25 300

1000

2000

3000

4000

5000

C47-30-300-C2-G

C47-30-300-C2-G-S

a b

c

Fig.18. Plots of axial load vs axial displacement for: (a) C47-30-300-A2-G and C47-30-300-A2-G-S, (b) C47-30-300-B2-G and C47-30-300-B2-G-S, (c) C47-30-300-C2-G andC47-30-300-C2-G-S specimens.

Fig. 19. FEM displacement-to-buckling (vertical displacement in mm) contours for C47-30-300-A2-G: (a) unstiffened and (b) stiffened specimens.



14/19

curve for a buckled specimen is shown inFig. 10. In order to have a

proper comparator intrinsic to the column, it is favorable to

identify a specic length, dened as the ratio between the length

and the cross section diameter, i.e. L D/ = . Otherwise, the out-

comes cannot be generalized for every similar column because a

long column with a large diameter would behave like a short

column as far as stability is concerned. A clever probe into stress

time plots reveals that specimens with 510

3 , which corre-

spond to all specimens with lengths below 3 m, will never sufferfrom bifurcation buckling or they would, in the worst case sce-

nario, face local buckling. However, specimens with higher specic

lengths those pertaining to a 3 m length will encounter an

abrupt stress failure signifying an overall buckled state. Since this

is more practically representative of full-sized columns in real

structures, further specimens have all been regarded to have 5> .

For instance, the stressstrain curve for the C47-40-300-A2-C

specimen is shown inFig. 11. The curve declares that, at point A,

with the stress and stress given in the gure, there exists slight

decrease in stress whereas the stress will continue to rise after-

wards. In fact, as for the Riks arc-length method in the FEM ana-

lyses[22], the curves will extend up to the last load step. However,

full agreement between experimental and FEM data would be

acquired if the instant when tearing in FRP strips occurs is eluci-

dated and the stressstrain curve is plotted up to that point. To this

aim, two alternative methods have been applied comparatively:

using the TsaiWu [21]and the maximum strain criteria [23]. Inthe former method, the compressive stress vs hoop tensile stress

was plotted for a FRP element, and the point of intersection with

the TsaiWu failure curve, as shown inFig. 12, was believed as the

tearing point for the FRP strip. In the latter, however, the FRP hoop

stress exceedingh,rupwould mark rupture in the FRP strip.Fig. 13shows the hoop stress and strain for the structure at the FRP

tearing instant on the basis of the TsaiWu criterion. The contour

legend for the given example shows that the hoop stress has

Table 9

Ratio between the ultimate axial displacements of stiffened and ordinary specimens ( RFstanding for the reaction force).

Specimen D D/CS C (%) RF RF /CS C (%)

C47-30-300-A2-G 182 119

C47-30-300-B2-G 127 102

C47-30-300-C2-G 126 107

Axial strain

Axialstress(MPa)

0 0.005 0.01 0.015 0.020

20

40

60

80

C47-40-300-A2-C

C47-40-300-B2-C

C47-40-300-C2-C

Hognestad

Axial strain

Axialstress(MPa)

0 0.005 0.01 0.015 0.020

20

40

60

80

C47-40-300-A2-C

C47-40-300-B2-C

C47-40-300-C2-C

Hognestad

Axial strain

Axialstress(MPa)

0 0.005 0.01 0.015 0.020

20

40

60

80

C47-40-300-A2-C

C47-40-300-B2-C

C47-40-300-C2-C

Hognestad

a b

c

Fig. 20. Axial load vs strain for specimens with varying hollow section ratios: (a) C47-40-300-A2-C, C47-40-300-B2-C, and C47-40-300-C2-C, (b) C47-50-300-A2-C, C47-50-

300-B2-C, and C47-50-300-C2-C, (c) C47-60-300-A2-C, C47-60-300-B2-C, and C47-60-300-C2-C.



15/19

exceeded 0.102, and thus both criteria imply tearing in FRP strips.

However, for the sake of further condence, the smaller strain to

tearing has been chosen as the determinant of tearing in FRP, and

the stressstrain curves have been extended up to the FRP tearing

point. It might be appealing to the reader that the FRP tearing

stress lies between 852 to 2678 MPa. Further clarication need be

made regarding the abrupt drop at point A (as shown inFig. 11). In

actual fact, nonlinear analysis in ABAQUS is identied by means of

time steps. Hence, the total time for every evidence can be tracked.

The time when the stress and strain reach those at point A is 0.018

for the given specimen atFig. 11. With that said, the stressstrain

curve for an element belonging to the middle of the height and

thickness of the column has been scrutinized at the 0.018 instant,

as shown inFig. 14. At this point, the FRP stressstrain curve shows

that FRP has not torn yet. Moreover, the concrete stressstrain

curve demonstrates that the concrete compressive stress has ex-

ceeded f0.5 c , and hence concrete is in the post-cracking nonlinear

zone. Finally, the steel stressstrain curve shows that steel has

yielded. Therefore, damage has initiated at this point, inducing a

sharp drop in the curve (Fig. 15).

5.2. Investigating the effect of column diameter

The effect of diameter was evaluated in 24 specimens, 12 of

them with CFRP and 12 with GFRP bers. All properties were kept

constant except diameter, which varied with 400, 500, and

600 mm values. A general comparison between the mechanical

behaviors of two columns demands, however, that the value of the

diameter be used with a specic length ratio . Fig. 15, exhibitingthe axial load vs strain plots for various specimens made with a

300 mm diameter, indicates that, with a constantratio, all suchspecimens would undergo buckling prior to FRP tearing. Moreover,

the ultimate axial stress experiences small difference with in-

creasing cross section diameter. To obviate this challenge, stiffen-

ing plates were used to delay buckling to occur after FRP strips

would tear. With the same column height, specimens made with

400, 500, and 600 mm, however, would buckle as soon as or

slightly after the FRP strips have torn, i.e. buckling occurs in the

hybrid column. Hence, these specimens would not demand being

stiffened. Fig. 16 depicts the axial vs hoop stress for composite

elements in the unstiffened specimens with 300 mm diameters

Axial strain

Axialload(

kN)

0 0.005 0.01 0.015 0.02 0.0250

2000

4000

6000

8000

10000

12000

14000

16000

C47-50-300-A2-C

Steel alone

Concrete alone

Sum (steel+conc)

C47-50-300-A2-G

Axial strain

Axialload(kN)

0 0.005 0.01 0.015 0.02 0.0250

2000

4000

6000

8000

10000

12000

14000

16000

C47-60-300-A2-C

Steel alone

Concrete alone

Sum (steel+conc)

C47-60-300-A2-G

a

b

Fig. 21. Axial load vs strain for equivalent steel and concrete cross sections as

compared with their summation and the hybrid counterparts in: (a) C47-50-300-

A2-G and C47-50-300-A2-C, (b) C47-60-300-A2-G and C47-60-300-A2-C.

Axial strain

Axialload(kN)

0 0.005 0.01 0.015 0.02 0.0250

2000

4000

6000

8000

10000

12000

14000

16000

C47-50-300-A2-C

Steel alone

Concrete alone

Sum (steel+conc)

C47-50-300-A2-G

Axial strain

Axialload(kN)

0 0.005 0.01 0.015 0.02 0.0250

2000

4000

6000

8000

10000

12000

14000

16000

C47-60-300-A2-CSteel alone

Concrete alone

Sum (steel+conc)

C47-60-300-A2-G

a

b

Fig. 22. Axial load vs strain for equivalent steel and concrete cross sections as

compared with their summation and the hybrid counterparts in: (a) C47-50-300-

B2-G and C47-50-300-B2-C, (b) C47-60-300-B2-G and C47-60-300-B2-C.



16/19

(made with GFR), in conjunction with the TsaiWu failure curve.

According to this criterion, a closed curve is identied as the

yield locus on the basis of the mechanical properties of the two

principal directions of the composite element. The point of inter-

section between this locus and the axial vs hoop stress curve de-

notes the pair of stresses at the yield onset. As clearly observed in

Fig. 16, the curves belonging to unstiffened specimens would di-

gress towards the hoop stress axis prior to intersecting with the

Tsai

Wu yield locus. To overcome this issue, steel stiffening plates

with a 6 mm thickness were connected to the steel tube. The

width of the stiffening plate was dictated such that there be al-

ways a 15 mm distance between the outer edge of the plate and

the inner surface of the FRP layer.

The properties of the stiffened specimens are tabulated in

Table 8as compared to their unstiffened counterparts. Obviously,

the naming follows a similar convention as in previous specimens,

with the only difference of adding an Ssufx to the end, symbo-

lizing the use of a stiffening plate. Fig. 17 shows the schematic

Axial strain

Axialload(kN)

0 0.005 0.01 0.015 0.02 0.0250

2000

4000

6000

8000

10000

12000

14000

16000

C47-50-300-C2-C

Steel alone

Concrete alone

Sum (steel+conc)

C47-50-300-C2-G

Axial strain

Axialload(kN)

0 0.005 0.01 0.015 0.02 0.0250

2000

4000

6000

8000

10000

12000

14000

16000

C47-60-300-C2-CSteel alone

Concrete alone

Sum (steel+conc)

C47-60-300-C2-G

a

b

Fig. 23. Axial load vs strain for equivalent steel and concrete cross sections as compared with their summation and the hybrid counterparts in: (a) C47-50-300-C2-G and

C47-50-300-C2-C, (b) C47-60-300-C2-G and C47-60-300-C2-C.

Table 10

Load bearing capacity in equivalent steel cross sections, showing the signicant reduction in the cross sectional area and thickness when a hybrid design is used.

Model PCFDST DSD tSD ASD DSeq tSeq ASeq A A/S eq S D

C47-50-300-A2-G-C 10447.1 125 6.3 2349.31 800 30 72570.9 30

C47-60-300-A2-G-C 14494.2 150 8 3568.84 1100 30 100845 28

C47-50-300-B2-G-C 9361.36 250 8 6082.12 750 30 67858 11

C47-60-300-B2-G-C 13065.5 300 8.8 8050.51 1000 30 91420 11

C47-50-300-C2-G-C 8183.08 375 10 11467 650 30 58433.6 5

C47-60-300-C2-G-C 11104.4 450 12 16512 900 30 81995.5 5



17/19

cross section of stiffened specimens.

Stiffened specimens would experience larger displacements

owing to their increased lateral stiffness. This can be easily ex-

plored fromFig. 18andTable 9. The axial displacement in all cases

has been measured at the column midpoint.

Table 9reveals that the ultimate displacement ratio is clearly

larger in stiffened columns than that in unstiffened specimens. It

might be tempting to see the displacement contours of C47-30-

300-A2-G and C47-30-300-A2-G-S at the buckling moment. Thiscan be seen inFig. 19. It could be observed that the buckling time

step and the displacement to buckling are clearly larger in stif-

fened specimens. For the given specimen, for instance, the ulti-

mate displacement in the stiffened and unstiffened counterparts

were 14 and 8 mm, respectively.

The combined effects due to diameter and thickness can be

sought through the D t/o o parameter, as the ratio between column

external diameter and outside FRP thickness. In fact, a decreasing

D t/o o parameter will result in increasing the FRP thickness, which

increases the maximum hoop stress and would accordingly

heighten the concrete ultimate compressive stress. By way of

contrast,D t/i i, as ratio between the internal counterparts, does not

tend to have a remarkable effect on the column compressive be-

havior (this could be observed inFig. 19).

5.3. Investigating the effect of hollow section ratio

Specimens corresponding to evaluating the effect of hollow

section ratio were subjected to have the specic length ratio of3000/400 7.5= , 3000/500 6.0000= , and 3000/600 5.0= and hol-

low section ratios of 0.25 (A), 0.5 (B), and 0.75 (C). The hollow

section ratios were selected far apart to ensure that the corre-

sponding effect is sufciently obvious (Fig. 20).Fig. 21portrays the

effect of hollow section ratio on the stressstrain behavior while

all other parameters have been kept invariant. It can be deduced

that the hollow section ratio does not remarkably affect the stress

strain behavior of the hybrid column in case that all other geo-

metric properties are kept constant.

6. Load bearing capacity of specimens compared at varying

constituents

This section is aimed at showing how the existence and con-

nectivity of different constituents of a hybrid column, including

steel, concrete, and GFRP or CFRP strips, would inuence the

stressstrain behavior. In this sense, the axial load vs strain curve

has been plotted for various specimens, each plot comprising the

equivalent steel and concrete constituents alone, the sum of axial

loads induced by equivalent steel and concrete, and the one with

steel, concrete, concrete, and FRP strips (either in glass or carbon

bers) all existing in the hybrid column inFigs. 2123.

The equivalent steel cross section is obtained by picking a trialcross section under identical axial loading and calculating theslenderness ratio kL r/ = , then checking the existing stress with

the allowable compressive stress Fa according to Ref. [24]. By de-

nition,k is the effective length factor, L is the unsupported length

(equal to the height of the column), and ris the minimum gyration

radius of the cross section. On the other hand, a concrete equiva-

lent cross section can be designed to bear the existing load in

absence of other constituents, in accordance with building code

requirements [25].

Table 10 reveals that an equivalent steel cross section should

have an area between 5 and 30 times that of the steel tube used in

the hybrid column. DSD and tSD could be dened as the hybrid

column steel tube diameter and thickness, respectively. Corre-

spondingly, DSeq and tSeqare the same parameters for the equiva-

lent steel cross section. Hence,ASD and ASeqwill be the steel cross

sectional area in the hybrid and the equivalent steel column, re-

spectively. The hybrid curves have continued up to the point

where FRP is torn, the steel curves have ended at the buckling

load, and the concrete curves have been plotted up to or slightly

past the concrete ultimate strain 0.004.

7. Concluding remarks

Specic focus has been placed over hybrid columns known as

CFDST in the literature over the past few decades. Of particular

importance is the effects of geometric properties on the me-

chanical behavior of these columns under compression. The pre-

sent work investigates the nonlinear behavior of CFDST using ex-

tended FEM analysis. The effect of various parameters including

the material and number of FRP layers and concrete compressive

strength as well as height, diameter, and hollow section ratio were

explored. Results are conducive to the following outcomes:

1. Designing a column in the form of CFDST would intensely in-

crease the load bearing capacity in comparison to equivalent

designs (under the same loading scheme) with the presence of

steel and concrete alone. The design proves even better than

the sum of steel and concrete designs, each designed against

the whole loading.

2. Increasing the number of FRP layers only from 2 to 6 would

induce a 45 percent increase in the concrete ultimate com-

pressive stress. This accounts for a great inuence within a

small range of improvement.

3. Changing bers from glass to carbon would increase the ulti-

mate compressive stress of concrete by 13 percent. In the

meantime, it would lower the strain to failure as for the more

brittle nature of carbon.

4. Increasing the concrete compressive strength would create a

more remarkable effect on the load bearing capacity in a hybrid

column than in an ordinarily reinforced column. That is, the

load bearing capacity and strain to failure were increased be-

tween 3090 percent and 460 percent, respectively in com-

parison to those in an ordinary reinforced concrete column.

5. With a specied length, increasing the overall diameter of the

column would signicantly increase the load bearing capacity,

irrespective of the hollow section ratio value. Quantitatively,

increasing the diameter by 100 and 200 mm would lead to a 45

and 200 percent increase in the ultimate load, respectively.

6. Employing steel stiffening plates in columns with high specic

lengths (e.g. 10 = ) would not only increase the ultimate dis-

placement by 2682 percent, but also delay the steel tubebuckling incidence up to the point of FRP tearing. This helps

maximizing the performance of the column under a combined

state of compressive and lateral loads (e.g. against earthquake).

7. An increase of 0.25 and 0.5 applied to the initial hollow section

ratio of 0.25 would lead to a 2070% increase in the ultimate

axial load, respectively.

Appendix A

SeeTable A1.



18/19

References

[1] H.T. Hu, C.S. Huang, M.H. Wu, Y.M. Wu, Nonlinear analysis of axially loaded

concrete-lled tube columns with connement effect, J. Struct. Eng. 129 (10)

(2003) 13221329.[2] E. Hognestad, Study of combined bending and axial load in reinforced concrete

members,University of Illinois. Engineering Experiment Station. Bulletin; no. 399,

1951.[3] H. Shakir-Khalil, S. Illouli, Composite columns of concentric steel tubes, 1989.[4] S. Wei, S.T. Mau, C. Vipulanandan, S.K. Mantrala, Performance of new sandwich

tube under axial loading: experiment, J. Struct. Eng. 121 (12) (1995)

18061814.[5] T.H. Han, K.H. Han, S.Y. Han, S.N. Kim, J.O. Kang, Y.J. Kang, The behavior of an

internallyconned hollow concretelled steel tube column, in: Proceedings of

the 8th KoreaJapan joint seminar, vol. 3, 2005.[6] X.L. Zhao, R. Grzebieta, Strength and ductility of concrete lled double skin

(SHS inner and SHS outer) tubes, Thin-Walled Struct. 40 (2) (2002) 199213.[7] Z. Tao, L.H. Han, X.L. Zhao, Behavior of concrete-lled double skin (CHS inner

and CHS outer) steel tubular stub columns and beam-columns, J. Constr. Steel

Res. 60 (8) (2004) 11291158.

[8] A.Z. Fam, S.H. Rizkalla, Flexural behavior of concrete-lled ber-reinforcedpolymer circular tubes, J. Compos. Constr. 6 (2) (2002) 123132.

[9] T.T.J.G. Yu, J.G. Teng, Y.L. Wong, Stress-strain behavior of concrete in hybrid

FRP-concrete-steel double-skin tubular columns, J. Struct. Eng. 136 (4) (2009)

379389.[10] S. Tokgoz, C. Dundar, Tests of eccentrically loaded L-shaped section steel bre

high strength reinforced concrete and composite columns, Eng. Struct. 38

(2012) 134141.[11] H.T. Hu, F.C. Su, Nonlinear analysis of short concrete-lled double skin tube

columns subjected to axial compressive forces, Mar. Struct. 24 (4) (2011)

319337.[12] Z. Tao, L.H. Han, Behaviour of concrete-lled double skin rectangular steel

tubular beamcolumns, J. Constr. Steel Res. 62 (7) (2006) 631646.[13] H. Huang, L.H. Han, Z. Tao, X.L. Zhao, Analytical behaviour of concrete-lled

double skin steel tubular (CFDST) stub columns, J. Constr. Steel Res. 66 (4)

(2010) 542555.[14] L.H. Han, Y.J. Li, F.Y. Liao, Concrete-lled double skin steel tubular (CFDST)

columns subjected to long-term sustained loading, Thin-Walled Struct. 49 (12)

(2011) 15341543.

Table A1

Geometric properties of specimens as for the study of height, diameter, and hollow section ratio.

No. of specimen Type Do(mm) H (mm) No. of FRP layers Di (mm) Hollow section ratio () ti (mm) Concrete compressive strength (f c )

11 C47-40-100-A2-G 400 1000 2 100 0.25 5.6 46.7

12 C47-40-100-B2-G 400 1000 2 200 0.50 6.3 46.7

13 C47-40-100-C2-G 400 1000 2 300 0.75 8.0 46.7

14 C47-40-100-A2-C 400 1000 2 100 0.25 5.6 46.7

15 C47-40-100-B2-C 400 1000 2 200 0.50 6.3 46.7

16 C47-40-100-C2-C 400 1000 2 300 0.75 8.0 46.717 C47-40-200-A2-G 400 2000 2 100 0.25 5.6 46.7

18 C47-40-200-B2-G 400 2000 2 200 0.50 6.3 46.7

19 C47-40-200-C2-G 400 2000 2 300 0.75 8.0 46.7

20 C47-40-200-A2-C 400 2000 2 100 0.25 5.6 46.7

21 C47-40-200-B2-C 400 2000 2 200 0.50 6.3 46.7

22 C47-40-200-C2-C 400 2000 2 300 0.75 8.0 46.7

23 C47-40-300-A2-G 400 3000 2 100 0.25 5.6 46.7

24 C47-40-300-B2-G 400 3000 2 200 0.50 6.3 46.7

25 C47-40-300-C2-G 400 3000 2 300 0.75 8.0 46.7

26 C47-40-300-A2-C 400 3000 2 100 0.25 5.6 46.7

27 C47-40-300-B2-C 400 3000 2 200 0.50 6.3 46.7

28 C47-40-300-C2-C 400 3000 2 300 0.75 8.0 46.7

29 C47-50-100-A2-G 500 1000 2 125 0.25 6.3 46.7

30 C47-50-100-B2-G 500 1000 2 250 0.50 8.0 46.7

31 C47-50-100-C2-G 500 1000 2 375 0.75 10.0 46.7

32 C47-50-100-A2-C 500 1000 2 125 0.25 6.3 46.7

33 C47-50-100-B2-C 500 1000 2 250 0.50 8.0 46.734 C47-50-100-C2-C 500 1000 2 375 0.75 10.0 46.7

35 C47-50-200-A2-G 500 2000 2 125 0.25 6.3 46.7

36 C47-50-200-B2-G 500 2000 2 250 0.50 8.0 46.7

37 C47-50-200-C2-G 500 2000 2 375 0.75 10.0 46.7

38 C47-50-200-A2-C 500 2000 2 125 0.25 6.3 46.7

39 C47-50-200-B2-C 500 2000 2 250 0.50 8.0 46.7

40 C47-50-200-C2-C 500 2000 2 375 0.75 10 46.7

41 C47-50-300-A2-G 500 3000 2 125 0.25 6.3 46.7

42 C47-50-300-B2-G 500 3000 2 250 0.50 8.0 46.7

43 C47-50-300-C2-G 500 3000 2 375 0.75 10.0 46.7

44 C47-50-300-A2-C 500 3000 2 125 0.25 6.3 46.7

45 C47-50-300-B2-C 500 3000 2 250 0.50 8.0 46.7

46 C47-50-300-C2-C 500 3000 2 375 0.75 10.0 46.7

47 C47-60-100-A2-G 600 1000 2 150 0.25 8.0 46.7

48 C47-60-100-B2-G 600 1000 2 300 0.50 8.8 46.7

49 C47-60-100-C2-G 600 1000 2 450 0.75 12.0 46.7

50 C47-60-100-A2-C 600 1000 2 150 0.25 8.0 46.7

51 C47-60-100-B2-C 600 1000 2 300 0.50 8.8 46.7

52 C47-60-100-C2-C 600 1000 2 450 0.75 12.0 46.7

53 C47-60-200-A2-G 600 2000 2 150 0.25 8.0 46.7

54 C47-60-200-B2-G 600 2000 2 300 0.50 8.8 46.7

55 C47-60-200-C2-G 600 2000 2 450 0.75 12.0 46.7

56 C47-60-200-A2-C 600 2000 2 150 0.25 8.0 46.7

57 C47-60-200-B2-C 600 2000 2 300 0.50 8.8 46.7

58 C47-60-200-C2-C 600 2000 2 450 0.75 12.0. 46.7

59 C47-60-300-A2-G 600 3000 2 150 0.25 8.0 46.7

60 C47-60-300-B2-G 600 3000 2 300 0.50 8.8 46.7

61 C47-60-300-C2-G 600 3000 2 450 0.75 12.0 46.7

62 C47-60-300-A2-C 600 3000 2 150 0.25 8.0 46.7

63 C47-60-300-B2-C 600 3000 2 300 0.50 8.8 46.7

64 C47-60-300-C2-C 600 3000 2 450 0.75 12.0 46.7

http://refhub.elsevier.com/S0263-8231(15)30044-6/sbref1http://refhub.elsevier.com/S0263-8231(15)30044-6/sbref1http://refhub.elsevier.com/S0263-8231(15)30044-6/sbref1http://refhub.elsevier.com/S0263-8231(15)30044-6/sbref1http://refhub.elsevier.com/S0263-8231(15)30044-6/sbref1http://refhub.elsevier.com/S0263-8231(15)30044-6/sbref1http://refhub.elsevier.com/S0263-8231(15)30044-6/sbref1http://refhub.elsevier.com/S0263-8231(15)30044-6/sbref1http://refhub.elsevier.com/S0263-8231(15)30044-6/sbref1http://refhub.elsevier.com/S0263-8231(15)30044-6/sbref1http://refhub.elsevier.com/S0263-8231(15)30044-6/sbref2http://refhub.elsevier.com/S0263-8231(15)30044-6/sbref2http://refhub.elsevier.com/S0263-8231(15)30044-6/sbref2http://refhub.elsevier.com/S0263-8231(15)30044-6/sbref2http://refhub.elsevier.com/S0263-8231(15)30044-6/sbref2http://refhub.elsevier.com/S0263-8231(15)30044-6/sbref2http://refhub.elsevier.com/S0263-8231(15)30044-6/sbref3http://refhub.elsevier.com/S0263-8231(15)30044-6/sbref3http://refhub.elsevier.com/S0263-8231(15)30044-6/sbref3http://refhub.elsevier.com/S0263-8231(15)30044-6/sbref3http://refhub.elsevier.com/S0263-8231(15)30044-6/sbref3http://refhub.elsevier.com/S0263-8231(15)30044-6/sbref3http://refhub.elsevier.com/S0263-8231(15)30044-6/sbref3http://refhub.elsevier.com/S0263-8231(15)30044-6/sbref4http://refhub.elsevier.com/S0263-8231(15)30044-6/sbref4http://refhub.elsevier.com/S0263-8231(15)30044-6/sbref4http://refhub.elsevier.com/S0263-8231(15)30044-6/sbref4http://refhub.elsevier.com/S0263-8231(15)30044-6/sbref4http://refhub.elsevier.com/S0263-8231(15)30044-6/sbref4http://refhub.elsevier.com/S0263-8231(15)30044-6/sbref4http://refhub.elsevier.com/S0263-8231(15)30044-6/sbref4http://refhub.elsevier.com/S0263-8231(15)30044-6/sbref5http://refhub.elsevier.com/S0263-8231(15)30044-6/sbref5http://refhub.elsevier.com/S0263-8231(15)30044-6/sbref5http://refhub.elsevier.com/S0263-8231(15)30044-6/sbref5http://refhub.elsevier.com/S0263-8231(15)30044-6/sbref5http://refhub.elsevier.com/S0263-8231(15)30044-6/sbref5http://refhub.elsevier.com/S0263-8231(15)30044-6/sbref5http://refhub.elsevier.com/S0263-8231(15)30044-6/sbref5http://refhub.elsevier.com/S0263-8231(15)30044-6/sbref5http://refhub.elsevier.com/S0263-8231(15)30044-6/sbref6http://refhub.elsevier.com/S0263-8231(15)30044-6/sbref6http://refhub.elsevier.com/S0263-8231(15)30044-6/sbref6http://refhub.elsevier.com/S0263-8231(15)30044-6/sbref6http://refhub.elsevier.com/S0263-8231(15)30044-6/sbref6http://refhub.elsevier.com/S0263-8231(15)30044-6/sbref6http://refhub.elsevier.com/S0263-8231(15)30044-6/sbref7http://refhub.elsevier.com/S0263-8231(15)30044-6/sbref7http://refhub.elsevier.com/S0263-8231(15)30044-6/sbref7http://refhub.elsevier.com/S0263-8231(15)30044-6/sbref7http://refhub.elsevier.com/S0263-8231(15)30044-6/sbref7http://refhub.elsevier.com/S0263-8231(15)30044-6/sbref7http://refhub.elsevier.com/S0263-8231(15)30044-6/sbref7http://refhub.elsevier.com/S0263-8231(15)30044-6/sbref7http://refhub.elsevier.com/S0263-8231(15)30044-6/sbref7http://refhub.elsevier.com/S0263-8231(15)30044-6/sbref7http://refhub.elsevier.com/S0263-8231(15)30044-6/sbref8http://refhub.elsevier.com/S0263-8231(15)30044-6/sbref8http://refhub.elsevier.com/S0263-8231(15)30044-6/sbref8http://refhub.elsevier.com/S0263-8231(15)30044-6/sbref8http://refhub.elsevier.com/S0263-8231(15)30044-6/sbref8http://refhub.elsevier.com/S0263-8231(15)30044-6/sbref8http://refhub.elsevier.com/S0263-8231(15)30044-6/sbref8http://refhub.elsevier.com/S0263-8231(15)30044-6/sbref8http://refhub.elsevier.com/S0263-8231(15)30044-6/sbref9http://refhub.elsevier.com/S0263-8231(15)30044-6/sbref9http://refhub.elsevier.com/S0263-8231(15)30044-6/sbref9http://refhub.elsevier.com/S0263-8231(15)30044-6/sbref9http://refhub.elsevier.com/S0263-8231(15)30044-6/sbref9http://refhub.elsevier.com/S0263-8231(15)30044-6/sbref9http://refhub.elsevier.com/S0263-8231(15)30044-6/sbref9http://refhub.elsevier.com/S0263-8231(15)30044-6/sbref9http://refhub.elsevier.com/S0263-8231(15)30044-6/sbref9http://refhub.elsevier.com/S0263-8231(15)30044-6/sbref10http://refhub.elsevier.com/S0263-8231(15)30044-6/sbref10http://refhub.elsevier.com/S0263-8231(15)30044-6/sbref10http://refhub.elsevier.com/S0263-8231(15)30044-6/sbref10http://refhub.elsevier.com/S0263-8231(15)30044-6/sbref10http://refhub.elsevier.com/S0263-8231(15)30044-6/sbref10http://refhub.elsevier.com/S0263-8231(15)30044-6/sbref10http://refhub.elsevier.com/S0263-8231(15)30044-6/sbref10http://refhub.elsevier.com/S0263-8231(15)30044-6/sbref11http://refhub.elsevier.com/S0263-8231(15)30044-6/sbref11http://refhub.elsevier.com/S0263-8231(15)30044-6/sbref11http://refhub.elsevier.com/S0263-8231(15)30044-6/sbref11http://refhub.elsevier.com/S0263-8231(15)30044-6/sbref11http://refhub.elsevier.com/S0263-8231(15)30044-6/sbref11http://refhub.elsevier.com/S0263-8231(15)30044-6/sbref11http://refhub.elsevier.com/S0263-8231(15)30044-6/sbref11http://refhub.elsevier.com/S0263-8231(15)30044-6/sbref11http://refhub.elsevier.com/S0263-8231(15)30044-6/sbref11http://refhub.elsevier.com/S0263-8231(15)30044-6/sbref11http://refhub.elsevier.com/S0263-8231(15)30044-6/sbref11http://refhub.elsevier.com/S0263-8231(15)30044-6/sbref10http://refhub.elsevier.com/S0263-8231(15)30044-6/sbref10http://refhub.elsevier.com/S0263-8231(15)30044-6/sbref10http://refhub.elsevier.com/S0263-8231(15)30044-6/sbref10http://refhub.elsevier.com/S0263-8231(15)30044-6/sbref9http://refhub.elsevier.com/S0263-8231(15)30044-6/sbref9http://refhub.elsevier.com/S0263-8231(15)30044-6/sbref9http://refhub.elsevier.com/S0263-8231(15)30044-6/sbref8http://refhub.elsevier.com/S0263-8231(15)30044-6/sbref8http://refhub.elsevier.com/S0263-8231(15)30044-6/sbref8http://refhub.elsevier.com/S0263-8231(15)30044-6/sbref8http://refhub.elsevier.com/S0263-8231(15)30044-6/sbref7http://refhub.elsevier.com/S0263-8231(15)30044-6/sbref7http://refhub.elsevier.com/S0263-8231(15)30044-6/sbref7http://refhub.elsevier.com/S0263-8231(15)30044-6/sbref7http://refhub.elsevier.com/S0263-8231(15)30044-6/sbref6http://refhub.elsevier.com/S0263-8231(15)30044-6/sbref6http://refhub.elsevier.com/S0263-8231(15)30044-6/sbref6http://refhub.elsevier.com/S0263-8231(15)30044-6/sbref6http://refhub.elsevier.com/S0263-8231(15)30044-6/sbref5http://refhub.elsevier.com/S0263-8231(15)30044-6/sbref5http://refhub.elsevier.com/S0263-8231(15)30044-6/sbref5http://refhub.elsevier.com/S0263-8231(15)30044-6/sbref4http://refhub.elsevier.com/S0263-8231(15)30044-6/sbref4http://refhub.elsevier.com/S0263-8231(15)30044-6/sbref4http://refhub.elsevier.com/S0263-8231(15)30044-6/sbref4http://refhub.elsevier.com/S0263-8231(15)30044-6/sbref3http://refhub.elsevier.com/S0263-8231(15)30044-6/sbref3http://refhub.elsevier.com/S0263-8231(15)30044-6/sbref3http://refhub.elsevier.com/S0263-8231(15)30044-6/sbref2http://refhub.elsevier.com/S0263-8231(15)30044-6/sbref2http://refhub.elsevier.com/S0263-8231(15)30044-6/sbref2http://refhub.elsevier.com/S0263-8231(15)30044-6/sbref2http://refhub.elsevier.com/S0263-8231(15)30044-6/sbref1http://refhub.elsevier.com/S0263-8231(15)30044-6/sbref1http://refhub.elsevier.com/S0263-8231(15)30044-6/sbref1http://refhub.elsevier.com/S0263-8231(15)30044-6/sbref1


19/19

[15] W. Li, L.H. Han, X.L. Zhao, Axial strength of concrete-lled double skin steeltubular (CFDST) columns with preload on steel tubes, Thin-Walled Struct. 56(2012) 920.

[16] M.F. Hassanein, O.F. Kharoob, Compressive strength of circular concrete-lleddouble skin tubular short columns, Thin-Walled Struct. 77 (2014) 165173.

[17] M.F. Hassanein, O.F. Kharoob, Analysis of circular concrete-lled double skintubular slender columns with external stainless steel tubes, Thin-WalledStruct. 79 (2014) 2337.

[18] Y.Z. Wang, B.S. Li, Finite Element Analysis for Concrete Filled Double-Skin SteelTubular Stub Columns, Adv. Mater. Res. 690 (2013) 696699.

[19] J.G. Teng, T. Yu, Y.L. Wong, S.L. Dong, Hybrid FRPconcretesteel tubular col-

umns: concept and behavior, Constr. Build. Mater. 21 (4) (2007) 846 854.

[20] J.G. MacGregor, J.K. Wight, S. Teng, P. Irawan, Reinforced Concrete: Mechanicsand Design, Prentice Hall, Upper Saddle River, NJ, 1997 .

[21] S.W. Tsai, E.M. Wu, A general theory of strength for anisotropic materials, J.Compos. Mater. 5 (1) (1971) 5880.

[22] Manual, ABAQUS UserS, Version 6.5, Hibbitt, Karlsson and Sorensen. Inc.,Pawtucket, RI, 2004.

[23] W.F. Chen, Plasticity in Reinforced Concrete, J. Ross Publishing, 2007.[24] C.G. Salmon, J.E. Johnson, F.A. Malhas, Steel Structures: Design and Behavior,

Harper and Row, New York, 1980.[25] ACI Committee, American Concrete Institute, and International Organization

for Standardization, Building Code Requirements for Structural Concrete (ACI

31808) and Commentary, American Concrete Institute, USA, 2008.

http://refhub.elsevier.com/S0263-8231(15)30044-6/sbref12http://refhub.elsevier.com/S0263-8231(15)30044-6/sbref12http://refhub.elsevier.com/S0263-8231(15)30044-6/sbref12http://refhub.elsevier.com/S0263-8231(15)30044-6/sbref12http://refhub.elsevier.com/S0263-8231(15)30044-6/sbref12http://refhub.elsevier.com/S0263-8231(15)30044-6/sbref12http://refhub.elsevier.com/S0263-8231(15)30044-6/sbref12http://refhub.elsevier.com/S0263-8231(15)30044-6/sbref12http://refhub.elsevier.com/S0263-8231(15)30044-6/sbref13http://refhub.elsevier.com/S0263-8231(15)30044-6/sbref13http://refhub.elsevier.com/S0263-8231(15)30044-6/sbref13http://refhub.elsevier.com/S0263-8231(15)30044-6/sbref13http://refhub.elsevier.com/S0263-8231(15)30044-6/sbref13http://refhub.elsevier.com/S0263-8231(15)30044-6/sbref13http://refhub.elsevier.com/S0263-8231(15)30044-6/sbref13http://refhub.elsevier.com/S0263-8231(15)30044-6/sbref14http://refhub.elsevier.com/S0263-8231(15)30044-6/sbref14http://refhub.elsevier.com/S0263-8231(15)30044-6/sbref14http://refhub.elsevier.com/S0263-8231(15)30044-6/sbref14http://refhub.elsevier.com/S0263-8231(15)30044-6/sbref14http://refhub.elsevier.com/S0263-8231(15)30044-6/sbref14http://refhub.elsevier.com/S0263-8231(15)30044-6/sbref14http://refhub.elsevier.com/S0263-8231(15)30044-6/sbref14http://refhub.elsevier.com/S0263-8231(15)30044-6/sbref15http://refhub.elsevier.com/S0263-8231(15)30044-6/sbref15http://refhub.elsevier.com/S0263-8231(15)30044-6/sbref15http://refhub.elsevier.com/S0263-8231(15)30044-6/sbref15http://refhub.elsevier.com/S0263-8231(15)30044-6/sbref15http://refhub.elsevier.com/S0263-8231(15)30044-6/sbref16http://refhub.elsevier.com/S0263-8231(15)30044-6/sbref16http://refhub.elsevier.com/S0263-8231(15)30044-6/sbref16http://refhub.elsevier.com/S0263-8231(15)30044-6/sbref16http://refhub.elsevier.com/S0263-8231(15)30044-6/sbref16http://refhub.elsevier.com/S0263-8231(15)30044-6/sbref16http://refhub.elsevier.com/S0263-8231(15)30044-6/sbref16http://refhub.elsevier.com/S0263-8231(15)30044-6/sbref16http://refhub.elsevier.com/S0263-8231(15)30044-6/sbref16http://refhub.elsevier.com/S0263-8231(15)30044-6/sbref17http://refhub.elsevier.com/S0263-8231(15)30044-6/sbref17http://refhub.elsevier.com/S0263-8231(15)30044-6/sbref17http://refhub.elsevier.com/S0263-8231(15)30044-6/sbref18http://refhub.elsevier.com/S0263-8231(15)30044-6/sbref18http://refhub.elsevier.com/S0263-8231(15)30044-6/sbref18http://refhub.elsevier.com/S0263-8231(15)30044-6/sbref18http://refhub.elsevier.com/S0263-8231(15)30044-6/sbref18http://refhub.elsevier.com/S0263-8231(15)30044-6/sbref19http://refhub.elsevier.com/S0263-8231(15)30044-6/sbref19http://refhub.elsevier.com/S0263-8231(15)30044-6/sbref19http://refhub.elsevier.com/S0263-8231(15)30044-6/sbref19http://refhub.elsevier.com/S0263-8231(15)30044-6/sbref19http://refhub.elsevier.com/S0263-8231(15)30044-6/sbref20http://refhub.elsevier.com/S0263-8231(15)30044-6/sbref20http://refhub.elsevier.com/S0263-8231(15)30044-6/sbref21http://refhub.elsevier.com/S0263-8231(15)30044-6/sbref21http://refhub.elsevier.com/S0263-8231(15)30044-6/sbref21http://refhub.elsevier.com/S0263-8231(15)30044-6/sbref22http://refhub.elsevier.com/S0263-8231(15)30044-6/sbref22http://refhub.elsevier.com/S0263-8231(15)30044-6/sbref22http://refhub.elsevier.com/S0263-8231(15)30044-6/sbref22http://refhub.elsevier.com/S0263-8231(15)30044-6/sbref22http://refhub.elsevier.com/S0263-8231(15)30044-6/sbref22http://refhub.elsevier.com/S0263-8231(15)30044-6/sbref22http://refhub.elsevier.com/S0263-8231(15)30044-6/sbref22http://refhub.elsevier.com/S0263-8231(15)30044-6/sbref22http://refhub.elsevier.com/S0263-8231(15)30044-6/sbref21http://refhub.elsevier.com/S0263-8231(15)30044-6/sbref21http://refhub.elsevier.com/S0263-8231(15)30044-6/sbref20http://refhub.elsevier.com/S0263-8231(15)30044-6/sbref19http://refhub.elsevier.com/S0263-8231(15)30044-6/sbref19http://refhub.elsevier.com/S0263-8231(15)30044-6/sbref18http://refhub.elsevier.com/S0263-8231(15)30044-6/sbref18http://refhub.elsevier.com/S0263-8231(15)30044-6/sbref18http://refhub.elsevier.com/S0263-8231(15)30044-6/sbref17http://refhub.elsevier.com/S0263-8231(15)30044-6/sbref17http://refhub.elsevier.com/S0263-8231(15)30044-6/sbref16http://refhub.elsevier.com/S0263-8231(15)30044-6/sbref16http://refhub.elsevier.com/S0263-8231(15)30044-6/sbref16http://refhub.elsevier.com/S0263-8231(15)30044-6/sbref15http://refhub.elsevier.com/S0263-8231(15)30044-6/sbref15http://refhub.elsevier.com/S0263-8231(15)30044-6/sbref15http://refhub.elsevier.com/S0263-8231(15)30044-6/sbref14http://refhub.elsevier.com/S0263-8231(15)30044-6/sbref14http://refhub.elsevier.com/S0263-8231(15)30044-6/sbref14http://refhub.elsevier.com/S0263-8231(15)30044-6/sbref14http://refhub.elsevier.com/S0263-8231(15)30044-6/sbref13http://refhub.elsevier.com/S0263-8231(15)30044-6/sbref13http://refhub.elsevier.com/S0263-8231(15)30044-6/sbref13http://refhub.elsevier.com/S0263-8231(15)30044-6/sbref12http://refhub.elsevier.com/S0263-8231(15)30044-6/sbref12http://refhub.elsevier.com/S0263-8231(15)30044-6/sbref12http://refhub.elsevier.com/S0263-8231(15)30044-6/sbref12

nonlinea rbehavior of frp-reinforced concrete-filled double-skin

Documents