Journal of Constructional Steel Research 90 (2013) 184–192

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Journal of Constructional Steel Research

Axial strength and ductility of square composite columns with twointerlocking spirals

Tsu-Han Shih a, Cheng-Chih Chen a,⁎, Cheng-Chiang Weng a, Samuel Yen-Liang Yin b, Jui-Chen Wang b

a Department of Civil Engineering, National Chiao Tung University, 1001 University Road, Hsinchu, 300, Taiwanb Ruentex Group, 14F, No. 308, Sec. 2, Bade Road, Taipei, 104, Taiwan

⁎ Corresponding author. Tel.: +886 3 571 2121x54915E-mail address: chrischen@mail.nctu.edu.tw (C.-C. Che

0143-974X/$ – see front matter © 2013 Elsevier Ltd. All rhttp://dx.doi.org/10.1016/j.jcsr.2013.07.021

a b s t r a c t

a r t i c l e i n f o

Article history:Received 18 March 2013Accepted 20 July 2013Available online 4 September 2013

Keywords:Composite columnSpiralAxial compressionStrengthDuctility

The axial compressive capacity and load–displacement behaviour of composite columns confined by twointerlocking spirals were experimentally and analytically investigated. The innovative spiral cage used for asquare column was fabricated by interlocking a circular spiral and a star-shaped spiral to enhance the confine-ment effect for the core concrete. Eight full-scale square composite columnswere tested undermonotonically in-creased axial compression. Experimental results demonstrated that, with significant savings of the transversereinforcement, the composite columns confined by two interlocking spirals achieved excellent axial compressivestrength and ductility capacity. Moreover, an analytical model was developed to take into account the concreteconfinement due to the structural steel in addition to the transverse reinforcement and distributions of the lon-gitudinal bars. The analytical results accurately predicted the axial compressive capacity and load–displacementbehaviour of the specimens. Consequently, the application of the two interlocking spirals in a square compositecolumn appears to be very affirmative.

© 2013 Elsevier Ltd. All rights reserved.

1. Introduction

Various experimental and numerical studies have shown that trans-verse reinforcement in columns functions as follows: (1) holding longitu-dinal bars in position; (2) preventing longitudinal bars from prematurebuckling; (3) providing shear strength for columns; (4) providing passiveconfinement for core concrete; and (5) improving axial compressivestrength and ductility of columns [1–7]. Square columns are traditionallyreinforcedwith rectangular hoops, and each hoop is formed froma singlesteel bar with hook at both ends [8]. However, field experiences revealthat hoops with a 135-degree bend are difficult to setup in a compositecolumn, and the entire construction is heavily relied on skilled laborsthat is time-consuming and costly.

Spirals are a continuously wound transverse reinforcement and canbe fabricated automatically in a factory. The fabrication of helical spiralsis faster and cheaper than that of rectilinear hoops. Moreover, helicalspirals in a column aremore effective in providing concrete confinementcompared to rectilinear hoops [9,10]. Mirza and Skrabek [11,12] studiedthe behaviour of short and slender composite columns subjected to axialforce and bending moment. Ricles and Paboojian [13] investigated theseismic behaviour of composite columns through experiments. Theyconcluded that the strength and toughness of composite columnswere affected by the confinement status of the core concrete. Exactlyhow the spirals apply to columnswith square cross section is of interest.Fig. 1(a) shows a square column reinforced by a circular helical spiral.

; fax: +886 3 572 7109.n).

ights reserved.

Because the concrete at the four corners of the square column cannotbe confined by the circular spiral, applications of the circular spiral tosquare columns are not common in engineering practice.

This research proposes an innovative spiral confinement as shown inFig. 1(b). The confinement is achieved by two interlocking spirals,consisting of a circular spiral and a star-shaped spiral, with longitudinalbars located around the perimeter of the square column. The interlockingspirals overcome the shortcomings of applications of a circular spiral tosquare cross-sectional columns, and facilitate sound confinement forthe concrete at the four corners of the square column. Moreover, themanpower and construction time to fabricate reinforcement cage canbe substantially reduced because the spirals can be fabricated by auto-matic machines in the factory. Fig. 2 illustrates the construction of thetwo interlocking spirals.

This work elucidates experimentally and analytically the effective-ness of the two interlocking spirals used in square composite columns.Eight full-scale columns, including six spirally reinforced composite col-umns and two reinforced concrete columns, were tested under mono-tonically increased axial compression. An analytical approach was alsoconducted to calculate the axial compressive strength and the load-deformation relationships of the specimens.

2. Experimental program

2.1. Design of test specimens

Table 1 presents the details of the specimens. Six of the specimens(SRC1 ~ 6) were composite columns reinforced with two spirals. The

(a) (b)

Fig. 1. Spiral confinements for a square column: (a) a circular spiral; (b) two interlockingspirals.

185T.-H. Shih et al. / Journal of Constructional Steel Research 90 (2013) 184–192

other two specimens (RC1 and RC2) were reinforced concrete columnswith rectilinear hoops. The test specimens were 600 mm square in thecross section and 1200 mm long. Two types of structural steel sectionsused were welded built-up box section (□250 × 250 × 6 × 6 and□300 × 300 × 9 × 9) and cross-H section (2-H220 × 100 × 6 × 9and 2-H350 × 175 × 6 × 9). The ratios of the area of structural steelsection to gross section of the column are presented in the table.

Regarding the design of the transverse reinforcement, different de-sign specifications were considered, including ACI 318 building code[8] andAISC seismic provisions [14]. SpecimenRC2, served as the bench-mark,was designed to haveminimum rectilinear hoops according to ACI318 building code.

Ash ¼ 0:3shcf ′cf yt

Ag

Ach−1

� �ð1aÞ

Ash ¼ 0:09shcf ′cf yt

ð1bÞ

where Ash is the total cross-sectional area of hoop reinforcement withinspacing s; Ag and Ach are the gross cross-sectional area of the column andthe cross-sectional area measured to outside edges of hoop reinforce-ment, respectively; f ′c is the specified compressive strength of concrete;fyt is the specified yield strength of hoop reinforcement; s is the center-to-center spacing of hoop reinforcement; and hc is thewidth of confinedcore concrete.

(Structural steel not shown for clarity)

(a) (b)

Fig. 2. Construction of the two interlocking spirals: (a) fabricated cage of the star-shapedspiral; (b) insert of the circular spiral.

For the spirally reinforced concrete column, specimen RC1, ACI 318building code stipulates that the volumetric ratio, ρs, defined as theratio of the volume of spiral reinforcement to the volume of core con-crete, shall not be less than the following requirement:

ρs ¼ 0:45f ′cf yt

Ag

Ach−1

� �ð2aÞ

ρs ¼ 0:12f ′cf yt

ð2bÞ

Regarding the transverse reinforcement used in composite columns,AISC seismic provisions propose a formula based on ACI 318 buildingcode. A reduction factor of (1 − fysAs/Pn) is used to reduce the require-ment for the tie reinforcement to take into account the structural steelcore. The minimum tie reinforcement shall meet the following:

Ash ¼ 0:09shcf ′cf yt

1−f ysAs

Pn

� �ð3Þ

in which As and fys are the cross-sectional area and specified yieldstrength of the structural steel, respectively; Pn is the nominal axialcompressive strength of the composite column calculated in accordancewith the AISC specification [15]. Hence, for designing the spirallyreinforced composite columns, specimens SRC1 ~ 3, a formula adoptinga reduction factor according to the same design philosophy is proposedas follows.

ρs ¼ 0:45f ′cf yt

Ag

Ach−1

� �1−

f ysAs

Pn

� �ð4Þ

Moreover, in recognition for the superior confinement provided bythe structural steel section in composite columns [12,16], as indicatedin Fig. 3, Weng et al. [17] proposed a formula to account for reducingtransverse reinforcement due to the highly confined concrete in com-posite columns. The following equationwas used to design the requiredspirals for specimens SRC4 ~ 6.

ρs ¼ 0:45f ′cf yt

Ag

Ach−1

� �1−Ps þ Phcc

Po

� �ð5aÞ

where

Po ¼ f ysAs þ f yrAr þ 0:85fc′Ac ð5bÞ

Ps ¼ f ysAs ð5cÞ

Phcc ¼ 0:85fc′Ahc ð5dÞ

where Po is the nominal axial compressive strength of the compositecolumn; Ps and Phcc are the compressive strength provided by the struc-tural steel and highly confined concrete, respectively; fyr is the specifiedyield strength of the longitudinal reinforcement; Ar is the cross-sectional area of the longitudinal reinforcement; Ac is the cross-sectional area of the concrete section; and Ahc is the area of highly con-fined concrete.

Accordingly, the use of the transverse reinforcement for each speci-men is shown in Table 1. Besides, the weights of the transverse rein-forcement per unit length of the column are also presented. On thebasis of the reduction for the transverse reinforcement specified inEqs. (4) and (5), composite columns (specimens SRC1 ~ SRC6) utilizedless transverse reinforcement compared to the reinforced concretecolumns (specimens RC1 and RC2). Fig. 4 depicts the details of thecross section of specimen SRC2, confined by two interlocking spirals.

Table 1Details of the specimens.

Specimendesignation

Structural steel Longitudinal bar Transverse reinforcement Weight oftransverse reinf.(N/m of col.)

Cross section

Size (mm) Arearatio

Size Arearatio

Circularspiral

Star-shapedspiral

Rectilinearhoop

Spacing(mm)

SRC1 □250 × 250 × 6 × 6 1.63% 12 No.8 1.69% No. 4 No. 4 - 115 325

SRC2 □300 × 300 × 9 × 9 2.91% 12 No.8 1.69% No. 4 No. 4 - 130 286

SRC3 □300 × 300 × 9 × 9 2.91% 12 No.8 1.69% No. 4 No. 3 - 100 282

SRC4 Two H220 × 100 × 6 × 9 1.66% 12 No.8 1.69% No. 4 No. 4 - 125 298

SRC5 Two H350 × 175 × 6 × 9 2.91% 12 No.8 1.69% No. 4 No. 4 - 150 248

SRC6 Two H350 × 175 × 6 × 9 2.91% 12 No.8 1.69% No. 4 No. 3 - 125 226

RC1 - - 8 No.108 No.11

4.05% No. 4 No. 4 - 100 376

RC2 - - 8 No.108 No.11

4.05% - - No. 4 90 405

186 T.-H. Shih et al. / Journal of Constructional Steel Research 90 (2013) 184–192

2.2. Material properties

Ready-mix normal weight concrete was used for the specimens andstandard cylinders of 150 × 300 mm were cast also. ASTM C39/C39M[18] test procedures were followed to determine the concrete compres-sive strength. Because concrete strength is highly depended on the cur-ing condition, the compressive strength of the cylinders cured in thesame condition as the columns was used. The average compressivestrength of three cylinders was 32.3 MPa measured at the time oftesting.

The steel plates used for the structural steel corewere all A572Gr. 50steel. All the longitudinal bars and circular spirals were ASTMA615 [19]Gr. 60 deformed bars. Owing to fabrication requirement, star-shapedspirals were deformed wires confirming ASTM A496 [20]. Three cou-pons were cut from each steel material and were tested in accordancewith ASTM A370 [21] to obtain the yield and ultimate strengths.

Partially confined concrete

Highly confined concrete

Unconfined concrete

Structural steel Lateral tie Longitudinal bar

Fig. 3. Concrete confinement in composite columns.

Table 2 presents the average material properties of the steel plates,deformed bars, and deformed wires. Instead of the specific strengths,the measured material strengths were adopted to evaluate the perfor-mance of the specimens.

2.3. Test setup

Fig. 5 shows the setup of the axial compression test for the speci-mens. A 58,800 kN hydraulic jack applied compressive force at a con-stant stroke rate of 0.03 mm/s. To achieve a uniform load distributionon the specimens, end capsweremounted on both column ends. Exten-someters of linear variable differential transformers were installed tomeasure the axial shortening of the specimens.

3. Experimental results and discussions

3.1. General behaviour and failure mode

All specimens demonstrated similar global behaviour. Before crackswere observed on the concrete surface, specimens exhibited linear elas-tic behaviour. Minor longitudinal cracks gradually appeared on the con-crete surface, and these cracks propagated longitudinallywhile the axialcompressive force was increased continuously. Caused by the seriouscracking, concrete cover began to spall when the specimens reachedtheir ultimate strengths. Post-peak behaviours of the specimens weremassive spalling of the concrete cover, buckling of the longitudinalbars, and rupturing of the spirals or hoops.

Fig. 6 shows the failure appearance of specimens RC2, SRC2, and SRC3after removing the spalled concrete cover. As indicated in Fig. 6(a), the

600

300

300

600

30 308No.8 longitudinal bar

300×300×9×9 structural steel

No.6 supplementary bar

No.4 deformed bar circular spiral

-13 deformed wire star-shaped spiral

(Unit: mm)

φ

Fig. 4. Cross section of spirally reinforced composite column, specimen SRC2.

187T.-H. Shih et al. / Journal of Constructional Steel Research 90 (2013) 184–192

rectilinear hoop in specimen RC2 ruptured at the hook. The circular spi-ral of specimen SRC2, having No. 4 circular and star-shaped spirals, rup-tured as presented in Fig. 6(b); however, the star-shaped spiral was notdamaged. As a result, the star-shaped spiral could still confine the coreconcrete and prevent buckling of the longitudinal bars located at the cor-ner of the column. Specimen SRC3 was designed to have No. 4 circularspiral and No. 3 star-shaped spiral. Because of the smaller size, thestar-shaped spiral ruptured but the circular spiral was undamaged asshown in Fig. 6(c). The rupture of the star-shaped spiral led to severebuckling of the longitudinal bars at the corner of the column, and, conse-quently, the axial compressive strength of the specimen deteriorated.

Fig. 7 depicts the axial compressive strength versus axial displace-ment relations of the specimens. The test axial compressive strengthwas normalized by dividing the squash strength, Psquash. The squashstrengthwas calculated the same as Po in Eq. (5b) but themeasuredma-terial strengths tabulated in Table 2were used. The two interlocking spi-rals could provide confinement to the core concrete and preventbuckling of the longitudinal bars, and then the confinement resultedin the increase of the axial compressive strength that can be observedfrom Fig. 7. Moreover, the spirally reinforced composite columnsexhibited gentle descending branch at the load–displacement curve.

3.2. Axial compressive strength and ductility

Table 3 tabulates the maximum test axial compressive strengths,Ptest, and squash strengths, Psquash, for all specimens. Squash strengthsof the columns represent the sum of all the axial compressive strengths

Table 2Measured strengths of steel materials used in the specimens.

Steel platethickness(mm)

Reinforcing bar

6 9 Deformedwire Deformed bar

No. 3 No. 4 No. 4 No. 8 No. 10 No. 11

Yield strength(MPa)

421 386 552 525 463 469 452 530

Ultimate strength(MPa)

571 529 635 601 707 658 705 756

contributed from each structural material, based on the assumption ofstrain compatibility. Thus, the increase of the axial compressivestrength due to concrete confinement was not considered. Therefore,the strength ratio of Ptest to Psquash implied degree of the concrete con-finement effect. As shown in Table 1, specimens RC1 (two interlockingspirals) and RC2 (rectilinear hoops) had the same amount of the longi-tudinal bars; however, specimen RC1 had fewer amount of the trans-verse reinforcement than specimen RC2. Specimen RC1 attained 9%higher axial compressive strength than specimen RC2 because of thegreat confinement effect provided by the two interlocking spirals.

Specimens SRC1 and SRC4 had lower structural steel ratio (1.63%and 1.66%, respectively) than other specimens (2.91%). The strength ra-tios of these two specimens were approximately the same as that ofspecimen RC1. Nevertheless, all other composite column specimenswith higher steel ratio attained higher strength ratio than specimenRC1 that implied the structural steel shape could provide superior con-finement to the core concrete.

To evaluate the ductility capacity of the specimens, a ductility indexwas defined as the ratio of the post-peak displacement corresponding to70% of the peak load, δ0:7Pu , to the displacement corresponding to thepeak load, δPu . The larger the ductility index, the better seismic perfor-mance of the column. As presented in Table 3, spirally reinforced con-crete column (specimen RC1) had better ductility capacity thanrectilinearly tied reinforced concrete column (specimen RC2). Further-more, because the structural steel shape enhanced the confinementfor the core concrete, spirally reinforced composite columns, specimensSRC1 ~ SRC6 having ductility indices ranging from 5.03 to 8.67, attainedmuch better ductility capacity than reinforced concrete columns, speci-mens RC1 and RC2 having ductility indices of 4.08 and 3.73, respective-ly. Cyclic behaviour is one of the most important issues while thecolumns are subjected to seismic load. The future research is neededto investigate seismic performance of the composite columns withtwo interlocking spirals.

3.3. Effect of the transverse reinforcement

Since the circular and star-shaped spirals are interlocking, the circu-lar spiral has a crosstie-like effect over the star-shaped spiral throughthe use of the longitudinal bars. When the specimens were subjectedto the axial compression, the circular spiral not only confined the con-crete but also suppressed the lateral deformation of the star-shapedspiral. The circular spiral functioned as a crosstie to improve theperformance of the star-shaped spiral. The two interlocking spirals

Max. force 58800 kNMax. displacement 500 mm

Max. stroke rate 0.58 mm/sec

StrongFrame

58800 kNHydraulic Jack

Test Specimen

Fig. 5. The 58,800 kN test machine and the test setup.

188 T.-H. Shih et al. / Journal of Constructional Steel Research 90 (2013) 184–192

simultaneously confined the core concrete and prevented the prema-ture buckling of the corner longitudinal bars. Therefore, the two inter-locking spirals increased the axial compressive strength and the ductilityof the columns.

Table 1 tabulates also the weights of the transverse reinforcementper unit length of the column used in the specimens. Spirally reinforcedconcrete specimen RC1 used less transverse reinforcement than recti-linearly tied reinforced concrete specimen RC2, but specimen RC1 de-veloped better strength ratio and ductility capacity than specimenRC2. All composite specimens used less transverse reinforcement thanRC columns. However, the spirally reinforced composite columnsnot only exhibited adequate strength and ductility performance butalso confirmed satisfactory economic benefit, especially for specimensSRC5 and SRC6.

(a) Specimen RC2 (b) Specimen

Ruptured circRuptured rectilinear hoop

Fig. 6. Failure appearance of specimens afte

4. Analytical prediction

4.1. Analytical modeling

An analytical approach was conducted to predict the axial compres-sive strength and load–displacement behaviour of the specimens. Thecross section of a composite column can be divided into several areasas shown in Fig. 8. The confined concrete in a composite column is dif-ferent from that in a reinforced concrete column. The concrete in com-posite column was assumed to be categorized into four differentareas: (1) a highly confined area that concrete confined simultaneouslyby the structural steel, circular spiral, and star-shaped spiral; (2) a dou-bly confined area that concrete confined by the circular and star-shapedspirals; (3) a singly confined area that concrete confined by either the

SRC2 (c) Specimen SRC3

Ruptured star-shaped spiralular spiral

r removing the spalled concrete cover.

(a) (b)

0 10 20 30 400

0.2

0.4

0.6

0.8

1

1.2

R C 1

SR C3

SR C6

0 10 20 30 400

0.2

0.4

0.6

0.8

1

1.2

R C1

R C2

Displacement (mm) Displacement (mm)

Pte

st/P

squa

s h

Pte

st/P

squa

s h

Fig. 7. Normalized load–displacement curves of RC and composite columns.

Table 3Experimental results.

Specimen Axial strength Strengthratio

Axialdisplacement

Ductilityindex

Ptest(kN)

Psquash(kN)

PtestPsquash

δPu

(mm)δ0:7Pu

(mm)

δ0:7PuδPu

SRC1 15,559 14,865 1.05 3.18 21.61 6.80SRC2 17,913 16,316 1.10 3.58 24.63 6.88SRC3 18,139 16,316 1.11 5.54 27.84 5.03SRC4 15,323 14,805 1.04 4.51 30.69 6.80SRC5 18,541 16,496 1.12 3.47 30.07 8.67SRC6 18,639 16,496 1.13 4.62 25.93 5.61RC1 17,501 16,700 1.05 5.22 21.31 4.08RC2 16,108 16,700 0.96 5.88 21.91 3.73

189T.-H. Shih et al. / Journal of Constructional Steel Research 90 (2013) 184–192

circular spiral or star-shaped spiral; and (4) an unconfined area thatconcrete located outside the transverse reinforcement. In accordancewith the stress–strain models of the different materials, the analyticalaxial compressive strength and load–displacement curve were calculat-ed by summing the strengths contributed from each material. Thestress–strain relations of variousmaterials used in the spirally reinforcedcomposite columns are briefly presented herein.

(

Lb

Unconfined area

Highly confined area

Doubly confined area

Singly confined area

Longitudinal bar

Steel Spiral

0 10 20 30 4Dis pla cemen tm(m)02.04.06.08.01

1.2

Ptest/Psquash RC1S RC3S RC60 1 0 2 0 3 0 4Disp lac emen(tmm)00.2

0.40.60.811.2

Ptest /Psqu ash

RC1RC2

(a) Box section structural steel

Fig. 8. Concrete confinement area

Awidely accepted stress–strainmodel proposed byMander et al. [5]wasused to establish the stress–strain relations of the confined concreteas follows.

f c ¼f ′ccxr

r−1þ xrð6aÞ

with

x ¼ εcεcc

ð6bÞ

r ¼ EcEc−E sec

ð6cÞ

f ′cc ¼ f ′co −1:254þ 2:254

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1þ 7:94 f ′l

f ′co

s−2

f ′lf ′co

0@

1A ð6dÞ

K ¼ −1:254þ 2:254

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1þ 7:94f ′l

f ′co

s−2

f ′lf ′co

ð6eÞ

b) Cross-H section structural steel

Unconfined area

Highly confined area

Doubly confined area

Singly confined area

ongitudinal ar

Steel Spiral

s of the composite columns.

(a) Longitudinal bar (b) Structural steel

Compressive Strain

Com

pres

sive

Stre

ss

fyr

0.4 fyr

εyrεco 10εco

Compressive StrainC

ompr

essi

veSt

ress

fys

εys

Fig. 9. Stress–strain curves used for longitudinal bar and structural steel.

Table4

Ana

lyticalm

odelingan

dcompa

risonbe

twee

nex

perimen

tala

ndan

alytical

resu

lts.

Specim

enCross-sectiona

larea(m

m2)

Conc

rete

confi

nemen

tfactor

Compressive

streng

th(kN)

Structural

stee

lLo

ngit.

bar

Unc

onfine

dconc

rete

Sing

lyco

nfine

dco

ncrete,

hoop

Sing

lyco

nfine

dco

ncrete,

circular

Sing

lyco

nfine

dco

ncrete,

star-sha

ped

Dou

bly

confi

ned

conc

rete

Highly

confi

ned

conc

rete

Sing

lyconfi

ned,

hoop

Sing

lyco

nfine

d,circular

Sing

lyco

nfine

d,star-sha

ped

Dou

bly

confi

ned

Highly

confi

ned

Test

Ana

lysis

P test

P ana

lysis

A sA r

A uc

A sc,hoo

pA s

c,circular

A sc,star

A dc

A hc

K s,hoo

pK s

,circular

Ks,star

Kd

K hP t

est

P analysis

SRC1

5856

6080

102,75

1-

18,719

33,869

136,08

156

,644

-1.24

11.20

41.33

01.51

215

,559

16,193

0.96

1SR

C210

,476

6080

102,75

1-

18,719

33,869

108,58

179

,524

-1.21

21.17

61.28

61.82

517

,913

17,856

1.00

3SR

C310

,476

6080

99,456

-17

,263

37,165

110,03

679

,524

-1.27

81.15

01.30

11.81

118

,139

17,902

1.01

3SR

C459

8860

8010

2,75

1-

18,719

33,869

164,58

128

,012

-1.22

11.18

51.30

01.36

315

,323

15,908

0.96

3SR

C510

,248

6080

102,75

1-

18,719

33,869

106,70

681

,627

-1.18

21.14

71.23

91.58

318

,541

17,590

1.05

4SR

C610

,248

6080

99,456

-17

,263

37,165

108,16

181

,627

-1.22

11.11

51.23

21.56

318

,639

17,567

1.06

1RC

1-

14,597

106,75

6-

28,664

31,912

178,07

0-

-1.29

01.29

41.32

1-

17,501

17,800

0.98

3RC

2-

14,597

102,64

724

2,75

6-

--

-1.31

2-

--

-16

,108

16,408

0.98

2Ave

rage

1.00

3Co

efficien

tof

variation

0.03

6

190 T.-H. Shih et al. / Journal of Constructional Steel Research 90 (2013) 184–192

εcc ¼ εco 1þ 5f ′ccf ′co

−1

!" #ð6fÞ

where f ′cc and εcc are the maximum compressive stress and the corre-sponding strain of the confined concrete, respectively; Ec is the tangentmodulus of elasticity of the concrete; Esec is the secant modulus of theconfined concrete at peak stress; f ′co and εco are the unconfined concretecompressive strength and the corresponding strain, respectively; f ′l isthe effective lateral confining stress; and K is the confinement factorfor confined concrete.

The stress–strain relations modeled for the longitudinal bar were as-sumed that the longitudinal bar would buckle when the concrete coverspalled. Therefore,when the axial compressive strain exceeded the strainεco, corresponding to the unconfined concrete compressive strength f ′co,the strength of the longitudinal bar gradually dropped to 40% of itsyield strength and maintained constant after the axial strain reachedten times of the strain εco, as shown in Fig. 9(a). The ten times of thestrain εco was assumed based on that the axial compressive strength ofthe double-spirally reinforced composite specimens was characterizedby a slow decrease at the descending branch of the load–displacementcurve as shown in the experiments.

The embedded structural steel effectively confined by the core con-crete because the core concrete remained undamaged until the end ofthe experiment. As a result, the local buckling of the structural steeldid not occur; thus, a linearly elastic-perfectly plastic stress–straincurve without any strength degradation was adopted for the structuralsteel, as shown in Fig. 9(b).

4.2. Analytical results

The concrete confinement factor K is mainly affected by the effectivelateral confining stress f ′l. At the highly confined concrete area, the later-al confining stress was enhanced by the structural steel section in addi-tion to the transverse reinforcement. Elements of the structural steelsection were considered to calculate the confining stress. Different con-finement factorswere determined based on the category of the confinedconcrete via Eq. (6e) suggested by Mander et al.

Table 4 tabulates the calculated confinement factors Ks, Kd and Kh forsingly, doubly and highly confined concrete, respectively. The confine-ment factor Ks for singly confined concrete is highly affected by thespacing of either the circular or star-shaped spiral, and the distributionof the longitudinal bars. Next, the confinement factor Kd for doubly con-fined concrete is influenced by both the circular and star-shaped spiralsin addition to the longitudinal bars. The confinement factor Kh for highlyconfined concrete is greatly dependent on the structural steel section.As a result, the confinement factor Kh is the greatest among the confine-ment factors while the confinement factor Ks is the smallest one,as evidenced in Table 4. Moreover, the confinement factors Kh of speci-mens SRC1 and SRC4, with smaller structural steel section than other

Compressive Strain

Com

pres

sive

Str

ess

Highly confined

Doubly confined

Singly confined

Unconfined

f 'co

ks f 'co

kd f 'co

kh f 'co

εco εscεdc εhc

Fig. 10. Compressive stress–strain curve of confined concrete based on different confine-ment factors.

191T.-H. Shih et al. / Journal of Constructional Steel Research 90 (2013) 184–192

composite specimens, are considerably lower than those of otherspecimens.

Calculated according to the equations mentioned before, the com-pressive stress–strain curves for various confined concrete are illustrat-ed in Fig. 10. The confinement factors mainly influenced the ultimatestrength and post-peak behaviour of the confined concrete.

On the basis of strain compatibility, the load–displacement curvesfor the specimens were calculated at a given axial compressive strainε. The analytic compressive strength Panalysis was determined as follows.

Panalysis ¼ f sAs þ f rAr þ f ucAuc þ f sc;circularAsc;circular þ f sc;starAsc;star

þ f dcAdc þ f hcAhc ð15Þ

where the definitions for the areas are shown in Table 4; and the vari-ables of f are the stresses corresponding to the areas.

Fig. 11 illustrates the analytical and experimental load-straincurves of specimens SRC2 and SRC5. A good agreement betweenthe analytical and experimental load-strain relationships is obtainedat both pre-peak and post-peak behaviour. Table 4 summarizes themaximum axial compressive strengths of the experiments and

0 0.005 0.01 0.015 0.020

5

10

15

20

Axi

al L

oad

(MN

)

Experiment

Analysis

Specimen SRC2

Strain

Fig. 11. Analytical and experimental load-str

analyses for all the specimens. The analytical predictions are veryclose to the experimental results. The ratios of the experimental toanalytical strength, Ptest/Panalysis, range from 0.961 to 1.061. The aver-age ratio is 1.003 and the coefficient of variation is 0.036. Moreover, theanalytical approach is more accurate to predict the maximum teststrengths than the calculated squash strengths because the squashstrengths did not take into account the confinement effect of the coreconcrete.

5. Conclusions

Six full-scale composite columns and two reinforced concrete col-umns were tested under axial compression. An analytical approachwas developed to predict axial compressive strengths and behaviourof the specimens. Based on the experimental and analytical results,the following conclusions can be drawn.

1. The experimental results revealed that the spirally reinforced con-crete column achieved better load-carrying capacity and behaviourthan the rectilinearly tied reinforced concrete column, although theamount of the spirals was less than that of the rectilinear hoops.

2. Compared to the spirally reinforced concrete column, the spirallyreinforced composite columns demonstrated excellent axial strengthand ductility performance attributed to the confinement resultingfrom structural steel.

3. The spirally reinforced composite columns with larger structuralsteel resulted in higher axial strength ratio because the structuralsteel provided superior confinement to the core concrete.

4. In general, experimental results have demonstrated the advantagesin strength and ductility improvement as well as economic benefitincrement in applying the two interlocking spirals to square compos-ite columns.

5. The analytical results exhibited that the analytical model can accu-rately predict not only the axial compressive strength but also theload–displacement relations of the spirally confined compositecolumns.

Acknowledgments

The authors would like to thank the Ruentex Engineering & Con-struction Co., Ltd. of Taiwan, for financially supporting this research.

0 0.005 0.01 0.015 0.020

5

10

15

20

Specimen SRC5

Axi

al L

oad

(MN

)

Experiment

Analysis

Strain

ain curves of specimens SRC2 and SRC5.

192 T.-H. Shih et al. / Journal of Constructional Steel Research 90 (2013) 184–192

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