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4th International Conference on Earthquake EngineeringTaipei, Taiwan

October 12-13, 2006

Paper No. 49

EXPERIMENTAL INVESTIGATION ON RECTANGULAR SRCCOLUMNS WITH MULTI-SPIRAL CONFINEMENTS

C.C. Weng 1, Y.L. Yin 2, J.C. Wang 3, C.Y. Liang 4 and C.M. Huang 4

ABSTRACT

Presented herein is a study on compression tests of a series of full-scale rectangular SRC (steelreinforced concrete) columns confined with a new type of multi-spiral cages. The multi-spiral is adevice of five interconnected spiral cages, named “5-spirals”or “Yin’s spirals”in this study, with alarge circular spiral at the center and four small ones at the corners. The innovation of applying the5-spirals to rectangular SRC columns is to take its superiority in concrete confinement as well as itsefficiency in automatic production for the precast construction industry. The major parameters of thisstudy included the cost effectiveness of the multi-spirals, and the strength and ductility of the spirallyconfined SRC columns. As compared to the reinforced concrete column tied with traditional rectilinearhoops, the test results showed that, with significant cost savings of the confinement steel, the SRCcolumns confined with 5-spirals demonstrated excellent performances in both strength and ductility.

Keywords: Rectangular SRC Column; Multi-Spiral Confinement; 5-Spirals; Precast Construction;Compression Test; Compressive Strength; Ductility Improvement; Cost Effectiveness.

INTRODUCTION

With the fast advances in construction technology, it has become increasingly popular in Taiwan toconstruct buildings with composite structural members. The SRC (steel reinforced concrete) columnis one of the major composite structural members, which renders a building with the advantages ofthe strength and stiffness of reinforced concrete as well as the ductility of structural steel. Additionalmerits of the SRC column extend to that the concrete also protects the imbedded steel section fromlocal buckling and fire damages (Weng and Wang, 2005).

Figure 1 shows two types of SRC columns commonly seen in Taiwan’s construction sites, in whichthe embedded structural steel can be a cross-H or a box section. It is noticed that the confinementreinforcements in rectangular SRC columns typically consists of rectilinear perimeter hoops (AIJ,2001). Each of the hoops is formed with a single steel bar and closed at both ends by two hookswith 135-degree bends. The confinement reinforcements in the column are designed to hold thelongitudinal bars in position and to provide the column with shear strength and passive confinement

---------------------------------1 Professor, Department of Civil Engineering, National Chiao Tung University, 1001 Ta-Hsueh Road, Hsinchu, 300, Taiwan.

frankweng@mail.nctu.edu.tw2 Professor, Department of Civil Engineering, National Taiwan University, No. 1, Roosevelt Road, Section 4, Taipei, 106,

Taiwan; CEO and Chief R&D Officer, Ruentex Group, 14F, No. 308, Sec. 2, Bade Road, Taipei, 104, Taiwan.samuel@mail.ruentex.com.tw

3 Manager, R&D Division, Runhorn Pretech Engineering Co., Ltd., 10F, No. 308, Sec. 2, Bade Road, Taipei, 104, Taiwan.4 Graduate Research Assistant, Department of Civil Engineering, National Chiao Tung University, 1001 Ta-Hsueh Road,

Hsinchu, 300, Taiwan.

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stress for the core concrete. However, experiences from the field practice indicated that the hoopswith 135-degree bends are not easy to setup in the SRC columns, and the entire process is heavilyrelied on skilled labors, which is time-consuming and expensive.

Fig. 1 Rectangular SRC columns with rectilinear perimeter hoop confinements

It is known that the confining efficiency of the confinement cage in a reinforced concrete column isinfluenced by both the geometry and the spacing of the confinement steel (Darwin, 1977; Mander etal., 1988; Pantazopoulou, 1998). As compared to the rectilinear hoops, the circular spirals in thecolumns have been shown to be more effective in concrete confinement (Shah et al., 1983; Sheikhand Toklucu, 1993). In addition, automatic production of the spiral cages are common in today’sprecast construction industry. Production of the continuous spirals and assembly of the cages can becarried out easily in the factory. It is because of the cost effectiveness and the lower demand of skilledlabors which make the spiral cages a potential competitor. However, applications of the circularspirals to the rectangular cross-section columns are not common in today’s engineering practice.

Fig. 2 Rectangular SRC column cross-sections with 5-spiral confinements

As shown in Fig. 2, the innovation of the multi-spiral confinements was originally proposed by Y.L.Yin for prefabricated rectangular reinforced concrete columns (Yin et al., 2004). The multi-spiral is adevice of five interconnected spiral cages, named “5-spirals”or “Yin’s spirals”in this study, with alarge central spiral at the center and four small ones at the corners. The idea of using the 5-spirals inrectangular SRC columns is to take its superiority in concrete confinement and its efficiency inautomatic production in prefabricated structural members. In practice, longitudinal bars in theprefabricated columns are located at four corners of the cross-section to create more working space atthe beam-column joint. The use of four small spiral cages at the corners successfully eliminates thebarrier for extending the application of circular spirals to the rectangular cross-section columns.

The objective of this research is to investigate experimentally the efficiency of applying the idea ofmulti-spiral confinements to the rectangular SRC columns. The major parameters of this study

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included the cost effectiveness of the multi-spirals, and the strength and ductility of the SRC columns.It is also hoped that this experimental investigation will provide further insight on the mechanicalbehavior and failure mechanism of the rectangular SRC columns with multi-spiral confinements.

DESIGN RULES FOR CONFINEMENT REINFORCEMENTS

The following sections briefly review the rules used in this study for the design of confinementreinforcements in the RC and SRC column specimens:

1. ACI-318 Code

The ACI-318 Code (2005) is one of the most widely accepted design guides for reinforced concretestructures. For a spirally confined reinforced concrete column, it is stated in section 21.4 of the ACICode that the volumetric ratio, ρs, defined as the ratio of the volume of spiral reinforcement to thevolume of core concrete, shall not be less than the following requirements:

0.45 1'

g cs

c yh

A fA f

(1)

and

0.12'c

syh

ff

(2)

in which 'cf is the compression strength of concrete; fyh is the yield stress of spiral steel; Ag and Ac are,

respectively, the gross and the confined core concrete areas.

For a reinforced concrete column tied with rectilinear hoops, it is stated that the cross-sectional area ofthe confinement reinforcement, Ash, shall not be less than

0.3 1'

gcsh c

yh ch

AfA sh

f A

(3)

and

0.09'

csh c

yh

fA sh

f

(4)

where s is the spacing; hc and Ach are, respectively, the width and the area of confined core concrete.

2. Taiwan SRC Code

In 2004, the Ministry of Interior of Taiwan published her first official edition of the design code forSRC buildings (MOI, 2004). To take into account the beneficial effect provided by the embedded steelsection in sharing the axial load of SRC column, the Taiwan SRC Code adopted a similar designapproach for composite columns used in the AISC Seismic Provisions (2005). For a spirally confinedSRC column, it is suggested that the volumetric ratio,ρs, of spiral reinforcement shall not be less than

0.4 15

'g c

sc yh

s ys

n u

A f

P

A f1

A f

(5)

and

10.12 s ys

n

'c

yh u

s

A f

Pff

(6)

in which fys and As, respectively, are the yield stress and the cross-sectional area of the steel section;(Pn)u is the nominal axial capacity of the SRC column.

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(Pn)u = fysAs + 0.85 'cf Ac + fyrAr (7)

In addition, for a SRC column tied with rectilinear hoops, it is suggested that the cross-sectional areaof the confinement reinforcement, Ash, shall not be less than

'

0.3 1 1g s yscsh c

yh ch n u

A A ffA sh

f A P

(8)

and

'

0.09 s 1 s yscsh c

yh n u

A ffA h

f P

(9)

3. Weng’s Formula

As shown in Fig. 3, the condition of concrete confinement in a SRC column is quite different from thatof an ordinary reinforced concrete column (Weng et al., 1998). It is observed from the figure that, dueto the confining effect to the core concrete provided by the flanges of the steel section in the SRCcolumn, the concrete is subjected to different degrees of confinement. The concrete in SRC columncan be categorized into three areas: (a) The highly confined concrete; (b) the ordinarily confinedconcrete; and (c) the unconfined area (Weng et al., 2004).

Fig. 3 Conditions of concrete confinement in a SRC column (Weng et al., 2004)

In recognition of the confining contribution provided by the flanges of the steel section, Weng et al.proposed a new set of formulas for the design of confinement reinforcements in SRC columns toaccount for this beneficial effect (Weng et al., 2004). It is proposed that

1. For a spirally confined SRC column, the volumetric ratio, ρs, of spiral reinforcement shall not beless than the followings:

1 10.45

'g c s h c

sc

uh nc y

PfP

A

fP

A

(10)

and

1 10. 2 s hcc

s

uyh

c

n

'f P PPf

(11)

2. For a SRC column tied with rectilinear hoops, the cross-sectional area of the confinementreinforcement, Ash, shall not be less than

Highly Confined Area

Ordinarily Confined Area

Unconfined Area

Longitudinal Bars Hoop ConfinementSteel Section

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0.3 1 1

'gc s hcc

sh cyh ch n u

Af P PA sh

f A P

(12)

and

0.09 1

'c s hcc

sh cyh n u

f P PA sh

f P

(13)

where (Pn)u is the nominal axial capacity of SRC column determined from equation (7). Ps and Phcc

are, respectively, the axial capacities provided by the steel section and the highly confined concrete.

s ys sP f A (14)

0.85 'chcc hccfP A (15)

where Ahcc is the area of highly confined concrete, as the dark shaded zone shown in Fig. 3. It is notedthat the bracket at the end of equations (10) to (13) is a reduction factor which accounts for thecontribution of the flanges of the steel section in confining the core concrete in the SRC column.

EXPERIMENTAL PROGRAM

As shown in Table 1, a total of eleven full-scale short columns were tested in this study, including twoRC columns and nine SRC columns. All column specimens are 600 mm square and 1200 mm height.Two types of confinement in the SRC columns were investigated, in which specimens SRC1 andSRC2 were tied with the traditional rectilinear hoops; specimens SRC3 to SRC9 were designed withthe 5-spirals. Specimens SRC1 and SRC2 were served as the benchmark for comparison purpose, andthey were given the same amount of steel section and longitudinal bars to provide the same magnitudeof expected compressive strength as designed for the SRC column specimens. Besides, the RC columnspecimens, RC1 and RC2, were also designed for comparison purpose, given the required amount oflongitudinal bars to provide the same expected compressive strength as for the SRC columns. Thespecimen RC1 was tied with the rectilinear hoops; and the specimen RC2 was confined with the 5-spirals.

In Table 1, the last column indicates the design guides used to determine the amount and spacing ofthe confinement reinforcement for each specimen. The reduction factor represents the percentage of“cost effectiveness”of confinement reinforcement for a specimen designed according to Taiwan SRCCode or Weng’s formula, relative to the amount of confinement needed if designed with the ACI-318requirements. In this study, the spacing of the confinement reinforcement varies from 75 to 110 mm.The smallest reduction factor is 65% for specimens SRC2 and SRC5; both were designed according toWeng’s formula. In addition, the volumetric ratio and the weight per unit length of confinementreinforcement for each specimen are also shown in the table. The volumetric ratios vary from 0.81% to1.67%; and the weight per unit length of confinement reinforcement ranges between 235 to 405 N/m.

The steel shapes in the SRC column specimens included the welded built-up cross-H and box sections.Steel plates of 6, 9 and 10 mm thick were used, and the yield stresses vary from 411 to 445 MPa. Thecompressive strength of the normal weight concrete is 41.1 MPa. The #8(D25) and #9(D29) deformedbars with yield stresses of 442 and 430 MPa, respectively, were served as longitudinal reinforcements.The #3(D10) and #4(D13) deformed bars with yield stresses of 485 and 463 MPa, respectively, wereused as the confinement reinforcements. As required by Taiwan SRC Code, one #4 supplementarylongitudinal bar was placed in the middle of each side of the SRC column, but was cut 50 mm short ateach end. It is note that, for the efficiency of confinement and automatic production, the #4 bar wasselected to form the large spiral cages and the #3 bar was used for the small ones.

Figure 4 shows two photos of the setup of the full-scale compression test of the short columns. A58,800 kN (6,000 metric ton) hydraulic jack was used to apply the axial compressive force at a

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constant strain rate of 0.03 mm/sec (25 με/sec). The expected maximum load to be applied to thespecimens was about 21,000 kN. To achieve a more uniform load distribution on the specimen, a steelend cap was mounted on each end of the column. During the test, a LVDT (linear variable differentialtransformer) extensometer was attached along the side of the specimen to monitor the axialshortening. To measure the variations of strains within the specimens, strain gages were glued on theselected surfaces of the steel section and the reinforcing bars before casting the concrete.

Table 1 Design details of columns tested in this study

Hoop/SpiralColumn

Cross-SectionSpecimen

Designation SmallCircle

LargeCircle

Hoop/SpiralSpacing( mm )

VolumetricRatioρs

Weight ofHoop/Spiral

( N / m )

ReductionFactor

DesignGuide

RC1-H-ACI-90 #4 90 ％1.67 405 100% ACI-318 Code

RC2-Y-ACI-75 #3 #4 75 ％1.25 360 100% ACI-318 Code

SRC1-HC-TWN-75 #4 75 ％1.34 298 79% Taiwan SRC Code

SRC2-HC-WENG-90 #4 90 ％1.11 248 65% Weng’s Formula

SRC3-YC-ACI-75 #3 #4 75 ％1.25 360 100% ACI-318 Code

SRC4-YC-TWN-95 #3 #4 95 ％0.99 283 79% Taiwan SRC Code

SRC5-YC-WENG-115 #3 #4 115 ％0.81 235 65% Weng’s Formula

SRC6-YC-S1-75 #3 #4 75 ％1.25 360 100% Spacing = SRC1

SRC7-YC-S2-90 #3 #4 90 ％1.04 299 83% Spacing = SRC2

SRC8-YB-TWN-95 #3 #4 95 ％0.99 283 79% Taiwan SRC Code

SRC9-YB-WENG-110 #3 #4 110 ％0.85 245 68% Weng’s Formula

：Note (1) Column dimensions：All column specimens are 600 mm square and 1200 mm height.(2) Steel sections in SRC columns:

(a) Cross-H: 2H350 × 175 × 6 × 9, ρsrc = 2.91% ; (b) Box section:□275 × 275 × 10 × 10, ρsrc = 2.94%(3) Longitudinal bars in SRC columns:

(a) Hoop columns (SRC1 & SRC2): 12 #9 (D29),ρr = 2.15% ; (b) Spiral columns: 16 #8 (D25), ρr = 2.25%(4) Longitudinal bars in RC columns (RC1 & RC2): 16 # 8 (D25) and 12 # 9 (D29); ρr = 4.40%

RESULTS AND DISCUSSIONS

Figure 5 makes a comparison between the load-displacement curves of the two reinforced columns,RC1 and RC2, in which both specimens were designed with same amount of longitudinal bars, and theconfinement reinforcements were arranged to meet the ACI-318 requirements. It is observed that theultimate compressive strengths of the two columns are quite close; however, the ductility of the spiral-confined column, RC2, is obviously better than that of the hoop-tied column, RC1. These observationsare in consistency with the test results reported by Wang in 2004. It is also noted from Table 1 that theweight of confinement reinforcement used for specimen RC2 is 360 N/m. It is much more cost-effective than that of the specimen RC1, which takes 405 N/m.

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0 10 20 30 40 50 60 70Displacement (mm)

0

10000

20000

30000

Com

pres

sive

Forc

e(k

N) SRC4

SRC5

RC2

SRC3

RC1

0 10 20 30 40 50 60 70Displacement (mm)

0

10000

20000

30000

Com

pres

sive

Forc

e(k

N)

RC1

RC2

(a) The 58800 kN compression test machine (b) Compression test of a SRC column

Fig. 4 The compression test machine and the setup of the experiment

In Fig. 6, three more load-displacement curves obtained from the SRC columns, SRC3, 4, and 5, wereadded to Fig. 5. For the purpose of comparison, all test specimens were initially designed with thesame expected compressive strength. It is observed from Fig. 6 that the three SRC columns all showedslightly higher ultimate capacities than those of the RC columns. More significantly, the ductility ofthe three SRC columns was found to be much better than that of the RC columns. It is also importantto observe from Table 1 that the confinements of columns SRC4 and SRC5 were designed accordingto Taiwan SRC Code and Weng’s formula, respectively. The amount of spiral steel used for these twoSRC columns were only 283 and 235 N/m, respectively, which are much less that those of columnsRC1 and RC2. From the reduction factors shown in Table 1, for column SRC5 which was designedaccording to Weng’s formula, only 65% of spiral reinforcement is needed as compared to the columndesigned with ACI Code. These observations demonstrated the advantages in“ductilityimprovement”as well as in“cost effectiveness”of applying the 5-spirals to rectangular SRC columns.

Fig. 5 Comparison of load-displacement curves Fig. 6 Comparison of load-displacement curvesbetween two RC columns: between RC and SRC columns:RC1(hoops) vs. RC2(5-spirals) RC1(hoops) vs. RC2, SRC3,4,5(5-spirals)

In order to compare the performances between the SRC columns tied with the rectilinear hoops andthose confined with the 5-spirals, Figs. 7(a) and (b) show the differences of the load-displacementbehavior of columns SRC1 versus SRC 6 and columns SRC2 versus SRC7, respectively. It isobserved that, given the same spacing of confinement reinforcement, the strength and the ductility ofthe spiral-confined SRC columns are all better than those of the hoop-tied SRC columns.

8

0 10 20 30 40 50 60 70Displacement (mm)

0

10000

20000

30000C

ompr

essi

veFo

rce

(kN

)

SRC1

SRC6

0 10 20 30 40 50 60 70Displacement (mm)

0

10000

20000

30000

Com

pres

sive

Forc

e(k

N)

SRC2

SRC7

0 0.02 0.04 0.06Strain

0

20

40

60

80St

ress

(MPa

)SRC2

u

u

0.7 P

P

0.023173.60

0.0088

0 0.02 0.04 0.06Strain

0

20

40

60

80

Stre

ss(M

Pa)

SRC4

u

u

0.7 P

P

0.05464.77

0.0115

u

u

0.7P

P

0.01631.82

0.0089

0 0.02 0.04 0.06Strain

0

20

40

60

80

Stre

ss(M

Pa)

RC1

(a) Spacing of confinement: both 75mm (b) Spacing of confinement: both 90mm

Fig. 7 Load-displacement curves of SRC columns with different types of confinement:SRC1 and SRC2 (with hoops) vs. SRC6 and SRC 7 (with 5-spirals)

(a) Spacing of hoops in RC1: 90mm (b) Spacing of hoops in SRC2: 90mm

(c) Spacing of spirals in SRC4: 95mm

Fig. 8 Comparison of ductility performances between RC and SRC columns:RC1 (hoops); SRC2 (hoops); SRC4 (5-spirals)

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Figures 8(a), (b) and (c) show a comparative study on the ductility performances among three differenttypes of columns: the traditionally hoop-tied RC and SRC columns, specimens RC1 and SRC 2,respectively, and the spiral-confined SRC column, specimen SRC4. A ductility index, μ, is definedherein as the ratio of the axial strain measured at 70% of the post-peak load, ε0.7Pu , to the strainrecorded at the peak load, εPu. It is observed from the figures that the ductility indexes are 1.82, 3.60and 4.77 for specimens RC1, SRC2 and SRC4, respectively.

The above observations indicated that the spiral-confined SRC column, SRC4, demonstrated the bestquality in absorbing inelastic strain energy. The capability of sustaining large deformation withoutquick loss of strength after the peak load of the SRC column with 5-spirals is one of the importantcharacteristics for achieving successful seismic resistance. To summarize, the ultimate strength andductility index of the columns tested in this study are shown in Table 2.

Table 2 Ultimate strength and ductility index of the columns tested in this study

Specimen RC1 RC2 SRC1 SRC2 SRC3 SRC4 SRC5 SRC6 SRC7 SRC8 SRC9

(Pu)t es t

(KN )18962 18109 18187 17952 20963 20198 20630 21336 20826 20208 19227

0.7 u

u

P

P

1.82 2.65 3.27 3.60 4.36 4.77 4.48 5.07 4.28 3.52 3.12

In addition, the photos presented in Figs. 9(a) and (b) may provide an explanation to the phenomenonof quick axial strength deterioration after reaching the peak load, as observed from the hoop-tiedcolumn, RC1. It is seen from Fig. 9(a) that the 135-degree hooks of the rectilinear hoops were openedup and resulted in buckling of the longitudinal bars. On the contrary, as shown in Fig. 9(b), the 5-spirals and the core concrete in the spiral-confined column, specimen SRC4, were found to be able tomaintain in a relatively sound condition after the peak load.

(a) Separation of the 135° hooks (b) The 5-spirals remained sound

Fig. 9 Comparison of failure modes between columns with different types of confinement:(a) Column RC1 with rectilinear hoops; (b) Column SRC4 with 5-spirals

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SUMMARY AND CONCLUSIONS

A series of full-scale rectangular SRC columns with multi-spiral confinements were tested undermonotonic compression. For comparison purpose, two reinforced concrete columns of the same sizewere also tested. The following conclusions can be drawn based on the test results of this study:

1. The new type of multi-spiral confinements, named “5-spirals”or “Yin’s spirals”which wasinnovated by Y. L. Yin in 2004, has been experimentally proven to be able to successfully extendits application to rectangular SRC columns.

2. As compared to the RC and SRC columns tied with rectilinear hoops, the SRC columns confinedwith 5-spirals demonstrated excellent performances in both strength and ductility.

3. The rectangular SRC columns with 5-spirals showed significant capability of sustaining largedeformation without quick deterioration of axial strength after reaching the peak load, which isone of the important characteristics for achieving successful seismic resistance.

4. As compared to the ACI-318 requirements for confinement reinforcements, the test resultsindicated that the Weng’s formula can provide significant cost benefit in the savings of the usageof confinement steel.

5. The experimental results showed that, with satisfactory performances in strength and ductility, thespiral confinements designed according to the Weng’s formula takes only 65% of the amount ofconfinement reinforcements needed if designed with the ACI Code.

6. In general, the test results have demonstrated the advantages in“ductilityimprovement”as well asin“cost effectiveness”of applying the newly innovated 5-spirals to rectangular SRC columns.

ACKNOWLEDGMENTS

The financial support of Runhorn Pretech Engineering Co., Ltd. is gratefully acknowledged. Thanksare also extended to China Engineering Consultant for providing the test facility for this investigation.

REFERRENCES

ACI (2005). Building Code Requirements for Structural Concrete (ACI 318) and Commentary (ACI 318R).American Concrete Institute, Farmington Hills, Michigan.

AIJ (2001). Standards for Structural Calculation of Steel Reinforced Concrete Structures. ArchitecturalInstitute of Japan, Tokyo.

AISC (2005). Seismic Provisions for Structural Steel Buildings, American Institute of Steel Construction,Chicago, Illinois.

Darwin, D., and Pecknold, D.A. (1977). “Nonlinear Biaxial Stress-Strain Law for Concrete,”J. of Eng. Mech.Div., ASCE, 103(2), 229-241.

Mander, J.B., Priestly, M.J.N., and Park, R. (1988). “Theoretical Stress-Strain Model forConfined Concrete,”J. of Struct. Div., ASCE, 114(8), 1804-1826.

MOI (2004). Building Code for Design of Steel Reinforced Concrete (SRC) Structures. Ministry of Interior,Taipei, Taiwan. (in Chinese)

Pantazopoulou, S.J., (1998). “Detailing for Reinforcement Stability in RC Members,” J. of Struct. Eng., ASCE,124(6), 623-632.

Shah, S.P., Fafitis, A., and Arnold, R., (1983).“Cyclic Loading of Spirally Reinforced Concrete,”J. of Struct.Div,. ASCE, 109(7), 1695-1710.

Sheikh, S.A., and Toklucu, M.T., (1993). “Reinforced Concrete Columns Confined byCircular Spirals andHoops,”ACI Struct. J., 90(5), 542-553.

Wang, P.H., (2004). The Study of New Confinement Details for Rectangular Concrete Columns, Master’s Thesis, Dept of Civil Eng., National Taiwan Univ., Taipei, Taiwan. (in Chinese)

Weng, C.C., and Wang, H.S., (2005). “Seismic Behavior of Steel Beam to Steel Reinforced Concrete ColumnConnections,” The 4th Int. Conf. on Adv. in Steel Structures, Shanghai, China, June.

Weng, C.C., Wang, H.S., Li, R., and Liang, C.Y., (2005). “Experimental Study on Seismic Behavior of Hoop-Confined SRC Columns,” Accepted, J. of Chinese Soc. of Struct. Eng., Oct. (in Chinese)

Weng, C.C., Yen, S.I., and Lin, C.C., (1998). “Influence of Steel Section on Hoop Confinement in Concrete-Encased SRC Columns,” J. of Chinese Soc. of Hydraulics and Civil Eng., 10(2), 193-204. (in Chinese)

Yin, Y.L., Chang, K.C., and Wang, J.C., (2004). “Experimental Studies ofRectangular Columns withInnovative Spiral Confinements,” The 17th KKCNN Symp. on Civil Eng., Ayuthaya, Thailand, Dec.