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International Conference on Earthquake Engineering and Disaster Mitigation, Jakarta, April 14-15, 2008

CONFINEMENT OF CIRCULAR RC COLUMNS WITH FINE MESH

Tavio1, R. Purwono1 and M.L. Ashari1

1 Department of Civil Engineering, Sepuluh Nopember Institute of Technology (ITS), Surabaya, Indonesia Email: [email protected]

ABSTRACT: The behavior of circular RC columns confined with fine mesh was investigated. The experimental investigation comprised strength and ductility tests using small-scale circular concrete column specimens with different grid spacing of fine mesh and diameter of fine mesh as lateral reinforcement. The column specimens were tested under concentric loading. The results indicate that fine mesh can be effective in confining the core concrete, resulting in significant improvements in strength and ductility of columns. These improvements were achieved even though the column specimens contained a relatively small percentage of fine mesh. Although some practical problems remain, fine mesh can potentially be used in earthquake-resistant structures as confinement reinforcement, particularly for retrofitting purposes.

1. INTRODUCTION

Tests of reinforced concrete columns have indicated that strength and ductility of concrete in compression are improved very significantly when confined by reinforcement. Concrete under high axial compression develops transverse strains due to internal cracking, but in the presence of reinforcement, the core concrete applies pressure on the steel, which in turn applies reactive pressure on the concrete.

Experimental and analytical research has been conducted in the past to investigate confinement of concrete by rectilinear ties (Sheikh, 1978). The main variables considered in that research were the size, amount, and spacing of lateral reinforcement. Prior to 1975, researchers ignored the effect of longitudinal reinforcement on concrete confinement. The effect of longitudinal reinforcement was discussed by Park and Paulay in 1975 and Vallenas et al. in 1977. However, it was not until 1978 that Sheikh and Uzumeri demonstrated the substantial improvement achieved in column strength and ductility by distributing the longitudinal steel around the core perimeter and providing a support for each bar by means of cross ties and/or hoops (Sheikh, 1978). This observation was later confirmed by large-scale column tests by Scott et al. in 1982 and Ozcebe and Saatcioglu in 1987.

It has become clear that both transverse and longitudinal bar spacings play important roles in confining the core concrete; therefore, it is reasonable to expect that concrete confinement will be increased if the concrete is placed in a cage that consists of closely spaced reinforcement in both longitudinal and transverse directions. Fine mesh (FM) appears to satisfy this requirement; however, no attempt has been made in the past to investigate the effect of FM on concrete confinement.

The use of FM as confining reinforcement in the structural members such as columns has not been investigated so far. Up to present, the implementation of FM is only limited for use in the non-structural elements, e.g., fences, animal cages, steel basket, etc. The idea to use FM as confining reinforcement in the structural components was raised from the following considerations: its economical price, higher precision (fabricated), lighter in weight, and easy to implement for existing buildings (retrofitting purposes).

The current research at the Sepuluh Nopember Institute of Technology (ITS) includes investigation of FM and WWF (Kusuma and Tavio, 2007a, b and c; Tavio et al., 2008) as confinement reinforcement. Twelve small-scale circular RC column specimens have been tested as part of this investigation. Various combinations of FM have been used as confinement steel. It is the objective of this paper to present the results of the experimental program.

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2. RESEARCH SIGNIFICANCE

The importance of ductility in earthquake-resistant structures has long been recognized. However, due to the brittle nature of plain concrete, the required ductility is difficult to achieve, especially in members subjected to high compressive stresses. The research project reported in this paper deals with a new application of fine mesh, i.e., to improve ductility of concrete in reinforced concrete members. Therefore, it has a potential application to earthquake-resistant structures (Purwono and Tavio, 2007).

3. EXPERIMENTAL PROGRAM

3.1 Test Specimens

Figure 1 illustrates the geometry of a typical column specimen. A total of twelve small-scale columns were prepared in one set, each cast from the same batch of concrete, then tested under concentric axial compression. Two identical specimens were prepared for each reinforcement configuration.

150

180 mm22,92 134,16

180 mm

22,92

450 mm

CROSS-SECTION ELEVATION180 mm

grid 50 x 50 mm 4 mmfine mesh

C 450

Figure 1 Specimen geometry.

The length of each FM piece used in a column was between 532 and 574 mm in the transverse direction. A summary of all test specimens and their properties is provided in Table 1.

Table 1 Summary of specimen properties. Fine mesh (FM)

Column pair

cf , MPa

Spacing, mm Gage

yfmf , MPa

fm , percent

Reinforcement configuration

C 000 26 N/A 1 C 225 26 27.1 27.1 4 678 0.44 2 C 250 26 52.1 52.1 4 657 0.23 3 C 325 26 28.2 28.2 4 690 0.95 4 C 350 26 53.2 53.2 4 691 0.50 5 C 450 26 54.2 54.2 4 697 0.83 6

Reinforcement configurations used in the specimens are illustrated in Figure 2. Configuration 1 did not include FM. Configuration 2 consisted of FM placed around the perimeter of the column with concrete cover.

The material properties, as determined from standard concrete cylinder tests and reinforcement coupon tests, are shown in Figures 3 and 4. The stress-strain relationships for FM also were obtained experimentally. The yield strength for the FM was taken as the stress corresponding to a strain of 0.35 percent as stipulated in ACI 318-08 and SNI 03-2847-2002 (Purwono et al., 2007) since no clear yield point was observed in the test results.



(1) (2) (3)

C 000 C 225 C 250

(4) (5) (6)

C 325 C 350 C 450

Figure 2 Reinforcement configurations.

0

5

10

15

20

25

30

0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40STRAIN (%)

STR

ESS

(MPa

)

Figure 3 Concrete stress-strain relationship.

0

100

200

300

400

500

600

700

800

900

1000

0 1 2 3 4 5 6 7 8STRAIN (%)

STR

ESS

(MPa

)

FM 250FM 350FM 450

Figure 4 Stress-strain relationships for fine mesh.

3.2 Instrumentation

Axial deformations of columns were measured by linear variable differential transformers (LVDTs). One LVDT with a gage length of 150 mm was placed on each column face. Strains in ties were measured using electric strain gages. The data were recorded using a computerized data acquisition system.

3.3 Test Setup and Procedure The columns were tested using a compression testing machine with a 2000-kN load capacity. Upon fixing the LVDTs, each column was placed in the center of the testing machine. An initial



load of 50 to 100 kN was applied, and the LVDTs were monitored to insure concentric loading. Shims were used when necessary to minimize accidental eccentricity.

The specimens were loaded slowly and the data were recorded at selected load and/or strain increments. The loading continued until a significant drop in load capacity was observed.

0

5

10

15

20

25

30

35

0.00 0.50 1.00 1.50 2.00 2.50 3.00 3.50 4.00STRAIN (%)

STR

ESS

(MPa

)

(a)

(b)

Figure 5 Response of column pair C 250: a) stress-strain relationship and b) Column C 250 after testing.

4. OBSERVED BEHAVIOR AND TEST RESULTS The columns showed similar response up to their peak loads. The peak load and corresponding axial strain varied somewhat depending on the confinement characteristics of the core concrete. The first set of cracks appeared on column faces at a strain of approximately 0.2 percent. These cracks propagated vertically and increased in width before the peak load was reached.

At ultimate load, concrete cover was spalled off in most of the specimens. It was noted that columns reinforced with closely spaced FM continued resisting the peak load even after the cover concrete had completely spalled off. Well-confined columns developed significant inelastic deformations at approximately the peak load level. The load resistance started dropping when bending and buckling of longitudinal bar of FM was observed. At this load stage, LVDT readings started deviating substantially from each other, indicating redistribution of the load resulting from eccentricity in columns.

The eccentricity in columns could be attributed to uneven spalling and buckling of longitudinal bars at different times. Once most of the longitudinal bars had buckled, the load was observed to be nearly concentric. The reduction in load resistance continued at different rates, depending on the confinement characteristics of specimens.



0

5

10

15

20

25

30

35

40

45

50

0.00 0.50 1.00 1.50 2.00 2.50 3.00 3.50 4.00STRAIN (%)

STR

ESS

(MPa

)

(a)

(b)

Figure 6 Response of column pair C 325: a) stress-strain relationship and b) Column C 325 after testing.

Typical results of column tests are shown in Figures 5 and 6 for lightly confined and well-confined columns. All figures contain curves of average values since the test results of each individual in column pairs were in very close agreement. A summary of test results is presented in Table 2. The table contains average values for the two columns with identical test parameters within each pair. The table includes computed and measured values determined as:

Table 2 Summary of test results.

Column Po, kN

Poconc, kN

Pocore, kN

Ptest, kN

Pcmax, kN Ptest/Po Pcmax/Pocore

1, percent

85, percent 85/1

C 000 664.9 664.9 670 670 1.008 0.195 0.281 1.439 C 225 712.3 663.0 328.7 900 851 1.263 2.588 0.278 1.306 4.691 C 250 689.0 663.9 306.0 760 735 1.103 2.402 0.270 0.595 2.205 C 325 777.0 660.5 372.6 1150 1033 1.480 2.774 0.453 1.098 2.425 C 350 723.7 662.6 334.9 950 889 1.313 2.654 0.311 1.055 3.393 C 450 767.2 660.9 365.4 1010 904 1.317 2.473 0.334 2.579 7.722

( ) yfmfmfmgco fAAAfP += (1) ( )fmgcoconc AAfP = (2) ( )fmcorecocore AAfP = (3)

testP = maximum column load applied in test (4)



yfmfmtestc fAPP =max (5) where is the ratio of unconfined concrete strength to cylinder strength. The value of was taken as 1.0 in computing the values given in Table 2 because of the similarities in size and shape of the column specimens and the standard cylinder. However, varies between 0.85 and 0.90 in large-size members. Strength enhancement of core concrete due to confinement is indicated in the table by the ratio Ptest/Po or Pcmax/Pocore. Ductility of concrete is indicated in the same table by the ratio 85/1. The significance of test variables and related test results are presented and discussed in the following section.

5. ANALYSIS OF TEST DATA The test data were analyzed to investigate the significance of the variables considered. The main variables studied in the research program included spacing/grid and diameter of FM. Responses of each column pair is compared with that of different spacing/grid and diameter. The comparisons are shown in Figures 7 and 8. The results indicate that FM can be used as lateral reinforcement if the ductility is to be expected from the column. Figure 7 indicates a ductile response of column pair C 225 after reaching the peak load. It was observed during the tests that FM could provide sufficient lateral support for the longitudinal bars. At ultimate load, the pressure applied by bending and buckling longitudinal bars caused FM to rupture suddenly. The closer the spacing, the more ductile the column is.

0

5

10

15

20

25

30

35

40

0.00 0.50 1.00 1.50 2.00 2.50 3.00 3.50 4.00STRAIN (%)

STR

ESS

(MPa

)

C 225C 250

Figure 7 Effect of FM spacing/grid as confinement reinforcement.

0

5

10

15

20

25

30

35

40

45

0.00 0.50 1.00 1.50 2.00 2.50 3.00 3.50 4.00STRAIN (%)

STR

ESS

(MPa

)

C 250C 350C 450

Figure 8 Effect of FM size as confinement reinforcement.

Different sizes of FM were used in column pairs C 250, C 350, and C 450. The comparison of results, shown in Figure 8, indicates that while all sizes of FM produce ductile response the one with less area results in a higher rate of strength drop after the peak load.



6. CONCLUSIONS

The following conclusions can be made based on the experimental investigation reported in this paper:

1. The use of FM as confinement reinforcement improves concrete strength and ductility very significantly. Concrete strength confined with FM was observed to increase by as much as 48 percent.

2. FM is effective in improving concrete ductility since buckling of longitudinal wires is prevented by lateral wires.

3. Columns confined with FM show ductile response with a slow strength drop after the peak load. FM is potential and promising of providing the necessary lateral support to longitudinal reinforcement.

4. FM can be used as confinement reinforcement either between the longitudinal and lateral tie reinforcement, outside the reinforcement cage, or outside the existing column for retrofitting purposes.

5. For approximately the same area of steel, finer mesh produces better confinement than coarser mesh.

7. ACKNOWLEDGMENTS

The fine mesh used in the research program reported in this paper was supplied by PT. Partiwa Unggul Abadi, Surabaya, Indonesia. The experimental program was conducted at the Laboratory of Concrete and Building Materials and Structures Laboratory, Department of Civil Engineering, Sepuluh Nopember Institute of Technology (ITS), Surabaya, Indonesia.

8. NOTATION

coreA = area of core concrete enclosed by center-to-center of exterior fine mesh

gA = gross area of column cross section

fmA = area of fine mesh (FM)

d = effective depth of column section measured from extreme compression fiber to the centroid of tension steel

cf = concrete cylinder strength yfmf = yield strength of fine mesh (FM)

maxcP = maximum axial load carried by concrete during a column test

oP = computed capacity of column under concentric loading

oconcP = computed concrete contribution to column strength under pure concentric loading

ocoreP = computed core concrete contribution to column strength under pure concentric loading

testP = maximum axial load recorded during a column test

s = spacing of fine mesh (FM)

= ratio of plain (unconfined) concrete strength in a member to concrete cylinder strength 1 = minimum axial strain corresponding to the maximum load resistance 85 = axial strain corresponding to 85 percent of the maximum load resistance on the falling

branch of the load-strain relationship



fm = ratio of volume of lateral wires in FM to volume of concrete core measured center-to-center of outer fine mesh

9. REFERENCES

ACI Committee 318 (2008). Building Code Requirements for Structural Concrete (ACI 318-08) and Commentary (ACI 318R-08), American Concrete Institute, Farmington Hills, Michigan, USA, 456.

Kusuma, B. and Tavio (2007a). Welded wire reinforcement sebagai tulangan pengekang pada kolom beton mutu tinggi, Proceeding of the Seminar Regional Material, Desain dan Rekayasa Konstruksi pada Bangunan Tahan Gempa, Universitas Merdeka, Malang, Indonesia, 7 June, 4449.

Kusuma, B. and Tavio (2007b). Studi perbandingan model-model pengekangan pada kolom beton mutu tinggi terkekang welded wire reinforcement, Proceeding of the Seminar Nasional Pascasarjana VII-2007, Institut Teknologi Sepuluh Nopember (ITS), Surabaya, Indonesia, 2 Aug., Paper No. SKH-14, 16.

Kusuma, B. and Tavio (2007c). Usulan kurva tegangan-regangan beton mutu tinggi terkekang welded wire reinforcement, Proceeding of the Seminar dan Pameran Teknik HAKI: Konstruksi Tahan Gempa di Indonesia, Hotel Borobudur, Jakarta, Indonesia, 21-22 Aug., Paper No. SPB-2, 113.

Kusuma, B. and Tavio (2008). Kurva tegangan-regangan eksperimental baja kawat-las mutu-tinggi, Proceeding of the Seminar Nasional Teknik Sipil IV-2008, Institut Teknologi Sepuluh Nopember (ITS), Surabaya, Indonesia, 13 Feb., B-102B-110.

Ozcebe, G. and Saatcioglu, M. (1987). Confinement of concrete columns for seismic loading, ACI Structural Journal, Vol. 84, No. 4, July-Aug., 308315.

Park, R. and Paulay, T. (1975). Reinforced Concrete Structures, John Wiley & Sons, New York, USA, 769.

Purwono, R., Tavio, Imran, I. and Raka, IG.P. (2007). Tata Cara Perhitungan Struktur Beton untuk Bangunan Gedung (SNI 03-2847-2002) Dilengkapi Penjelasan (S-2002), ITS Press, Surabaya, Indonesia, Mar., 408.

Purwono, R. and Tavio (2007). Evaluasi Cepat Sistem Rangka Pemikul Momen Tahan Gempa, ITS Press, Surabaya, Indonesia, Sept., 51.

Scott, B.D., Park, R. and Priestley, M.J.N. (1982). Stress-strain behavior of concrete confined by overlapping hoops at low and high strain rates, ACI Journal, Proceedings, Vol. 79, No. 1, Jan.-Feb., 1327.

Sheikh, S.A. (1978). Effectiveness of Rectangular Ties as Confinement Steel in Reinforced Concrete Columns, Ph.D. Dissertation, Department of Civil Engineering, University of Toronto, 256.

Tavio, Suprobo, P. and Kusuma, B. (2007). Effects of grid configuration on the strength and ductility of hsc columns confined with welded wire fabric under axial loading, Proceeding of the 1st International Conference on Modern, Construction and Maintenance of Structures, Vol. 1, 10-11 Dec., Hanoi, Vietnam, 178185.

Vallenas, J., Bertero, V.V. and Popov, E.P. (1977). Concrete confined by rectangular hoops and subjected to axial loads, Report No. UCB/EERC-77/13, Earthquake Engineering Research Center, University of California, Berkeley, USA, 114.



UNIFIED STRESS-STRAIN MODEL FOR CONFINED COLUMNS OF ANY CONCRETE AND STEEL STRENGTHS

B. Kusuma1 and Tavio1

1Department of Civil Engineering, Sepuluh Nopember Institute of Technology (ITS), Surabaya, Indonesia Email: [email protected]

ABSTRACT: In this paper, a unified stress-strain model of confined concrete columns is developed and presented. The model is based on the extensively obtained data from tests of column specimens subjected to concentric compression loading. The model covers a wide range of varieties including both normal- and high-strength concretes and steels. The model is sensitive to the influencing parameters of confinement, such as concrete strength, yield strength of confining reinforcement, volumetric ratio of confining reinforcement to concrete core, spacing between confining reinforcement, cross section of confined core, configuration of lateral confining reinforcement, and distribution of longitudinal bars. The model can also be used for various concrete columns confined by spirals, crossties, and even combinations of these reinforcements. Comparison with extensive experimental data available in the literatures illustrates the validity of the proposed model in predicting the actual stress-strain curves of any confined columns of various concrete and steel strengths.

1. INTRODUCTION

The stress-strain relationships of confined concrete columns, including their empirical formulas, have long been developed and proposed by many researchers in a way to describe the actual stress-strain relationships of confined concrete columns. To date, several available analytical models for predicting the actual stress-strain relationship do not provide similar predictions on the descending branch of the curves beyond the peak stress.

The behavior of confined concrete column is normally characterized by its strength and ductility enhancements. The increase of the strength and ductility of confined concrete column highly depends on the lateral confining stress in the concrete core produced by the transverse steel. The value considerably depends on the configuration, yield strength, size, and spacing of lateral and longitudinal reinforcements.

The objective of this study is to present a comprehensive and relatively simple analytical stress-strain model for confined concrete column. The model was developed from a large database of NSC and HSC column confined by normal- and high-strength steel ties with or without crossties as well as spiral with square and circular column cross sections. The compiled database involves a total of 231 square and circular column specimens from extensive experimental tests involving monotonic and concentric axial compression loading. The concrete strength considered ranges from approximately 20 to 124 MPa, whereas the yield strength of lateral steel (fyh) ranges from about 260 to 1390 MPa. The model is shown to be applicable for a wide range of quantity and configuration of lateral reinforcement with volumetric ratio to concrete ranges from 0.2 to 5.6 percent. In addition, the peak stress and strain of the relationship are presented in a comparative study for different confinement situations.

2. AVAILABLE EXPERIMENTAL DATA FROM LITERATURE

The reviewed stress-strain models for confined NSC and HSC were applied to predict the results of experimental tests on small and large-scale specimens carried out and reported by Sheikh and Uzumeri (1980), Yong et al. (1988), Nagashima et al. (1992), Sheikh and Toklucu (1993), Cusson and Paultre (1994), Pessiki and Pieroni (1997), Saatcioglu and Razvi (1998), Razvi and Saatcioglu (1999), Li et al. (2001), Assa et al. (2001), Lin et al. (2004), and Sharma (2005). Table 1 presents the experimental work used in the analysis including 231 concrete column specimens with



different cross sections, heights, compressive strengths, and transverse reinforcements. The range of material strength is shown in Figure 1, while the range of volumetric ratio of transverse reinforcement in Figure 2.

Table 1 Experimental work included in the analysis.

Sheikh (1980) 24 Square 305 1,960 31.3 - 40.8 0.76 - 2.40 269 - 767Yong (1988) 6 Square 152 457 83.6 - 93.5 0.55 - 1.64 496Nagashima (1992) 20 Square 225 716 57.3 - 112.1 1.66 - 3.98 807 - 1,387Sheikh (1993) 27 Circular 203 - 356 812 - 1,424 35 0.58 - 2.30 452 - 629Cusson (1994) 27 Square 235 1,400 52.6 - 115.9 1.40 - 4.80 392 - 770Pessiki (1997) 8 Circular 559 2,235 37.9 - 84.7 1.32 - 2.61 476 - 537Saatcioglu (1998) 24 Square 250 1,500 60 - 124 0.99 - 4.59 400 - 1,000Razvi (1999) 16 Circular 250 1,500 60 - 124 0.41 - 3.05 400 - 1,000Li (2001) 13 Circular 240 720 52.0 - 82.5 0.82 - 2.94 445 - 1,318Assa (2001) 24 Circular 145 300 20 - 90 1.13 - 4.15 909 - 1,296Lin (2004) 24 Square 300 1,400 27.6 - 41.3 0.86 - 2.16 365 - 554

9 Square 150 600 61.85 - 83.15 2.2 - 5.62 412 - 5209 Circular 150 600 61.85 - 83.15 2.2 - 5.5 412 - 520

Sharma (2005)

Author Height (mm)

Cross section (mm)

ShapeNumber of specimens

Transverse reinforcement

Volumetric ratio (%)

Yield strength (MPa)

Compressive strength (MPa)

0200400600800

1000120014001600

0 20 40 60 80 100 120 140

f' c (MPa)

f yh (M

Pa)

Figure 1 Range of material strength in database.

0

1

2

3

4

5

6

0 20 40 60 80 100 120 140

f' c (MPa)

s (%

)

Figure 2 Range of volumetric ratio of transverse reinforcement in database.

3. ANALYTICAL STRESS-STRAIN MODEL

3.1 Stress-Strain Relation

Figure 3 shows the proposed complete stress-strain curve of confined NSC and HSC column. In most of the previously proposed stress-strain models, the ascending branch was formulated by the modified Sargins curve (Sargin, 1971). This is because a fractional equation is a simple mathematical expression and it represents well the stress-strain relation. The equation is given by:

( ) bbbbb

ccc KKff

21

2

+= for ccc < (1)

where; cc

cccb f

EK = , cc

cb

=

cf is the confined concrete stress at strain of c , and and ccf cc are the peak stress and the corresponding strain. is calculated as per ACI 318-08 equation as follows: cE



ccc fwE = 5.1043.0 (2) where is the unit weight of concrete in kg/m3, and cw cf is in MPa. The descending branch of the stress-strain curve consists of a linear segment originating from the peak, as indicated by the test results from literature shown in Figure 3. The slope of this segment is defined as . The stress-strain relation of the descending branch can be determined by: desE

( cccdesccc Eff ) = (3) where, = deterioration rate, which is developed from regression analysis of test data in the range of

desE

cc to cu .

Figure 3 Proposed stress-strain curve and definition of ultimate strain.

3.2 Formulation of Confinement Effect

In the proposed model, expressed by Eqs. (1) and (3), factors for controlling the stress-strain relation of confined concrete are the peak stress, the strain at the peak stress and the slope of the falling branch. The effect of confinement on these three parameters was determined based on the test results from literature, as described next.

The main parameters that are likely to influence the confinement effect are the strength of concrete, yield strength of the confining reinforcement, volumetric ratio of the confining reinforcement to the concrete core as well as spacing between confining reinforcement, cross section of confined core, configuration of lateral confining reinforcement, and distribution of longitudinal bars. All these parameters are considered in the presented model.

In the study, the effective confinement index was defined as the effective lateral pressure ( ) calculated from Eq. (4).

lef

yhsele fkf 5.0= (4) where, s is the volumetric ratio of the confining reinforcement to the concrete core; is the yield strength of the confining reinforcement; and is the modified Sheikh and Uzumeri (1982) factor for calculating the effectiveness of confinement given by the following formula.

yhf

ek

For square hoops/ties, 22

16

1

=

ccc

ie b

sdbb

k (5)

For circular hoops/spirals, 5.0

1

=

ce b

sk (6)



where, is the center-to-center distance between consecutive restrained longitudinal bars, ib s the center-to-center spacing of transverse reinforcement, and the center-to-center width and height of the outer tie, respectively.

cb cd

A regression analysis was performed using the experimental results to formulate the peak strength , the strain at peak strength ( ccf ) ( )cc , and the slope of the descending branch ( in terms of

(see Figures 4, 6, and 8). The results of regression analyses are presented in Eqs. (7) to (9), respectively.

)desElef

1

2

3

4

5

6

0.0 0.2 0.4 0.6 0.8 1.0

f le /f' c

f cc/f'

c

f cc /f' c = 1.0+3.7 f le /f' cfor Square and Circular; R2 = 0.888

Figure 4 Relation between the effective lateral pressure and peak stress.

Figure 4 shows the relation between an effective lateral pressure, cle ff , and the ratio of peak stress to the strength of concrete, ccc ff , for the circular and square experimental specimens. The following relationships are deduced from regression analysis to predict the compressive strength of confined concrete columns;

+= c

leccc f

fff 7.31 (7)

Figure 5 shows the relationship between the experimentally recorded results for the confined concrete strength versus the values derived analytically from the proposed model. The correlation between the two sets of values is terrific for most of the specimens. The calculated, , value is 0.9299 that displays the fine matching between experimental and analytical results.

2R

R2 = 0.9299

020406080

100120140160180

0 20 40 60 80 100 120 140 160 180f cc Analytical - MPa

f cc E

xper

imen

tal -

MP

a

Figure 5 Correlation between experimental and analytical concrete confined strengths.

Figure 6 shows general relationship between the confining pressure ratio to the concrete strength, cle ff , and the peak strain, cc , of the experimented specimens. Clearly the cle ff versus cc

relation may be approximated by a linear function. The following relations are obtained from regression analyses:

c

lecc f

f+= 055.00029.0 (8)



0.00

0.01

0.02

0.03

0.04

0.05

0.0 0.2 0.4 0.6 0.

f le /f' c

cc

8

cc = 0.0029+0.055 f le /f' cfor Square and Circular; R2 = 0.823

Figure 6 Relation between the effective lateral pressure and strain at peak stress.

R2 = 0.8245

0.00

0.01

0.02

0.03

0.04

0.05

0.06

0 0.01 0.02 0.03 0.04 0.05 0.06

cc Analytical

cc E

xper

imen

tal

Figure 7 Correlation between experimental and analytical strains at peak point.

Figure 7 shows the correlation between the prediction of cc calculated by Eq. (8) and the experimental results. The calculated, , value is 0.8245 that displays good performance between experimental and analytical results.

2R

Figure 8 shows a confinement index factor ( )2cyhs ff versus the deterioration rate, . is defined as the slope of the straight line connecting the point of the peak strength and the point at which the stress drops to 50 percent of the peak strength. The following expression can approximate the test data for both circular and square sections, and approximate relation is written as

desE desE

( )22.12

cyhsdes ff

E = (9)

The experimental results reported by Li et al. (2001) and Assa et al. (2001), in which the value of strain along the descending branch of the confined concrete curve when stress drops to

ccf50.0 ( 50cc ) is not available. The strain corresponding to 50 percent of the peak stress is assumed as the ultimate strain

ccf

cu because the strain at is usually close to the point of failure due to hoop fracture and/or shear failure of the confined core (Cusson and Paultre, 1994). The definition of ultimate strain,

ccf50.0

cu , is important.

05

10152025303540

0 3 6 9 12 15

s f yh /f' c 2 (x10-3)

E d

es (x

103 )

E des = 12.2f' c2 / s f yh

for Square and Circular; R2 = 0.713

Figure 8 Relation between confinement index factor and deterioration rate.

By substituting into Eq. (3), the ultimate strain ccc ff 50.0= cu is obtained as



des

cccccu E

f2

+= (10)

Figure 9 compares the prediction of cu calculated by Eq. (10) to the experimental results. The calculated, , value is 0.6955 represent well between experimental and analytical results. 2R

R2 = 0.6955

0.00

0.01

0.02

0.03

0.04

0.05

0.06

0.00 0.01 0.02 0.03 0.04 0.05 0.06

cu Analytical

cu E

xper

imen

tal

Figure 9 Correlation between experimental and analytical ultimate strains.

4. COMPARISON OF PROPOSED MODEL

To show the effectiveness of the proposed model, the stress-strain relations predicted by the previous models were computed for all the test specimens, and compared against the experimental results. Curves obtained from the models of Hoshikuma et al. (1997), Kappos and Konstantinidis (1999), Legeron and Paultre (2003), and El-Dash and El-Mahdy (2006) are also shown in Figures 10 and 11 for four selected specimens, besides those from the proposed model. It is shown that significant scatter exists in the post-peak range.

0

10

20

30

40

50

60

0.000 0.005 0.010 0.015 0.020

Strain

Stre

ss (M

Pa)

SU (1980) : 2C1-16ProposedHKNT modelKK modelLP modelDM model

(a) 2C1-16 (Sheikh and Uzumeri, 1980)

020406080

100120140160180

0.000 0.005 0.010 0.015 0.020 0.025 0.030

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ss (M

Pa)

NSKI (1992) : HL08LAProposedHKNT modelKK modelLP modelDM model

0

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60

80

100

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160

0.000 0.005 0.010 0.015 0.020 0.025

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ss (M

Pa)

CP (1994) : 1DProposedHKNT modelKK modelLP modelDM model

(b) HL08LA (Nagashima et al., 1992) (c) 1D (Cusson and Paultre, 1994)

Figure 10 Comparison of stress-strain curves for square specimens.

From the figures, it can also be seen that the model derived in this study is reasonably accurate in predicting the actual response of both normal- and high-strength concrete and steel for either circular or rectangular column cross-section with various confinement types. The proposed model can simulate very well the actual response of confined column specimens, prior to and beyond the peak stress. By those plots, it is also observed that the proposed curve predicts the peak stress, the strain at the peak stress and the deterioration rate reasonably better than the previous models.



0

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LPT (2001) : 6HBProposedHKNT modelLP modelDM model

0

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Pa)

SBK (2005) : CFProposedHKNT modelLP modelDM model

(a) 6HB (Li et al., 2001) (b) CF (Sharma et al., 2005)

Figure 11 Comparison of stress-strain curves for circular specimens.

From the previous comparison, it may be said that the proposed model generally provides better agreement with the stress-strain relation of confined concrete over a wider range of concrete strength, yield strength of confining reinforcement, volumetric ratio of confining reinforcement to concrete core, spacing between confining reinforcement, cross-section of confined core, configuration of lateral confining reinforcement, and distribution of longitudinal bars than the previous models.

The model proposed by Kappos and Konstantinidis (1999) is not capable to predict the confined column specimens with circular cross-section. This is because the proposed model, which was derived from the regression analysis, was mainly based on a few test data of rectangular column specimen only. All the predictions from the other models indicate that the actual stress-strain relationships, except those from Legeron and Paultre (2003) model, overestimate the strength gain of confined concrete columns.

5. CONCLUSIONS

A unified model is presented to predict the stress-strain relationship for normal- and high-strength concrete columns of square and circular cross-sections confined with spirals, ties, and/or crossties. The model is based on the experimental results of 231 concrete column specimens subjected to different types and amounts of transverse reinforcement and tested under concentric loading. Comparisons are made between the predictions of the model and the available experimental results. It can be concluded from the study that:

1. The model demonstrates good predictive capability and is applicable for a wide range of variables that include range of concrete compressive strength from 20 to 124 MPa and yield strength of confining reinforcement from 270 to 1390 MPa.

2. All models predict the ascending branch of the stress-strain curve fairly well, whereas the predicted descending branch is not consistent, except for the proposed model.

3. The statistical model proposed in the present study, which is based on a large experimental database, resulted in lower uncertainties than other models for most parameters.

4. The maximum strength of confined concrete is well predicted by the proposed than the other models as well as the strain along the descending branch of the confined concrete curve when stress drops to ccf50.0 .

5. The proposed model provides more reasonable values than the other relations.

6. REFERENCES

ACI Committee 318 (2008). Building Code Requirements for Structural Concrete (ACI 318-08) and Commentary (ACI 318R-08), American Concrete Institute, Farmington Hills, Michigan, USA, 456.

Assa, B., Nishiyama, M. and Watanabe, F. (2001). New approach for modeling confined concrete i: circular columns, Journal of Structural Engineering, ASCE, 127(7), 743-750.

Cusson, D. and Paultre, P. (1994). High strength concrete columns confined by rectangular ties, Journal of Structural Engineering, ASCE, 120(3), 783-804.



International Conference on Earthquake Engineering and Disaster Mitigation 2008

El-Dash, K.M. and El-Mahdy, O.O. (2006). Modeling the stress-strain behavior of confined concrete columns, International Symposium on Confined Concrete, ACI, SP-238, China, 177-192.

Hoshikuma, J., Kawashima, K., Nagaya, K. and Taylor, A.W. (1997). Stress-strain model for confined reinforced concrete in bridge, Journal of Structural Engineering, ASCE, 123(5), 624-633.

Kappos, A.J. and Konstantinidis, D. (1999). Statistical analysis of confined high strength concrete, Materials and Structures, 32, 734-748.

Li, B., Park, R. and Tanaka, H. (2001). Stress-strain behavior of high-strength concrete confined by ultra-high- and normal-strength transverse reinforcements, ACI Structural Journal, 98(3), 395-406.

Lin, C.H., Lin, S.P. and Tseng, C.H. (2004). High-workability concrete columns under concentric compression, ACI Structural Journal, 101(1), 85-93.

Legeron, F. and Paultre, P. (2003), Uniaxial confinement model for normal-and high-strength concrete columns, Journal Structural Engineering, 129(2), 241-252.

Nagashima, T., Sugano, S., Kimura, H. and Ichidawa, A. (1992). Monotonic axial compression test on ultra-high strength concrete tied columns, Proceedings of 10th World Conference on Earthquake Engineering, Madrid, 5, 2983-2988.

Pessiki, S. and Pieroni, A. (1997). Axial load behavior of large-scale spirally-reinforced high-strength concrete columns, ACI Structural Journal, 94(3), 304-314.

Razvi, S.R. and Saatcioglu, M. (1999). Circular high-strength concrete columns under concentric compression, ACI Structural Journal, 96(5), 817-825.

Sargin, M., Ghosh, S.K. and Handa, V.K. (1971). Effects of lateral reinforcement upon the strength and deformation properties of concrete, Magazine of Concrete Research, 23(75-76), 99-110.

Sheikh, S.A. and Uzumeri, S.M. (1980). Strength and ductility of tied concrete columns, Journal of Structural Division, ASCE, 106(ST5), 1079-1101.

Sheikh, S.A. and Uzumeri, S.M. (1982). Analytical model for concrete confinement in tied columns, Journal of Structural Division, ASCE, 108(ST12), 2703-2722.

Sheikh, S.A. and Toklucu, M.T. (1993). Reinforced concrete columns confined by circular spirals and hoops, ACI Structural Journal, 90(5), 542-553.

Saatcioglu, M. and Razvi, S.R. (1998). High-strength concrete columns with square section under concentric compression, Journal of Structural Engineering, ASCE, 124(12), 1438-1447.

Sharma, U.K., Bhargava, P. and Kaushik, S.K. (2005). Behavior of confined high strength concrete columns under axial compression, Journal of Advanced Concrete Technology, 3(2), 267-281.

Yong, Y.K., Nour, M.G. and Nawy, E.G. (1988). Behavior of laterally confined high strength concrete under axial load, Journal of Structural Engineering, ASCE, 114(2), 332-351.



STUDY OF CONFINEMENT MODELS FOR HIGH-STRENGTH CONCRETE COLUMNS CONFINED BY HIGH-STRENGTH STEEL

Zulfikar Djauhari1 and Iswandi Imran2

1PhD Student of Civil Engineering Study Program at Institut Teknologi Bandung, Indonesia 2Faculty of Civil and Environmental Engineering, Institut Teknologi Bandung, Indonesia

Email: [email protected]

ABSTRACT: The analysis of structural members requires an analytical model for the full stress-strain relationship of concrete in compression, both in confined and unconfined states. Many empirical confinement models for normal strength materials have been developed and documented in the literature during the last three decade. However, the models developed for normal strength material are not applicable to high-strength material. This paper reviews the various proposed stress-strain model for high-strength concrete materials confined by high-strength steel.

The main objective of the study is to examine the capabilities of the various models available in literature to predict the actual experimental behavior of high-strength concrete columns confined by high-strength steel. The experimental data used are the results of the tests conducted by the author, involving testing of 18 short column specimens with 110 mm diameter circular section confined by 6 mm spirals or hoops made of wire rod reinforcement. The test variables include yield strength, type (spiral or hoops), spacing and volumetric ratio of confining steel. The resulting stress-strain curves from the tests are then compared with the various models available in the literature. It is shown from this study that there is no models which can accurately predict the complete behavior of high-strength concrete columns confined with high-strength steel. 1. INTRODUCTION

The most fundamental requirement in predicting the behavior of reinforced concrete structures is the knowledge of stress-strain behavior of the constituent materials. As concrete is basically used to resist compression, the knowledge of its behavior in compression is very important. If the behavior of unconfined and confined concrete in uniaxial compression is known, its flexural behavior can be predicted. A considerable volume of research has been directed towards generating the stress-strain relationship for compressed concrete both in confined and unconfined state. As a result, many empirical stress-strain models have been proposed for confined concrete, both for normal and high-strength concretes.

Inelastic deformability of reinforced concrete columns is essential for overall stability of structures in order to sustain strong earthquakes. This can be achieved through proper confinement of the core concrete. The increase in the strength and ductility of normal and high-strength concrete confined by normal strength steel has been well documented (Assa et al., 2001; Li et al., 2001; Legeron and Paultre, 2003; Sharma et al., 2005; Hong et al., 2006). Question, however, have been asked as to whether a similar amount of confinement is suitable for high-strength concrete columns confined by high-strength steel. Existing code provisions for minimum amount of confining reinforcement are based on experiences with normal strength materials (ACI 318, 2005). However, the influence of the increase in material strength used needs to be taken into account. This initiates research studies on the effect of high strength materials on the behavior of confined concrete in various countries. Most of these studies have unanimously concluded that high-strength concrete columns need a considerably higher amount of confinement to attain the level of ductility that is commonly achieved by a nominal amount of confining reinforcement in normal-strength concrete columns (Sharma et al., 2005). It means that the confining pressure required for high-strength concrete columns is significantly higher than that for normal-strength concrete columns. The research findings have also indicated that for well confined columns, increasing the yield strength of confining steel results in an increase in strength and ductility, and can alleviate



the congestion of reinforcement (Li et al., 2001; Legeron and Paultre, 2003; Sharma et al., 2005). So, the higher confinement requirement of high-strength concrete columns can be satisfied by either increasing the volumetric ratio of lateral steel or by using higher grade of lateral steel. Li et al. (2001) have recommended the use of lateral steel grades above 1000 MPa for high-strength concrete columns.

2. SUMMARY OF CONFINEMENT MODELS

Many confinement models had been proposed for high-strength concrete columns confined by high strength steel (Muguruma et al., 1993; Cusson and Paultre, 1995; Azizinamini et al., 1994; Nakatsuka et al., 1995; Razvi and Saatcioglu, 1999; Li et al., 2001; Legeron and Paultre, 2003; and Hong et al., 2005). However, the models reported had various limitations. For example, Lis model is only applicable to certain range of concrete compressive strength. Moreover, Azizinamini and Hongs concluded in their studies that there is no significance effect on the use of high-strength steel for confining reinforcement. All the models, except Lis model, do not take into account a reinforcement type as a parameter. Among the models available in the literature, Legerons model is the most unified, widely accepted and with a wider scope than those of other models.

Cusson and Paultre (1995) developed a confinement model for high-strength concrete on the basis of test results of 50 large-scale high-strength concrete tied columns tested under concentric loading. Out of them, 30 high-strength concrete tied columns (225 x 225 mm) were tested by authors themselves and 20 high-strength concrete tied columns (225 x 225 mm) were tested by Nagashima et al. (1992). The concrete compressive strengths of the specimens ranged from 60 to 120 MPa. The ties with yield strength from 400 to 800 MPa were used. The proposed model takes into account tie yield strength, tie configuration, and longitudinal reinforcement ratio. Two-part of stress-strain relationship with separate expressions for ascending and descending parts were formulated in their study (Figure 1).

Azizinamini et al. (1994) modified the model developed by Yong et al. (1988) based on their test data, as well as test data obtained by Yong et al. The model consists of a linear ascending branch, followed by a linear descending branch with a constant residual at 30% of peak stress (Figure 1). The model was developed on the basis of test results of nine 2/3-scale column specimens with square cross section. The main test parameters were in place concrete strength (54 to 101 MPa), spacing of confining reinforcement (41.3 to 66.7 mm), axial load, and yield strength of confining reinforcement (414 to 828 MPa).

Razvi and Saatcioglu (1999) proposed a model for confined normal and high strength concrete columns using extensive test data from the authors own test results as well as experimental results from other research studies. This included the test results of nearly full size specimens of different shapes, sizes, reinforcement configuration, tie yield strength (ranging from 400 to 1387 MPa) and concrete strength (ranging from 30 to 130 MPa). The parameters incorporated in the model were type, volumetric ratio, spacing, yield strength, and arrangement of transverse reinforcement, distribution and amount of longitudinal steel as well as concrete strength and geometry. The two-part stress-strain model proposed by the authors is in the form of the ascending parabolic branch up to peak and a linear descending branch up to 20% of the peak stress (Figure 1).

Silva (2000) proposed a model for circular confined high strength concrete columns. He tested 15 circular columns that were made of normal and high strength concrete with compressive strength ranging from 35.5 to 125.4 MPa, confined with spiral reinforcement with yield strength of 440 to 560 MPa. The variable considered in the tests were diameter, spacing, volumetric ratio and yield strength of confining reinforcement. A two-part stress-strain relation was proposed to predict the constitutive behavior of confined high-strength concrete. He developed the confinement model based on the Popovics model (1973) for ascending branch and Fafitis and Shahs model (1985) for descending branch.

Assa et al. (2001) proposed the steel concrete interaction model to predict the strength and stress-strain curves of confined concrete. This model is based on the confining stiffness of transverse reinforcement. A total of thirty-two 150 x 300 mm concrete cylinders were tested under monotonic



concentric compression. No concrete cover was provided in all the specimens. The target strength of concrete ranged from 20 MPa to 90 MPa. The confining reinforcement of 6.25 mm helical spirals and welded circular hoops were used. The nominal yield strengths of the confining reinforcement were 1300 MPa and 800 MPa, respectively. The spacing of spirals or circular hoops was varied from 19 mm to 75 mm. The test results can be used to model the stress-strain behavior of concrete confined by several types of reinforcement configurations. If the lateral pressure for any lateral strain is theoretically obtained for any transverse reinforcement configuration as indicated by lateral pressure-lateral strain line, the lateral pressure at peak load can be easily obtained at the intersection point between the peak load condition line and lateral pressure-lateral strain line. Then, stress-strain coordinate at peak load can be obtained.

Li et al. (2001) proposed a three-part stress-strain model for high-strength concrete confined by high-strength steel based on their experimental results (Figure 1). Fourty reinforced concrete short columns of both cylindrical (240 mm diameter) and square (240 x 240 mm) cross sectional shapes were tested. The main parameters were in place concrete strength (35.2 to 82.5 MPa) and lateral steel grade (445 and 1318 MPa). Other parameters like spacing and volumetric ratio of lateral steel, were also varied in the tests. From test results, a confinement model was developed based on Mugurumas model (1993).

Legeron and Paultre (2003) proposed a stress-strain confinement model for normal and high-strength concrete columns based on the large number of test results of circular, square, and rectangular columns tested by themselves and by a number of other researchers. The concrete compressive strength ranged from 20 to 140 MPa and tie yield strength ranged from 300 to 1400 MPa. The model incorporates almost all the parameters of confinement. The stress-strain relationship is basically the same as that proposed by Cusson and Paultre (1995), but the parameters of the model were recalibrated on the basis of large number of test data collected by the authors.

Most of those models have limited validity in terms of concrete strengths, column geometry, transverse reinforcement yield strength and loading conditions. With exception of the models proposed by Razvi and Saatcioglu (1999), Li et al. (2001), Legeron and Paultre (2003), which cover both circular and rectilinear sections, all other models are applicable to only square or rectilinear shapes.

It has now been proven experimentally by many researchers that for high-strength concrete columns confined with high yield strength ties, lateral confining ties may not yield when the peak of confined concrete stress-strain is reached (Li et al., 2001; Cusson and Paultre, 2003). Even for lower yield strength of lateral confining steel, if enough degree of confinement is not provided, the transverse steel may not yield at peak confined strength. However, most of the models use yield strength of lateral steel to calculate lateral confining pressure at peak confined strength. Only Razvi and Saatcioglu (1999) and Legeron and Paultre (2003) have incorporated this fact into their respective models by proposing procedures to calculate actual confining stress at peak of confined stress-strain response. Li et al. (2001) has also accounted for this indirectly by suggesting a different expression for confined strength when higher grades of lateral steel are to be used, but no explicit expression for finding the confining stress at peak is proposed. In addition, none of the models take into account all the loading conditions, namely monotonic, cyclic, strain rate, and eccentric loading.

A critical review of the expression for ascending and descending portions proposed in the various confinement models indicates that the basic forms of these expressions are mostly the same and only the evaluation of the parameters differed from model to model. The expression of ascending branches as proposed by Li et al. (2001) is basically the same with those proposed by Muguruma et al. (1993). The ascending curves proposed by Cusson and Paultre (1995), Razvi and Saatcioglu (1999), Legeron and Paultre (2003) are also quite similar. The expression of descending curves proposed by Muguruma et al.(1993), Razvi and Saatcioglu (1999), Li et al. (2001) are basically the same and those given by Cusson and Paultre (1995) and Legeron and Paultre (2003) are also similar.



Figure 1 Example of stress-strain relationship of confined high strength concrete.

3. COMPARISON OF ANALYTICAL AND EXPERIMENTAL STRES-STRAIN BEHAVIOR

In this section, an attempt has been made to investigate the relative performance of the various proposed analytical models with regard to their capabilities of producing the experimentally observed stress-strain profiles on different test specimens. For this purpose, eighteen short column specimens (height of 600 mm) with 110 mm diameter circular section confined by 6 mm spirals or hoops made of wire rod reinforcement tested by Zulfikar et al. (2006) are used. The key parameters in the tests include yield strength, type (spiral or hoops), spacing and volumetric ratio of confining steel. The test parameters of the test specimens are shown in Table 1.

It should be noted that all the six confinement models of the study are applicable to square sections whereas only three, namely Razvi and Saatcioglus model (1999), Li et al.s model (2001), Legeron and Paultres model (2003), can also be applied to circular sections. Figure 2 to 9 illustrate the uniaxial stress-strain curves obtained using the various models for circular columns.

Table 1 The test parameters.

Pitch Volumetric ConfinementConcrete Confining Reinforcement (mm) ratio Index

1 2 3 4 5 6 7 81 S400P30 30 0.0419 0.242 S400P60 60 0.0209 0.123 S800P30 30 0.0419 0.484 S800P60 60 0.0209 0.245 S800P120 120 0.0105 0.126 S960P30 30 0.0419 0.577 S960P60 60 0.0209 0.298 S960P70 70 0.0180 0.259 S960P120 120 0.0090 0.12

10 H400P30 30 0.0419 0.2411 H400P60 60 0.0209 0.1212 H800P30 30 0.0419 0.4813 H800P60 60 0.0209 0.2414 H800P120 120 0.0105 0.1215 H960P30 30 0.0419 0.5716 H960P60 60 0.0209 0.2917 H960P70 70 0.0180 0.2518 H960P120 120 0.0090 0.12

960

Spiral

70

400

800

960

Hoop

400

800

No Confining Type Strength (MPa)Specimen



In order to judge the predictive capability of various analytical models, the computations were carried out for the peak confined stress fcc and the corresponding strain cc for all the specimens. The ratios of the predicted peak confined strengths to respective experimental peak values for all the specimens are shown in Table 2. The corresponding ratios for peak strains are shown in Table 3. It should be emphasized that the post-peak description of the stress-strain curve is of greater significance in order to ascertain the ductility and failure related aspects of concrete columns. Keeping this fact in mind, the study also aimed to determine the strain values at one specified stress levels in descending portion; i.e. 85% of the peak stress fcc. It is apparent from Figure 1 that linear or exponential descending branch belonged to most of the models employs either the definition of strain at 85% of peak stress, c85, or strain at 50% of peak stress, c50, or ultimate failure strain u as an alternate means to characterize the post-peak curve. These expressions for softening branches enabled us to compute c85 and c50 strain for various models. Most of the reported experimental stress-strain curves of the test specimens do not reach down to a strain value of 50% of the peak stress. So, for these cases, no comparison is possible at strain of 50% of peak stress. The comparison at post-peak is only made at strain of 85% of peak stress. Table 4 show the ratios of these predicted to experimental post-peak strains.

Most of the confinement models assume that the lateral reinforcement stress to attain its yield value at the confined strength of concrete columns is irrespective of whether a high yield strength or normal yield strength reinforcement are being used. However, some of the recently developed confined models propose a method to work out the actual stress level in the lateral confining reinforcement. This issue has also been addressed in the present work by computing the ratios of predicted confining reinforcement stress at peak by various models to real stress of confining reinforcement obtained from the test, as shown in Table 5.

Table 2 Comparisons for peak confined stress fcc.

Assa Azizinamini Legeron Li Razvi SilvaS400P30 88.61 1.11 0.92 1.05 0.95 1.04 0.98S400P60 73.03 1.15 1.05 1.16 0.99 1.13 0.95S800P30 100.06 1.26 0.92 1.08 1.18 1.09 1.21S800P60 80.67 1.22 1.03 1.16 0.99 1.14 1.07S800P120 70.76 1.19 1.11 1.19 1.00 1.16 0.98S960P30 125.94 1.09 0.77 0.90 1.09 0.92 1.07S960P60 83.30 1.25 1.03 1.16 1.01 1.15 1.12S960P70 78.24 1.26 1.08 1.20 1.01 1.18 1.12S960P120 71.80 1.21 1.12 1.20 0.99 1.18 1.01H400P30 86.23 1.11 0.92 1.05 0.93 1.04 0.98H400P60 71.65 1.15 1.05 1.16 0.99 1.13 0.95H800P30 99.55 1.26 0.92 1.08 1.06 1.09 1.21H800P60 73.91 1.22 1.03 1.16 1.01 1.14 1.07H800P120 68.65 1.19 1.11 1.19 1.02 1.16 0.98H960P30 102.50 1.09 0.77 0.90 1.18 0.92 1.07H960P60 75.50 1.25 1.03 1.16 1.01 1.15 1.12H960P70 72.46 1.26 1.08 1.20 1.01 1.18 1.12H960P120 70.38 1.21 1.12 1.20 1.00 1.18 1.01

5.20 10.99 8.52 6.53 7.44 7.75

Specimen fcc exp (MPa)fcc predicted/fcc experiment

COV (%)



Table 3 Comparisons for peak confined strain cc.

Assa Azizinamini Legeron Li Razvi SilvaS400P30 0.0062 1.74 0.76 1.07 2.41 0.72 1.89S400P60 0.0055 1.25 0.63 0.83 0.89 0.64 0.94S800P30 0.0178 1.04 0.33 0.63 1.12 0.34 1.84S800P60 0.0072 1.50 0.55 0.92 3.74 0.62 1.63S800P120 0.0047 1.45 0.54 0.96 3.19 0.75 1.09S960P30 0.0346 0.62 0.18 0.38 1.29 0.19 1.27S960P60 0.0035 3.48 1.17 2.12 8.37 1.36 4.28S960P70 0.0208 0.53 0.18 0.32 1.27 0.22 0.58S960P120 0.0059 1.30 0.44 0.84 2.77 0.63 1.06H400P30 0.0081 1.74 0.76 1.07 1.39 0.72 1.89H400P60 0.0036 1.25 0.63 0.83 1.06 0.64 0.94H800P30 0.0099 1.04 0.33 0.63 1.72 0.34 1.84H800P60 0.0070 1.50 0.55 0.92 3.19 0.62 1.63

H800P120 0.0046 1.45 0.54 0.96 2.18 0.75 1.09H960P30 0.0229 0.62 0.18 0.38 1.80 0.19 1.27H960P60 0.0211 3.48 1.17 2.12 1.17 1.36 4.28H960P70 0.0020 0.53 0.18 0.32 10.70 0.22 0.58

H960P120 0.0047 1.30 0.44 0.84 2.27 0.63 1.0658.55 56.54 56.66 93.13 56.27 65.08

cc predicted/cc experimentSpecimen cc exp

COV (%)

S400P30

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0 0.02 0.04 0.06 0.08

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Azizinamini (1994)Legeron (2003)Li (2004)Razvi (1999)Silva (2000)Experiment

Figure 2 Stress-strain curve for specimens S400P30. Figure 3 Stress-strain curve for specimens S400P60.

S800P30

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S960P30

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H400P60

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H960P60

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Figure 8 Stress-strain curve for specimens H400P60. Figure 9 Stress-strain curve for specimens H960P60.

4. DISCUSSION The relative performance of the various confinement models of high-strength concrete columns confined by high-strength steel in terms of their capabilities to predict the actual confined compressive test behavior has been evaluated. The behavior parameters considered are experimental peak confined strengths fcc, corresponding peak strain cc, post-peak strains c85, stress level in confining reinforcement fs at peak and stress-strain curves. In the absence of any conclusive pattern with respect to these parameters for the selected specimens, the coefficient of variation concept has been employed to quantify the performance index of each model.

The analysis using Azizinamini et al.s model (1994) indicates that this model, in general, underestimate the peak confined strength, fcc, and the associated peak strain, cc, and post-peak strain, c85, of the test results. The coefficient of variation in estimating peak confined stress, fcc, for this model are the largest among all models considered (i.e. 10.99 % (Table 2)). This model proposes that the confining reinforcement always yield as the peak confined strength is reached. Therefore, the model is not able to predict the actual level of spiral or hoop stress at the peak confined stress for those specimens having higher spiral content or hoop yield strengths.

The Razvi and Saatcioglu model (1999) has the advantages of being applicable to all the cross-sectional shapes, covering a wider concrete strength range (60-124 MPa) and considers the implications of using high-strength steel, although it suffers from the limitations of being unable to produce an ascending and descending branch that is in agreement with the experimental results. However, the peak stress fcc parameter obtained from this model shows close agreement with the test values (Table 2). Nevertheless, the predictions of post-peak strain, c85, and descending branches of predicted stress-strain curves indicate that the model consistently overestimate with considerable magnitude the actual post-peak behavior. But, strain at peak stress, cc, is underestimated by the model. The procedure adopted in the model to compute the actual spiral or hoop stress at peak, fs appears to be more rational as its predictions for the specimens are better if not more accurate than those given by the other models considered in this study. The coefficient of variation in estimating the actual spiral or hoop stress at peak from this model is the minimum of all models (i.e. 43.12% (Table 5)).

The Li et al. model (2001) can predict stress-strain curves both for circular and square confined specimens. Its prediction of the peak confined strength, fcc is close enough to the test values for almost all test specimens (Table 2). It is evident from the study that the model is quite erroneous in predicting peak strains, cc. The model produces the largest COV in this case (Table 3). For the specimens confined by normal and high strength steel in particular, the errors corresponding to the estimation of post-peak strain parameters c85 are also significant (Table 4). A separate expression for calculating peak strength of column confined by high-strength steel is included in this model to account for delayed confining effect in such cases. So, the fact that high-strength steel spiral or hoop in high-strength concrete columns may not yield at peak is taken into account, but still the model give more erroneous results for specimens having high-strength confining steel. As no specific expression is given to calculate the level of stress in the lateral confining reinforcement at peak confined strength, then the ratio of actual lateral spiral or hoop stress at peak to yield strength can not be obtained for this model. The present study shows that this model is capable of



predicting reasonably the peak strength of high-strength concrete columns confined by high-strength steel only.

The Legeron and Paultre model (2003) can also be used to predict the stress-strain behavior of columns of all cross sectional shapes. This model predicted both peak strength, fcc and peak strain, cc of the test value remarkably well. However, the stress-strain curves predicted by the model overestimate the experimental stress-strain curves for almost all specimens (Figure 2 to 9). The expression proposed in the model to calculate the actual level of confining reinforcement stress at peak confined strength produces higher estimate than the experimentally reported values as indicated in Table 5.

Table 4 Comparisons for strain at 85% of peak stress c85.

Assa Azizinamini Legeron Li Razvi SilvaS400P30 0.0155 1.82 1.33 2.37 1.68 1.73 1.11S400P60 0.0036 8.12 4.16 4.01 2.41 3.49 2.03S800P30 0.0205 1.88 1.39 4.78 1.70 2.53 2.08S800P60 0.0090 3.13 1.99 4.09 5.20 2.31 1.92S800P120 -S960P30 0.0368 1.17 0.86 3.35 2.14 1.68 1.45S960P60 0.0570 0.53 0.34 0.85 0.90 0.42 0.39S960P70 0.0200 1.42 0.86 1.92 2.31 0.99 0.90S960P120 0.0100 2.72 1.16 1.78 2.84 1.11 0.89H400P30 0.0137 2.06 1.50 2.69 1.44 1.96 1.26H400P60 0.0088 3.29 1.69 1.62 0.77 1.41 0.82H800P30 0.0205 1.88 1.39 4.78 1.46 2.53 2.08H800P60 0.0064 4.41 2.80 5.75 6.13 3.25 2.69H800P120 0.0100 2.88 1.14 1.42 1.75 1.00 0.72H960P30 0.0714 0.60 0.44 1.73 1.01 0.86 0.75H960P60 0.0159 1.88 1.20 3.03 2.70 1.50 1.38H960P70 0.0350 0.81 0.49 1.10 1.07 0.57 0.51H960P120 -

76.73 67.13 52.58 67.28 53.44 51.31COV (%)

Specimen c85 exp c85 predicted/c85 experiment

Table 5 Comparisons for stress in confining reinforcement at peak stress.

fs exp (MPa) Cusson Hong Legeron RazviS400P30 570.67 0.94 0.70 0.70 1.79S400P60 211.60 2.40 1.89 1.89 4.11S800P30 483.69 2.68 1.41 1.41 2.43S800P60 843.81 0.78 0.81 0.81 1.19S800P120 735.12 0.62 0.93 0.93 1.23S960P30 525.17 4.18 1.78 1.78 1.69S960P60 293.14 1.15 3.20 3.20 2.57S960P70 261.05 6.43 3.59 3.59 2.80S960P120 385.94 1.47 2.43 0.63 1.68H400P30 273.20 2.47 1.46 1.46 3.75H400P60 221.00 1.55 1.81 1.81 3.94H800P30 444.75 1.85 1.54 1.54 2.65H800P60 444.75 1.44 1.54 1.54 2.25H800P120 347.24 1.27 1.97 1.97 2.61H960P30 179.99 8.68 5.20 5.20 4.93H960P60 319.97 5.10 2.93 2.93 2.36H960P70 228.10 0.85 4.11 4.11 3.21H960P120 764.95 0.59 1.22 0.32 0.85COV (%) 90.71 57.09 66.33 43.12

Specimenfs predicted/ fs experiment

5. CONCLUSIONS

The use of high strength steel is now being advocated for confining reinforcement in concrete columns to compensate for the lower ductility of high-strength concrete columns. Given the fact



that confining reinforcement may not yield when the peak confined strength of columns is reached, there are only few models available in the literature which include procedures to calculate the actual stress of confining reinforcement. Only the models proposed by Razvi and Saatcioglu (1999) and Legeron and Paultre (2003) cover a wide range of concrete strength, is applicable to all the cross-sectional shapes and can be used for both normal and high-strength confining steel.

A comparative study was undertaken to evaluate the capabilities of the various confinement models of high-strength concrete columns available in literature in predicting the actual experimental behavior of the specimens tested by the author. The study indicated that almost all the models are able to correctly estimate the ascending part of the experimental stress-strain curve. However, there are wide variation in the prediction of peak strength, peak strain, post peak strain and the descending part of stress-strain curves, with a few models underestimating and a few overestimating the test values.

There is no model which correctly predicts the stress in the confining reinforcement at peak confined stress. The resulting coefficient of variation in predicting experimental values for all specimens ranges from 43.12 to 90.71. The large values of COV show that the models considered are not accurate enough in predicting the stress in confining reinforcement at peak.

6. REFERENCES

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

Assa, B., Nishiyama, M. and Watanabe, F. (2001). New approach for modeling confined concrete I : circular columns, Journal of Structural Engineering, V.127, No.7, July, pp 743-750.

Azizinamini, A., Baum Kuska, S.S., Brungardt, P. and Hatfield, E. (1994). Seismic behavior of square high-strength concrete columns, ACI Structural Journal, V.91, No.3, May-June, pp. 336-345.

Cusson, D. and Paultre, P. (1995). Stress-strain model for confined high-strength concrete, Journal of Structural Engineering, V.121, No.3, March, pp. 468-477.

Fafitis, A. and Shah, S.P. (1985). Lateral reinforcement for high-strength concrete columns, SP-87-12, American Concrete Institute, Detroit, pp. 213-232.

Hong, K.N., Akiyama, M., Yi, S.T. and Suzuki, M. (2006). Stress-strain behavior of high-strength concrete columns confined by low-volumetric ratio rectangular ties, Magazine of Concrete Research, V.58, No.2, March, pp. 101-115.

Legeron, F. and Paultre, P. (2003). Uniaxial confinement model for normal- and high-strength concrete columns, Journal of Structural Engineering, V.129, No.2, February, pp. 241-252.

Li, B., Park, R. and Tanaka, H. (2001). Stress-strain behavior of high-strength concrete confined by ultra-high- and normal-strength transverse reinforcement, ACI Structural Journal, V. 98, No. 3, May-June, pp. 395-406.

Mugurama, H., Nishiyama, M. and Watanabe, F. (1993). Stress-strain curve model for concrete with a wide-range of compressive strength, Proceeding High-Strength Concrete, Lillehammer, Norway, pp. 314-321.

Nakatsuka, T., Nakagawa, H. and Suzuki, K. (1995). Strength deformation characteristic of confined concrete and spiral reinforcement: of high strength, Concrete 95 toward Better Concrete Studies, pp. 427-469.

Popovics, S. (1973). Analytical approach to complete stress-strain curves, Cement and Concrete Research, 3 (5), pp. 583-599.

Razvi, S. and Saatcioglu, M. (1999). Confinement model for high-strength concrete, Journal of Structural Engineering, V. 125, No. 3, March, pp. 281-289.

Sharma, U., Bhargava, P. and Kaushik, S.K. (2005). Comparative study of confinement models for high-strength concrete columns, Magazine of Concrete Research, V. 57, No. 4, May, pp. 185-197.



International Conference on Earthquake Engineering and Disaster Mitigation 2008

Silva, P. (2000). Effect of Concrete Strength on Axial Load Response of Circular Columns, Department of Civil Engineering and Applied Mechanics, Mc Gill University, Montreal, Canada.

Yong, Y.K., Nour, M.G. and Nawy, E.G. (1988). Behavior of laterally confined high-strength concrete under axial loads, Journal of Structural Engineering, V. 114, No. 2, February, pp. 332-350.

Zulfikar, D., Imran, I. and Setio, H.D. (2007). Strength and ductility behaviour of high-strength concrete confined by high-strength steel (in Indonesia), Proceeding Earthquake Resistant Construction in Indonesia, Jakarta, pp. 23-34.



STUDY ON THE SEISMIC PERFORMANCE CURVES OF REINFORCED CONCRETE SHORT COLUMNS FAILED IN SHEAR

Shyh-Jiann Hwang 1, Yi-An Li 2 and Pu-Wen Weng 3

1Department of Civil Engineering, National Taiwan University, Taipei, 106, Taiwan 2Department of Civil Engineering, National Taiwan University, Taipei, 106, Taiwan

3National Center for Research on Earthquake Engineering, Taipei, 106, Taiwan [email protected], [email protected], [email protected]

ABSTRACT: Reinforced concrete (RC) columns failed in shear were commonly observed during Chi-Chi earthquake. Especially, the shear failure of RC short columns was one of the major failure modes which caused building collapse. Therefore, this study focuses on the behavior of shear failure till collapse. Eight specimens were constructed and tested to study the seismic behavior of short columns. These specimens with different height-to-depth ratio, shear reinforcement detailing and axial load ratios were subjected to double curvature bending with constant axial forces to observe the behavior of the shear and axial failure. Test results show that the different shear reinforcement detailing results in different behavior and the axial failure takes place much early with high axial load ratio. Finally, this study recognizes that the RC short column can possess the gravity-load carrying capacity even its lateral-load strength is lost completely.

1. INTRODUCTION

During Chi-Chi Earthquake in Taiwan (1999), we have found the failure of the columns was the major damage in the reinforced concrete (RC) buildings, especially low-rise RC school buildings. In order to understand the characteristic of the columns in low-rise RC school buildings, we observed that the typical columns become the captive columns because of the windowsill which commonly exist in low-rise RC school buildings. The shear failure of RC captive columns was one of the major failure modes which caused building collapse. However, it is noted that the columns still possess its gravity-load carrying capacity even the columns have been failed by shear. Therefore, this study focuses on understanding the post-strength behavior of the short columns after shear failure.

According to the experience surveyed during Chi-Chi earthquake, we found the low-rise RC school buildings collapsed due to the failure of the columns on the first story. The collapse of low-rise RC school buildings results from the lost of the gravity-load carrying capacity of columns. In order to understand the seismic behavior of low-rise RC school buildings, we should know the failure modes of short columns subjected to the horizontal and vertical loads. In this research, we varied three different parameters of short columns, such as height-to-width ratio, the amount of transverse steel and axial load ratio. We want to study the failure modes and the collapse behavior of the captive columns failed by shear.

2. EXPERIMENTAL PROGRAM

The experimental program consists of eight tests under cyclic lateral and vertical load. We totally have three parameters of the specimens such as height-to-width ratio, ductile or nonductile detailing and axial load ratio. The specimens were divided into four groups and every group has two specimens. These two specimens are subjected to low axial load ( , where gc Af 1.0 cf = designed concrete compressive strength and = gross cross-sectional area) and high axial load ( ) separately. Table 1 shows the parameters of the specimens. 3 and 4 represent the height-to-width ratio. D and N represent ductile detailing and nonductile detailing, respectively. L and H represent low axial load (

gA

gc Af 3.0

gc Af 1.0 ) and high axial load ( gc Af 3.0 ), respectively. Figure 1 shows the reinforcement details of the specimens. First group of specimens is the nonductile



shorter columns shown in figure 1(a). The second group is the ductile shorter columns shown in figure 1(b). The third group is the nonductile longer columns shown in figure 1 (c). The fourth group is the ductile long columns shown in figure 4 (d). The height of the columns are 150 cm and 200 cm and the columns have a cross section of 5050 cm.

Table 1 Specimens layout. Parameters

Specimens Aspect ratio Detailing Axial load

4DL gc Af 1.0 (L) 4DH

Ductile (D) gc Af 3.0 (H)

4NL gc Af 1.0 (L) 4NH

4

Nonductile (N) gc Af 3.0 (H)

3DL gc Af 1.0 (L) 3DH

Ductile (D) gc Af 3.0 (H)

3NL gc Af 1.0 (L) 3NH

3

Nonductile (N) gc Af 3.0 (H)

5

7015

070

50

(a) 3NL & 3NH (b) 3DL & 3DH

Unit : cm

10

8585

150

200

50

#8 longitudinal bars

#3 ties @ 30 cm

90-degree hooks

#3 ties @ 30 cm

16#8 longitudinal bars

50

(c) 4NL & 4NH (d) 4DL & 4DH

Figure 1 Specimen details.



The specified concrete compressive strength was 210 kgf/cm2 at 28 days. Mean concrete strengths obtained from standard compression tests on 152305 mm cylinders on the day of column testing ranged from 303 to 352 kgf/cm2 (Table 2). Mean yield and ultimate strengths of the 25.4-mm diameter (No.8) deformed longitudinal bars were 4812 kgf/cm2 and 7004 kgf/cm2, respectively. Mean yield and ultimate strengths of the 9.5 mm-diameter (No.3) deformed longitudinal bars were 4570 kgf/cm2 and 6707 kgf/cm2, respectively. The axial loads of the specimens L and H are 63.75 tf and 191.25 tf.

Table 2 Material strength. reinforcement Specimens cf ( kgf/cm2) No. fy(kgf/cm2) fu(kgf/cm2)

4DL 310 4DH 303 4NL 347 4NH 314

#3 4570 6707

3DL 352 3DH 344 3NL 331 3NH 341

#8 4812 7004

The lateral support consists of four steel columns and two steel braces. It is designed to restrain the testing columns against lateral movement. Figure 2 shows the test setup in the laboratory. The loading systems are composed of two horizontal actuators and two vertical actuators. The force of horizontal actuators goes through the L shaped steel frame to the specimens. The vertical actuators apply axial load on the specimen. Figure 3 shows the loading history, which consists of the following lateral drift cycles: three cycles each at 0.25%, 0.5%, 0.75%, 1%, 1.5%, 2%, 3%, 4%, 5%, 6%. The control of actuator loading system is mixed with displacement and force controls. The loading systems which consist of four actuators are shown in Figure 4. The horizontal actuator 1 is the displacement control. It followed the loading history (shown in Figure 3). The horizontal actuator 2 provided the same load of the actuator 1. The resultant of the actuators 1and 2 went through the center of the column. The displacement of the vertical actuator 3 is equal to actuator 4. The resultant of the vertical actuators 3 and 4 was maintained as the targeted value throughout the test. The reason that we choose this kind of loading systems is to confirm the column deformed in double curvature.

Figure 2 Test setup.



drift

rat

io (%

)

Figure 3 Loading history.

Figure 4 Actuator control.

3. EXPERIMENTAL RESULTS AND DISSCUSION

3.1 Test Results According to the crack patterns shown in Figure 5, we observed not only a lot of diagonal cracks after the specimens reach the maximum strength but also the vertical cracks, especially for ductile detailing columns. From Figure 5, it is noted that the inclined angle of the principal cracks with respect to the horizontal axis is larger when the axial load applied on the specimens is higher. Table 3 shows the test results contains the peak point of the test data and the observed failure modes. We think the failure mode of the short columns is the shear failure because of the diagonal crack patterns of the specimens. However, we note that there is another failure mode of the short columns, which is the vertical bond splitting along the column longitudinal bars.

Figure 6 shows the load-displacement hysteretic relationship of the specimens. We can see that the maximum strength of the specimens can not reach the flexural strength. The nominal flexural strength (Mn) of the test columns in Figure 6 were calculated according to ACI Committee 318 (2005). Therefore, we confirmed all the tested short columns were failed by shear. According to the hysteretic loop of testing (Figure 6), we concluded that the displacement of the nondcutile detailing specimens at the ultimate strength is lower than ductile detailing specimens and that the displacement of the specimens with high axial load is also higher than those of low axial load.

More details of the test results can be found in the reference of Weng (2007).



(a) 4DL (b) 4DH (c) 4NL (d) 4NH

(e) 3DL (f) 3DH (g) 3NL (h) 3NH

Figure 5 Failure patterns of the specimens.



Table 3 Test results. Peak Point

Specimens Strength (tonf) Displacement (cm) Description of Failure

4DL 73.7 3.5 shear failure with bond splitting

4DH 80.1 2.5 shear failure with bond splitting

4NL 47.9 1.7 shear failure

4NH 68.5 1.6 shear failure

3DL 78.5 1.7 shear failure with bond splitting

3DH 87.4 1.9 shear failure with bond splitting

3NL 48.2 0.8 shear failure

3NH 71.9 0.7 shear failure

Mn-8 -4 0 4 8 12

-18 -12 -6 0 6 12 18-120

-80

0

60

120

Late

ralf

orce

(ton

f)

-12 -8 -4 0 4 8 12

-12 -6 0 6 12 18

-8 -4 0 4 8 12

-12 -6 0 6 12 18

-8 -4 0 4 8 12

-120

-60

0

60

120

-12 -6 0 6 12 18

-8 -4 0 4 8 12

3DL 3NL 3DH 3NHDisplacement (cm)

Drift Ratio (%)

Late

ralF

orce

(ton

f)

-16 -8 0 8 16 24

-8 -4 0 4 8 12

-24 -16 -8 0 8 16 24-100

-50

0

50

100

-12 -8 -4 0 4 8 12

-16 -8 0 8 16 24

-8 -4 0 4 8 12

-100

-50

0

50

100

-16 -8 0 8 16 24Displacement (cm)

Drift Ratio (%)

4DL 4NL 4DH 4NH

Figure 6 Load-displacement relationship of the specimens.



3.2 Compare with ASCE 41

Some empirical equations to predict the drift ratio of the flexural shear failure (Elwood and Moehle, 2005a) and the drift ratio of the axial failure (Elwood and Moehle, 2005b) are available. Some of these findings were incorporated into the ASCE 41 (2007). Figure 7 shows the prediction of strength and displacement by the ASCE 41 (2007) and the envelope of the test results. According

iceedm08 str

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