Bull Earthquake EngDOI 10.1007/s10518-014-9617-x

ORIGINAL RESEARCH PAPER

Performance of HSC columns under severe cyclic loading

Hakim Bechtoula · Susumu Kono ·Fumio Watanabe · Youcef Mehani ·Abderrahmane Kibboua · Mounir Naili

Received: 3 December 2013 / Accepted: 30 March 2014© Springer Science+Business Media Dordrecht 2014

Abstract Experimental and analytical results of seismic investigation of high strength rein-forced concrete columns performance is summarized in this paper. Twelve cantilever columnswith different sizes and concrete compressive strengths were tested. The column sizes were325×325 mm, 520×520 mm and 650×650 mm for the small, medium and large scale spec-imens, respectively. Concrete compressive strength was 80, 130 and 180 MPa. All specimenswere designed in accordance with the Japanese design guidelines. It was noticed that spallingof cover concrete was very brittle for specimens made of 180 MPa followed by a significantdecrease in strength independently of the column size. It was also observed that, while con-crete compressive strength increases, the drift corresponding to the peak load decreases aswell as the ductility of the specimen. Curvature was much important for the small size thanfor the medium size columns. Specimens with high concrete compressive strength showed ahigher equivalent viscous damping at all drift angles. An equation was proposed for predict-ing the moment-drift envelope curves for the medium and large scale columns knowing thatof the small scale columns. Experimental moment-drift and axial strain-drift histories werewell predicted using a fiber model developed by the authors.

Keywords High strength concrete · Column · Performance · Scale effect · Curvature ·Damage

1 Introduction

A few years ago, concrete with a compressive strength of 34 MPa was considered as a HighStrength Concrete (HSC). Today, HSC is defined as concrete with a specified compressive

H. Bechtoula (B) · Y. Mehani · A. Kibboua · M. NailiNational Earthquake Engineering Research Center, C.G.S 01 Rue Kaddour Rahim, BP252,Hussein Dey, Alger, Algeriae-mail: bechhakim@gmail.com; hbechtoula@cgs-org.dz

S. Kono · F. WatanabeDepartment of Architecture, Kyoto University, Katsura Campus, Nishikyo, Kyoto 615-8540, Japan

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strength of 55 MPa or higher (ACI Committee-363 2005). In many markets, concrete havinga specified compressive strength in excess of 69 MPa is routinely produced on a daily basis(Antonius 2013; Bechtoula et al. 2009; Campione 2008). Although 55 MPa was selectedas the current lower limit, it is not intended to imply that any drastic change in materialproperties or in production techniques occurs at this compressive strength (Ramadoss andNagamani 2012; Ching and Ho 2011; Bo and Li 2009; Lu and Chen 2008). In reality, allchanges that take place at or above 55 MPa represent a process which starts with the lowerstrength concretes and continues into the high strength realm (Han Qiang and Xiuli 2013;Hadi and Zhao 2011; Dias-da-Costa and Júlio 2010; Hamid et al. 2008; Tomosawa andNoguchi 1995; Martinez et al. 1982).

Use of Reinforced Concrete (RC) structures to erect high-rise buildings has rapidlyincreased in Japan especially after the publication of the “New RC Project” report (JICE1988–1993). This research project took into account the results of many research programcarried in the past (Nishiyama 1993; Muguruma and Watanabe 1990; Nakamura and Yokoo1977). The results of “New RC Project” and the succeeding progress of structural analysesand construction technology have made the realization of high-rise buildings of RC struc-tures more possible. For the first time, in Japan in 1997, concrete of specified compressivestrength of 100 MPa was applied to the columns of the residential River-City 21 North-BlockN-building (Namiki et al. 1999) with 43 stories and 145 m in height.

Using HSC can reduce the section dimensions and dead loads of structures; these advan-tages of high strength concrete are more remarkable when used for longer span and tallerstructures. As a result, the application of HSC in the construction industry has steadilyincreased in recent years. However, concrete with higher strength demonstrates a more brit-tle property, and with the increase of compressive strength, the ratio of tensile strength tocompressive strength usually decreases. High strength concrete can improve the strengthof structures, but reduce their ductility (Liu 2009a,b; Huang et al. 2005; Kuramoto et al.1995). Higher strength concrete exhibits a less ductile post peak response in compressionthan normal strength concrete. This, together with the tendency for splitting cracks to formcan result in a reduction of the compressive capacity of columns and has led to greater con-finement requirements for high strength concrete columns (Collins et al. 1993; Saatciogluand Razvi 1998; Nishiyama 2009). Various researches have been undertaken on the usageof HSC for axially loaded reinforced concrete columns that are subjected to seismic loading(Parande 2013; Yu-Chen et al. 2012; Cengiz and Serkan 2012; Paultre et al. 2009; Paultreand Légeron 2008; Ozbakkaloglu and Saatcioglu 2006; Rogerio et al. 2005; Seung-Hun et al.2004). However, it is apparent that further investigation is necessary due to limited researchdata especially for large scale specimens.

Here after, some of the main results drawn from tests and numerical simulations of twelvehigh strength reinforced concrete columns with different sizes and concrete compressivestrengths, tested under severe vertical and horizontal cyclic loading, are reported. The purposeis to investigate the seismic behavior of HSC columns by analyzing the effect of some crucialcolumn parameters on the overall performance and capacities. These tests were carried outat Kyoto University for a period of two years.

2 Material characteristic and test setup

Twelve high strength reinforced concrete cantilever columns were designed according to theJapanese guide lines (AIJ 1999) and tested at Kyoto University. Due to time consuming,money and efforts needed to achieve this testing program, it was decided to carry out this

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Full scale(100%) Large scale

(76%) Medium scale(61%) Small scale

(38%)

(a)

(b) (c)

(d)

Fig. 1 Size and steel arrangement of the columns. a Model and prototype. b Small scale column. c Mediumscale column. d Large scale column

research in two phases by dividing the test program to two series, series A and series B, with6 specimens in each. Three types of column sections were selected: the small scale columns(S) were 325 × 325 mm, the medium scale columns (M) were 520 × 520 mm and the largescale columns (L) were 650 × 650 mm. These specimens represent models of a prototypewith a cross section of 850 × 850 mm, as illustrated in Fig. 1.

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The test variables were mainly the column dimensions and the concrete compressivestrength. Shear span ratio, longitudinal and transversal reinforcement and the normalizedaxial load were the same for all specimens except for specimens under variable axial load.Three types of concrete compressive strength were used, 80, 130 and 180 MPa as shown inTable 1. Concrete admixture for series A and B are shoxn in Tables 2 and 3, respectively,whereas Table 4 summarizes the mechanical characteristics of the reinforcements. Smallscale column were tested vertically using the loading frame of the laboratory, see Fig. 2a.Whereas, medium and large scale columns were tested horizontally using the reaction wallas a support due to the important axial load intensity. As illustrated in Fig. 2b; two 8MN andtwo 3MN hydraulic jacks were used to apply the axial load. For the reversed cyclic loadingtwo 2MN jacks were used. Fig. 3 shows the three type of reversed cyclic loading historyapplied during the test for the different specimens.

3 Experimental results

3.1 Bending moment-drift relationships

Experimental bending moment-drift hysteresis loops are shown in Figs. 4 and 5 for series Aand B, respectively. Yielding of the longitudinal reinforcements in tension and compressionare shown in the figures by black marks. As it will be discussed furthermore, the first andthe second peak denote, respectively, the maximum elastic moment (before spalling of coverconcrete) and the maximum peak moment (after spalling of cover concrete) of the specimen.Spalling of the cover concrete was very brittle especially for specimens with 130 and 180 MPa.After the spalling, a rapid decrease in the moment capacities was observed as shown forexample for specimens S180-C-A and S130-V-B. However, for specimens made of 80 MPa,the capacity of the specimens continued to increase even after the spalling of concrete asseen for specimens S080-C-B, M080-C-A and L080-C-B.

3.2 Effect of concrete compressive strength and scale on the performance

Effect of the concrete compressive strength on the seismic performance of the columns wasobserved clearly wile comparing the normalized horizontal load versus the drift of columnsof the same scale, as illustrated clearly in Fig. 6, respectively for the small and medium scalecolumns.

Drift corresponding to the maximum capacity, horizontal load, decreased with an increasein the concrete compressive strength. Also, slope of the descending branch increased withan increase in the concrete compressive strength.

Size effect was not clearly seen in this experiment, especially for specimens made of130 MPa, as illustrated in Fig. 7 that shows the normalized horizontal load versus the drift ofcolumns with the same concrete compressive strength and different sizes.

3.3 Curvature distribution

Fifteen Linear Variable Displacement Transducers, LVDTs, were set at the lower part of thecolumns to monitor the deformations at the plastic hinge region. Figure 8 shows the settingof the LVDTs for the small, medium and large scale columns. Curvature was computed fora height equal to the column depth, D, for all specimens.

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Tabl

e1

Spec

imen

’sch

arac

teri

stic

san

dte

stva

riab

les

Seri

esC

olum

nsA

xial

load

ratio

N/f

′ cD2

Shea

rsp

anra

tioa/

DC

olum

nw

idth

D(m

m)

Shea

rsp

ana

(mm

)L

ongi

tudi

nal

reba

rT

rans

vers

alre

bar

Con

cret

est

reng

thf′ c

(Mpa

)

Axi

allo

ad(M

N)

AM

180-

C-A

0.30

2.5

520

1300

16-D

25(3

.01

%)

UD

10@

70(0

.78

%)

180

13.6

M13

0-C

-A13

010

.6

M08

0-C

-A80

5.32

S180

-C-A

325

812.

516

-D16

(3.0

1%

)U

D6@

50(0

.78

%)

180

5.31

S130

-C-A

130

4.13

S080

-C-A

802.

08

BL

130-

C-B

0.30

2.5

650

1625

16-D

32(3

.01

%)

UD

13@

100

(0.7

8%

)13

015

.22

L08

0-C

-B0.

3080

10.1

4

M13

0-V

-BM

ax:0

.55

Min

:−0.

7σy�

As

520

1300

16-D

25(3

.00

%)

UD

10@

55(1

.01

%)

130

Max

:17.

83M

in:−

4.11

S130

-V-B

Max

:0.5

5M

in:−

0.7σ

y�A

s32

581

2.5

16-D

16(3

.00

%)

UD

6@40

(0.9

8%

)13

0M

ax:7

.49

Min

:−1.

67

S130

-C-B

0.30

16-D

16(3

.00

%)

UD

6@50

(0.7

8%

)13

04.

20

S080

-C-B

0.30

802.

67

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(a)

(b)

Fig. 2 Test setup. a Test setup of the small scale columns. b Test setup of the medium and large scale columns

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Table 2 Concrete admixture forseries A

Item Concrete compressivestrength (MPa)

180 130 80

Slump flow (cm) 70 60 23

Maximum aggregate size (mm) 20 20 20

Air (%) 1.5 2.0 3.0

Cement (kg/m3) 1,000 705 495

Water (l/m3) 150 155 173

Fine aggregate (kg/m3) 493 606 780

Corse aggregate (kg/m3) 817 912 896

Water cement ratio W/C (%) 15 22 35

Table 3 Concrete admixture forseries B

Item Concrete compressivestrength (MPa)

130 80

Slump flow (cm) 70 65

Maximum aggregate size (mm) 20 20

Air (%) 1.5 2.0

Cement (kg/m3) 773 528

Water (l/m3) 150 170

Fine aggregate (kg/m3) 704 865

Corse aggregate (kg/m3) 842 842

Water cement ratio W/C (%) 19.4 32.2

Table 4 Reinforcementscharacteristics

Yield strength(MPa)

Tensile strength(MPa)

Young modulus(GPa)

Rebar (series A)

D25 729 925 196

D16 757 967 195

UD10 920 986 201

UD6 964 1,005 207

Rebar (series B)

D32 723 928 198

D25 723 921 196

D16 754 958 194

UD13 934 1,104 181

UD10 973 1,130 182

UD6 951 1,191 190

Concrete compressive strength and size effect on curvature distribution are shown inFigs. 9 and 10, respectively. In general, curvatures measured for the small scale columnswere slightly higher than that measured for the medium and large scale columns. Effect of

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-3

-2

-1

0

1

2

3

0 2 4 6 8 10 12 14

Dri

ft a

ng

le (

%)

Cumulative cycles

M130-V-B and S130-V-B M180-C-A and S180-C-A

-3

-2

-1

0

1

2

3

0 2 4 6 8

Cumulative cycles

Dri

ft a

ng

le (

%)

(a) (b)

Remaining specimens

-6

-4

-2

0

2

4

6

0 2 4 6 8 10 12 14 16 18

Cumulative cycles

Dri

ft a

ng

le (

%)

(c)

Fig. 3 Loading history of the specimens. a M130-V-B and S130-V-B. b M180-C-A and S180-C-A. c Remain-ing specimens

concrete compressive strength was more pronounced for the small scale column than for themedium and large scale column as illustrated in Fig. 9.

3.4 Damage at column’s bases

Damage was less important for columns made of low concrete compressive strength thanfor those made of high concrete compressive strength. This can be seen, for example, ifwe compare the last state of specimen S080-C-A and S180-C-A from series A, or by com-paring specimen L080-C-B and L130-C-B from series B shown, respectively, in Figs. 11and 12.

For columns made of the same concrete compressive strength, it was observed that smallscale column suffered less damage than the medium and large scale columns, as seen forexample, for the case of specimens S080-C-A and M080-C-A under constant axial load, andfor specimens S130-V-B and M130-V-B under variable axial load.

Also, the authors observed that the damage was extended until the top of the column.This is due to the contribution of the axial load (P-delta effect) to the total moment appliedto the column. Fig. 13 shows the moment distribution during the loading and unloading. Itcan be observed that during the loading phase, contributions of the axial load, N, and thehorizontal force, Q, to the total moment are on the same side of the column. This gives abending moment at the column base, MB, greater that the moment at the top column, MA.

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M180-C-A

-3000

-2000

-1000

0

1000

2000

3000

-4 -2 0 2 4 6 8 10

Drift (%)

Ben

din

g m

om

ent

(kN

.m)

First peakSecond peakYielding steel compressionYielding steel tension

M130-C-A

-3000

-2000

-1000

0

1000

2000

3000

-6 -4 -2 0 2 4 6 8 10

Drift (%)

Ben

din

g m

om

ent

(kN

.m)

First peakSecond peakYielding steel compressionYielding steel tension

(a) (b)

M080-C-A

-2000

-1500

-1000

-500

0

500

1000

1500

2000

2500

-6 -4 -2 0 2 4 6 8 10

Drift (%)

Ben

din

g m

om

ent

(kN

.m)

First peak

Second peak

Yielding steel compressionYielding steel tension

S180-C-A

-800

-600

-400

-200

0

200

400

600

800

-4 -2 0 2 4 6 8 10

Drift (%)

Ben

din

g m

om

ent

(kN

.m)

First peakSecond peakYielding steel compressionYielding steel tension

(c) (d)

S130-C-A

-800

-600

-400

-200

0

200

400

600

800

-6 -4 -2 0 2 4 6 8 10

Drift (%)

Ben

din

g m

om

ent

(kN

.m)

First peakSecond peak

Yielding steel compressionYielding steel tension

S080-C-A

-600

-400

-200

0

200

400

600

-6 -4 -2 0 2 4 6 8 10

Drift (%)

Ben

din

g m

om

ent

(kN

.m)

First peak

Second peak

Yielding steel compressionYielding steel tension

(e) (f)

Fig. 4 Bending moment-drift relationships for series A. a M180-C-A. b M130-C-A. c M080-C-A. d S180-C-A. e S130-C-A. f S080-C-A

However, while reversing the loading direction, unloading phase, contributions of N and Qto the total moment are in opposite sides. This state gives a bigger moment at the top of thecolumn than the base of the column, MA greater than MB, especially for specimens underlarge value of axial load.

3.5 Equivalent viscous damping variation

Variation of the equivalent viscous damping factor was computed using the first cycle loops ateach of the imposed drift angle (Shibata and Sozen 1976). The equivalent viscous damping,ξeq , was computed using the following expression:

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L130-C-B

-6000

-4000

-2000

0

2000

4000

6000

-4 -2 0 2 4 6 8 10

Drift (%)

Ben

din

g m

om

ent

(kN

.m)

First peakSecond peakYielding steel compressionYielding steel tension

L080-C-B

-6000

-4000

-2000

0

2000

4000

6000

-6 -4 -2 0 2 4 6 8 10

Drift (%)

Ben

din

g m

om

ent

(kN

.m)

First peakSecond peakYielding steel compressionYielding steel tension

(a) (b)

M130-V-B

-1000

-500

0

500

1000

1500

2000

2500

3000

-4 -2 0 2 4 6 8 10

Drift (%)

Ben

din

g m

om

ent

(kN

.m)

First peakSecond peak

Yielding steel compressionYielding steel tension

S130-V-B

-200

-100

0100

200

300

400

500600

700

800

-2 0 2 4 6 8 10

Drift (%)

Ben

din

g m

om

ent

(kN

.m)

First peakSecond peakYielding steel compressionYielding steel tension

(c) (d)

S130-C-B

-800

-600

-400

-200

0

200

400

600

800

-4 -2 0 2 4 6 8 10

Drift (%)

Ben

din

g m

om

ent

(kN

.m)

First peakSecond peakYielding steel compressionYielding steel tension

S080-C-B

-600

-400

-200

0

200

400

600

800

-6 -4 -2 0 2 4 6 8 10Drift (%)

Ben

din

g m

om

ent

(kN

.m)

First peakSecond peakYielding steel compressionYielding steel tension

(e) (f)

Fig. 5 Bending moment-drift relationships for series B. a L130-C-B. b L080-C-B. c M130-V-B. d S130-V-B.e S130-C-B. f S080-C-B

ξeq = 1

4π

�W

�e(1)

where: �W is the area enclosed by one cycle hysteresis loop and �e is the equivalent potentialenergy, see Fig. 14.

Variations of the equivalent viscous damping are shown in Figs. 15 and 16. The equivalentviscous damping, ξeq , increased with an increase of the concrete compressive strength eitherfor the small, medium and large scale columns as seen in Fig. 15. In the same time and asillustrated in Fig. 16, the equivalent viscous damping decreased while the scale of the columnincreased. This was observed for columns under constant and variable axial load.

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-1.5

-1

-0.5

0

0.5

1

1.5

-6 -4 -2 0 2 4 6 8 10

No

rmal

ized

ho

rizo

nta

l lo

ad

(Q/Q

max

)

Drift (%)

S080-C-AS130-C-AS180-C-A

-1.5

-1

-0.5

0

0.5

1

1.5

-6 -4 -2 0 2 4 6 8

No

rmal

ized

ho

rizo

nta

l lo

ad

(Q/Q

max

)

Drift (%)

M080-C-AM130-C-AM180-C-A

(a) (b)

Fig. 6 Normalized horizontal load-drift relationships for the same size. (a) Small scale columns. b Mediumscale columns

-1.5

-1

-0.5

0

0.5

1

1.5

-10 -5 0 5 10

No

rmal

ized

ho

rizo

nta

l lo

ad

(Q/Q

max

)

Drift (%)

L080-C-BM080-C-AS080-C-A

-1.5

-1

-0.5

0

0.5

1

1.5

-6 -4 -2 0 2 4 6

No

rmal

ized

ho

rizo

nta

l lo

ad

(Q/Q

max

)

Drift (%)

L130-C-B

M130-C-A

S130-C-A

(a) (b)

Fig. 7 Normalized horizontal load-drift relationships for the same concrete strength. a Columns with 80 MPaconcrete. b Columns with 130 MPa concrete

3.6 Prediction of the cracking moment

During the testing, and while possible, crack widths and moment corresponding to the onsetof the first crack Mexp were listed. The cracking moment, was compared to the calculated oneusing the following procedure. It is well known that for a given rectangular section, B × D,under bending moment, Mcal , and axial load, N , the maximum stress at the extreme fiber isgiven by:

Mcal = B D2

6fr + N D

6(2)

with,

fr = 0.623√

f ′c (M Pa)

Table 5 shows a comparison between the experimental and the calculated onset crackingmoments, for the positive and the negative loading. As it can be observed, Eq. (2) underesti-mated too much the cracking moment of four specimens (M080-C-A, S130-C-A, S080-C-Aand S130-C-B) were the ratio Mexp/Mcal was greater than 1.5. For the other specimens, moreor less good agreements were obtained.

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12

3

4

56

7

8

910

11

12

1314 15

Zone 1

Zone 2

Zone 3Zone 4

3@16

2.5

135.131

210

1

2 3 45

6 7 89

10 11 121314 15

Zone 1

336

210

503@

260

Zone 2

Zone 3

Zone 4

1

2 3 45

6 7 89

10 11 12

1314 15

Zone 1

Zone 2

Zone 3

Zone 4

420

325

262

6332

532

5

(a) (b) (c)

Fig. 8 LVDT’s positions and dimensions of the different monitored zones on the columns. a Small size. bMedium size. c Large size

-3

-2

-1

0

1

2

3

-3 -2 -1 0 1 2 3

Φ*D

(10

-2)

Drift (%)

S080-C-B

S130-C-B

S080-C-A

S130-C-A

S180-C-A

-3

-2

-1

0

1

2

3

-3 -2 -1 0 1 2 3

Φ*D

(10

- 2)

Drift (%)

M080-C-A

M130-C-A

M180-C-A

(a) (b)

-3

-2

-1

0

1

2

3

-3 -2 -1 0 1 2 3

Φ*D

(10

-2

Drift (%)

L080-C-B

L130-C-B

(c)

)

Fig. 9 Concrete strength effect on curvature distribution. a Small scale. b Medium scale. c Large scale

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-2

-1

0

1

2

3

-2 -1 0 1 2 3

Φ*D

(10

-2)

Drift (%)

L130-C-B

M130-C-A

S130-C-B

S130-C-A

0

1

2

3

-3 -2 -1 0 1 2 3

Φ*D

(10

-2)

Drift (%)

L080-C-B

M080-C-A

S080-C-B

S080-C-A

(a) (b)

-2

-1

-3

Fig. 10 Size effect on curvature distribution. a Columns with 130 MPa concrete. b Columns with 80 MPaconcrete

(a) (b) (c)

(d) (e) (f)

Fig. 11 Observed damage for series A columns. a M180-C-A. b M130-C-A. c M080-C-A. d S180-C-A. eS130-C-A. f S080-C-A

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(a) (b) (c)

(d) (e) (f)

Fig. 12 Observed damage for series B columns. a L130-C-B. b L080-C-B. c M130-V-B. d S130-V-B. eS130-C-B. f S080-C-B

3.7 Prediction of the first peaks

The first peaks shown in Figs. 4 and 5 are those corresponding to the maximum elasticmoments, spalling of cover concrete. In total, four procedures were used to predict thesemoments:

1. The linear elastic method2. Fiber model calculation3. Calculation based on Muramatsu’s method4. Calculation based on Muramatsu’s method and taking into account Kumagai’s assump-

tion.

Details about the 2nd and the 4th calculation methods are given in Sect. 4, Analytical results.Hereafter, a brief introduction to Muramatsu’s et al. assumptions is introduced.

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Horizontal force Q

A

B

MA

MB

If Q>0Axial force N

Bending moment due to the axial load N

Bending moment due to the horizontal

force Q

Global bending moment

(a)

A

B

MA

MB

Horizontal force Q

If Q<0Axial force N Bending moment due

to the axial load NBending moment due

to the horizontalforce Q

Global bending moment

(b)

Fig. 13 Moment distribution. a Loading phase. b Unloading phase

Fig. 14 Definition of theparameters to compute theequivalent viscous damping

Mom

ent

Curvature

We

ΔW

In general, the stress block in the compression zone of a flexure member can be defined bythree parameters: k1, k2 and k3 as illustrated in Fig. 17. The parameter k1 is defined as the ratioof the average compressive stress to the maximum compressive stress in the compressionzone k3 f ′

c . The parameter k2 is the ratio of the depth of the resultant compressive forceC to the depth of the compression zone xn D. The parameter k3 is the ratio of the maximumcompressive stress in the compression zone to the compressive strength measured by concretecylinder f ′

c . The design values of the stress block parameters are determined when the strainsat the extreme fibers, εc, reach the ultimate strain of the concrete εcu .

The ultimate strain of concrete member subjected to flexure is generally higher thanthat of concrete cylinder subjected to pure compression. The linear strain gradient in thecompression zone of flexural members helps in achieving higher strain value at failure. Other

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0

5

10

15

20

25

30

35

0 1 2 3 4 5 6Eq

uiv

alen

t vi

sco

us

dam

pin

g (

%)

Drift (%)

S080-C-AS130-C-AS180-C-A

0

5

10

15

20

25

0 0.5 1 1.5 2 2.5Eq

uiv

alen

t vi

sco

us

dam

pin

g (

%)

Drift (%)

L130-C-BL080-C-B

(a) (b)

Fig. 15 Effect of concrete compressive strength on the equivalent viscous damping variation. a Small scale.b Large scale

0

5

10

15

20

25

30

35

0 1 2 3 4 5 6Eq

uiv

alen

t vi

sco

us

dam

pin

g (

%)

Drift (%)

0

5

10

15

20

25

30

0 0.5 1 1.5 2 2.5 3 3.5Eq

uiv

alen

t vi

sco

us

dam

pin

g (

%)

Drift (%)(a) (b)

0

2

4

6

8

10

12

0 0.25 0.5 0.75 1 1.25 1.5Eq

uiv

alen

t vi

sco

us

dam

pin

g (

%)

Drift (%)

S080-C-BS080-C-AM080-C-AL080-C-B

S130-C-B

S130-C-A

M130-C-A

L130-C-B

S130-V-B

M130-V-B

(c)

Fig. 16 Size effect on the equivalent viscous damping variation. a Columns with 80 MPa. b Columns with130 MPa. c Columns with 130 MPa under variable axial load

reasons for higher strain are the shape and size effects of the concrete cylinder comparedwith the actual reinforced concrete structural member (Mertol et al. 2008). Furthermore, theloading rate of a structural member is usually much slower than that of a concrete cylinder.The stress distribution of concrete in flexure, however, may still be represented adequately

123

Bull Earthquake Eng

Table 5 Prediction of thecracking moment

Columns Driftangle (%)

Mexp(KN m)

Mcal(KN m)

Mexp/Mcal

(a) Positive loading

M180-C-A 0.45 1,908 1,368 1.39

M130-C-A 0.29 1,311 1,085 1.21

M080-C-A 0.35 1,070 579 1.85

S180-C-A 0.34 424 334 1.27

S130-C-A 0.50 495 265 1.87

S080-C-A 0.25 222 142 1.56

L130-C-B 0.26 2,348 1,962 1.20

L080-C-B 0.23 1,604 1,354 1.18

M130-V-B – – – –

S130-V-B – – – –

S130-C-B 0.37 414 269 1.54

S080-C-B 0.20 227 177 1.28

(b) Negative loading

M180-C-A – – −1,368 –

M130-C-A −0.33 −1,398 −1,085 1.29

M080-C-A −0.25 −728 −579 1.26

S180-C-A – – −334 –

S130-C-A – – −265 –

S080-C-A – – −142 –

L130-C-B −0.30 −2,681 −1,962 1.37

L080-C-B −0.24 −1,778 −1,354 1.31

M130-V-B – – – –

S130-V-B – – – –

S130-C-B −0.33 −359 −269 1.33

S080-C-B −0.23 −237 −177 1.34

Fig. 17 Equivalent stress block (Muramatsu et al. 2005)

by the stress-strain relationship of the concrete cylinder using an empirical constant k3 toaccount for these differences.

Based on experiment test program carried out on HSC columns, Muramatsu et al. (2005)proposed equations for evaluating the shape form based on the three parameters k1, k2 andk3 given by:

123

Bull Earthquake Eng

k1k3 =∑

S

f ′cεc

(3)

k2 =(εc − εg

)

εc(4)

with:

εc : Concrete strain at the extreme compression fiber∑S : Area enclosed by the concrete stress-strain curve up to εc

εg : Strain at the gravity center of the enclosed area by the concrete stress-strain curvef ′c : Concrete compressive strength (MPa).

For simplicity, the first peak can be obtained assuming a triangular stress-strain curve witha maximum strain of εc = 0.00278. In this case k1k3 and k2 are given by:

k1k3 = 0.5 (5)

k2 = 1/3 (6)

For confined concrete, Muramatsu et al. introduced a confinement coefficient, Cc, that takesinto account the confinement effect in order to compute the three parameters k1, k2 and k3.This coefficient can be calculated using the following equation:

Cc = 0.313ρs

√fy

f ′c

(1 − 0.5

s

W

)(7)

with:

ρs : Volume ratio of the horizontal reinforcement.fy : Yield strength of the lateral reinforcement (MPa)s : Spacing of horizontal reinforcement (mm)W : Minimum dimension of the restraint core cross section (mm)f ′c : Concrete compressive strength (MPa)

The value of εc corresponding to the smallest ratio k2/(k1k3) is defined as the straincorresponding to the second peak, εc2. Muramatsu et al. found that εc2 depends on the valueof the confinement coefficient Cc. The stress strain shape factors, k1k3 and k2, can be assessedusing the following equations:

If Cc < 0.0013

εc2 = 3.08 × 10−1Cc + 3.25 × 10−3

k1k3 = 4.62 × 10Cc − 6.25 × 10−4 f ′c + 6.65 × 10−1

k2 = −2.25 × 10−4 f ′c + 3.84 × 10−1 (8)

If 0.0013 < Cc < 0.0030

εc2 = 2.49Cc + 4.24 × 10−4

k1k3 = 1.73 × 102Cc − 6.25 × 10−4 f ′c + 5.01 × 10−1

k2 = 4.08 × 10Cc − 2.25 × 10−4 f ′c + 3.31 × 10−1 (9)

Table 6 summarizes the experimental and the calculated first peaks of the twelve speci-mens. Calculation based on Muramatsu assumptions (Muramatsu et al. 2004; Komuro et al.2004; Muramatsu et al. 2005) gave good results that are better than those obtained using alinear elastic calculation. Fiber model also gave a good estimation of the first peaks as shown

123

Bull Earthquake Eng

on the same table. Reducing the concrete compressive strength, by taking into account thescale effect as suggested by Kumagai (Kumagai et al. 2005), underestimated the first peakmoments for nearly all specimens as shown at the last column of Table 6.

3.8 Prediction of the moment-drift envelope curves of the large and medium scale columnsknowing those of the small scale

Analyzing the test results, a relationship between the moment-drift envelope curve of thelarge (or medium) scale columns and the small scale columns was established having theform of:

ML

MS=

(DL

DS

)α f ′cL

f ′cS

(10)

with,

α = −0.002

(f ′cL + f ′

cS

2

)+ 3.04 (11)

where ML , MS, DL and DS are the moment and the column depth for the large (or medium)and small size columns, respectively. Alpha, α, is a factor depending on the concrete com-pressive strength of the large and small scale specimens, f ′

cL and f ′cS .

Using the test results of the 12 specimens shown in Table 6, a regression analysis wasdone to establish Eq. (11) relating the variation of α with respect to the concrete compressivestrength, as illustrated in Fig. 18.

Figure 19 shows a comparison between the moment-drift envelope curves of the large(or medium) size columns and the modified moment-drift envelope curves of the small sizecolumns using the proposed equation, Eq. (10). As it can be observed, a good agreement isobtained along the full loading history, either for specimens under constant or variable axialload.

4 Analytical results

Modeling approaches of material nonlinearities in frame analysis typically fall into two maincategories: lumped and distributed models as illustrated in Fig. 20 for a double fixed column.The lumped plasticity approach is characterized by insertion of discrete nonlinear moment-rotation hinges at the ends of linear elements. Such an approach provides an efficient means ofmodeling and controlling plastic hinge formation, but requires a prior knowledge of plastichinge locations. On the other hand, distributed plasticity models provides a more generalframework to nonlinear frame analysis, but may suffer from inaccuracies that derive fromthe numerical integration performed to compute the element forces and stiffness matrix.The behavior of discrete and lumped plasticity models can be compared to that of discreteand smeared crack models in continuum finite elements. In the first case the location anddirection of the possible cracks is predetermined, while in the second case cracks may developanywhere in the structures (Shing and Tanabe 2001).

Several lumped-plasticity models have been proposed in the last decades, starting by thefirst studies by Clough et al. (1965), subsequently developing with the consideration of thebending and axial force interaction (Galal and Ghobarah 2003), biaxial bending interaction

123

Bull Earthquake Eng

Tabl

e6

Com

pari

son

betw

een

the

calc

ulat

edan

dth

eex

peri

men

tal1

stpe

aks

Col

umns

Loa

ding

dire

ctio

nTe

stre

sult

Me

(kN

m)

Lin

ear

elas

ticca

lcul

atio

nFi

ber

Mod

elca

lcul

atio

nM

uram

atsu

Mur

amat

suan

dZ

Mel

s(k

Nm

)M

e/M

els

Mfib

(kN

m)

Me/

Mfib

Mm

(kN

m)

Me/

Mm

Mm

k(k

Nm

)M

e/M

mk

M18

0-C

-APo

sitiv

e2,

417

2758

0.88

2,48

50.

972,

513

0.96

1,98

91.

22

Neg

ativ

e−2

093

0.76

0.84

0.83

1.05

M13

0-C

-APo

sitiv

e2,

130

2128

1.00

2,32

90.

912,

044

1.04

1,66

81.

28

Neg

ativ

e−2

043

0.96

0.88

1.00

1.22

M08

0-C

-APo

sitiv

e1,

642

1074

1.53

––

1,24

01.

321,

077

1.52

Neg

ativ

e−1

455

1.35

1.17

1.35

S180

-C-A

Posi

tive

643

685

0.94

604

1.07

619

1.04

524

1.23

Neg

ativ

e−7

111.

041.

181.

151.

36

S130

-C-A

Posi

tive

590

532

1.11

572

1.03

503

1.17

436

1.35

Neg

ativ

e−5

771.

091.

011.

151.

32

S080

-C-A

Posi

tive

438

278

1.58

––

311

1.41

280

1.57

Neg

ativ

e−4

391.

581.

411.

57

L13

0-C

-BPo

sitiv

e4,

224

3848

1.10

4,43

00.

9537

501.

133,

017

1.40

Neg

ativ

e−4

,304

1.12

0.97

1.15

1.43

L08

0-C

-BPo

sitiv

e3,

024

2563

1.18

––

2781

1.09

2,33

21.

30

Neg

ativ

e−3

034

1.18

1.09

1.30

M13

0-V

-BPo

sitiv

e2,

378

––

2,12

61.

1217

011.

401,

078

2.21

Neg

ativ

e–

––

−403

–−3

94–

S130

-V-B

Posi

tive

592

––

533

1.11

438

1.35

310

1.91

Neg

ativ

e–

––

−103

–−1

01–

S130

-C-B

Posi

tive

626

531

1.18

572

1.09

505

1.24

436

1.44

Neg

ativ

e−5

611.

060.

981.

111.

29

S080

-C-B

Posi

tive

486

337

1.44

––

358

1.36

319

1.52

Neg

ativ

e−4

461.

321.

251.

40

123

Bull Earthquake Eng

Fig. 18 Variation of α factor

y = -0.002x + 3.0389

0

0.5

1

1.5

2

2.5

3

3.5

0 50 100 150 200

Average concrete strength (MPa)C

oeff

icie

nt α

Constant axial load

Variable axial load

(Sfakianakis and Fardis 1991) and bending and shear interaction (D’Ambrisi and Filippou1999).

The lumped-plasticity models are simplifications of the real behavior, for which theypresent some deficiencies. The first is related with the assumption of the concentrated inelas-ticity in the hinge, thus ignoring the damage spread along the element, which takes higherimportance in large resisting elements like RC walls (Aktan and Bertero 1985), whereinthe combination of plasticity concentration in the element ends (mainly due to bending)with a significant contribution of shear can induce major inclined cracks spreading intothe element inner region; clearly, for such cases, the consideration of concentrated plas-ticity in the member ends is not an accurate option (Sezen 2000). Furthermore, lumpedmodels simplify some aspects of the hysteretic response of RC members since the sectionbehavior characteristics are defined a priori. The principal proposals can be found in theliterature, namely those resumed by Otani (1981), Fardis (1991) and by Filippou and Fenves(2004).

Another approach of modeling at element level is associated with the distribution ofthe nonlinearity along the element, providing the element with a certain number of controlsections, where the inelastic behavior is integrated to obtain the global inelasticity of theelement. This concept was first introduced by Otani (1974) and the major advantage ofthese models is the nonexistence of a predetermined length where the inelasticity can occur,because all the sections can have incursions in the non-linear response. While this approachis a closer approximation to reality, it also requires more computational capacity (Calabrese2008). Exhaustive reviews describing these formulations can be found in the works of Tauceret al. (1991), Spacone et al. (1992) and Arêde (1997).

The fiber model is the most popular distributed plasticity model being used for the non-linear modeling, where cross section of the structural element is subdivided into concretefiber and steel fibers (Spacone et al. 1996; Petrangeli et al. 1999; Filippou and Fenves 2004;Alemdar and White 2005; Scott and Fenves 2006; Mpampatsikos 2008; Mpampatsikos et al.2008; Wijesundara et al. 2011). Since the response is obtained in terms of uniaxial deforma-tion of the fibers, the load versus deformation response of a fiber model is defined in termsof uniaxial stress-strain relations specified for concrete and reinforcements. Although fibermodel is more advanced compared to plastic hinge model, its use in beams and columns isnot warranted from practical viewpoint. In such elements, abundance of test data regardingstiffness modeling and rotation capacities leads instead to a wide use of the plastic hingemodeling (Garevski and Ansal 2010).

123

Bull Earthquake Eng

-2500

-2000

-1500

-1000

-500

0

500

1000

1500

2000

2500

-6 -4 -2 0 2 4 6 8 10

Ben

din

g m

om

ent

(kN

.m)

Drift (%)

M080-C-A

Modified S080-C-A

-3000

-2000

-1000

0

1000

2000

3000

-4 -2 0 2 4 6

Ben

din

g m

om

ent

(kN

.m)

Drift (%)

M130-C-A

Modified S130-C-A

-3000

-2000

-1000

0

1000

2000

3000

-4 -3 -2 -1 0 1 2 3 4

Ben

din

g m

om

ent

(kN

.m)

Drift (%)

M180-C-A

Modified S180-C-A

-6000

-4000

-2000

0

2000

4000

6000

-6 -4 -2 0 2 4 6

Ben

din

g m

om

ent

(kN

.m)

Drift (%)

L080-C-B

Modified S080-C-B

-6 -4 -2 0 2 4 6

Ben

din

g m

om

ent

(kN

.m)

Drift (%)

L130-C-B

Modified S130-C-B

-1000

-500

0

500

1000

1500

2000

2500

3000

-3 -2 -1 0 1 2 3 4

Ben

din

g m

om

ent

(kN

.m)

Drift (%)

M130-V-B

Modified S130-V-B

-6000

-4000

-2000

0

2000

4000

6000

Fig. 19 prediction of the moment-drift envelope curves of the large/medium scale columns knowing those ofthe small scale columns

4.1 Fiber model results

4.1.1 Envelope curves

Moment-drift envelope curves were predicted using a fiber model developed by the authorsassuming a lumped plasticity approach. Section analysis was carried out assuming Bernoulli’stheory (plane sections remain plane) for concrete and longitudinal steel. Based on previousresearch program results carried out by the authors, the plastic hinge length, l p , was takenequal to the column depth, D. The column cross section was subdivided into concrete fiber

123

Bull Earthquake Eng

Plastic hinges

Linear elastic

Node

Node

Integration points

Node

Node

Fig. 20 Lumped and distributed models

Fig. 21 Meshes and signs convention

elements and reinforcing steel fiber elements. Section response was obtained by integratingall fiber element stresses and stiffness.

For a section under biaxial horizontal loading as illustrated in Fig. 21, the axial strain εi j

of the element i j located at (yi j , zi j ) from the center of the section can be derived as:

εi j (yi j , zi j ) = (1, zi j ,−yi j )

⎧⎨

⎩

ε0

φy

φz

⎫⎬

⎭(12)

where ε0, φy and φz are the section axial strain, the curvatures along the y-axis and z-axis,respectively. Using the stress increment, �σi j , and the area, Ai j , of each element, the sec-tion axial load variation, �N , and the bending moments variation, �My and �Mz , can bewritten as:

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Bull Earthquake Eng

�N =m∑

i=1

n∑

j=1

∫

Ai j

�σi j d Ai j (13)

�My =m∑

i=1

n∑

j=1

∫

Ai j

zi j�σi j d Ai j (14)

�Mz =m∑

i=1

n∑

j=1

∫

Ai j

(−yi j )�σi j d Ai j (15)

The above equations can be rearranged in a matrix form as:⎧⎪⎪⎪⎨

⎪⎪⎪⎩

�Nbh f ′

c

�My

b2h f ′c

�Mzbh2 f ′

c

⎫⎪⎪⎪⎬

⎪⎪⎪⎭

=

⎡

⎢⎢⎢⎢⎣

∑mi=1

∑nj=1

Ei j Ai jbh f ′

c

∑mi=1

∑nj=1

Ei j Ai j zi j

b2h f ′c

−∑mi=1

∑nj=1

Ei j Ai j yi j

bh2 f ′c

∑mi=1

∑nj=1

Ei j Ai j zi j

b2h f ′c

∑mi=1

∑nj=1

Ei j (Iy+Ai j z2i j )

b3h f ′c

−∑mi=1

∑nj=1

Ei j (Iyz+Ai j yi j zi j )

b2h2 f ′c

−∑mi=1

∑nj=1

Ei j Ai j yi j

bh2 f ′c

− ∑mi=1

∑nj=1

Ei j (Iyz+Ai j yi j zi j )

b2h2 f ′c

∑mi=1

∑nj=1

Ei j (Iz+Ai j y2i j )

bh3 f ′c

⎤

⎥⎥⎥⎥⎦

×⎧⎨

⎩

�ε0

b�φy

h�φz

⎫⎬

⎭(16)

where: Ei j is the Young’s modulus, f ′c is the concrete compressive strength, Iy, Iz and Iyz

are the section moments of inertia.In our analysis, �N/bh f ′

c, b�φy and h�φz are taken as an input data, whereas,�My/b2h f ′

c,�Mz/bh2 f ′c and �ε0 are the output.

Steel fiber elements followed Nakamura’s stress-strain relation (Nakamura and Yokoo1977), whereas concrete fiber elements followed Popovic’s stress-strain relation (Popovics1997). Concrete strength enhancement was taken into account using Sakino’s et al. equation(Sakino and Sun 1994). The enhanced concrete strength, f peak , shown in Fig. 22, due toconfinement is expressed as follows:

f peak = f ′c + κρh fhy

κ = 11.5α

(d

c

) (1 − s

2Dcore

)(17)

where: f ′c is the concrete compressive strength without confinement, κ is a coefficient of

strength enhancement due to confinement, ρh, fhy, d , and c are the ratio, yield strength,diameter and the unsupported length of the shear reinforcing bars, respectively. s is thedistance between adjacent shear reinforcements, and Dcore is the width of confined concrete.The coefficient, α, was added to the original equation to take into account the effects of straingradient. More details can be found elsewhere (Bechtoula 2005)

As an example Fig. 23 shows the concrete stress-strain models used for the cover concrete(plain concrete) and inside concrete (core concrete) for specimens S130-C-B and L130-C-B.

A comparison between the experimental and the analytical moment-drift envelope curvesare shown in Fig. 24 for some specimens of series A and series B. As a general trend, a good

123

Bull Earthquake Eng

Fig. 22 Concrete stress-strainrelationship

0

20

40

60

80

100

120

140

160

0.0 0.5 1.0 1.5 2.0

Str

ess

(MP

a)

Strain (%)

S130-C-B Cover concrete

Core concrete

Test cylinder 1

Test cylinder 2

Test cylinder 3

0

20

40

60

80

100

120

140

160

0.0 0.5 1.0 1.5 2.0

Str

ess

(MP

a)

Strain (%)

L130-C-B Cover concrete

Core concrete

Test cylinder 1

Test cylinder 2

(a) (b)

Fig. 23 Confined and unconfined concrete models. a S130-C-B. b L130-C-B

estimation was obtained. It can be also seen that, the fiber model grasp the drop in strengthfor specimens made of 130 and 180 MPa (Figure 25).

4.1.2 Axial strain and moment drift hysteresis curves

Figures 24 to 26 show some results of the hysteresis moment-drift curves and the axial strain(shortening and/or elongation) variation computed at the center of the column’s sections ofseries A and B, respectively. Elongation of the column has a positive sign in the figures.Good agreements between the experimental and the predicted results can be observed exceptfor the axial strain of specimens M180-C-A, S130-C-B and L130-C-B where the predictionsunderestimated the real measured axial strain. It is clearly shown that when the concrete com-pressive strength of the specimen increases, 130 and 180 MPa, only shortening is observed asillustrated, as an example, for specimen M180-C-A and L130-C-B. In the same time it wasobserved that for a concrete compressive strength of 80 MPa, small size column S080-C-Ashowed both shortening and elongation, where medium size column M080-C-A and largesize column L080-C-B showed nearly only shortening.

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Bull Earthquake Eng

0

1000

2000

3000

0 2 4 6

Ben

din

g m

om

ent

(kN

.m)

Drift (%)

M180-C-A

EXP

CAL

0

2000

4000

6000

0 2 4 6

Ben

din

g m

om

ent

(kN

.m)

Drift (%)

L130-C-B

EXP

CAL

(a) (d)

-3000

-2000

-1000

0

1000

2000

3000

-6 -4 -2 0 2 4 6

Ben

din

g m

om

ent

(kN

.m)

Drift (%)

M130-C-A

EXP

CAL

0

2000

4000

6000

0 2 4 6

Ben

din

g m

om

ent

(kN

.m)

Drift (%)

L080-C-B

EXP

CAL

(b) (e)

0

250

500

750

0 2 4

Ben

din

g m

om

ent

(kN

.m)

Drift (%)

S180-C-A

EXP

CAL

0

250

500

750

1000

-3000

-2000

-1000

-4 -2-6000

-4000

-2000

-6 -4 -2

-6000

-4000

-2000

-6 -4 -2

-1000

-750

-500

-250

-4 -2 -750

-500

-250

-6 -4 -2 0 2 4 6

Ben

din

g m

om

ent

(kN

.m)

Drift (%)

S130-C-B

EXP

CAL

(c) (f)

Fig. 24 comparison between the experimental and the calculated pushover curves. a M180-C-A. b M130-C-A.c S180-C-A. d L130-C-B. e L080-C-B. f S130-C-B

4.2 ACI results

A comparison between the test results and the ACI results, in term of peak moment, is reportedhereafter. The analytical results were evaluated using the ACI guidelines (ACI 2011) for twoassumed concrete compressive strengths:

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Bull Earthquake Eng

0

1000

2000

3000

0 2 4 6

Ben

din

g m

om

ent

(kN

.m)

Drift (%)

M180-C-A

EXP

CAL

0

0.2

0 2 4 6

Axi

al s

trai

n (

kN.m

)

Drift (%)

M180-C-A

EXPCAL

(a)

0

250

500

750

0 2 4

Ben

din

g m

om

ent

(kN

.m)

Drift (%)

S180-C-A

EXPCAL

0

0.2

0 2 4

Axi

al s

trai

n (

%)

Drift (%)

S180-C-A

EXP

CAL

(b)

0

250

500

750

0 2 4 6 8 10

Ben

din

g m

om

ent

(kN

.m)

Drift (%)

S080-C-A

EXP

CAL

0

0.2

0.4

0.6

-3000

-2000

-1000

-4 -2-1

-0.8

-0.6

-0.4

-0.2

-4 -2

-1000

-750

-500

-250

-4 -2-1

-0.8

-0.6

-0.4

-0.2

-4 -2

-750

-500

-250

-6 -4 -2-0.4

-0.2

-6 -4 -2 0 2 4 6 8 10

Axi

al s

trai

n (

%)

Drift (%)

S080-C-A

EXPCAL

(c)

Fig. 25 Cyclic loading results -series A-. a M180-C-A. b S180-C-A. c S080-C-A

1- Cylinder test values2- Reduced values, which is based on the cylinder’s results and taking into account the scale

effect. This was done based on Kumagai et al. assumption (Kumagai et al. 2005).

123

Bull Earthquake Eng

0

2000

4000

6000

0 1 2 3

Ben

din

g m

om

ent

(kN

.m)

Drift (%)

L130-C-B

EXPCAL

0

0.05

0 1 2 3

Axi

al s

trai

n (

%)

Drift (%)

L130-C-B

EXPCAL

(a)

0

250

500

750

0 2 4 6 8

Ben

din

g m

om

ent

(kN

.m)

Drift (%)

S130-V-B

EXP

CAL

0

0.3

0.6

0.9

1.2

1.5

0 2 4 6 8

Axi

al s

trai

n (

%)

Drift (%)

S130-V-B

EXPCAL

(b)

0

250

500

750

0 2 4 6

Ben

din

g m

om

ent

(kN

.m)

Drift (%)

S080-C-B

EXPCAL

0

0.1

0.2

0.3

-6000

-4000

-2000

-2 -1-0.25

-0.2

-0.15

-0.1

-0.05

-2 -1

-250-2

-0.6

-0.3

-2

-750

-500

-250

-6 -4 -2-0.5

-0.4

-0.3

-0.2

-0.1

-6 -4 -2 0 2 4 6

Axi

al s

trai

n (

%)

Drift (%)

S080-C-B

EXP

CAL

(c)

Fig. 26 Cyclic loading results -series B-. a L130-C-B. b S130-V-B. c S080-C-B

Kumagai et al. suggested that the concrete compressive strength given by a cylinder testshould be modified in order to take into account the scale effect. The real concrete compressivestrength that should be considered is given by:

σc = kdkhσB (18)

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Bull Earthquake Eng

Table 7 Reduced concrete compressive strength

Columns σB (MPa) h (mm) dmin (mm) d (mm) a kd kh σC (MPa)

M180-C-A 168 1,040 520 586.8 −0.164 0.748 1.00 125.7

M130-C-A 130 −0.145 0.774 1.00 100.6

M080-C-A 65.5 −0.113 0.819 1.00 53.7

S180-C-A 170 650 325 366.7 −0.165 0.807 1.00 137.2

S130-C-A 132 −0.146 0.827 1.00 109.2

S080-C-A 68.2 −0.114 0.862 1.00 58.8

L130-C-B 120.1 1,300 650 733.6 −0.140 0.756 1.00 90.9

L080-C-B 80.0 −0.120 0.787 1.00 63.0

M130-V-B 119.9 1,040 520 586.9 −0.140 0.781 1.00 93.6

S130-V-B 129.0 650 325 366.8 −0.145 0.829 1.00 106.9

S130-C-B 132.6 −0.146 0.827 1.00 1096

S080-C-B 84.2 −0.122 0.853 1.00 71.8

with:

kd = (d/100)α

α = −0.08 − σB/200

kh = 0.95 + 0.2 (h/dmin)−2 (19)

where, σB is the cylinder concrete compressive strength with 100 mm diameter, σc is thereduced compressive strength, h is the clear height of the considered column, dmin is theminimum dimension of the column cross section and d is the diameter of the equivalentcircular section for the column.

Based on Eqs. (18) and (19), the reduced concrete compressive strengths for the twelvecolumns were computed and summarized in Table 7.

The experimental moments (shown as the 2nd peaks in Figs. 4, 5) and the analytical ACIpeak moments for the tested columns are summarized in Tables 8 and 9 for two assumptions:section with and without cover concrete, respectively. As shown in the tables, Kumagaiand Moramatsu methods underestimated the columns capacities. The nearest values to theexperimental ones were those obtained using the fiber model as show in the last column ofTable 8 taking into account the cover concrete.

Figure 27 shows the scale effect by comparing the peak moment ratios of the experi-mental, Mexp, to the calculated the ACI code, Maci , and the concrete compressive strengthfor the three different scales, small medium and large. The comparison was carried outfor two concrete strengths: (a) from the cylinder test and (b) from the reduced cylindertest using Kumagai assumption. As illustrated in the figure, the moment ratio

(Mexp/Maci

)

seems to be affect by the concrete compressive strength as well as by the column size.It is clearly shown that the scale effect increases while the column size decreases fol-lowing a linear variation with respect to the concrete compressive strength. It is worth tomention here that more experimental test data are needed for large scale columns in thefuture.

123

Bull Earthquake Eng

Tabl

e8

Com

pari

son

betw

een

the

calc

ulat

edan

dth

eex

peri

men

talp

eaks

mom

ents

(with

cove

rco

ncre

te)

Col

umns

Loa

ding

dire

ctio

nM

e(k

Nm

)W

ithco

ver

conc

rete

Fibe

rM

odel

calc

ulat

ion

AC

IA

CI

and

Kum

agai

Mor

amat

suM

oram

atsu

and

Kum

agai

Mac

i(kN

m)

Me/

Mac

iM

k(k

Nm

)M

e/M

kM

m(k

Nm

)M

e/M

mM

mk

(kN

m)

Me/

Mm

kM

mk

(kN

.m)

Me/

Mfb

M18

0-C

-APo

sitiv

e2,

477

2,83

30.

8722

941.

081,

948

1.27

1554

1.59

2,48

51.

00

Neg

ativ

e−1

,952

0.69

0.85

1.00

1.26

0.79

M13

0-C

-APo

sitiv

e2,

343

2,31

91.

0119

901.

181,

735

1.35

1484

1.58

2,28

21.

03

Neg

ativ

e−2

,302

0.99

1.16

1.33

1.55

1.01

M08

0-C

-APo

sitiv

e2,

026

1,45

31.

3912

801.

5814

541.

3913

761.

471,

785

1.14

Neg

ativ

e−1

,737

1.20

1.36

1.19

1.26

0.97

S180

-C-A

Posi

tive

586

699

0.84

600

0.98

478

1.23

405

1.45

611

0.96

Neg

ativ

e−7

121.

021.

191.

491.

761.

17

S130

-C-A

Posi

tive

672

574

1.17

502

1.34

427

1.57

384

1.75

568

1.18

Neg

ativ

e−6

271.

091.

251.

471.

631.

10

S080

-C-A

Posi

tive

536

364

1.47

330

1.62

366

1.47

352

1.52

451

1.19

Neg

ativ

e−4

881.

341.

481.

331.

391.

08

L13

0-C

-BPo

sitiv

e4,

835

4,25

91.

1434

881.

393,

292

1.47

2,83

41.

714,

328

1.12

Neg

ativ

e−4

465

1.05

1.28

1.36

1.58

1.03

L08

0-C

-BPo

sitiv

e3,

665

3,20

81.

1427

231.

352,

968

1.23

2,75

21.

333,

781

0.97

Neg

ativ

e−3

761

1.17

1.38

1.27

1.37

0.99

M13

0-V

-BPo

sitiv

e2,

627

2,10

41.

251,

469

1.79

1,22

22.

1575

63.

4721

021.

25

Neg

ativ

e(−

468)

−410

−−3

99–

−351

–−3

51–

––

S130

-V-B

Posi

tive

687

544

1.26

418

1.64

298

2.31

202

3.40

513

1.34

Neg

ativ

e(−

61)

−105

–−1

03–

−90

–−9

0–

––

123

Bull Earthquake Eng

Tabl

e8

cont

inue

d

Col

umns

Loa

ding

dire

ctio

nM

e(k

Nm

)W

ithco

ver

conc

rete

Fibe

rM

odel

calc

ulat

ion

AC

IA

CI

and

Kum

agai

Mor

amat

suM

oram

atsu

and

Kum

agai

Mac

i(kN

m)

Me/

Mac

iM

k(k

Nm

)M

e/M

kM

m(k

Nm

)M

e/M

mM

mk

(kN

m)

Me/

Mm

kM

mk

(kN

.m)

Me/

Mfb

S130

-C-B

Posi

tive

673

571

1.18

499

1.35

425

1.58

383

1.76

568

1.19

Neg

ativ

e−6

341.

111.

271.

491.

661.

12

S080

-C-B

Posi

tive

559

412

1.36

369

1.51

384

1.46

367

1.52

489

1.14

Neg

ativ

e−5

071.

231.

371.

321.

381.

04

123

Bull Earthquake Eng

Tabl

e9

Com

pari

son

betw

een

the

calc

ulat

edan

dth

eex

peri

men

talp

eaks

mom

ents

(with

outc

over

conc

rete

)

Col

umns

Loa

ding

dire

ctio

nM

e(k

Nm

)W

ithou

tcov

erco

ncre

te

AC

IA

CI

and

Kum

agai

Mor

amat

suM

oram

atsu

and

Kum

agai

Mac

i(kN

m)

Me/

Mac

iM

k(k

Nm

)M

e/M

kM

m(k

Nm

)M

e/M

mM

mk

(kN

m)

Me/

Mm

k

M18

0-C

-APo

sitiv

e2,

477

1,87

81.

321,

414

1.75

1,71

91.

441,

381

1.79

Neg

ativ

e−1

,952

1.04

1.38

1.14

1.41

M13

0-C

-APo

sitiv

e2,

343

1,58

01.

481,

259

1.86

1,56

71.

5013

861.

69N

egat

ive

−2,3

021.

461.

831.

471.

66M

080-

C-A

Posi

tive

2,02

610

981.

8596

72.

101,

436

1.41

1362

1.49

Neg

ativ

e−1

,737

1.58

1.80

1.21

1.28

S180

-C-A

Posi

tive

586

464

1.26

379

1.55

422

1.39

354

1.66

Neg

ativ

e−7

121.

531.

881.

692.

01S1

30-C

-APo

sitiv

e67

239

01.

7233

02.

0438

51.

7535

61.

89N

egat

ive

−627

1.61

1.90

1.63

1.76

S080

-C-A

Posi

tive

536

274

1.96

248

2.16

361

1.48

348

1.54

Neg

ativ

e−4

881.

781.

971.

351.

40L

130-

C-B

Posi

tive

4,83

529

371.

652,

309

2.09

3,01

41.

602,

678

1.81

Neg

ativ

e−4

,465

1.52

1.93

1.48

1.67

L08

0-C

-BPo

sitiv

e3,

665

2,34

41.

561,

968

1.86

2,91

61.

262,

717

1.35

Neg

ativ

e−3

,761

1.60

1.91

1.29

1.38

M13

0-V

-BPo

sitiv

e2,

627

943

2.79

293

8.97

1119

2.35

701

3.75

Neg

ativ

e(−

468)

––

––

−351

–−3

51–

S130

-V-B

Posi

tive

687

235

2.92

104

6.61

262

2.62

184

3.73

Neg

ativ

e(−

61)

––

––

−90

–−9

0–

S130

-C-B

Posi

tive

673

388

1.73

329

2.05

383

1.76

354

1.90

Neg

ativ

e−6

341.

631.

931.

661.

79S0

80-C

-BPo

sitiv

e55

929

81.

8826

42.

1237

71.

4836

21.

54N

egat

ive

−507

1.70

1.92

1.34

1.40

123

Bull Earthquake Eng

0.60

0.80

1.00

1.20

1.40

1.60

1.80

40 60 80 100 120 140 160 180

Rat

io M

exp

/Mac

i

Concrete strength (MPa)

S size M size L size

Small

Medium

Large

0.60

0.80

1.00

1.20

1.40

1.60

1.80

40 60 80 100 120 140 160 180

Rat

io M

exp

/Mac

i

Concrete strength (MPa)

Small

Medium

Large

(a) (b)

S size M size L size

Fig. 27 Relationships between moment ratios and concrete strength for different scales. a Concrete strengthfrom cylinder. b Reduced concrete strength by Kumagai

5 Conclusions

Twelve high strength reinforced concrete columns with a cross section of 325×325, 520×520and 650 × 650 mm were tested under severe vertical and horizontal cyclic loading. Concretewith 80, 130 and 180 MPa was used in the testing program. Shear span ratio and normalizedaxial load were identical for all specimens, except for two specimens that were tested undervariable axial load. The test results showed that spalling of cover concrete was very brittle forspecimens made of 180 MPa concrete. The spalling was followed by a significant decreasein strength. It was observed that damage was more severe for large and medium scale columnthan for small scale columns. The measured curvature at the column’s bases for a heightequal to the column depth was much important for the small scale columns than for themedium and large scale columns. The equivalent viscous damping increased with an increaseof the concrete compressive strength either for the small, medium and large scale columns,however, decreased while the scale of the column increased. A simple equation was suggestedfor evaluating the moment-drift envelope curves for the large and medium scale columnsknowing those obtained from the small scale columns. This equation is based only on thegeometrical and material characteristics of the columns; hence its advantage to be used inpractice. Analytical investigation was carried out using the ACI code and a fiber modeldeveloped by the authors. As a general trend, a good estimation was obtained using the fibermodel for the moment-drift and axial strain-drift hysteresis curves. The fiber model graspthe drop in strength for specimens made of 130 and 180 MPa. In general the fiber modelgave a bitter prediction than the ACI code. The experimental to the ACI peak moment ratiosvaried between 0.69 and 1.47. These values were 0.79 and 1.34 for the fiber model. Scaleeffect was affected by the concrete compressive strength as well as by the column size. It wasmore pronounced for the small scale column than for the medium and large scale columns.The relation between the ratio

(Mexp/Maci

)and the concrete compressive strength varied

linearly for a give column scale.

Acknowledgments The authors are thankful to: Sakashita M., Shibata S., Matsuda T., Oda M. and Ryu N.former students at Kyoto University. The authors also acknowledge TAISEI and KAJIMA companies for theirfinancial support. The first author is grateful to JSPS for their 2 years financial support as Post Doctor at KyotoUniversity.

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