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ARTICLE IN PRESS

Engineering Structures xx (xxxx) xxx–xxxwww.elsevier.com/locate/engstruct

Experimental validation of seismic code provisions for RC columns

Elizabeth Vintzileou∗, T.P. Tassios, M. Chronopoulos

National Technical University of Athens, Greece

Received 20 March 2006; received in revised form 20 July 2006; accepted 21 August 2006

Abstract

The aim of the experimental programme was to check the validity of the provisions of Eurocode 8 regarding the confining reinforcement ofcolumns. Cyclic tests on 37 full-scale specimens were subjected to large cyclic displacements under constant axial load. Single rectangular hoops,even closely spaced, proved to be inadequate, as in most cases the target ductility was not reached. On the contrary, double or triple arrangementof hoops ensured satisfactory behaviour; they ensured acceptable force response degradation (lower than 20%), when the columns were subject tolarge displacement reversals (compatible with the target ductility).c© 2006 Published by Elsevier Ltd

Keywords: RC columns; Confinement; Cyclic actions; Force–response degradation; Ductility

1. Introduction1

According to Eurocode 8 (2004), the confining reinforce-2

ment that should be provided within the critical regions of3

columns is calculated as a function of several parameters, such4

as the normalized axial force (ν), the in-section and in-height5

arrangement of hoops, the confined part of the section as a6

percentage of the gross cross sectional area (Ac/A0), etc. The7

volumetric mechanical percentage of hoops, ωw, calculated ac-8

cording to the code, is assumed to provide to the column a9

corresponding value of curvature ductility factor, µ1/r . The10

value of the required curvature ductility factor depends on the11

ductility class to which the structure should belong. A value12

for the required curvature ductility factor µ1/r = 10 corre-13

sponds roughly to the Medium Ductility Class according to Eu-14

rocode 8.15

Following the definition of the code, a column is considered16

to behave satisfactorily under the following conditions: (a) the17

column is able to sustain displacement reversals at a maximum18

value compatible with the target ductility and (b) after three full19

reversals, the force response degradation of the column does not20

exceed 15% of its maximum resistance.21

∗ Corresponding address: Laboratory of Reinforced Concrete, NationalTechnical University of Athens, 5, Iroon Polytechniou Str., 15773 Zografou,Greece. Tel.: +30 210 7721272; fax: +30 210 7721273.

E-mail address: elvintz@central.ntua.gr (E. Vintzileou).

In the Laboratory of Reinforced Concrete at National 22

Technical University of Athens (NTUA), an extensive 23

experimental programme was carried out with the aim of 24

checking whether the behaviour of columns reinforced in 25

accordance with the code requirements is in conformity with 26

the anticipated behaviour. 27

Thirty-seven (37) full-scale columns were tested in cyclic 28

shear and bending, under constant axial load. In this paper, the 29

results of this programme are presented and commented upon, 30

whereas the efficiency of relevant code provisions is assessed. 31

2. The confinement model used 32

(a) The model for confinement adopted by Eurocode 8, 33

based on the model presented in Tassios et al. [2], is valid 34

for symmetrically reinforced sections, where the curvature at 35

yield is expressed in terms of the normalized axial force (ν) of 36

the element and the percentage of longitudinal reinforcement 37

(ρ), taking into account the degree of mobilization of the 38

compressed longitudinal reinforcement (σs/ fy ≤ 1.0, where 39

σs and fy denote the stress and the yield strength of the 40

compressed reinforcement). For the calculation of the curvature 41

at yield, the following assumptions were made in the model: (i) 42

the part of the concrete section that is not enclosed by the hoops 43

has spalled, (ii) the properties of the confined concrete of the 44

core follows the model adopted by CEB-FIP Model Code 1990, 45

(iii) the percentage of the longitudinal reinforcement is taken 46

0141-0296/$ - see front matter c© 2006 Published by Elsevier Ltddoi:10.1016/j.engstruct.2006.08.013

Please cite this article as: Elizabeth Vintzileou et al., Experimental validation of seismic code provisions for RC columns, Engineering Structures (2006),doi:10.1016/j.engstruct.2006.08.013

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equal to 0.04 (the maximum allowed by the code), whereas1

(iv) both tensioned and compressed longitudinal reinforcement2

are assumed to have entered into the hardening branch of3

the stress–strain curve. Thus, an expression was derived for4

the effective confinement ratio (αωw) needed both to ensure5

sufficient curvature ductility and that the section will be able6

to carry the imposed design action effects after spalling of the7

concrete cover:8

αωw = k0µ1/rεyλν − 10εcu (1)9

where:10

ωw denotes the volumetric mechanical ratio of confining11

reinforcement (closed hoops and ties),12

α denotes the effectiveness of confinement, i.e. an indicator13

of the volume of the core that is effectively confined by hoops14

and ties,15

µ1/r denotes the targeted curvature ductility factor,16

εy denotes the yield strain of the steel,17

ν denotes the normalized axial force of the element, ν =18

N/Ac fc,19

λ = Ac/A0 denotes the gross cross sectional area20

normalized to the core section,21

εcu = 0.0035 is the strain at failure of the unconfined22

concrete and23

k0 is a coefficient depending on the ‘ductility class’ which24

was adopted for the design of the entire structure. In the final25

text of Eurocode 8, a value k0 = 30 was adopted for both26

ductility classes.27

(b) Moreover, EC8 requires that a minimum ωw-value is28

observed, equal to 0.08 or 0.12, for medium and high ductility29

class; this may roughly be translated into a minimum ‘αωw’30

requirement equal to 0.05, approximately.31

Finally, according to the code, spacings ‘s’ of consec-32

utive hoops should nor exceed specific maximum values33

(max s: db = 8, for medium ductility class, where ‘db’ denotes34

the diameter of longitudinal reinforcement).35

It is understood that these two additional requirements had36

the meaning that the analytical model of Eq. (1) is not valid37

unless both of these conditions are observed.38

3. Research objectives39

It is broadly accepted that confinement offers a more40

ductile behaviour to RC columns under post-yield reversed41

displacement [see i.a. [4–7]]. Such behaviour, however, is42

influenced by a large number of (at least five) parameters,43

as mentioned in the previous Section 2. Consequently,44

experimental research accounting simultaneously for such a45

large number of parameters is rather scarce. That is why the46

combination of available experimental data, taking into account47

only a limited number of parameters each time, is not an48

easy task. Since the model adopted in EC8 (Eq. (1)) was only49

analytically derived, the basic scope of this paper is to attempt50

an experimental overall check of the validity of the provisions51

of the Code, as follows:52

(a) By means of a large variety of combination of the53

aforementioned parameters, the validity of Eq. (1) will be54

experimentally checked, as explained in Section 4(b): checking 55

the ‘cyclic stability’ of force–response, after three full cycles at 56

the targeted ductility level. To this end, 37 different full-scale 57

columns were tested under identical experimental conditions. 58

(b) On the other hand, the validity of the two minimal 59

requirements of EC8 will also be checked, namely the 60

minimum ωw-values and the minimum (s/db)-values, as 61

explained in Section 2(b). 62

4. Description of the research programme 63

Specimens and tests were designed as follows: 64

(a) Several parameters affecting confinement were selected 65

for investigation, namely the in-section arrangement (the 66

format) of hoops, the diameter of hoops, the spacing of hoops 67

and the ratio between the gross cross-sectional area and the 68

core area of the column. To a number of specimens, the simple 69

square arrangement of hoops was applied, although the rule of 70

not having hoops legs arranged at a distance larger than 200 mm 71

from each other is not respected in this case. This arrangement 72

of hoops was tested, because in real structures, a large number 73

of columns (especially, corner columns in upper storeys) are 74

having sectional dimensions not larger than 300 mm. 75

It should be noted that the specimens were designed to fail 76

in flexure. 77

(b) Each specimen was allotted a target curvature ductility 78

factor ranging between 7 and 13 (see Table 1), whereas 79

the effective confinement ratio, αωw, and the Ac/A0 ratio 80

were predetermined. Thus, introducing the appropriate values 81

of the various parameters in Eq. (1), the maximum axial 82

load was calculated for each specimen, for which the target 83

curvature ductility factor can be reached. This axial force 84

value was imposed on each specimen during testing. Thus, all 85

code-conditions being respected, the cyclic stability of each 86

specimen was tested experimentally. In other words, it was to be 87

checked whether the specimens being reinforced and loaded in 88

conformity with the code and submitted to the target ductility, 89

show a force response degradation not exceeding 15% after 90

three full reversals. This is a final and comprehensive check of 91

the validity of code provisions in a multi-parameter field. 92

The maximum displacement ‘dmax’ to apply in correspon- 93

dence with the targeted ductilities µ1/r were calculated as fol- 94

lows: assuming a nominal value for the expected length of the 95

plastic hinge (equal to approximately 10% of the length of the 96

element), the mean dmax/dy-values corresponding to these cur- 97

vature ductility factors were calculated: 98

µ1/r = 7 − dmax/dy ∼ 3.0, µ1/r = 10 − dmax/dy ∼ 4.0, 99

µ1/r = 13 − dmax/dy ∼ 5.0. 100

(c) The geometry of specimens tested within this programme 101

is shown in Fig. 1: specimens were 3.0 m long. The cross- 102

sectional dimensions were 250 × 250 [mm]. The specimen 103

is meant to simulate two cantilever columns fixed to a stiff, 104

heavily reinforced element 500×500 [mm]. It should be noted, 105

however, that in a real column fixed at floor level, horizontal 106

displacements due to an earthquake would generate tension (or 107

compression) to toe ‘A’ of the upper column and compression 108

Please cite this article as: Elizabeth Vintzileou et al., Experimental validation of seismic code provisions for RC columns, Engineering Structures (2006),doi:10.1016/j.engstruct.2006.08.013

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Table 1Combination of parameters

In-sectionarrangementof hoops

Specimennumber

Diameterand spacingof hoops

Qualityofsteel(hoops)

Targetcurvatureductilityµ1/r

effectiveness ofconfinementα = αnαs

Effectiveconfinementratio αωw

Ac/A0 AxialforceN (kN)

Normalizedaxial force ν

1 ∅6/100 S220 10 0.19 0.01 1.42 50 0.022 2∅10/50 S220 10 0.26 0.14 1.42 450 0.183 ∅6/100 S220 10 0.18 0.01 1.64 50 0.024 ∅8/75 S220 10 0.22 0.03 1.64 200 0.086 ∅6/100 S220 10 0.18 0.01 1.83 20 0.017 2∅10/50 S220 10 0.25 0.15 1.83 840 0.348 ∅8/50 S220 13 0.25 0.05 1.64 100 0.049 ∅8/100 S220 10 0.19 0.02 1.42 290 0.1210 ∅8/100 S400 10 0.18 0.02 1.83 90 0.0411 ∅6/100 S220 10 0.19 0.01 1.42 221 0.0912 ∅8/125 S220 10 0.16 0.01 1.42 30 0.0113 ∅8/125 S220 10 0.15 0.01 1.79 26 0.0114 ∅6/100 S220 10 0.18 0.01 1.83 193 0.0815 ∅8/125 S220 10 0.15 0.01 1.83 25 0.01

16 ∅6/100 S220 10 0.39 0.03 1.42 100 0.0417 ∅8/75 S220 10 0.45 0.09 1.42 335 0.1318 ∅10/50 S220 10 0.52 0.23 1.42 700 0.2819 ∅6/100 S220 10 0.37 0.03 1.64 80 0.0320 ∅8/75 S220 10 0.44 0.09 1.64 419 0.1721 ∅10/50 S220 10 0.51 0.24 1.64 727 0.2922 ∅6/100 S220 10 0.36 0.03 1.83 80 0.0323 ∅8/75 S220 10 0.42 0.09 1.83 391 0.1624 ∅10/50 S220 10 0.50 0.25 1.83 699 0.2825 ∅8/75 S220 13 0.44 0.09 1.64 391 0.1626 ∅8/50 S220 7 0.52 0.15 1.42 1063 0.4327 ∅8/50 S220 7 0.51 0.16 1.64 690 0.2828 ∅8/50 S220 7 0.50 0.16 1.83 727 0.2929 ∅8/100 S400 10 0.39 0.07 1.42 391 0.1630 ∅8/100 S400 10 0.36 0.07 1.83 273 0.11

31 ∅6/100 S220 10 0.45 0.04 1.42 335 0.1332 ∅10/50 S220 10 0.60 0.32 1.42 913 0.3733 ∅6/100 S220 10 0.43 0.04 1.64 130 0.0534 ∅8/75 S220 10 0.51 0.12 1.64 475 0.1935 ∅10/50 S220 10 0.59 0.33 1.64 1006 0.4036 ∅6/100 S220 10 0.41 0.04 1.83 120 0.0537 ∅10/50 S220 10 0.58 0.35 1.83 1062 0.4238 ∅8/50 S220 13 0.59 0.21 1.64 600 0.24

Specimen No 5 was defective; it was not tested.

(or tension) respectively to toe ‘A’ of the lower column. In1

the case of specimens tested within this programme, however,2

tensioned (or compressed) zones of upper and lower column3

coincide. On the other hand, longitudinal reinforcements in4

the specimens were continuous throughout the toe, without5

lap splices; such an experimental set up does not allow a free6

pullout of bars to contribute to plastic rotations. Consequently,7

this testing arrangement will give rather conservative results.8

However, the magnitude of all action effects (axial load,9

bending moment and shear force) was the same as for a real10

double half-column subassembly.11

In the same Fig. 1, one can see the arrangement of both12

longitudinal and transverse reinforcement, as well as the testing13

sequence: the specimen is pinned at both ends. The axial load14

is applied (up to a predetermined value) and held constant15

during testing. At mid-height of the column (at ‘floor’ level)16

horizontal cyclic displacements are imposed, by means of a 17

500 kN actuator. 18

5. Construction of specimens—materials 19

5.1. Construction 20

Reinforcement cages were mounted and placed in the 21

wooden moulds. Strain gauges were glued on several 22

longitudinal bars and on hoops within the critical regions of 23

columns (Fig. 2). Ready mixed concrete was used for the 24

construction of the specimens in horizontal position. Specimens 25

were cured wet for seven days. Subsequently, they were stored 26

in the Laboratory up to their testing, without any further curing. 27

Please cite this article as: Elizabeth Vintzileou et al., Experimental validation of seismic code provisions for RC columns, Engineering Structures (2006),doi:10.1016/j.engstruct.2006.08.013

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Fig. 1. Dimensions and reinforcement of specimens, and loading history.

Fig. 2. Instruments for strains and displacements measurements: Strain gauges1–12 (measuring strains of longitudinal reinforcement and hoops), LVDTs 1measures the horizontal displacement at mid-height of the specimen, LVDTs2–5 (to measure the vertical deformation of regions close to the central stiffelement).

5.2. Concrete1

The mean compressive strength of concrete at the time2

of testing of the columns was measured on conventional3

specimens (cylinders 150 mm diameter and 300 mm height);4

it was found to be equal to 40 N/mm2. The characteristic5

compressive strength (5% fractile) was approximately equal6

to 35 N/mm2. Due to the very low scatter of this property,7

small differences in concrete compressive strength from one8

specimen to another were not taken into account. The mean9

value of the modulus of elasticity of concrete was equal to10

34 000 N/mm2.11

5.3. Steel12

Deformed bars 12 mm and 14 mm in diameter were used13

as longitudinal reinforcement. Their mean yield strength and14

tensile strength was equal to 450 N/mm2 and 650 N/mm215

respectively. The mean uniform deformation at failure was 16

approximately equal to 20%. Hardening was initiated at a strain 17

approximately equal to 4%. 18

Smooth or deformed bars were used for hoops: (a) smooth 19

bars S220, with yield strength and tensile strength equal to 20

350 N/mm2 and 450 N/mm2 respectively. Hardening was 21

initiated at a strain value of 3.5% approximately. The mean 22

uniform strain at failure was varying between 25% και 35%, 23

(b) deformed bars 8 mm in diameter, S400 with yield strength 24

and tensile strength of 450 N/mm2 and 650 N/mm2. Their 25

remaining characteristics were as for longitudinal bars. 26

6. Investigated parameters 27

The parameters investigated within the programme are the 28

following: 29

(a) In-section arrangement of hoops: The three alternative 30

formats of Fig. 1 were used. 31

(b) Quality of reinforcing steel: S220 and S400. 32

(c) Diameter and spacing of hoops: 6 mm, 8 mm or 10 mm 33

bars, at 50 mm or 75 mm or 100 mm or 125 mm. 34

(d) Ratio of the gross cross sectional area to the area of the core 35

(Ac/A0). By varying the clear concrete cover, ratio values 36

between 1.42 and 1.83 were used. 37

(e) Target curvature ductility factor: 7, 10 and 13. 38

(f) Normalized axial force, ν = N/ fc Ac: varying between 0.02 39

and 0.43. 40

The combination of parameters (a)–(d) led to a relatively 41

wide range of values for the effective confinement (between 42

0.01 and 0.35). It should be noted that effective confinement 43

values, αωw, as well as normalized axial load values, ν, were 44

calculated on the basis of mean values of mechanical properties 45

of materials. 46

The combination of parameters applicable to each individual 47

specimen is shown in Table 1. 48

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7. Measurements—loading history1

During testing, the following measurements were made2

(Fig. 2): (a) axial load (held constant during testing) and shear3

force; (b) horizontal displacement at mid-height of specimen4

(LVDT1); (c) rotation of sections in the region of maximum5

bending moments (LVDTs 2–5); (d) strain of longitudinal bars6

(strain gauges 1–4); (e) strain of hoops (strain gauges 5–12)7

close to the critical regions.8

The loading history imposed on all specimens is the9

following (Fig. 1(b)): Step 1—The axial load is imposed up to10

a predetermined value (calculated as described in Section 4(b)).11

The axial load is held constant during testing. Step 2—12

Horizontal displacement is imposed at mid-height of the13

column up to a value dy , corresponding to the yield of the14

specimen. Displacement at yield is estimated during testing15

as follows: Since strains in longitudinal bars are measured, it16

may be assumed that the specimen reaches its yield moment17

when the tensioned bars yield. Moreover, the force vs. mid-18

height displacement curve was continuously recorded and19

observed; the point of initiation of inelastic response was then20

considered as the yield point of the specimen. It should be21

noted that the yield displacement values estimated according22

to the two methods showed a fairly good agreement. Once the23

displacement at yield is determined, a full cycle is performed at24

±dy . Step 3—The specimen is subjected to three full cycles at25

maximum horizontal displacement equal to 3dy or 4dy or 5dy ,26

depending on the magnitude of the target curvature ductility27

factor (7, 10 and 13 respectively). Step 4—The specimen28

is subjected to monotonically increasing displacements, until29

substantial response degradation is recorded. At this point, the30

test is considered completed. In all tests, displacements were31

applied almost statically; thus six to eight hours were needed32

for the completion of each test.33

8. Experimental results34

8.1. Failure mode35

As anticipated by the design of specimens, all columns36

exhibited a flexural failure mode. Initially, flexural cracks37

appeared within the critical regions on both sides of the38

simulated floor level. For larger values of imposed horizontal39

displacement, spalling of the concrete cover occurred within40

a length varying between 0.5h and h, h being the cross41

sectional dimension of the column. As expected, damage was42

mainly concentrated more to one of the two critical regions43

located on both sides of the central stiff element. In fact, in44

19 columns, damage was concentrated in the critical region45

above the simulated floor level, whereas in 18 columns the46

critical region of the lower column was more damaged. The47

behaviour of specimens during cycling at the predetermined48

displacement level depends on various parameters, mainly49

the in-section arrangement of hoops and their spacing. In50

general, two cases can be distinguished. In specimens with51

low confinement and/or large spacing of hoops, after the52

occurrence of concrete spalling, buckling of longitudinal bars53

Photo 1. Test set-up: 1-specimen, 2-Jack for the application of the axial load,3-reaction frame for the support of the actuator.

Photo 2. Test set-up: 1-specimen, 4-actuator (in horizontal position-duringtesting), 5-hinged head in front of the actuator.

was observed, as well as fracture of the closest to ‘floor 54

level’ hoops; in some cases, fracture of some longitudinal bars 55

was observed, as well as disintegration of the concrete core 56

(Photo 1); as a result, substantial force response degradation 57

of specimens was recorded. In well-confined specimens and/or 58

in specimens with closely spaced hoops, limited disintegration 59

of core concrete was observed (Photo 2), whereas limited 60

buckling of longitudinal bars occurred. Those specimens were 61

characterized by a stable behaviour with limited force–response 62

degradation due to cycling at the predetermined level of 63

displacement. 64

8.2. Hysteretic behaviour 65

In Fig. 3 hysteretic loops for some of the tested columns are 66

presented. One can observe that the behaviour of specimens is 67

indeed governed by flexure, as indicated by the large area of 68

hysteretic loops and the absence of pinching effect. 69

Moreover, one may distinguish specimens that exhibited 70

satisfactory cyclic behaviour (e.g. Specimens 2, 23 και 71

32) characterized by limited force response degradation for 72

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Fig. 3. Hysteresis loops. Horizontal axis: Mid-height displacement (in mm). Vertical axis: Shear force (in kN).

maximum imposed displacement compatible with the target1

ductility, as well as specimens (e.g. columns 6, 11, 15) that2

exhibited substantial force response degradation. It should be3

noted that only horizontal force vs. horizontal displacement4

curves are presented: due to the geometry of specimens, there5

are two critical regions (both sides of the stiff mid-height part6

of the specimen). As damage is inevitably concentrated in one 7

of the two critical regions, for the same imposed displacement 8

the two half-columns exhibit unequal rotations (partly due to 9

the partial pullout of the longitudinal reinforcement). Thus, 10

second order bending moments are also unequal for the two 11

parts of the specimens. Moreover, the measurements taken 12

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Photo 3. Failure of specimen No 23 d/dy = 4.

Photo 4. Failure of specimen No 38 d/dy = 5.

by LVDTs 2–5 were not reliable up to the completion of1

the testing procedure. Consequently, it was preferred not to2

translate the force–displacement curves to moment-curvature3

diagrams. Fig. 4 illustrates basic data of hysteretic behaviour4

of all specimens: the force response degradation for the third5

cycle is plotted for each of the tested specimens, along with the6

respective hysteretic damping, ζ , calculated as follows:7

ζ =1

4π

area of loopelastic energy

. (2)8

One may observe that significant force response degradation is9

associated with higher hysteretic damping values. Specimens10

with acceptable force response degradation (≤20%) exhibit11

practically the same ζ -value (∼0.20).12

8.3. Force–response degradation due to cycling—Mobilization13

of hoops14

(a) Fig. 5 shows the force–response degradation characteris-15

tics of the tested columns: the force–response (Vn) during the16

nth cycle normalized to the force–response (V1) during the first17

cycle, is plotted against the number of cycles of the imposed18

displacement ductility. As previously mentioned, in order to19

evaluate the seismic behaviour of the specimens, the follow-20

ing criterion (in conformity with Eurocode 8) is applied: It is21

assumed that a column designed for a given curvature ductility22

factor, behaves according to its design requirements if (when23

subjected to displacement reversals compatible with the target24

ductility) it exhibits during the third reversal a force–response 25

degradation not exceeding 15%. Based on this criterion, one 26

may observe that the majority of specimens 1–15 (specimens 27

with single rectangular hoops) do not fulfil the design require- 28

ments, although they do observe Eq. (1). In fact, most of the 29

specimens 1–15 exhibit force–response degradation larger than 30

15%; moreover, the recorded Vn/V1 values are extremely scat- 31

tered. The first impression is that the arrangement of ‘single 32

rectangular hoops’ cannot offer a completely reliable behaviour 33

of these columns, whereas the results for columns with double 34

or triple hoops are liable to substantially smaller uncertainties. 35

In Fig. 6, the V3/V1 values are plotted for all specimens, against 36

the effective confinement ratio, αωw. It is clear that for confine- 37

ment values smaller than 0.05, the results are very scattered, 38

independently of the in-section arrangement of hoops. This ob- 39

servation proves that a minimum value of the confining rein- 40

forcement is indeed needed and it should be expressed in terms 41

of effective confinement αωw > 0.05 rather than in terms of ωw 42

alone. Moreover, one should also mention that independently of 43

the value of confining reinforcement provided to a column, the 44

double and triple arrangement of hoops leads to less scattered 45

(hence, to less uncertain) results, possibly because of a better 46

fixing of longitudinal bars against buckling. 47

(b) It was also confirmed that another parameter affecting 48

the cyclic behaviour of columns is the spacing of hoops, 49

normalized to the diameter of longitudinal bars. Fig. 7 shows 50

the force–response at the third cycle, normalized to that of the 51

first cycle, as a function of the spacing of hoops normalized 52

to the longitudinal bars diameter. It is observed that when 53

the normalized spacing of hoops increases, both the scatter 54

of experimental results and the force–response degradation 55

increase. It is expected that as the spacing of hoops increases, 56

the probability of longitudinal bars to buckle increases, whereas 57

the disintegration of core concrete becomes more probable as 58

well; these phenomena lead to a substantial premature decrease 59

of the force–response. On the data plotted in Fig. 7, it may 60

also be observed that for s/db values equal or larger to 7.0, the 61

V3/V1 ratio exhibits unacceptably low values and large scatter. 62

It should be remembered here that the value s/db = 8.0 is set by 63

Eurocode 8 (Medium Ductility Class) as an upper value against 64

buckling of longitudinal bars. 65

(c) Obviously, the aforementioned three examined parame- 66

ters (namely the in-section arrangement of hoops, their spacing, 67

as well as the effective confinement ratio), are interconnected. 68

Experimental results have proved, however, that all three should 69

comply with some minimum requirements, in order to allow the 70

target ductility to be realized. 71

This observation is illustrated in Fig. 8, which shows the 72

effect of the normalized spacing of hoops on the force–response 73

degradation (as for Fig. 7), for specimens provided with 74

αωw larger than 0.05. It may now be observed that the 75

majority of results are over the threshold of the 0.85 residual 76

force–response level. 77

It should be noted, however, that the buckling of 78

longitudinal reinforcing bars per se remains to be systematically 79

investigated; however, such an investigation was out of the 80

scope of this research work. 81

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Fig. 4. Hysteretic behaviour of specimens after three full displacement reversals: Force response degradation, ∆V , normalized to the maximum monotonic responseand hysteretic damping, ζ .

Fig. 5. Force response degradation at code-targeted cyclic displacement ductility levels, for various in-section hoop arrangements. The validity of Eq. (1) is ratherdoubtful in some cases where simple square hoops’ arrangement is used.

(d) A final very important remark concerns the stressing1

of hoops: single rectangular arrangement of hoops allows for2

premature disintegration of the concrete core and, subsequently, 3

for premature buckling of longitudinal bars, a feature more 4

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Fig. 6. Force response degradation as a function of confinement ratio for various in-section hoops arrangements, required by code for given ductility levels. It isclearly shown that for αωw-values lower than 0.05, the quantitative confinement provisions of EC8 (Eq. (1)) are not valid.

Fig. 7. Effect of hoops spacing (normalized to the diameter of longitudinalbars) on the force response degradation due to cycling, when the code-requirement regarding effective confinement for targeted ductility-levels isobserved.

pronounced for large spacing of hoops. As a result, hoops are1

not fully mobilized (they do not reach their yield strength).2

This phenomenon is illustrated in Fig. 9 where the strain of3

hoops, normalized to their yield strain, is plotted against the in-4

section arrangement of hoops. It is clear that as the arrangement5

becomes more dense in-section, the mobilization of hoops is6

enhanced, and the scatter of the results is substantially reduced.7

Thus, in the more dense arrangement ‘3’, yield of hoops was8

reached in all tested columns.9

8.4. Displacement and curvature ductility factors10

(a) Another criterion in order to evaluate the seismic11

behaviour of specimens tested within this programme, is that12

Fig. 8. Effect of hoops spacing (normalized to the diameter of longitudinalbars) on force response degradation, for specimens with effective confinementratio at least equal to 0.05.

of the ratio between the targeted and the effective displacement 13

ductility: remembering that each specimen was subjected to 14

three large amplitude displacement cycles. The amplitude of the 15

displacement reversals (equal to several times the displacement 16

at yield) was compatible with the target curvature ductility, 17

and it was selected on the basis of the respective model of 18

Eurocode 8 (Eq. (1)). On the other hand, the actual ductility 19

exhibited by the specimens can be assessed on the basis of 20

hysteresis loops, as follows: (i) the hysteresis loops envelope 21

for the third loading cycle is traced for both loading directions, 22

(ii) a horizontal line is traced at a force–response level equal to 23

85% of the maximum response; thus, two points are determined 24

on each curve (one on the ascending branch, the other on 25

the descending branch). It is assumed that the mobilized 26

displacement ductility factor is equal to the ratio between 27

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Fig. 9. Effect of in-section arrangement of hoops on the degree of theirmobilization, at the stage of targeted ductility: the average strain of hoops atthis stage seems to increase in arrangements of multi-leg hoops.

the displacement determined on the falling branch and that1

determined on the ascending branch of each curve. Fig. 102

summarizes the results regarding the displacement ductility3

factors (for both loading directions) as a function of the4

effective confinement ratio. As expected, the results are similar5

to those regarding the previous criterion of the force response-6

degradation V3/V1. In fact, for αωw values smaller than 0.05,7

the value of the normalized displacement ductility exhibits8

unacceptably large scatter (effective to target ductility varying9

between 0.20 and 1.70 approximately), whereas for a large10

number of specimens this ratio is lower than unity. On the11

contrary, for effective confinement ratio values larger than 0.05,12

the ratio between achieved and target ductility lies between 0.8013

and 1.20. This variation is considered to be acceptable, taking14

into account the inherent scatter of experimental results.15

(b) Strain gauges used to measure strains of longitudinal16

bars allowed for the calculation of experimental curvature17

values. On the other hand, moment-curvature diagrams were18

calculated for all specimens. Thus, experimentally obtained19

curvature ductilities can be compared to analytical ones:20

in Fig. 11(a), analytical µ1/r -values are plotted against21

experimentally derived curvature ductility values (on the basis22

of LVDT measurements in both loading directions, as well23

as using strain gauge measurements on different pairs of24

longitudinal bars). In Fig. 11(b), the same analytical values25

are plotted against the average experimental curvature ductility26

value for each specimen. One may observe that, although the27

scatter of experimental values in Fig. 11(a) is pronounced,28

the average values of µ1/r are close to the analytical ones.29

Furthermore, it is observed that, with the exception of those30

specimens that exhibited very poor cyclic behaviour (mainly31

those with single rectangular hoops), the columns reached or32

exceeded the target curvature ductility factor (µ1/r = 10 for33

the vast majority of specimens).34

Fig. 10. Normalized displacement ductility as a function of the confinementratio of columns.

8.5. Residual displacement 35

As shown in the hysteresis loops of Fig. 3, after cycling 36

to displacements as large as 40–100 mm in some cases, there 37

is a quite large residual displacement (of the order of several 38

millimetres). The evaluation of test results has shown that 39

the magnitude of the axial load or the effective confinement 40

ratio does not seem to affect the ratio between residual 41

and maximum imposed displacement. On the other hand, as 42

expected, the magnitude of the residual displacement seems 43

to increase with increasing maximum imposed displacement. 44

Moreover, as shown in Fig. 12, the ratio between residual 45

and maximum imposed displacement seems to increase for 46

larger displacement amplitudes. This is an important aspect of 47

the seismic behaviour of columns, as it may affect the post- 48

earthquake stability of the entire building. In the opinion of 49

the authors of this paper, in addition to the measures taken to 50

enhance the ductility properties of columns, an effort should 51

be made to reduce (via an appropriate conceptual design of the 52

structure) the absolute value of the displacements likely to be 53

imposed to the building. 54

9. Summary and concluding remarks 55

9.1 56

Eurocode 8 (EC8) provisions regarding the necessary 57

confinement of RC columns are based on an analytically 58

derived model (Eq. (1)), explicitly taking into account the 59

following parameters: targeted curvature ductility (µ1/r ), 60

longitudinal steel strain at yield (εsy), gross cross-sectional 61

area normalized to the core section (λ), normalized axial 62

load (ν), hoops arrangement leading to specific efficiency 63

factors (α), an allowable force response degradation lower than 64

15% after three post-yield reversed displacements compatible 65

with targeted curvature ductility. Moreover, by definition, the 66

mechanical volumetric ratio of the hoops to be provided is a 67

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Fig. 11. Comparison between calculated and experimentally derived curvature ductility factors: (a) experimental values from LVDTs and from strain gauges onlongitudinal bars, (b) mean values per specimen of measurements plotted in (a).

Fig. 12. The effect of maximum cyclic drift on the ratio between residual andmaximum imposed drift.

function of their yield strength ( fyw) and the concrete strength1

of the column ( fc).2

Available experimental investigations, simultaneously tak-3

ing into account all of these six basic parameters are rather4

scarce, although results of more than 450 tests on RC columns5

are available (Vintzileou and Statathos [8])-investigating how-6

ever the role of only some of the aforementioned parameters7

each time.8

That is why it was decided to undertake an overall9

experimental checking of the validity of the basic equation10

(1), by means of an experimental research on 37 columns,11

accounting for all the above parameters tested under identical12

conditions. The testing philosophy was performance-oriented:13

columns designed in conformity with Eq. (1) were subjected to14

post-yield reversed displacements compatible with the targeted15

curvature ductility level; it was checked whether after three16

such cycles, the residual force response capacity of the column17

was higher than 85% of its maximum capacity under monotonic18

loading.19

It was found that, under the minimal conditions discussed20

in the subsequent paragraph, the tested columns observed this21

performance condition; thus, Eq. (1) was experimentally proven 22

to be an appropriate design tool (Figs. 5, 10 and 11). 23

9.2 24

On the other hand, it was found that the following 25

prerequisites set forth by EC8 for the application of Eq. (1), 26

may need a slight modification. 27

For Medium Ductility Class (i.e. for targeted µ1/r = 10), it 28

is not sufficient to require that ωw > 0.10. This experimental 29

investigation has shown that the minimal requirement had better 30

be formulated in terms of ‘effective volumetric mechanical ratio 31

of confinement’ αωw > 0.05 (Figs. 6 and 10). 32

9.3 33

In order to avoid undesirable post-seismic second-order 34

effects, the residual displacements after the three code-required 35

cycles of post-yield displacements compatible with the targeted 36

ductility level, should if possible also be limited by means of an 37

appropriate new code provision, which however, was out of the 38

scope of this paper (Fig. 12). 39

9.4 40

It has to be noted that because of a particularity of the 41

tested specimen (Section 4(c)), the results of this experimental 42

investigation may be considered as somewhat conservative: 43

the contribution of pullout of anchorage lengths towards an 44

increase of available plastic rotation of the column base, was 45

smaller than in most real cases with spliced longitudinal bars. 46

But it should also be noted that the translation of the 47

targeted curvature ductility factors (µ1/r ) into displacement 48

ductility factors (dmax/dy) was made (Section 4(b)) by means 49

of somehow unconservative coefficients: in fact, the simple 50

numerical values used reflect rather average than worse 51

conditions; in view of these two opposite trends, however, it 52

may be said that the results of this investigation are valid for 53

practical design purposes. 54

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9.51

Finally, it should be noted that the results presented in this2

paper seem to be in accordance with the experimental results3

available in the literature (more than 450 tests of RC columns),4

as evaluated in [8].5

Uncited references6

Photo 3 and Photo 4. [1] and [3].7

References8

[1] CEN (2004) EN 1998-1. Eurocode 8: Design of structures for earthquake9

resistance—Part 1: General rules, seismic actions and rules for buildings.10

[2] Tassios TP, Vintzileou E, Chronopoulos M. Confinement of RC columns

for a given ductility factor. In: Duma, editor. 10th ECEE, vol. 3. Balkema; 11

1994. p. 1649–55. 12

[3] CEB-FIP Model code 1990. Bulletins d’ Information. No 213/214. 13

Lausanne; May 1993. 14

[4] Mo YL, Wang SJ. Seismic behaviour of reinforced concrete columns with 15

various tie configurations. Journal of Structural Engineering, ASCE 2000; 16

126:1122–30. 17

[5] Saatcioglu M, Ozcebe G. Response of reinforced concrete columns to 18

simulated seismic loading. ACI Structural Journal 1989;3–12. 19

[6] Watson S, Park R. Simulated seismic load tests on reinforced concrete 20

columns. Journal of Structural Engineering, ASCE 1994;120 ST(6): 21

1825–48. 22

[7] Wehbe N, Saiidi MS, Sanders D. Confinement of rectangular bridge 23

columns for moderate seismic areas. National center for earthquake 24

engineering research (NCEER) Bulletin 1998; 12 No. 1. 25

[8] Vintzileou E, Stathatos A. Assessment of the cyclic behaviour of RC 26

columns. Engineering Structures. 2006 [in press]. 27

Please cite this article as: Elizabeth Vintzileou et al., Experimental validation of seismic code provisions for RC columns, Engineering Structures (2006),doi:10.1016/j.engstruct.2006.08.013