TOWARDS THE DESIGN OF DUCTILE REINFORCED · PDF fileTOWARDS THE DESIGN OF DUCTILE REINFORCED...

TOWARDS THE DESIGN OF DUCTILE REINFORCED HIGH STRENGTH CONCRETE COLUMNS

SKKaushik Indian Institute of Technology Roorkee India

Pradeep Bhargava Indian Institute of Technology Roorkee India Umesh Sharma Indian Institute of Technology Roorkee India

29th Conference on OUR WORLD IN CONCRETE amp STRUCTURES 25 - 26 August 2004 Singapore

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SKKaushik Indian Institute of Technology Roorkee India Pradeep Bhargava Indian Institute of Technology Roorkee India

Umesh Sharma Indian Institute of Technology Roorkee India

ABSTRACT

High strength concrete (HSC) has gained wide acceptance in the recent years owing to its many advantages over normal strength concrete One of the potential applications of HSC is in the lower story columns of multistory buildings But high strength concrete has poor post-peak deformation capacity which questions its applicability in seismic regions In this analytical amp experimental study the behavior of reinforced high strength concrete columns was investigated under axial loads as well a s a xial load with flexure The viability of applying the various present codes requirements of providing special confining reinforcement to HSC columns in the potential plastic hinge regions was examined The study shows that the present code specifications do not impart the same ductility to columns made of higher concrete grades as that to normal strength concrete columns As a solution to the problem of lower ductility of high strength concrete columns the concept of using a combination of suitable fibers along with lateral confining steel has been mooted

Keywords Confinement Columns Ductility Fibers

59

1 Introduction

In the seismic design of reinforced concrete columns of buildings and bridge substructures the potential plastic hinge regions need to be carefully detailed for ductility in 0 rder toe nsure that the shaking from large earthquakes will not cause collapse Recently concrete strengths much higher than 60MPa have gained acceptance in the construction industry Higher compressive strengths greater modulus of elasticity and substantial savings resulting from the reduction in cross sections are all properties of high strength concrete that appeal to designers One of the main applications of HSC is in the lower-story columns of tall buildings The use of HSC allows a significant reduction of column sizes which increases the floor area leading to economic advantages But the high strength concrete when subjected to short term or sustained loads tends to be brittle when loaded to failure lacking the plastic deformation typical of normal strength concrete This type of behavior raises questions on the suitability of HSC to structures in seismic regions Therefore it becomes important that the structural design and detailing of HSC columns should allow for post-elastic deformations so that energy dissipation can take place and this can be incorporated by proper deSign of confinement devices

One of the ways in which the building codes of various countries ensure ductility in concrete columns is by specifying the amount of transverse reinforcement in critical regions of columns However these code equations specifying the minimum amount of transverse steel for columns are empirical and have been developed based upon experimental data obtained from the testing of normal strength concrete columns Therefore the major objectives of this study are (1) To study the behavior of HSC columns under a xiall oad a nd a xiall oad with flexure (ii) To investigate t he validity 0 f a pplying the current AC1318-02 IS-13920-93 and NZS-3101-95 requirements to high strength concrete columns and (ii) To explore the possibility of adding steel fibers to HSC columns in order to achieve desired ductility The work reported here is a part of ongoing comprehensive analytical and experimental research work at the Civil Engineering Department Indian Institute of Technology Roorkee to investigate the confinement requirements of high strength concrete columns

2 Behavior of HSC Columns Under Concentric Loads

Thirty reinforced concrete axially loaded columns were designed satisfying the requirements of ACI 318 [1] and IS-13920 [2] Both circular and square columns were deSigned The columns of both cross-sectional shapes were deSigned for three ultimate load levels For each ultimate load level five concrete grades ranging from M20 to M100 were used amounting to fifteen columns each for circular and square shapes All cross sectional and reinforcement details are shown in Table 1 for circular columns and Table 2 for square columns

The notations PI d l and n stand for volumetric ratio diameter and number of longitudinal steel bars

whereas d hand S h for diameter and spacing of lateral ties In the circular columns longitudinal bars

were distributed equally along the periphery Whereas in the case of square columns they were provided at the comers except in the cases where due to requirement of cross ties longitudinal bars were given in between the corners also These are the columns where 8 numbers of longitudinal bars were required But in each case codal provisions were followed To be able to compare the post peak performance of the columns for different concrete grades the design ultimate load longitudinal steel ratio concrete cover (40mm) and yield strength of steel (415 Mpa) were kept constant Lateral steel for each column was deSigned as per these codes requirements of confining steel for critical regions Further to be able to compare the behavior of different columns actual calculated sectional dimensions and reinforcement diameters were employed That is why cross sectional sizes and bar diameters are in fractions (Tables 1 amp2) Uniaxial stress-strain curves for the deSigned confined concrete column sections under monotonic loading have been computed

The complete stress-strain curves for confined reinforced concrete columns were predicted using a most relevant theoretical model ie Legeron amp Paultre (2003) model [3]

60

Table1 Design Details for Circular Section Columns

Ultimate Capacity (Pu) kN

Concrete Grade

Section Diameter (mm)

Longitudinal Steel Lateral Steel Ties

Peak Strain

E cc

Strain at 50 of Peak Stress

E cc50

Ductility Ratio

cent PI n dJ

mm

d h

mm

Sh

mm

1500 M20 412 012 8 16 88 100 00396 02069 525 M40 316 012 6 141 109 79 006466 026036 4027 M60 266 012 6 12 125 75 007741 0279 361 M80 234 012 6 12 14 75 008848 02893 327 M100 211 012 6 12 153 75 01 0299 298

2000 M20 500 0082 8 16 85 100 002935 01703 58 M40 376 0082 8 12 117 94 005371 02126 396 M60 313 0082 6 12 128 79 00677 0243 359 M80 274 0082 6 12 139 75 007836 025474 325 M100 247 0082 6 12 157 75 0095 0283 298

3000 M20 563 015 10 21 8 86 100 00279 01615 578 M40 438 015 10 17 117 100 003704 015 407 M60 3705 015 10 1435 1361 92 63 005741 020182 3515 M80 327 015 10 1267 142 81 77 006622 02118 3198 M100 296 015 8 1282 15 75 007862 02315 294

Post-peak portion of the curves gave an idea about the inelastic deformation capacity of the columns In the past various researchers have established from their research that the point corresponding to the first hoop fracture could be taken as the limiting or ultimate compressive strain before the final failure [4-5] It has also been concluded that this point happens to be very close to the instance when stress drops to 50 of the peak confined stress in the descending side Therefore in this study the

ductility has been found as the ductility ratio (cent ) which is the ratio of strain (E cc50 ) at 50 of the peak

confined strength in the post peak part divided by strain (EcJ corresponding to the peak confined

stress

Table 2 Design Details for Square Section Columns


Concrete Grade

Section Dimension (mm)

Longitudinal Steel

Lateral Steel Ties

Peak Strain

E cc


Ecc50

Ductility Ratio

cent PI n dJ

mm

d h

mm

Sh

mm

1315 M20 350 01 4 198 11 37 876 005366 0258 481 M40 2657 01 4 15 145 75 007678 031055 405 M60 2226 01 4 126 168 75 009771 035361 362 M80 200 01 4 12 1823 75 011073 036217 327 M100 200 01 4 12 1985 75 011747 035083 298

1715 M20 400 01 8 16 85 100 004314 021432 496 M40 304 01 4 1715 145 76 006632 026742 4032 M60 255 01 4 1435 167 75 008293 03 361 M80 224 01 4 126 186 75 01 033 33 M100 202 01 4 12 1985 75 011594 034634 298

2665 M20 47026 015 8 23 85 100 003401 019082 561 M40 366 015 8 1787 115 91 5 005977 023933 4004 M60 310 015 4 21 4 178 77 5 007505 027071 361 M80 27326 015 4 189 1787 75 007976 025959 325 M100 24731 015 4 171 194 75 00927 027616 2979

61

middot

Uniaxial stress-strain curves of all the designed confined reinforced concrete columns indicate that for the given design ultimate capacity and longitudinal steel ratio and keeping concrete cover and yield strength constant the post peak curves become steeper and steeper as the concrete grade is

p o M40 -- M50 ____ M30 - M100 I _WO - lIMO ___ M50 ___ MBO - M~ _ 140 shy 140 120 120

100100middot III

III 80 I) 80 III CII

~ 60f 60 rn 40-rn

40 20

20 0 0 0 001 002 003 004 005

Strain

Figure 2 Stress-Strain Curves ( Circular Columns Pu=2000 kN)

increased A few representative curves have been shown in the Figures 1 amp 2 Steeper post peak curves indicate that if a column section is designed using higher concrete grades as per ACI 318 amp ISshy13920 the ductility goes down Ductility ratios (cent ) for all the columns were found as per the adopted

definition ie pound cc50 divided by pound cc They are indicated in Table 1 for circular columns and in Table 2 for

square columns The declining trend of ductility ratios from M20 grade columns to M100 grade columns shows that the post elastic deformation capacity of the columns gets reduced as the concrete of higher compressive strength is used Ductility ratio values at M 100 concrete are almost half the values achieved for M20 concrete The ductility ratios have been plotted with various concrete grades for all the columns designed in this investigation Figure 3 shows the plot for circular columns and the same is shown for square columns in Figure 4 These curves clearly show the downward trend of ductility ratios as the concrete grade increases

[-PU=1500Kn --Pu=2000Kn --Pu=3000Kn I C-Pu=1315 Kn --Pu=2665 Kn J

0 001 002 003 004 005

Strain

Figure 1 Stress-Strain Curves (Square Columns Pu=2665 kN)

7 6

0 551 5 10 40~ 4 ~ ~3

6

3 - bull bull ~ ~ 2 ~ 2 ~ c c

1

o +-~-~--~--~------~-

M20 M40 M60 MBO M100M20 M40 M60 M80 M100

Concrete Grade Concrete Grade Figure 3 Variation of Ductility Ratio with

Figure 4 Variation of Ductiliity Ratio withConcrete Grade ( Circular Section Concrete Grade (Square Columns)Columns)

3 Behavior of HSC Columns Under Axial Load amp Flexure

In this part of the study an attempt has been made to investigate the effect of concrete strength and axial load level on the ductility of concrete columns with lateral steel designed strictly according to the seismic requirements of ACI 318 NZS 3101 [6] a nd IS 1 3920 In this way it could be possible to

62

evaluate the provisions of these codes and thereby to compare their performances To this end a square tie confined reinforced concrete column cross section with cross ties was selected to study the behavior of HSC columns under combined axial load and flexure (Fig 5) The confining lateral reinforcement for the various concrete strengths (35-100 MPa) and axial load levels (015-05) were designed strictly according to the various codes as shown in Table 3 The size of cross section concrete cover to longitudinal steel bars amount and distribution of longitudinal steel bars material properties of longitudinal and lateral steel and configuration of lateral ties were kept fixed These section and material properties are Size of cross section = 400x400mm Cover concrete = 40mm i Longitudinal steel = 8 nos 16mm diameter bars Iy = 415Mpa

-----___T ~1----400--middot

Fieure 5 - Cross Section In each case the lateral tie steel area was provided just equal to the area required by the code in order to evaluate the performance of the codes more meaningfully Table 3 gives the ratio of the tie area provided to that required in each case and it can be seen that the provided area was never more than 107 times that required Using the analytical procedure the theoretical moment curvature relations were found for all the cases of columns of above~mentioned different concrete strengths and axial load levels

Table 3 Lateral Confining Steel Requirements of the Codes for Different Concrete Strengths and Axial Load Levels

IS 13920 and ACI 318 do not include the effect of axial load levels in their requirements of lateral confining steel in critical hinge regions of columns Therefore they required the same tie steel area for

f c IS 13920 ACI318 NZS 3101

Mpa p -shy

p -shy

p -shy

f c Ag fc Ag fc Ag

01503 amp 05 01503 amp 05 015 03 05

d mm

s mm ~

Ashcode

d mm

s mm ~

ASh code

d mm

s mm ~

Ash code

d mm

s mm ~

ASh code

d mm

s mm ~

Ash code

35 12 75 1020 10 59 1020 7 70 1050 10 75 1015 13 60 1034 50 14 75 1010 12 60 1043 - - - 12 60 1033 - - -70 16 75 1014 13 50 1080 10 65 1066 14 50 1070 17 42 1039 85 18 75 1070 14 50 1070 - - - 15 45 1070 - - -100 19 75 1070 14 43 1070 12 56 1048 16 42 1070 19 35 1042

different axial load levels Whereas the confinement prOVIsions of NZS 3101 does include the influence of axial load levels and therefore needed different lateral tie areas for different axial load levels Figure 6 compares the confinement requirements of the three codes by showing the variation

of Ah normalized to spacing of ties s and core dimension c with concrete strength at different axial

load levels The tie area requirements of IS and ACI codes were almost the same with the former needing slightly more area for all the concrete strengths At 015 load level NZS code provided tie area which was always less than the other two codes of the study Whereas at 05 axial load level the lateral steel requirements of NZS code were considerably more than that of IS and ACI codes for all the concrete strengths with the margin of difference being more at higher concrete strengths The NZS code required almost two and half times the confinement steel needed by IS and ACI codes for 100 Mpa concrete at 05 axial load level For axial load level of 03 NZS provisions needed lesser tie area than IS and ACI codes up to 50 Mpa concrete and slightly more for higher concrete strengths Therefore it can be said that for the reinforced concrete columns having low axial load levels laquo03) with both low and high concrete strengths and even for columns having moderate axial load levels (03) with low concrete strengths NZS code specifies less confinement steel than that required by IS and ACI codes However for concrete columns having high axial load levels (gt03) and with low or

63

high concrete strengths the confinement steel provisions of NZS code are more stringent than those of IS and ACI codes The curvature ductility factors ~ were computed for all the design cases of the study using the bilinear idealization of the computed moment curvature relations Figure 7 gives the variation of the curvature ductility factor ~ with the concrete cylinder strength fc for the columns designed according to the codes for the various axial load levels Also shown in this figure is a horizontal line giving the minimum limit of desired curvature ductility factor for the potential plastiC hinge regions of the reinforced

007

006 ACI

u 005 (pfcAg=OIS O3OS)

= It)

lt 004

001002

-

-

-shy

- -

NZS (PfcAg=O IS)

NZS(pfcAg=O3)

001

o --- --------------~------

- --shy NZS (PfcAg=OS)

20 40 60 80 100

fc(MPa)

008 ---IS (PfcAg=O lSO3OS)

Figure 6 - Confinement Reinforcement Requirements of Various Codes

concrete columns IS and ACI code designed confined column sections showed fairly enough ductility at 015 axial load level and the curvature ductility factor remained almost the same at all the concrete strengths This shows that the confinement requirements of both these codes are sufficient to take care of high concrete strengths up to 100 Mpa at low axial load levels However the column sections with lateral ties designed according to NZS code produced lesser ductility at this axial load level for all the concrete strengths In this case the ductility factors for only high concrete strength column sections were more than the desired minimum It indicates that the recommendations of NZS 3101 provide slightly less confinement steel than required for low concrete strengths at low axial load levels

The ductility factors decreased from the values of 22 94 and 2137 for 35 Mpa concrete to 1554 and 1625 for the 100 Mpa concrete for the columns with ties designed as per IS and ACI codes respectively at 03 axial load level Though the ductility factors reduced by a bout two third as the concrete strength increased from 35 to 100 Mpa still the ductility was satisfactory for all the concrete strengths except in the case of IS designed column with 100 Mpa concrete where the value of the ductility factor fell slightly short of the minimum limit of 16 This shows that the confinement provisions of AC I and IS codes are more than required a t low concrete strengths and just sufficient for high concrete strengths at 03 axial load level In the case of columns designed according to NZS code at 03 load level the ductility factor in fact increased from a value of 16 to 2256 as the concrete cylinder strength increased from 35 to 100 Mpa indicating that the NZS code provisions are satisfactory at this axial load level though slightly over-conservative at higher concrete strengths

64

IS (PfcAg=03)30 NZS(PlfcAg=03) s 25 -_-- middot ~ bull ACI(PlfcAg=O3) u

ca IS(PlfcAg=015)u 20 bull~ NZS(PlfcAg=015)bull~ 15 r--===sectS=2~S~ bull AC~PlfcAg=O 15)middot o IS(PlfcAg=05)2 10 bulla ca NZS(PlfcAg=05)bull ~ 5 bull bullbullbull ACI(PlfcAg=O5)(J

o+-_~__---__~__------__--_ _ ---Desirable ~ctility

20 35 50 65 80 95 110

fe (MPa)

Figure 7 - Variation of Curvature Ductility Factor with Concrete Strength

The IS and ACI designed confined column sections produced ductility factors of 1404 and 1301 respectively for 35 Mpa concrete strength at 05 axial load level and their values were 578 and 605 respectively for 100 Mpa concrete at the same load level It shows that the confinement requirements of both these codes are not sufficient for high concrete strengths at high axial load levels to impart enough ductility to critical hinge regions of columns Even for low concrete strength sections IS and ACI codes do not ensure enough ductility at high axial loads However the ductility performance of column sections designed as per NZS code at 05 axial load level was reasonably satisfactory for low concrete strengths and just sufficient for high concrete strengths more than 70 Mpa showing that the confinement reinforcement recommendations of the code are sufficient even for high strength concretes and at high axial loads At the same time it is also apprehended that NZS code may also result into insufficient ductility at axial loads more than 05 and concrete strength more than 70 Mpa It may be noted here that the NZS code required considerably higher amount of confining steel at 05 axial load level than that needed by IS and ACI codes to provide desired ductility In fact NZS code needed almost two and half times the lateral confining steel than that provided by the other two codes for high strength concretes at such high axial load levels

4 Benefits of Using Fibers

It is observed from the previous sections that the reinforced high strength concrete columns at high axial load levels need tremendously high amount of lateral confining steel in their critical hinge regions to sustain the seismic loads The placing of such amount of transverse steel shall entail much cost and effort and shall render these column regions too much congested High yield strength steel may be one solution to reduce the quantities required or otherwise to simplify the fabrication process in these regions the use of fibers coupled with moderate lateral steel may be undertaken A wide range of fibers is commercially available now It is well documented now that the addition of small closely spaced and uniformly dispersed discrete fibers to concrete substantially improves many of its engineering properties such a s tensile strength flexural strength fracture toughness resistance to fatigue impact and thermal shock The fibers added to concrete serve as crack arresters delaying the appearance of cracks and creating a stage of slow crack propagation The ductility of the composite is increased compared to the unreinforced matrix as the fibers are known to improve the post-cracking behavior of concrete Many researchers have studied the behavior of fibre-reinforced normal and high strength concretes under compression Typical stress-strain curves of fibre reinforced concrete in compression show an increase in the strain at the peak stress and substantially higher toughness where toughness is a measure of the ability to absorb energy

65

Figure S Test Set up

An experimental study has been undertaken at Indian Institute of Technology Roorkee to investigate the post-peak behavior of steel fiber reinforced HSC columns The variables of the study are concrete strength cross sectional shape tie yield strength tie configuration volume fraction and aspect ratio of crimped steel fibers Different series of short column specimens (150x600mm) were tested under monotonic loading to study the effect of various parameters on the post-peak behavior of columns (Figure 8) The uniaxial stress-strain curves were drawn for all the specimens of the study It has been observed that the addition of steel fibers to reinforced high strength concrete columns improves their inelastic deformation capacity The study has indicated that the peak strain of the axial stress-strain curves 0 f t he fiber reinforced columns increased in the range of 12 to 2 times that of non-fibrous reinforced columns depending on the volume fraction and aspect ratio of fibers Similarly an increase of 15 to 4 times in strain at 85 of peak stress in descending portion was observed in case of fiber reinforced concrete columns as compared to plain reinforced concrete columns Typical experimental stress-strain curves are shown in the Figure 9

100 --MBO (WIthout90 Fibres) BO ---MBO (With Fibres) 70ii

Q 60 ~ III 50 III III 40

(fJ 30 20 10 0

0 001 002 003 004 005

Strain (mmmm)

Figure 9 Stress-Strain Curves for MSO concrete grade RCC Columns with amp With out Fibres Figure 10 Failure Modes

The failure mode of the RCC columns was also improved by the addition of fibers from sudden shear failure to ductile bulging type failure It was also noticed that the sudden spalling of cover of the high strength concrete columns was prevented by the addition of fibres Figure 10 shows the typical failure modes of three columns SE1 is a M80 concrete grade RCC column without fibres and SE2 and SE3

are the fiber reinforced M80 concrete RCC columns having short (I =25mm amp Vf =15) and long (I = 50mm Vf = 15) fibers respectively

66

5 Conclusions

The study concludes that if the columns are designed using higher concrete grades for the same ultimate load capacity keeping all other design parameters namely steel yield strength cover and longitudinal steel ratio constant then the ductility imparted by the confining reinforcement des5igned according to the ACI 318 and IS 13920 code provisions gets reduced The slope of the post peak part of t he uniaxial stress-strain curves predicted u sing a n analytical model becomes steeper with the increase in concrete grade Ductility defined by ductility ratio comes down to almost half as the concrete grade is increased from M20 to M100

The behavior of columns under axial load and flexure has indicated that the RCC columns with concrete compressive strength between 35 to 100 Mpa and axial loads of 50 percent of axial load capacity of the column and designed as per the provisions of IS and ACI codes exhibited inadequate ductility particularly for high strength concretes where ductility factors of almost one third of the minimum desired values were noticed NZS code designed columns produced enough ductility even at axial load of 50 percent of column axial capacity for all the concrete strengths but required more than double the confining lateral steel area as compared to that provided by IS and ACI codes It is strongly recommended that IS13920 and ACI 318 seismic provisions of confinement steel should be revised to take into account the influence of axial load levels on the lines of NZS 3101

As a solution to the problems of reduced ductility and the congestion caused by the bigger bars and smaller spacing of lateral steel required in high strength concrete columns for the potential plastic hinge regions the concept of using suitable fibres along with lateral ties has been encouraged The study shows that only nominal amount of steel fibres (volume fraction1-15) are required to compensate the ductility loss of high strength concrete columns and to render them adequately ductile

Acknowledgement

This study is a part of ongoing PhD work of the third author

References

1 ACI Committee 318 Building Code Requirements for Structural Concrete (ACI 318- 02) and Commentary (ACI 318R-02) American Concrete Institute Farmington Hills Mich1995 pp 369

2 IS 13920-1993 Indian Standard Code of Practice for Ductile Detailing of Reinforced Concrete Structures Subjected to Seismic Forces Indian Standards Institution New Delhi 1993

3 Legeron F and Paultre P Uniaxial Confinement Model for Normal and High Strength Concrete Columns ASCE Journal of Structural Engineering Vo129 No2 2003 Pp 241shy252

4 Mander JB Priestly MJN and Park R Theoretical Stress-Strain Model for Confined Concrete ASCE Journal of Structural Engineering Vo1114 No8 1988 pp 1804-1826

5 Cusson D and Paultre P High Strength Concrete Columns Confined by RectangUlar Ties ASCE Journal of Structural Engineering Vo1120 No3 1994 pp 783-804

6 NZS 3101 Part 1 1995 Code of Practice for the Design of Concrete Structures Standards Association of New Zealand Wellington New Zealand 1995

67



SKKaushik Indian Institute of Technology Roorkee India Pradeep Bhargava Indian Institute of Technology Roorkee India

Umesh Sharma Indian Institute of Technology Roorkee India

ABSTRACT

High strength concrete (HSC) has gained wide acceptance in the recent years owing to its many advantages over normal strength concrete One of the potential applications of HSC is in the lower story columns of multistory buildings But high strength concrete has poor post-peak deformation capacity which questions its applicability in seismic regions In this analytical amp experimental study the behavior of reinforced high strength concrete columns was investigated under axial loads as well a s a xial load with flexure The viability of applying the various present codes requirements of providing special confining reinforcement to HSC columns in the potential plastic hinge regions was examined The study shows that the present code specifications do not impart the same ductility to columns made of higher concrete grades as that to normal strength concrete columns As a solution to the problem of lower ductility of high strength concrete columns the concept of using a combination of suitable fibers along with lateral confining steel has been mooted

Keywords Confinement Columns Ductility Fibers

59

1 Introduction









60



Concrete Grade



Peak Strain

E cc


E cc50

Ductility Ratio

cent PI n dJ

mm

d h

mm

Sh

mm

1500 M20 412 012 8 16 88 100 00396 02069 525 M40 316 012 6 141 109 79 006466 026036 4027 M60 266 012 6 12 125 75 007741 0279 361 M80 234 012 6 12 14 75 008848 02893 327 M100 211 012 6 12 153 75 01 0299 298

2000 M20 500 0082 8 16 85 100 002935 01703 58 M40 376 0082 8 12 117 94 005371 02126 396 M60 313 0082 6 12 128 79 00677 0243 359 M80 274 0082 6 12 139 75 007836 025474 325 M100 247 0082 6 12 157 75 0095 0283 298

3000 M20 563 015 10 21 8 86 100 00279 01615 578 M40 438 015 10 17 117 100 003704 015 407 M60 3705 015 10 1435 1361 92 63 005741 020182 3515 M80 327 015 10 1267 142 81 77 006622 02118 3198 M100 296 015 8 1282 15 75 007862 02315 294




stress



Concrete Grade


Longitudinal Steel

Lateral Steel Ties

Peak Strain

E cc


Ecc50

Ductility Ratio

cent PI n dJ

mm

d h

mm

Sh

mm

1315 M20 350 01 4 198 11 37 876 005366 0258 481 M40 2657 01 4 15 145 75 007678 031055 405 M60 2226 01 4 126 168 75 009771 035361 362 M80 200 01 4 12 1823 75 011073 036217 327 M100 200 01 4 12 1985 75 011747 035083 298

1715 M20 400 01 8 16 85 100 004314 021432 496 M40 304 01 4 1715 145 76 006632 026742 4032 M60 255 01 4 1435 167 75 008293 03 361 M80 224 01 4 126 186 75 01 033 33 M100 202 01 4 12 1985 75 011594 034634 298

2665 M20 47026 015 8 23 85 100 003401 019082 561 M40 366 015 8 1787 115 91 5 005977 023933 4004 M60 310 015 4 21 4 178 77 5 007505 027071 361 M80 27326 015 4 189 1787 75 007976 025959 325 M100 24731 015 4 171 194 75 00927 027616 2979

61

middot



100100middot III


~ 60f 60 rn 40-rn

40 20

20 0 0 0 001 002 003 004 005

Strain






0 001 002 003 004 005

Strain


7 6

0 551 5 10 40~ 4 ~ ~3

6

3 - bull bull ~ ~ 2 ~ 2 ~ c c

1

o +-~-~--~--~------~-

M20 M40 M60 MBO M100M20 M40 M60 M80 M100





62


-----___T ~1----400--middot




f c IS 13920 ACI318 NZS 3101

Mpa p -shy

p -shy

p -shy

f c Ag fc Ag fc Ag

01503 amp 05 01503 amp 05 015 03 05

d mm

s mm ~

Ashcode

d mm

s mm ~

ASh code

d mm

s mm ~

Ash code

d mm

s mm ~

ASh code

d mm

s mm ~

Ash code

35 12 75 1020 10 59 1020 7 70 1050 10 75 1015 13 60 1034 50 14 75 1010 12 60 1043 - - - 12 60 1033 - - -70 16 75 1014 13 50 1080 10 65 1066 14 50 1070 17 42 1039 85 18 75 1070 14 50 1070 - - - 15 45 1070 - - -100 19 75 1070 14 43 1070 12 56 1048 16 42 1070 19 35 1042




63


007

006 ACI


= It)

lt 004

001002

-

-

-shy

- -

NZS (PfcAg=O IS)

NZS(pfcAg=O3)

001

o --- --------------~------


20 40 60 80 100

fc(MPa)





64




20 35 50 65 80 95 110

fe (MPa)





65





(fJ 30 20 10 0

0 001 002 003 004 005

Strain (mmmm)




66

5 Conclusions




Acknowledgement


References







67

1 Introduction









60



Concrete Grade



Peak Strain

E cc


E cc50

Ductility Ratio

cent PI n dJ

mm

d h

mm

Sh

mm

1500 M20 412 012 8 16 88 100 00396 02069 525 M40 316 012 6 141 109 79 006466 026036 4027 M60 266 012 6 12 125 75 007741 0279 361 M80 234 012 6 12 14 75 008848 02893 327 M100 211 012 6 12 153 75 01 0299 298

2000 M20 500 0082 8 16 85 100 002935 01703 58 M40 376 0082 8 12 117 94 005371 02126 396 M60 313 0082 6 12 128 79 00677 0243 359 M80 274 0082 6 12 139 75 007836 025474 325 M100 247 0082 6 12 157 75 0095 0283 298

3000 M20 563 015 10 21 8 86 100 00279 01615 578 M40 438 015 10 17 117 100 003704 015 407 M60 3705 015 10 1435 1361 92 63 005741 020182 3515 M80 327 015 10 1267 142 81 77 006622 02118 3198 M100 296 015 8 1282 15 75 007862 02315 294




stress



Concrete Grade


Longitudinal Steel

Lateral Steel Ties

Peak Strain

E cc


Ecc50

Ductility Ratio

cent PI n dJ

mm

d h

mm

Sh

mm

1315 M20 350 01 4 198 11 37 876 005366 0258 481 M40 2657 01 4 15 145 75 007678 031055 405 M60 2226 01 4 126 168 75 009771 035361 362 M80 200 01 4 12 1823 75 011073 036217 327 M100 200 01 4 12 1985 75 011747 035083 298

1715 M20 400 01 8 16 85 100 004314 021432 496 M40 304 01 4 1715 145 76 006632 026742 4032 M60 255 01 4 1435 167 75 008293 03 361 M80 224 01 4 126 186 75 01 033 33 M100 202 01 4 12 1985 75 011594 034634 298

2665 M20 47026 015 8 23 85 100 003401 019082 561 M40 366 015 8 1787 115 91 5 005977 023933 4004 M60 310 015 4 21 4 178 77 5 007505 027071 361 M80 27326 015 4 189 1787 75 007976 025959 325 M100 24731 015 4 171 194 75 00927 027616 2979

61

middot



100100middot III


~ 60f 60 rn 40-rn

40 20

20 0 0 0 001 002 003 004 005

Strain






0 001 002 003 004 005

Strain


7 6

0 551 5 10 40~ 4 ~ ~3

6

3 - bull bull ~ ~ 2 ~ 2 ~ c c

1

o +-~-~--~--~------~-

M20 M40 M60 MBO M100M20 M40 M60 M80 M100





62


-----___T ~1----400--middot




f c IS 13920 ACI318 NZS 3101

Mpa p -shy

p -shy

p -shy

f c Ag fc Ag fc Ag

01503 amp 05 01503 amp 05 015 03 05

d mm

s mm ~

Ashcode

d mm

s mm ~

ASh code

d mm

s mm ~

Ash code

d mm

s mm ~

ASh code

d mm

s mm ~

Ash code

35 12 75 1020 10 59 1020 7 70 1050 10 75 1015 13 60 1034 50 14 75 1010 12 60 1043 - - - 12 60 1033 - - -70 16 75 1014 13 50 1080 10 65 1066 14 50 1070 17 42 1039 85 18 75 1070 14 50 1070 - - - 15 45 1070 - - -100 19 75 1070 14 43 1070 12 56 1048 16 42 1070 19 35 1042




63


007

006 ACI


= It)

lt 004

001002

-

-

-shy

- -

NZS (PfcAg=O IS)

NZS(pfcAg=O3)

001

o --- --------------~------


20 40 60 80 100

fc(MPa)





64




20 35 50 65 80 95 110

fe (MPa)





65





(fJ 30 20 10 0

0 001 002 003 004 005

Strain (mmmm)




66

5 Conclusions




Acknowledgement


References







67



Concrete Grade



Peak Strain

E cc


E cc50

Ductility Ratio

cent PI n dJ

mm

d h

mm

Sh

mm

1500 M20 412 012 8 16 88 100 00396 02069 525 M40 316 012 6 141 109 79 006466 026036 4027 M60 266 012 6 12 125 75 007741 0279 361 M80 234 012 6 12 14 75 008848 02893 327 M100 211 012 6 12 153 75 01 0299 298

2000 M20 500 0082 8 16 85 100 002935 01703 58 M40 376 0082 8 12 117 94 005371 02126 396 M60 313 0082 6 12 128 79 00677 0243 359 M80 274 0082 6 12 139 75 007836 025474 325 M100 247 0082 6 12 157 75 0095 0283 298

3000 M20 563 015 10 21 8 86 100 00279 01615 578 M40 438 015 10 17 117 100 003704 015 407 M60 3705 015 10 1435 1361 92 63 005741 020182 3515 M80 327 015 10 1267 142 81 77 006622 02118 3198 M100 296 015 8 1282 15 75 007862 02315 294




stress



Concrete Grade


Longitudinal Steel

Lateral Steel Ties

Peak Strain

E cc


Ecc50

Ductility Ratio

cent PI n dJ

mm

d h

mm

Sh

mm

1315 M20 350 01 4 198 11 37 876 005366 0258 481 M40 2657 01 4 15 145 75 007678 031055 405 M60 2226 01 4 126 168 75 009771 035361 362 M80 200 01 4 12 1823 75 011073 036217 327 M100 200 01 4 12 1985 75 011747 035083 298

1715 M20 400 01 8 16 85 100 004314 021432 496 M40 304 01 4 1715 145 76 006632 026742 4032 M60 255 01 4 1435 167 75 008293 03 361 M80 224 01 4 126 186 75 01 033 33 M100 202 01 4 12 1985 75 011594 034634 298

2665 M20 47026 015 8 23 85 100 003401 019082 561 M40 366 015 8 1787 115 91 5 005977 023933 4004 M60 310 015 4 21 4 178 77 5 007505 027071 361 M80 27326 015 4 189 1787 75 007976 025959 325 M100 24731 015 4 171 194 75 00927 027616 2979

61

middot



100100middot III


~ 60f 60 rn 40-rn

40 20

20 0 0 0 001 002 003 004 005

Strain






0 001 002 003 004 005

Strain


7 6

0 551 5 10 40~ 4 ~ ~3

6

3 - bull bull ~ ~ 2 ~ 2 ~ c c

1

o +-~-~--~--~------~-

M20 M40 M60 MBO M100M20 M40 M60 M80 M100





62


-----___T ~1----400--middot




f c IS 13920 ACI318 NZS 3101

Mpa p -shy

p -shy

p -shy

f c Ag fc Ag fc Ag

01503 amp 05 01503 amp 05 015 03 05

d mm

s mm ~

Ashcode

d mm

s mm ~

ASh code

d mm

s mm ~

Ash code

d mm

s mm ~

ASh code

d mm

s mm ~

Ash code

35 12 75 1020 10 59 1020 7 70 1050 10 75 1015 13 60 1034 50 14 75 1010 12 60 1043 - - - 12 60 1033 - - -70 16 75 1014 13 50 1080 10 65 1066 14 50 1070 17 42 1039 85 18 75 1070 14 50 1070 - - - 15 45 1070 - - -100 19 75 1070 14 43 1070 12 56 1048 16 42 1070 19 35 1042




63


007

006 ACI


= It)

lt 004

001002

-

-

-shy

- -

NZS (PfcAg=O IS)

NZS(pfcAg=O3)

001

o --- --------------~------


20 40 60 80 100

fc(MPa)





64




20 35 50 65 80 95 110

fe (MPa)





65





(fJ 30 20 10 0

0 001 002 003 004 005

Strain (mmmm)




66

5 Conclusions




Acknowledgement


References







67

middot



100100middot III


~ 60f 60 rn 40-rn

40 20

20 0 0 0 001 002 003 004 005

Strain






0 001 002 003 004 005

Strain


7 6

0 551 5 10 40~ 4 ~ ~3

6

3 - bull bull ~ ~ 2 ~ 2 ~ c c

1

o +-~-~--~--~------~-

M20 M40 M60 MBO M100M20 M40 M60 M80 M100





62


-----___T ~1----400--middot




f c IS 13920 ACI318 NZS 3101

Mpa p -shy

p -shy

p -shy

f c Ag fc Ag fc Ag

01503 amp 05 01503 amp 05 015 03 05

d mm

s mm ~

Ashcode

d mm

s mm ~

ASh code

d mm

s mm ~

Ash code

d mm

s mm ~

ASh code

d mm

s mm ~

Ash code

35 12 75 1020 10 59 1020 7 70 1050 10 75 1015 13 60 1034 50 14 75 1010 12 60 1043 - - - 12 60 1033 - - -70 16 75 1014 13 50 1080 10 65 1066 14 50 1070 17 42 1039 85 18 75 1070 14 50 1070 - - - 15 45 1070 - - -100 19 75 1070 14 43 1070 12 56 1048 16 42 1070 19 35 1042




63


007

006 ACI


= It)

lt 004

001002

-

-

-shy

- -

NZS (PfcAg=O IS)

NZS(pfcAg=O3)

001

o --- --------------~------


20 40 60 80 100

fc(MPa)





64




20 35 50 65 80 95 110

fe (MPa)





65





(fJ 30 20 10 0

0 001 002 003 004 005

Strain (mmmm)




66

5 Conclusions




Acknowledgement


References







67


-----___T ~1----400--middot




f c IS 13920 ACI318 NZS 3101

Mpa p -shy

p -shy

p -shy

f c Ag fc Ag fc Ag

01503 amp 05 01503 amp 05 015 03 05

d mm

s mm ~

Ashcode

d mm

s mm ~

ASh code

d mm

s mm ~

Ash code

d mm

s mm ~

ASh code

d mm

s mm ~

Ash code

35 12 75 1020 10 59 1020 7 70 1050 10 75 1015 13 60 1034 50 14 75 1010 12 60 1043 - - - 12 60 1033 - - -70 16 75 1014 13 50 1080 10 65 1066 14 50 1070 17 42 1039 85 18 75 1070 14 50 1070 - - - 15 45 1070 - - -100 19 75 1070 14 43 1070 12 56 1048 16 42 1070 19 35 1042




63


007

006 ACI


= It)

lt 004

001002

-

-

-shy

- -

NZS (PfcAg=O IS)

NZS(pfcAg=O3)

001

o --- --------------~------


20 40 60 80 100

fc(MPa)





64




20 35 50 65 80 95 110

fe (MPa)





65





(fJ 30 20 10 0

0 001 002 003 004 005

Strain (mmmm)




66

5 Conclusions




Acknowledgement


References







67


007

006 ACI


= It)

lt 004

001002

-

-

-shy

- -

NZS (PfcAg=O IS)

NZS(pfcAg=O3)

001

o --- --------------~------


20 40 60 80 100

fc(MPa)





64




20 35 50 65 80 95 110

fe (MPa)





65





(fJ 30 20 10 0

0 001 002 003 004 005

Strain (mmmm)




66

5 Conclusions




Acknowledgement


References







67




20 35 50 65 80 95 110

fe (MPa)





65





(fJ 30 20 10 0

0 001 002 003 004 005

Strain (mmmm)




66

5 Conclusions




Acknowledgement


References







67





(fJ 30 20 10 0

0 001 002 003 004 005

Strain (mmmm)




66

5 Conclusions




Acknowledgement


References







67

5 Conclusions




Acknowledgement


References







67

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