BEHAVIOR AND DESIGN OF HSC MEMBERS SUBJECTED TO AXIAL COMPRESSION AND FLEXURE

Transcription

1 BEHAVIOR AND DESIGN OF HSC MEMBERS SUBJECTED TO AXIAL COMPRESSION AND FLEXURE Halit Cenan Mertol, SungJoong Kim, Amir Mirmiran, Sami Rizkalla and Paul Zia Synopsis: This paper identiies the undamental design issues related to the behavior o high-strength onrete (HSC) members with ompressive strengths up to 124 MPa (18 ksi) subjeted to axial ompression loads. The indings are based on ritial assessment and synthesis o available data, the experienes o bridge owners, onrete abriators, and urrent bridge design odes rom North Ameria, Europe, Australia, and Asia. The paper disusses the various ators believed to aet the design and behavior o HSC ompression members, inluding the undamental properties o onrete, member geometry, support onditions, main and lateral reinorement, and type o onstrution. The signiiane o modeling o the stress-blok, potential early spalling o onrete and reliability issues o HSC olumns is also disussed. This paper represents the urrent eorts by the authors to reommend revisions to the AASHTO-LRFD Bridge Design Speiiations, whih urrently limits the ompressive strength o onrete to 69 MPa (10 ksi). Keywords: olumn; ombined ompression and lexure; ompression members; highstrength onrete; stress blok parameters

2 Halit Cenan Mertol is a member o ACI. He obtained his BSCE (1999) and MSCE (2002) rom Middle East Tehnial University in Turkey. He is urrently a Ph. D. student in Civil, Constrution and Environmental Engineering in North Carolina State University, Raleigh, North Carolina. His main interests are high-strength onrete and iber reinored polymer materials. SungJoong Kim is a Ph. D. student in the Department o Civil, Constrution and Environmental Engineering at North Carolina State University. He reeived his BS (1997) and MS (2000) degrees rom the Dept. o Civil and Environmental Engineering o Chung-Ang University, Seoul, Korea. His main researh interests inlude the strutural use o high-strength onrete and design o high-strength onrete olumns. Amir Mirmiran is Proessor and Chair o the Department o Civil and Environmental Engineering at the Florida State International University in Miami, FL. He has served on the aulty o the North Carolina State University, University o Cininnati and the University o Central Florida. His researh interests inlude high-perormane onrete and omposite materials. Sami Rizkalla is a Distinguished Proessor o Civil and Constrution Engineering in the Department o Civil, Constrution and Environmental Engineering, North Carolina State University. He is the Diretor o the Construted Failities Laboratory and NSF I/UCRC in Repair o Strutures and Bridges at North Carolina State University. He is a ellow o ACI, ASCE, CSCE, EIC and IIFC. ACI member Paul Zia is a Distinguished University Proessor Emeritus at North Carolina State University. He served as ACI president in 1989, and is a member o the ACI Committee 363, High-Strength Conrete; Conrete Researh Counil; and Joint ACI-ASCE Committee 423, Prestressed Conrete; and ACI Committee 445, Shear and Torsion. INTRODUCTION Development o high-strength onrete (HSC) dates bak to 1930's, but these early developments were eonomially prohibitive or pratial appliations. In the 1960 s, superplastiizers were developed in Japan and Germany and made it possible to derease the water-to-ement ratio o onrete while maintaining its workability. In the 1970 s, the ombined use o super-plastiizers and ultra-ine materials suh as silia ume, inely ground granulated blast urnae slag or anhydrous gypsum led to urther improvement o onrete perormane measures inluding its strength. Sine the mid s, HSC has gained popularity in both preast and ast-in-plae onstrution or either reinored or prestressed members. In Japan, onrete strengths as high as 11.4 ksi (79 MPa) were used in the 1970 s or railway bridges (ACI 363R ).

3 In the early 1990 s, the Federal Highway Administration (FHWA) began sponsoring the use o High Perormane Conrete (HPC) in several demonstration projets. Sine 1993, a number o HPC bridges have been onstruted aross the ountry. The FHWA ompilation projet (Russell et al. 2003) reports on 19 suh bridges in 14 states. While the highest design onrete strength in these bridges was reported as 14 ksi (97 MPa) in Texas, the ahieved strength at the design age reahed as high as 15.9 ksi (110 MPa) in South Dakota. The AASHTO LRFD Bridge Design Speiiations, irst published in 1994, inludes an artile ( ) limiting its appliability to a maximum onrete strength o 10 ksi (69 MPa), unless physial tests are made to establish the relationship between onrete strength and its other properties. These limitations releted the lak o researh data at the time, rather than the inability o the material to perorm its intended untion. Many design provisions stipulated in the LRFD Speiiations are still based on test results obtained rom speimens with ompressive strengths up to 6 ksi (41 MPa). Although suh a strength limit is not expliitly imposed by other odes suh as the ACI (2002), exept in the provisions or development length, their appliability to HSC is not ully addressed either. The National Cooperative Highway Researh Program has initiated our separate projets to expand the LRFD Speiiations, allow broader use o HSC, and meet the needs o the bridge design ommunity. The objetive o NCHRP Projet 12-64, whih is the ous o this paper, is to reommend revisions to the LRFD Speiiations to extend the appliability o its ompressive and ombined ompressive and lexural design provisions or reinored and prestressed onrete members to onrete strengths up to 18 ksi (124 MPa). AFFECTING FACTORS FOR HIGH-STRENGTH CONCRETE The ators that aet the ompressive and ombined ompressive and lexural behavior o reinored and prestressed high-strength onrete members were identiied rom the databank assembled by the authors. Compressive Strength and Ultimate Strain o Conrete The ompressive strength o onrete diretly aets the load arrying apaity o reinored and prestressed onrete members subjeted to ompression and ombined ompression and lexure. However, there is not a ommon deinition or HSC. The FHWA Compilation Report (Russell et al. 2003) suggests the ollowing three grades: Grade 1 or 8 ksi (55 MPa) < 10 ksi (69 MPa), Grade 2 or 10 ksi (69 MPa) < 14 ksi (97 MPa) and Grade 3 or 14 ksi (97 MPa).

4 The stress-strain response o onrete, its ompressive strength and its ultimate strain are untions o several parameters, inluding the mix proportions, type o ement and ementitious materials, type o admixtures, and type and grading o aggregates. Other ators that inluene the ompressive strength and ultimate strain o onrete inlude uring, speimen type and size, moisture ontent and end onditions o test speimens, speimen age at the time o testing, and rate o loading. Some parameters are known to aet ertain properties o onrete more than others. For example, aggregate type has a proound eet on the elasti modulus o onrete. Figure 1 shows typial axial stress-strain urves or a range o onrete ompressive strengths up to nearly 16 ksi (110 MPa). As the onrete strength inreases, the strain at the peak stress inreases slightly, the shape o the asending branh o the stress-strain urve beomes more linear and steeper, and the slope o the desending part also beomes steeper. As seen in Figure 1 above, the eetive (useable) ultimate strain o onrete dereases as the strength inreases. All design odes in the U.S. suggest a onservative value o or design, whereas some o the oreign odes (e.g., Belgium, Sweden, Germany, and Canada) use Codes in the U.K. use an ultimate strain o or a onrete ompressive strength o 1.8 ksi (12 MPa), but gradually redue it to or a onrete ompressive strength o 7.3 ksi (50 MPa). Modulus o Elastiity o Conrete Modulus o elastiity o onrete aets the elasti deormation o reinored and prestressed onrete members, lateral stiness o olumns, and the loss o prestress. The modulus inreases with the strength, however, at a somewhat lower rate. The FHWA Compilation Report (Russell et al. 2003) suggests hanging the limits o elasti modulus or dierent grades o onrete whih are 5,000 ksi (34,475 MPa) E < 6,000 ksi (41,370 MPa) or Grade 1, 6,000 ksi (41,370 MPa) E < 7,000 ksi (48,265 MPa) or Grade 2 and 7,000 ksi (48,265 MPa) E or Grade 3. Figure 2 shows over 300 available test results rom the databank on the modulus o elastiity in omparison with the design expressions o the LRFD Speiiations and ACI 363R-92 (1997), the latter o whih ollows the equation proposed by Carrasquillo et al. (1981). Poisson s Ratio o Conrete The Poisson s ratio aets lateral expansion o onrete, thereby inluening the eetiveness o the transverse reinorement. The limited test data suggests a range o or the Poisson s ratio o HSC between ompressive strengths o 8 and 11.6 ksi

5 (55 and 80 MPa) (Perenhio and Khieger 1978). The predominant ator in this regard appears to be the water-to-ement ratio. The ACI 363R-92 (1997) reommends using the same Poisson s ratio or HSC as that o NSC in the elasti range. Modulus o Rupture o Conrete The modulus o rupture o onrete represents its lexural tensile strength. It aets raking moment or onrete members, and thereore, inluenes the minimum lexural reinorement that is required to prevent sudden ailure o the beam under lexural loads. It also aets strain limits in prestressed onrete members. The literature review suggests values or the modulus o rupture o HSC in the range o 0.24 to 0.38 ksi (0.62 to MPa). Carrasquillo et al. (1981) suggested a higher value o 0.37 (0.97 MPa) or onrete ompressive strengths o up to 12 ksi (83 MPa). Figure 3 shows some o the experimental values o the modulus o rupture in omparison with dierent design odes and researh publiations. Based primarily on a number o SHRP projets (Zia et al. 1993), Russell et al. (2003) has proposed a revision to the modulus o rupture equations in the LRFD Speiiations to inlude an upper bound o 0.37 ksi (0.97 MPa) and a lower bound o 0.24 ksi (0.62 MPa) or onrete ompressive strengths o up to 15 ksi (103 MPa). Creep Properties o Conrete Creep is the hange in length o a onrete member under onstant sustained axial load. Creep properties o onrete aet long-term deletions o onrete members. The amount and rate o reep depend on the mix proportions and the onstituent materials o onrete, age and strength o onrete at the time o loading, length o time under load, size o the member, amount o non-prestressed reinorement, and the ambient environment. The FHWA ompilation report (Russell et al. 2003) suggests the ollowing three grades o onrete based on its speii reep (ultimate reep per unit stress), whih are 0.52 x 10 3 /ksi (75 /MPa) C > 0.38 x 10 3 /ksi (55 /MPa) or Grade 1, 0.38 x 10 3 /ksi (55 /MPa) C > 0.21 x 10 3 /ksi (30 /MPa) or Grade 2 and 0.21 x 10 3 /ksi (30 /MPa) C or Grade 3. Parrott (1969) reported that the total strain observed in a sealed HSC speimen under a sustained loading o 30% o its ultimate strength was the same as that o a sealed NSC speimen when expressed as a ratio o the short-term strain. On the other hand,

6 reent researh (Tadros et al. 2003) has indiated that HSC undergoes less ultimate reep than NSC, while its reep develops relatively more rapidly than in NSC. Shrinkage Properties o Conrete Drying shrinkage is a shortening that results rom loss o moisture rom the onrete. Shrinkage will aet the long-term deormation and raking o onrete members. Aording to ACI 363R-92 (1997), a relatively high initial rate o shrinkage has been reported or HSC, as ompared to NSC. However, ater drying or about 180 days, there is little dierene between the shrinkage o HSC and NSC made with dolomite or limestone. The magnitude and rate o shrinkage depend on many ators inluding mix proportions and onstituent materials o onrete, size o member, amount o nonprestressed reinorement, uring proedure and duration, and the ambient environment. DESIGN ISSUES FOR HIGH-STRENGTH CONCRETE The design issues or high-strength in ompression and ombined ompression and lexure o reinored onrete members were identiied rom the databank assembled by the authors. Also, a detailed review o Setion 5 o the LRFD Speiiations and their historial development was perormed to ensure a thorough understanding o the impliations o using HSC in ompression and ombined ompression and lexure. Axial Resistane or Compression Members This issue is primarily related to Artile whih limits the maximum strain at the extreme onrete ompression iber to 0.003, Artiles and o the LRFD Speiiations whih use 0.85 or the redution ator or axial ompression. In order to evaluate the above equations in the LRFD Speiiations, it is neessary to review their basis and historial development. It is generally understood that the strength o onrete in a member is dierent rom that in a onrete ylinder. Thereore, the strength obtained rom testing a onrete ylinder is oten multiplied by a ator to aount or this dierene. This ator originated rom the olumn tests o Rihart et al. in the early 1930 s, as o ( Ag Ast ) y Ast P = k ' + (1) 3

7 The k 3 parameter in the above equation an be obtained either rom onentrially loaded olumn tests or rom ombined ompressive and lexural tests. In this equation, it is assumed that longitudinal steel bars in the olumn (i any) yield when onrete reahes its peak stress o. This assumption is generally justiied, as the strain ε o orresponding to the peak stress is usually about For onentrially loaded olumns with lateral steel reinorement, P o is taken as the irst peak load that orresponds to the spalling o over onrete. Figure 4 shows the experimental values o k 3 rom all available tests o onentrially loaded olumns in the databank as a untion o the onrete ompressive strength. There is learly signiiant satter in the test results. Moreover, a sarity o test data or onrete strengths above 14 ksi (97 MPa) is apparent. Some o the satter may be explained by the at that dierent investigators have used dierent size ylinders in determining the onrete ompressive strength. It is generally aepted that ompressive strength o onrete measured on 4 x 8 in (102 x 203 mm) ylinders is about 1% to 5% higher than the strength measured rom the 6 x 12 in (152 x 305 mm) ylinders (Carino 1994). The k 3 parameter may also be determined rom ombined ompressive and lexural tests in omparison with ompression tests, i.e., ylinder tests, as below: k = 3 Maximum Conrete Stress in Combined Compressive and Flexural Tests Maximum Conrete Stress in Compression Cylinder Tests (2) In these ombined ompressive and lexural tests, a C-shaped speimen is loaded with two axial ompression loads at two dierent eentriities to reate a ompression only ross setion (Figure 5). While loading the braket to ailure, the neutral axis is maintained at the outside ae o the speimen throughout the test. The maximum stress in the above equation is obtained rom losely spaed, onseutive readings o strain data in these eentri braket tests. Subsequently, an approximate stress an be alulated or onrete at every strain level. The maximum value o the stress obtained in this step is then used in the k 3 alulations. Figure 6 shows the experimental values o k 3 that were obtained rom the available ombined ompression and lexural tests in the databank. A ursory omparison o Figures 4 and 6 shows that the values o k 3 obtained rom onentrially loaded olumns are generally lower than those rom ombined ompression and lexural tests. This dierene may be explained as ollows: The over onrete in olumns ails due to instability long beore rushing o ore onrete. The onnetion plane between the ore onrete and the over onrete is espeially weak when large amounts o longitudinal and transverse steel reinorement are provided. Thereore, separation o the over onrete at this plane rom the ore onrete may be triggered very easily beore rushing o ore onrete. In ombined ompression and lexural tests, deletion o the member is suh that the ompression side is always on the onave side o the olumn, whih is the side

8 that is suseptible to over bukling and instability. The over onrete on this side has a tendeny to bukle towards the ore onrete, and thereore, is onstrained against suh instability. As a result, over bukling is not an issue in members under bending. The quality o over onrete is generally lower than the ore onrete, simply beause o inadequate ompation o the over onrete espeially or HSC mixes with low workability. Moreover, there is a dierene between the drying shrinkage o the ore onrete and that o the over onrete. Low permeability o HSC leads to drying shrinkage strain in the over onrete, while the ore remains relatively moist. As a result, tensile stresses are developed in the over onrete o HSC olumns more rapidly than those in NSC olumns. In summary, the design issue o atored axial resistane is o great signiiane and o high priority. There is adequate test data to establish the neessary parameters desribed above. However, due to large satter o the available test data and the sarity o data or onrete ompressive strengths above 14 ksi (97 MPa), validation tests are needed. Behavior o Conrete in Compression Zones using Retangular Stress Distribution This issue is primarily related to Artile whih limits the maximum strain at the extreme onrete ompression iber to and Artile whih deines the stress blok parameters, while it also aets the lexural resistane in Artile o the LRFD Speiiations. As disussed earlier, the axial stress-strain relationship o onrete varies with its strength. The asending and desending portions o the urve beome steeper with inreasing strength. The urves tend to beome more linear or higher strength onretes. As a result, the equivalent stress blok or high-strength onrete is expeted to be dierent rom that o normal-strength onrete. A generalized stress blok is deined by three parameters, k 1, k 2 and k 3. The design values o the stress blok parameters are determined at the ultimate strain ε u, whih orresponds to the maximum moment o the setion. These parameters are depited in Figure 7. They originated rom the eentri braket tests perormed by Hognestad et al. in the 1950 s. The k 1 k 3 value and the k 2 value an be obtained rom the equilibrium o the external and internal ores as ollows: P = k k ' b + A ' n M n 1 3 = k k ' b 1 3 s su ( d k ) + A ' ( d d' ) 2 + A s s su su (3)

9 The three-parameter generalized stress blok an be redued to a two-parameter equivalent retangular stress blok, by keeping the resultant o the ompression ore at the mid-depth o the assumed retangular stress blok. The two parameters o α 1 and β 1 an be deined as 1 3 α 1 = 2k (4) 2 β = 2k 1 k k 2 The nominal axial and lexural resistane o the setion an then be shown as: P = α β ' b + A ' n M n A β1 = α1β1 ' b d + As ' 2 s su s su su ( d d') (5) Table 1 shows how the stress blok parameters are treated in a number o dierent design odes. Table 2 shows the proposed equations in dierent reports and researh publiations. The ultimate ompressive strain o onrete is also shown in these tables, as it aets the stress blok parameters and the lexural resistane o the setion. Figures 8 through 10 show graphs o the experimental values o α 1 and β 1 obtained rom eentri braket tests perormed by Hognestad (1955), Nedderman (1973), Kaar (1976), Swartz (1985), Shade (1992) and Ibrahim and MaGregor (1996) and the produt α 1 β 1 as a untion o onrete ompressive strength in omparison with dierent design odes. These results indiate that as the strength o onrete inreases, α 1 β 1 dereases. These igures onirm earlier indings o the ACI 441R-96 (1996) that there are onliting test results over the appliability o the urrent retangular stress blok approah to the olumns made o HSC. While some studies have ound the urrent approah or NSC olumns to underestimate the lexural resistane o HSC olumns at a given axial load, there are others who have ound the approah to be quite un-onservative. Reinorement and Strain Limits or Compression Members This issue is primarily related to Artile o the LRFD Speiiations whih limits the maximum and minimum reinorement. The equations in the LRFD Speiiations are extrapolated or a range o onrete ompressive strengths between 5 and 20 ksi (34 and 138 MPa), in the absene o any prestressing steel in the setion. It was observed that the allowable longitudinal nonprestressing steel ratio ρ l in a olumn to be between 4% to 8% or an 18 ksi (124 MPa) onrete and a Grade 60 ksi (414 MPa) steel. The upper bound is limited to 6% in

10 seismi appliations. Suh high levels o minimum reinorement would be quite unusual and need to be veriied. In order to evaluate these reinorement limits, it is neessary to review their basis and historial development. Limits or longitudinal reinorement in ompression members originated rom the early olumn tests by Rihart et al. at the University o Illinois in 1930 s. When a olumn is subjeted to sustained servie loads, the stress distribution between steel and onrete hanges over time due to reep and shrinkage o onrete. With its reep and shrinkage progressing, onrete relieves itsel rom its initial share o the axial load. As a result, longitudinal steel reinorement arries a larger portion o the sustained load over time. Thereore, it is theoretially possible that in olumns with small amounts o longitudinal reinorement, the steel ould yield, resulting in reep rupture o the olumn. Tests by Rihart et al. ( ) showed the inrease o stress in steel reinorement to be inversely proportional to the perentage o the longitudinal steel. Results rom these tests that were arried out on a range o onrete strengths between 2 and 8 ksi (14 and 55 MPa), indiated that a minimum reinorement ratio o 1% was appropriate. The upper limit was initially established based on pratial onsiderations o onrete plaement, and has sine been maintained or all ranges o onrete strengths. The same rational proedure o Rihart et al. ( ) an be ollowed to establish the minimum reinorement limits or HSC olumns. Sine reep properties o HSC are expeted to be dierent rom the NSC, the reinorement limits are also expeted to be hanged. Using the same saety ators and the same duration o sustained loads as those in the early study o Rihart et al. ( ), the lower reinorement limits an be rationally established or HSC with any ombination o mild and prestressing steel. The two strain limits o onern in ompression members are the ultimate strain ε u o onrete at the ultimate limit state, and the strain ε o o onrete orresponding to its peak stress. Figure 11 shows the variation o ε u as a untion o. These results are obtained rom tests on olumns, beams, and ylinders. A review o the literature indiates that as the strength o onrete inreases, ε u dereases. However, the igure shows that the urrent value o or ε u in the LRFD Speiiations remains valid or HSC. Figure 12 shows the variation o ε o as a untion o, using all available results in the databank rom tests on olumns, beams, and ylinders. The igure learly shows that as the strength o onrete inreases, the strain at peak stress also inreases. This has a proound eet on determining the axial resistane o ompression members, sine with higher ε o the assumption o yielding o longitudinal steel reinorement is well justiied. It is not expeted that the above strain limits or HSC ompression members will hange.

11 Coninement and Lateral Reinorement This issue is primarily related to Artiles and d o the LRFD Speiiations whih limits the volume ratio o the spiral reinorement and the total gross setional area o retangular hoop reinorement. Transverse reinorement in olumns provides a passive orm o oninement or onrete, as the lateral steel reats to the expansion o onrete. Sine HSC is expeted to undergo less internal miro-raking, its lateral strains are less than those seen in NSC olumns. For that reason, a number o researh experiments have shown the oninement reinorement to be less eetive in HSC olumns, as ompared to NSC olumns. Thereore, lateral oninement pressure required or HSC olumns may be signiiantly higher than that or NSC olumns. The higher level o oninement pressure may be ahieved using higher grades o lateral steel to avoid ongestion o the reinorement age. On the other hand, HSC has been slow to gain aeptane in seismi regions due to its more brittle behavior in ompression than the NSC. The parameters that aet the oninement o onrete inlude yield strength, spaing, size, distribution, shape, and eetiveness o the oninement reinorement, as well as distribution and yield strength o the longitudinal reinorement, spalling o over onrete, and level o axial load on the setion. The strength o onined onrete an be written as = ' Cσ 2 (6) + Subsequently, the minimum volumetri ratio o spiral reinorement an be ound as 2 ' ( Ag Ast A ) ρ s = (7) min C yw A Equation (7) leads to Equation ( ) in the LRFD Speiiations using a value o 4.44 or the C parameter. It should be noted that the tests by Rihart et al. (1928) identiied the C parameter as 4.1 or NSC olumns. Table 3 provides a summary o the oninement equations proposed in dierent researh publiations. Table 4 summarizes the minimum oninement reinorement ratios speiied in design odes or proposed in various researh publiations.

12 CONCLUSIONS The design issues or normal-strength onrete must be veriied and extended or high-strength onrete. There is available test data to establish the neessary parameters desribed above. However, beause o the large satter o the available test data and the sarity o data or onrete ompressive strengths above 14 ksi (97 MPa), validation tests are needed. Ater these validation tests, the revisions to the LRFD Speiiations to extend the appliability o its lexural and ompression design provisions or reinored and prestressed onrete members to onrete strengths up to 18 ksi (124 MPa) will be reommended. The reommended provisions should be seamless and uniied over the ull range o onrete strengths. ACKNOWLEDGEMENTS The authors would like to aknowledge the support o the NCHRP through the projet and the Senior Program Oier, David Beal. The authors also thank the ontributions o Dr. Henry Russell o Henry Russell, In. and Robert Mast o Berger/ABAM Engineers, In. who also serve as onsultants on the projet. The indings and the onlusion reported here are however o a preliminary nature and are those o the authors alone, and not neessarily those o the supporting ageny. REFERENCES AASHTO LRFD Bridge Design Speiiations, Seond Edition, Amerian Assoiation o State Highway and Transportation Oiials, Washington DC, ACI Committee 318, Building Code Requirements or Strutural Conrete (ACI ) and Commentary (318R-02), Amerian Conrete Institute, Farmington Hills, MI, 2002, 443 pp. ACI Committee 363, State-o-the-Art Report on High-Strength Conrete (ACI 363R- 92), Amerian Conrete Institute, Detroit, MI, 1992 (Revised 1997), 55 pp. ACI Committee 363, Guide to Quality Control and Testing o High-Strength Conrete (ACI 363.2R-98), Amerian Conrete Institute, Detroit, MI, 1998, 18 pp. Ansari, F. and Li, Q., High Strength Conrete Subjeted to Triaxial Compression, ACI Materials Journal, Vol. 95, No. 6, 1998, pp Attard, M. M. and Setunge, S., Stress-Strain Relationship o Conined and Unonined Conrete, ACI Strutural Journal, Vol. 93, No. 5, 1996, pp

13 Attard, M. M. and Stewart, M. G., A Two Parameter Stress Blok or High Strength Conrete, ACI Strutural Journal, Vol. 95, No. 3, 1998, pp Azizinamini, A., Kuska, S. S. B., Brungardt, P. and Hatield, E., Seismi Behavior o Square High-Strength Conrete Columns, ACI Strutural Journal, Vol. 91, No. 3, 1994, pp Bae, S. and Bayrak, O., Stress Blok Parameters or High-Strength Conrete Members, ACI Strutural Journal, Vol. 100, No. 5, 2003, pp Bayrak, O. and Sheikh, S. A., Coninement Reinorement Design Considerations or Dutile HSC Columns, Journal o Strutural Engineering, Vol. 124, No. 9, 1998, pp Bing, L., Park, R. and Tanaka, H., Stress Strain Behavior o High Strength Conrete Conined by Ultra-High- and Normal-Strength Transverse Reinorement, ACI Strutural Journal, Vol. 98, No. 3, 2001, pp Canadian Standards Assoiation, Design o Conrete Strutures, CSA A , Rexdale, Ontario, 1994, 199 pp. Carino, N. J., Predition o Potential Strength at Later Ages, Conrete and Conrete- Making Materials, 1994, 140 pp. Carrasquillo, R. L., Nilson, A. H. and Slate, F., Properties o High Strength Conrete Subjet to Short- Term Loads, ACI Strutural Journal, Vol. 78, No.3, 1981, pp Carrasquillo, R. L., Slate, F. and Nilson, A. H., Miro-Craking and Behavior o High Strength Conrete Subjet to Short- Term Loading, ACI Strutural Journal, Vol. 78, No.3, 1981, pp Comite European de Normalisation (CEN), Euroode 2 : Design o Conrete Strutures, Part 1 General Rules and Rules or Buildings, pren , 2002, 211 pp. Cusson, D. and Paultre, P., High-Strength Conrete Columns Conined by Retangular Ties, Journal o Strutural Engineering, Vol. 120, No. 3, 1994, pp Dahl, K. K. B., Uniaxial Stress-Strain Curves or Normal and High-Strength Conrete, ABK Report No. R282, Department o Strutural Engineering, Tehnial University o Denmark, Dong Z. and Keru, W., Frature Properties o High-Strength Conrete, Journal o Materials in Civil Engineering, Vol. 13, No. 1, 2001, pp

14 Ho, J. C. M. and Pam, H. J., Inelasti Design o Low-Axially Loaded High Strength Conrete Reinored Columns, Engineering Strutures, Vol. 25, No. 8, 2003, pp Hognestad, E., Hanson, N. W. and MHenry, D., Conrete Stress Distribution in Ultimate Strength Design, ACI Journal, Vol. 52, No. 4, 1955, pp Ibrahim, H. H. H. and MaGregor, G., Tests o Eentrially Loaded High-Strength Conrete Columns, ACI Strutural Journal, Vol. 93, No. 5, 1996, pp Ibrahim, H. H. H. and MaGregor, G., Modiiation o the ACI Retangular Stress Blok or High-Strength Conrete, ACI Strutural Journal, Vol. 94, No. 1, 1997, pp Iravani, S., Mehanial Properties o High-Perormane Conrete, ACI Materials Journal, Vol. 93, No. 5, 1996, pp Issa, M. A. and Tobaa, H., Strength and Dutility Enhanement in High-Strength Conined Conrete, Magazine o Conrete Researh, Vol. 46, No. 168, 1994, pp Kaar, P. H., Hanson, N. W. and Capell, H. T., Stress-Strain Charateristis o High Strength Conrete, ACI Speial Publiation-55, Douglas MHenry International Symposium on Conrete and Conrete Strutures, Mihigan, MI, 1978, pp Kahn, L. F. and Meyer, K. F., Retangular Stress Blok or Non-retangular Compression Zone, ACI Strutural Journal, Vol. 92, No. 3, 1995, pp Li, B., Strength and Dutility o Reinored Conrete Members and Frames Construted Using High Strength Conrete, Ph. D. Thesis in Civil Engineering, University o Canterbury, Christhurh, New Zealand, Legeron, F. and Paultre, P., Predition o Modulus o Rupture o Conrete, ACI Materials Journal, Vol. 97, No. 2, 2000, pp Legeron, F. and Paultre, P., Behavior o High-Strength Conrete Columns under Cyli Flexure and Constant Axial Load, ACI Strutural Journal, Vol. 97, No. 4, 2000, pp Le Roy, R., Instantaneous and Time Dependant Strains o High-Strength Conrete, Laboratoire Central des Ponts et Chaussees, Paris, Frane, 1996, 376 pp. Liu, J., Foster, S. J. and Attard, M. M., Strength o Tied High Strength Conrete Columns Loaded in Conentri Compression, ACI Strutural Journal, Vol. 97, No. 1, 2000, pp

15 Nedderman, H., "Flexural Stress Distribution in Very-High Strength onrete, M.S. Thesis, University o Texas at Arlington, 1973, 182 pp. Noguhi Laboratory Data, Department o Arhiteture, University o Tokyo, Japan, ( Ozbakkaloglu, T. and Saatioglu, M., Retangular Stress Blok or High-Strength Conrete, ACI Strutural Journal, Vol. 101, No. 4, 2004, pp Parrot, L. J., The Properties o High-Strength Conrete, Tehnial Report No , Cement and Conrete Assoiation, Wexham Springs, 1969, 12 pp. Paultre, P. and Mithell, D., Code Provisions or High-Strength Conrete - An International Perspetive, Conrete International, 2003, pp Razvi, S. R. and Saatioglu, M., Coninement Model or High Strength Conrete, Journal o Strutural Engineering, Vol. 125, No. 3, 1999, pp Pendyala, R. and Mendis, P. A., A Retangular Stress Blok or High Strength Conrete, Strutural Engineering Journal, Institution o Engineers, Australia, Vol. CE39, No. 4, 1998, pp Perenhio, W. F. and Khieger, P., Some Physial Properties o High Strength Conrete, Researh and Development Bulletin No. RD056.01T, Portland Cement Assoiation, Skokie, IL, 1978, 7 pp. Rihart, F. E., Brandtzaeg, A. and Brown, R. L., A Study o the Failure o Conrete under Combined Compressive Stresses, Bulletin 185, University o Illinois Engineering Experiment Station, Urbana, Illinois, 1928, 104 pp. Rihart, F. E. and Staehle, G. C., Progress Report on Column Tests at the University o Illinois, Journal o Amerian Conrete Institute, Vol. 27, 1931, pp Rihart, F. E. and Staehle, G. C., Seond Progress Report on Column Tests at the University o Illinois, Journal o Amerian Conrete Institute, Vol. 27, 1931, pp Rihart, F. E. and Staehle, G. C., Third Progress Report on Column Tests at the University o Illinois, Journal o Amerian Conrete Institute, Vol. 28, 1931, pp Rihart, F. E. and Staehle, G. C., Fourth Progress Report on Column Tests at the University o Illinois, Journal o Amerian Conrete Institute, Vol. 28, 1932, pp

16 Rihart, F. E., Reinored Conrete Column Investigation, Journal o Amerian Conrete Institute, Vol. 29, 1933, pp Russell, H. G., Miller, R. A., Ozyildirim, H. C. and Tadros, M. K., Compilation and Evaluation o Results rom High Perormane Conrete Bridge Projets, Volume 1, Federal Highway Administration, Russell, H. G., Miller, R. A., Ozyildirim, H. C. and Tadros, M. K., Compilation and Evaluation o Results rom High Perormane Conrete Bridge Projets, Volume 2, Federal Highway Administration, Saatioglu, M. and Baingo, D., Cirular High Strength Columns under Simulated Seismi Loading, Journal o Strutural Engineering, Vol. 125, No. 3, 1999, pp Saatioglu, M. and Razvi, S. R., High Strength Conrete Columns with Square Setions under Conentri Compression, Journal o Strutural Engineering, Vol. 124, No. 12, 1998, pp Shade, J. E., Flexural Conrete Stress in High Strength Conrete Columns, M. S. Thesis in Civil Engineering, the University o Calgary, Calgary, Alberta, Canada, Swartz, S. E., Nikaeen, A., Narayan Babu, H. D., Periyakaruppan, N. and Reai, T. M. E., Strutural Bending Properties o Higher Strength Conrete, ACI Speial Publiation- 87, High-Strength Conrete, 1985, pp Tadros, M., Al-Omaishi, N., Seguirant, J. S. and Galit, J. G., Prestress Losses in Pretensioned High-Strength Conrete Bridge Girders, NCHRP Report 496, Transportation Researh Board, Xie, J., Elwi, A. E. and MaGregor, J. G., Mehanial Properties o Three High Strength Conretes Containing Silia Fume, ACI Strutural Journal, Vol. 92, No. 2, 1995, pp Yong, Y. K., Nour, M. G. and Nawy, E. G., Behavior o Laterally Conined High Strength Conrete under Axial Loads, Journal o Strutural Engineering, Vol. 114, No. 2, 1988, pp Zia, P., Leming, M. L., Ahmad, S., Shemmel, J. J., Elliot, R. P. and Naaman, A. E., Mehanial Behavior o High Perormane Conrete, Vol. 1 Vol. 5, SHRP Report C , Strategi Highway Researh Program, National Researh Counil, Washington, D. C., 1993.

17 LIST OF NOTATIONS a: depth o equivalent retangular stress blok A 1 : area under bearing devie, A : area o ore measured to the outside diameter o the spiral A g : gross ross-setional area o member A ps : area o prestressing steel A s : area o tension reinorement A sh : total ross-setional area o tie reinorement (inluding supplementary rossties) A st : total area o longitudinal steel b: width o web, whih is the same as the width o ompression lange in retangular setions : distane between the neutral axis and the extreme ompression iber C: oninement eetiveness parameter. C : speii reep d: depth o tension steel rom the extreme ompression iber d : depth o ompression steel rom the extreme ompression iber E : modulus o elastiity e x : eentriity o the applied atored axial ore in the X diretion e y : eentriity o the applied atored axial ore in the Y diretion : speiied ompressive strength o onrete at 28 days, unless another age is speiied : strength o onined onrete pe : eetive prestress ater losses pu : speiied tensile strength o prestressing steel su : ultimate strength o longitudinal steel y : yield strength o longitudinal steel yh : speiied yield strength o spiral reinorement, h : ore dimension HSR: High-strength reinorement k 1 : ratio o the average ompressive stress to the maximum ompressive stress k 2 : ratio o the depth o the resultant ompressive ore to the depth o neutral axis k 3 : ratio o the maximum ompressive stress to the ompressive strength o onrete ylinder. m: modiiation ator. M n : nominal Flexural resistane o the setion NSR: normal-strength reinorement P n : nominal axial resistane o the setion P o : maximum load arried by an axially loaded member P rx : atored axial resistane determined on the basis that only eentriity e y is present P ry : atored axial resistane determined on the basis that only eentriity e x is present P rxy : atored axial resistane in biaxial lexure

18 s: vertial spaing o hoops (not exeeding 4 in) α 1 : redution ator o onrete strength β 1 : stress blok parameter ε o : strain o onrete orresponding to its peak stress. ε u : strain o onrete at the ultimate limit state ρ l : allowable longitudinal non-prestressing steel ratio in a olumn ρ s : ratio o the volume o spiral reinorement to the total volume o onrete ore ρ smin : minimum volumetri ratio o spiral reinorement σ 2 : equivalent lateral onining pressure or a spirally reinored onrete olumn φ: resistane ator or members in axial ompression

19 Table 1 Retangular Stress Blok Parameters in Dierent Design Codes Reerene α 1 β 1 ε u 0.85 or ' 4ksi LRFD and ACI ( ' 4) (2002) or ' > 4ksi NZS 3101 (1995) (see Li, Park and Tanaka 1994) 0.85 or ' 8 ksi or ' > 8 ksi ( ' 8) or ' 4.35ksi or ' > 4.35ksi ( ' 4.35) CSA A23.3 (1994) ' ' EC2-02 (2002) α or ' k ' k 7.25 α 1 29 or 7.25 ksi ' ksi 7.25 ksi k 0.80 or ' k ' k or 7.25 ksi ' 7.25 ksii k ksi or ' k 7.25 ksi ' k or 7.25 ksi ' ksi NS 3473 (1995) or ' k 8 ksi CEB-FIB (1990) ' AFREM (1995) ' ACI 441-R96 (1996) or ' > 10 ksi ( ' 10) 0.60 k ' or ' 10 ksi

20 Table 2 Proposed Retangular Stress Blok Parameters in Dierent Publiations Reerene α 1 β 1 ε u 0.85 or ' 10 ksi 0.85 or ' 4.35ksi Azizinamini et al ( ' 10) ( ' 4.35) (1994) or ' > 10 ksi or ' > 4.35ksi Ibrahim and MaGregor (1997) Pendyala and Mendis (1998) ' ' ( ' 8.7) ( ' 8.7) or 8.7 ksi ' 14.5 ksi or 8.7 ksi ' 14.5 ksi ' or Dogbone Tests Attard and Stewart (1998) ' ' or Sustain Load Tests Bae and Bayrak (2003) Ozbakkaloglu and Saatioglu (2003) 0.85 or ' or ' 0.85 or ' or ' 10.2 ksi > 10.2 ksi ( ' 10.2) ( ' 4) > 4 ksi 4 ksi or ' or ' 0.85 or ' or ' 4.35 ksi > 4.35 ksi > 4 ksi ( ' 4.35) 4 ksi ( ' 4) or ' 8ksi or ' 8ksi 0.003

21 Table 3 Proposed Coninement Equations or NSC and HSC Columns Reerene Proposed Equations Rihart (1928) NSC: = ' + 4.1σ 2 Xie, Elwi and MaGregor (1995) Attard and Setunge (1996) Ansari and Li (1998) Bing, Park and Tanaka (2001) σ NSC and HSC: 2 = 1+ ( ' ) ' ' σ ( ' ) ' NSC and HSC: σ 2 = 1 ' + t NSC and HSC: ' ' σ = + HSC, NSR, Retilinear, Cirular: = ' + 4σ 2 HSC, HSR, Cirular: = ' + 2.7σ 2 HSC, HSR, Retilinear: = ' + 1.9σ 2 Table 4 Coninement Requirements in Dierent Design Codes and Publiations Reerene LRFD Speiiations and ACI (2002) NZS Ho and Pam (2003) Requirement A g ' ρ S or spiral reinorement A y ' ρ S 0.12 or spiral olumns in seismi regions y ' A g A sh 0.30sh 1 or retangular olumns in seismi y A regions ' A sh 0.12sh or ret. ol. in seismi regions or LRFD y ' A sh 0.09sh or ret. ol. in seismi regions or ACI y y 1.3 ρ g sh" 0.85 ' Ag ' P Ash 0.006sh" 3.3 A y Ag ' φ A ρ = S A g ρl u y P Ag u 0.9 u yh

22 Table 4 Coninement Requirements in Dierent Design Codes and Publiations (ontinued) Saatioglu and Baingo (1999) Razvi and Saatioglu (1999) Saatioglu and Razvi (1998) Bayrak and Sheikh (1998) ' ρ S 0.17 or spiral, yt P = 0.43xP 0, A g /A 1 = 0.23 and 0.05 lateral drit ρ 0.09 ' or spiral, A g /A 1 = 0.4 S min ' yt ρ Styp 0.14 or spiral, A g /A 1 = 0.4 yt ' ρ S min 0.07 k or retangular 2 yt ' ρ Styp 0.10 k or retangular 2 yt 5 P [ ] ( µ 80 ) A = φ sh Ash( ACI ) α P Tests by Dahl (1992) 120 Axial Compressive Stress (ksi) Axial Compressive Stress (MPa) Axial Compressive Strain Figure 1 Axial Compressive Stress-Strain Curves or Dierent Strengths o Conrete 0

23 Conrete Compressive Strength ' (MPa) Modulus o Elastiity E (10 3 ksi) Le Roy (1996) Dong and Keru (2000) Chin and Mansur (1997) Carrasquillo et al. 1981) Khan et al. (1995) Iravani (1996) Cusson and Paultre (1994) Noguhi Lab, AIJ (1993) LRFD Speiiations ACI 363R-92 (1997), Carrasquillo et al. (1981) Conrete Compressive Strength ' (ksi) Figure 2 Test Data and Design Expressions or Modulus o Elastiity o Conrete Modulus o Elastiity E (GPa) Modulus o Rupture r (ksi) Conrete Compressive Strength ' 0.5 (MPa) University o Sherbrooke (Legeron and Paultre 2000) University o Minnesota (Legeron and Paultre 2000) Li, Park and Tanaka (Paultre and Mithell 2003) Noguhi laboratory ACI Canadian Code New Zealand Code ACI 363 (1997), Carrasquillo et al. (1981) Modulus o Rupture r (MPa) Conrete Compressive Strength ' 0.5 (ksi) Figure 3 Test Data and Design Expressions or Modulus o Rupture o Conrete

24 Conrete Compressive Strength ' (MPa) k Yong, Nour and Nawy (1988) Cusson and Paultre (1994) Liu, Foster and Attard (2000) Issa and Tobaa (1994) Conrete Compressive Strength ' (ksi) Figure 4 k 3 Parameter rom Conentrially Loaded Column Tests Figure 5 C-Shaped Speimen

25 Conrete Compressive Strength ' (MPa) k Kaar (1978) Swartz (1985) Shade (1992) Ibrahim and MaGregor (1996) Conrete Compressive Strength ' (ksi) Figure 6 k 3 Parameter rom Combined Compressive and Flexural Tests b ε u k 3 α 1 k 2 C = k 1 k 3 b β 1 β 1 /2 C = α 1 β 1 b d A s Strain Distribution Generalized Stress Blok Parameters Retangular Stress Blok Parameters Setion Figure 7 Stress Blok Parameters or Retangular Setions

26 1.1 Conrete Compressive Strength ' (MPa) α CEB - FIB (1990) 0.5 NZS 3101 (1995) CSA A23.3 (1994) LRFD (1998) - ACI 312 (2002) - AFREM 0.4 ACI 441 (1995) Test Data Conrete Compressive Strength ' (ksi) Figure 8 Comparison o Experimental Values and Design Codes or α Conrete Compressive Strength ' (MPa) CEB-FIB (1990) NZS 3101 (1995) - Li, Park and Tanaka (1994) CSA 3 A23.3 (1994) LRFD (1998) - ACI 318 (2002) Test Data 0.9 β Conrete Compressive Strength ' (ksi) Figure 9 Comparison o Experimental Values and Design Codes or β 1

27 Conrete Compressive Strength ' (MPa) CEB-FIB (1990) NZS 3101 (1995) - Li, Park and Tanaka (1994) CSA 3 A23.3 (1994) Test Data LRFD (1998) - ACI 318 (2002) α1 x β Conrete Compressive Strength ' (ksi) Figure 10 Comparison o Experimental Values and Design Codes or α 1 β 1 Conrete Compressive Strength ' (MPa) εu εo ε50u Paultre, Legeron (2001) (e50u) (ylinder) Paultre, Legeron (2000) (e50u) (ylinder) Ibrahim and MaGregor (1996) (eu) (test) (retangular) Cusson and Paultre (1994) (e50u) (ylinder) Shade 1992 (eu) (ylinder) Shade 1992 (eu) (test) (retangular) Ibrahim and MaGregor (1996) (eu) (test) (triangular) Kaar, Hanson and Capell (1976) (eu) (test) (retangular) Conrete Compressive Strength ' (ksi) Figure 11 Variation o ε u As a Funtion o

28 Conrete Compressive Strength ' (MPa) εo Khaloo and Bozorgzadeh (2001) Cusson and Paultre (1994) Issa and Tobaa (1994) Nagashima (1992) Yong, Nour and Nawy (1988) Paultre, Legeron (2001) Paultre, Legeron (2000) Shade (1992) 0.5 Sun and Sakino (1993-2) Muguruma (1992) Kabeyasawa (1990) εo ε50u Swartz (1985) Conrete Compressive Strength ' (ksi) Figure 12 Variation o ε o As a Funtion o