ACI Structural Journal / July-August 1997

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2 Shamim A. Sheikh is a professor of ivil engineering at the University of Toronto. He is hairman of joint ACI-ASCE Committee 441, Reinfored Conrete Columns, a member of joint ACI-ASCE Committee 442, Response of Conrete Buildings to Lateral Fores, and of ACI Committee 368, Earthquake Resisting Conrete Strutural Elements and Systems. His researh interests inlude onfinement of onrete, earthquake resistane of reinfored onrete, and expansive ement and its appliation in deep foundations. Shafik S. Khoury is an assistant professor in the Department of Strutural Engineering at Alexandria University, Alexandria, Egypt. He reeived his PhD from the University of Houston in His researh ativities inlude onrete materials and reinfored onrete olumns. ρ s 0.45 A g f A f yh (1) The spiral pith was limited to 3 in. (76 mm) and the maximum enter-to-enter spaing between ties was 4 in. (102 mm). The minimum ross setional area of tie (one leg) was speified as A tie l h ρ s s where l h the maximum unsupported length of the perimeter tie, s tie spaing, and ρ s is the larger of the value alulated from Eq. (1) and (2). In the format of the urrent Code requirements, 1 the amount of tie steel for square olumns with only perimeter ties an be written as (3) where A g gross area of setion, A area of the onrete ore measured to the outside diameter of spiral, f ompressive strength of onrete, and f yh yield strength of lateral steel. The only signifiant differene between the two editions of ode was that related to steel detailing. While the 1956 Code required all the longitudinal bars to be laterally supported by tie bends, this requirement was onsiderably relaxed in the 1963 edition (see Fig. 1) in whih unsupported middle bars were permitted as long as the lear distane between an unsupported bar and a supported bar did not exeed 6 in. (152 mm). This hange was primarily based on experiments in whih the ultimate olumn strength was the only riterion used. Sine no attempt was made to evaluate dutility, this relaxation in interior ties appeared plausible. Whereas the hange was tehnially sound for most steel arrangements, allowing perimeter ties only for all situations is not appropriate as it is now well-known that olumns with only four orner bars supported by tie bends may fail in a brittle manner. 7-9 The single perimeter tie is not able to support the middle longitudinal bars effetively after over spalling; these bars would bukle and push the ties outward, thus releasing a onsiderable amount of onfinement. The 1956 Code provided very effiient steel detailing whih would have provided exellent onfinement with small tie spaing. Sine 1963, this provision of the Code has not hanged. The 1971 and 1977 Codes The speial provisions for seismi design were introdued in the 1971 edition of the Code in Appendix A and were retained without any substantial hanges in the 1977 Code. The importane of dutility was outlined, and related signifiant terms were defined. The plasti hinge was defined as the region where ultimate setion moment apaity may be developed and maintained while the inelasti deformation is inreased signifiantly. The onept of Strong Column-Weak Beam was introdued in an attempt to prevent olumn hinging. The volumetri ratio of spiral ρ s was given as in Eq. (1) with the lower limit provided by Eq. (2) that will be appliable to large olumns in whih A g /A is less than sh A g f , A h f 0.12sh where A h A, the total ross setional area of retilinear steel perpendiular to dimension h ( 2A tie ), and h l h. Eq. (4) assumes that for olumns with square perimeter hoops only, the effiieny of retilinear onfining steel is 50 perent of that of spirals. For the ase of square hoop with one supplementary rosstie in eah diretion, the implied effiieny of the retilinear ties is inreased to 66 perent of that of spirals. Appliation of lateral pressure on the onrete ore at larger number of points results in better onfinement; 4 therefore the Code s assumption was quite rational. The minimum bar size allowed for ties was also inreased from #2 (6.4 mm) as speified in the 1963 Code, to #3 (9.5 mm) for longitudinal bars #10 (31.8 mm) or smaller and at least #4 (12.7 mm) for #11 (34.9 mm) or larger longitudinal bars. The 1983 Code The maximum tie spaing was hanged from 4 in. (102 mm) to the smaller of 4 in. (102 mm) and one-quarter of the minimum setion dimension. While the requirements for the amount of spiral reinforement were f yh f yh (4) ρ s 0.12 f --- f y (2) Fig. 1 Redution of interior ties in 1963 ACI Code 422 ACI Strutural Journal / July-August 1997

3 similar to those speified in the previous edition [Eq. (1) and (2)], the total ross setional area of retilinear lateral steel (inluding rossties) was given by, 0.3sh A g f -, A h f 0.12sh --- f y f y (5) It an be seen that this requirement is similar to that given by Eq. (4) exept for the numerial oeffiient 0.45 whih has been redued to 0.3. No lear explanation for this hange from the 1977 Code was provided. From Eq. (1), (2), and (5), it an be shown that for olumns with square perimeter ties, the effiieny of ties as onfining steel varied from 50 to 75 perent of that of spirals (Fig. 2). As for spirals, the lower limit in Eq. (5), whih is appliable to olumns in whih A g /A h 1.4 sets the minimum onfinement for the purpose of dutility. The Code also required that this lateral steel be distributed over regions where inelasti ation is onsidered to be likely. The length of this region was defined to be above and below eah onnetion and on both sides of any setion where flexural yielding is likely to our, or in other words, where plasti hinges are expeted. The use of rossties with a 180 deg hook at one end and a 90 deg hook at the other end was allowed for the first time to provide ease of onstrution. Effiieny of the 90 deg hooks in onfining the onrete ore and preventing the premature bukling of longitudinal bars has proven to be somewhat doubtful, espeially under high axial load levels. 7-9 The 1989 and 1995 Codes In view of the importane of providing reinfored onrete strutures with adequate toughness to respond inelastially under severe seismi attaks, Appendix A was moved to form Chapter 21 in the main body of the 1989 Code. 1 Eq. (1), (2), and (5) remained unhanged exept that the fator 0.12 in Eq. (5) was hanged to This hange was based on the observed behavior of tied olumns, whih had properly detailed hoops and rossties, and made the relative effiieny of retilinear lateral reinforement reasonably uniform for all sizes of olumns (Fig. 2). Fig. 3 shows a omparison of the behavior of olumns with different steel arrangements tested under onentri ompression. 10,11,14 It is lear that the relationship between the effiienies of irular and retilinear lateral steel is not as simple as assumed in the ode. The following points an be made in this regard: 1. The urrent ode equations assume that all steel onfigurations in tied olumns result in similar olumn behavior. Extensive experimental evidene indiates that setion dutility and strength varied signifiantly from one onfiguration to another 7-12 under axial load only as well as under ombined axial load and bending moment; 2. The Code philosophy of maintaining axial load apaity of a setion after spalling of the over onrete ignores the most important parameter, dutility, when a olumn is subjeted to axial load and flexure. A measure of dutility should be inluded in the design equations; 3. The axial load level in the olumn has a great effet on the olumn behavior. 7-9,12,13 Sine onsiderably high levels of axial load are permitted by many odes for seismi design of olumns, ACI Strutural Journal / July-August 1997 Fig. 2 Comparison of effetiveness of spirals and retilinear ties Fig. 3 Comparison of irular and retilinear onfinement the detrimental effets of higher axial loads must be ompensated for by using larger amounts and more effiient onfiguration of lateral steel. The onfinement equations in the 1982 NZS Code 2 were almost similar to Eq. (5) exept for the additional multipliation fator of (P e /φf A g ) where P e is the olumn axial load, and φ is the strength redution fator. At values of P e /φf A g less than 0.4, the ACI Code was more onservative than the 1982 NZS Code and for higher axial load, the NZS Code requires more lateral steel than the ACI Code, up to 50 perent more for P e /φf A g equal to Neither ode attempted to quantitatively relate the required amount of lateral steel to olumn performane. In the 1995 version of the New Zealand Code, 2 the amount of lateral steel is related to the level of axial load and is aimed at produing highly dutile olumns. RESEARCH SIGNIFICANCE In the light of the previous researh and ensuing onlusions about the inability of the existing ACI Code provisions 423

4 for onfinement to provide olumns with an adequate level of dutility in many irumstanes, the need for a proedure for the design of onfining steel beomes lear. Suh a proedure that relates onfinement parameters to the olumn performane is proposed here on the basis of results from an extensive experimental program. This proedure inludes the effets of two additional variables whih are not onsidered in the urrent Code equations and have been proven 4,5,7-13 to signifiantly affet the onfinement effetiveness and onsequently the olumn behavior. These variables are the level of axial load and the steel onfiguration. In the proposed method the required amount of onfining steel is inreased with an inrease in dutility demand. The proposed proedure lends itself to a design hart whih should be of interest to researhers, and pratitioners engaged in the design of dutile moment-resisting reinfored onrete frames. PROPOSED APPROACH The proposed approah was developed using the experimental results of twenty-nine large-sized speimens reported elsewhere. 7-9,14 Initial development of this design proedure is given in Ref. 15. Some bakground data and the proedure is briefly explained here. Column performane In evaluating the olumn performane and studying the effets of different variables, dutility and toughness parameters defined in Fig. 4 were used. These inlude urvature dutility fator µ φ, umulative dutility ratio N φ, and energy-damage indiator E. Wherever used, subsripts t and 80 indiate, respetively, the value of the parameter until the end of the test (total value) and the value until the end of the yle in whih the moment is dropped to 80 perent of the maximum value. Energy parameter e i represents the area enlosed in yle i by the M-φ loop. All other terms are defined in Fig. 4 exept L f and t whih represent the length of the most damaged region and setion depth of the speimen, respetively. The energy-damage indiator E is similar to the one proposed by Ehsani and Wight 16 for fore-defletion urves. Table 1 lists the available dutility parameters for all the speimens onsidered in this analysis. In order to relate various dutility parameters, energy index E 80 and umulative dutility ratio N φ80 are plotted against urvature dutility fator µ φ in Fig. 5. Data from nine similar speimens that were tested under similar onditions with onstant axial load and yli lateral loads were used in the onstrution of this figure. A reasonable orrelation exists between the parameters in the figure. For µ φ of 16, the values for N φ80 and E 80 are 64 and 575, respetively. A olumn setion with this level of deformability is defined as highly dutile. With a µ φ value of 8 to 16, the setion is defined as moderately dutile and the low dutility olumn has µ φ < 8. With this orrelation between dutility parameters, the speimens tested under monotoni flexure (last 15 speimens in Table 1) ould also be onsidered in the analysis. In typial olumns of framed strutures urvature dutility fator µ φ and displaement dutility fator µ are diretly related. Assuming an elasto-plasti setion response and onstant urvature over an equivalent plasti hinge length (L p ), the main variables that affet the relationship between µ φ and µ are L p, the olumn length L between the point of maximum moment and the point of ontraflexure and the type of lateral load applied. The equivalent plasti hinge length has been found to depend on several fators suh as length L, setion size, and longitudinal bar diameter, but it is unaffeted by parameters that omprise onfining steel. 7,8,13,17 Sine onfinement of onrete in olumns will only affet µ φ diretly, urvature dutility rather than displaement dutility is therefore used as a parameter in the proposed proedure. For drift-based design story/olumn drift an then be easily alulated using µ φ and plasti hinge length for speifi geometri and loading onditions. Axial load level Inreased axial load redues dutility signifiantly. 7-9 The level of axial load is generally measured by indies P/f A g and P/P o. For olumns with similar f, both these indies provide similar omparison. However, for different f values in olumns the omparison using P/f A g may not remain valid. Fig. 6 shows moment-urvature responses of 4 olumns. Effet of a hange in axial load on the olumn behavior an be evaluated from Speimens AS-3 and AS-17, whih are almost idential in every other regard. Inrease in load from 0.66 f A g to 0.77 f A g resulted in a sig- Fig. 4 Dutility parameters 424 Fig. 5 Relationships between urvature and displaement dutility fators ACIStruturalJournal/July-August1997

5 nifiantly less dutile behavior. Curvature dutility fator µ φ was redued by about 45 perent. Speimens AS-3 and AS-3H ontained the same amount of tie steel and were tested under similar axial loads as represented by index P/f A g. Speimen AS-3H made with higher onrete strength, f, displayed muh lower dutility. Speimens AS-3 and AS-18H ontained about 45 perent more tie steel than that required by the ACI Code 1 and both were tested under P/f A g approximately equal to 0.6. Dutility and energy dissipation apaity of the higher strength onrete speimen is onsiderably lower. Speimen AS-17 is omparable to Speimen AS-18H from a point of view that both ontained about 150 perent of the ode-required tie steel ontents and both were subjeted to axial loads that were approximately 60 perent of the ultimate load apaity P o. Moment-urvature responses and dutility parameters of these two speimens are reasonably similar. It an be onluded that the amount of tie steel required for a ertain flexural response of olumns for a given P/P o is approximately proportional to the onrete strength. Steel onfiguration The effetiveness of onfining steel primarily depends on the area of the effetively onfined onrete and the distribution of onfining pressure whih are in turn highly affeted by the distribution of longitudinal and lateral steel and the extent of lateral restraint provided to the bars. 4,5,9 Fig. 7 explains the onept of effetively onfined onrete area within a olumn ore in two different steel onfigurations. 5 With larger number of longitudinal bars laterally supported by tie bends, the area of effetively onfined onrete is inreased and the effiieny of onfinement improves onsiderably. From a four-bar onfiguration to an eight-bar onfiguration the effiieny improvement is very large. Beyond the eight-bar onfiguration, the onfinement effiieny does not inrease as signifiantly with the inrease in the number of laterally-supported longitudinal bars. Fig. 8 shows moment-urvature responses of two olumn speimens ES-13 and FS-9. These speimens and Speimen AS-17 in Fig. 6 are almost idential in all regards exept steel onfiguration. Speimen AS-17 displayed more dutile behavior (also see Table 1) than Speimen FS-9 whih in turn is tougher than Speimen ES-13. Based on this onept and extensive experimental data 4,7,8,9,12,14 steel onfigurations may be divided into the following three main ategories (see Fig. 9): Category I: where only single-perimeter hoops are used as onfining steel Table 1 Details of speimens Researhers Khoury and Sheikh 10 Sheikh, Shah, and Khoury 11 Patel and Sheikh 16 Yeh and Sheikh 12 Speimen Lateral steel Axial load level Dutility ratio Energy indiator f, Spaing, ρ s, f yh, P P ksi in. perent ksi, f P o µ φ AS * FS ES AS AS AS F-9H E-13H AS-3H AS-18H AS-20H F-9L* E-13L A-17L E A F D F D E F E A F E D D A * Lightweight aggregate onrete speimens N φ 80 N φ t E 80 E t ACI StruturalJournal/July-August

6 Fig. 7 Conept of effetively onfined onrete area Fig. 8 Effet of steel onfiguration Fig. 6 Effets of axial load and onrete strength Category II: in addition to the perimeter hoops supporting four orner bars, at least one middle longitudinal bar at eah fae is supported at alternate points by hooks that are not anhored in the ore. At other points the supporting hooks are anhored in the ore. Category III: in whih a minimum of three longitudinal bars are effetively supported by tie orners on eah olumn fae and hooks are anhored into the ore onrete. Limiting onditions for steel onfigurations For earthquake design, it is believed that only the two top ategories of dutility, high and moderate, are needed to be disussed here. 426 Among the speimens tested during this researh program none of the speimens with Configuration E (Category I) resulted in high setion dutility fator (µ φ ). The axial load level in these speimens was high but in other studies (e.g., Ref. 12) olumns with E setions tested under low axial load level (P < 0.3P o ) also showed unsatisfatory behavior. Based on the observed experimental performane and the analytial evidene (Fig. 8), Category I onfiguration is not reommended for high dutility olumns. Speimen ES-13, whih ontained 34 perent more steel than required by the Code, showed very poor behavior with µ φ 2.5. Also under medium level of axial load (about P o ), Speimen E-2 with 1.45 times the Code required steel exhibited µ φ of only about 10. Therefore, the use of Configuration E in moderately dutile olumns should be limited to lower range of axial load (P < 0.40P o ). For onser- ACI Strutural Journal / July-August 1997

7 vative design, the Category I onfigurations are reommended for moderate dutility olumns only if the applied axial load is less than the balaned load P b. With regard to Category II onfigurations, the effetiveness of hooks not anhored in the ore has been a ontroversial issue. Although some researhers onluded that the supplementary rossties allowed olumns to perform in a dutile manner, 12,18,19 the axial load levels in these tests were low (about 0.1P o to 0.3P o ). Reent researh 7-9 has shown that the use of 90 deg hooks in Setion F (Fig. 9) may provide suffiient restraint to the middle bars up to a ertain stage of loading, but at large deformations the 90 deg hooks tend to open, and the restraint provided to the bars beomes ineffetive resulting in a loss of onfinement. None of the reported speimens showed satisfatory performane under high levels of axial load even when lateral steel ontent was in exess of the Code requirements (see Table 1). Although Speimen F-4 indiates very dutile performane, the same setion in Speimen F-9 under higher axial load level shows undesirable behavior for seismi resistane. It should be noted that the 90 deg hooks were not always in the zone of maximum deformation due to the monotoni nature of flexural loading in this set of speimens. Therefore, high apparent dutility in some speimens may not be repeatable. Aordingly, it is reommended that the use of Category II onfigurations to produe high-dutility olumns be limited to ases with low levels of axial load. These olumns an be used for moderate dutility if axial load does not exeed 0.4P o. The limiting onditions under whih the three ategories of steel onfigurations may be reliably used for moderate and high dutility olumns are outlined in Fig. 10. It should be emphasized here that some onfigurations under suh onditions may require a higher amount of lateral steel than other onfigurations. AMOUNT OF CONFINING STEEL General form of proposed equation The relationship between the amount of lateral steel as reommended by the urrent Code, and the suggested amount of lateral steel is taken as: where Y is a fator expressed as Y (, )Y αy p Y φ where α is a parameter that aounts for the onfinement effiieny inluding onfiguration and the lateral restraint provided to the longitudinal bars. Parameters Y p and Y φ take into aount the effet of axial load level and the setion dutility demand, respetively. Parameter α Parameter α is assumed to be equal to unity for Category III onfigurations. This fator is expeted to be greater than unity for Category I onfigurations even for their use under limiting onditions presribed earlier. For suh a ase, the value for α is estimated in a later setion. Use of Category II onfigurations is subjeted to imposed limitations beause some of the hooks are not anhored in the ore ACI Strutural Journal / July-August 1997 (6) (7) Fig. 9 Categories of steel onfigurations Fig. 10 Limiting onditions for steel onfigurations as previously disussed. It is reasonable to assume a value of α equal to unity for these onfigurations in situations where opening of these hooks does not take plae until after suffiient dutility is exhibited. 7-9 In the event of high axial load levels, the value of α would be muh greater than unity; however suh an appliation should be avoided. Development of expressions for parameters Y p and Y φ Eq. (6) and (7) for setions with at least three longitudinal bars effetively restrained on eah fae (α 1) redue to Y p Y φ, After investigating several possible forms of expressions for Y p and Y φ, the following simple forms were seleted, Y p a 1 + a P a 3, and Y φ P o b 1 ( µ φ ) b 2 (8) (9) (10) 427

8 where a 1, a 2, a 3, b 1, and b 2 are onstants to be determined empirially. As a starting point, sine the two parameters Y p and Y φ are independent of eah other, the value of Y φ is assumed to be unity for highly dutile setions with µ φ equal to or greater than 16. Speimens meeting this requirement are AS-3, AS- 18, AS-19, AS-20H, A-3 and F-4. Using the results from these speimens, a least squares analysis was performed to find onstants a 1 and a 2 for seleted values of a 3 that ranged from 1 to 6. Corresponding to eah hosen value of a 3, and onsequently obtained values for a 1 and a 2, the onstants b 1 and b 2 in the expression for Y φ (Eq. 10) were then determined using the test results for those 16 speimens in whih α 1.0. These inluded all the speimens with A and D onfigurations and Speimens F-4 and F-12 from Table 1. Speimen A-3 was not inluded in the analysis sine its µ φ was unusually large ompared with other similar speimens. Minimization of the total umulative error for all the 16 speimens was the only riterion used to selet the final values of the empirial onstants. The umulative error e 2 was alulated as Fig. 11 Required amount of tie steel as affeted by axial load 16 e 2 ( Y exp Y pred ) 2 1 (11) where Y exp /,, and Y pred Y p Y φ. The best fit urves from this analysis are shown in Fig. 11 and 12. The expressions for parameters Y p and Y φ are given below Y p P 5 P o (12) Fig. 12 Required amount of tie steel as affeted by urvature dutility fator and Y φ ( µ φ ) (13) The orrelation oeffiients for Eq. (12) and (13) are 0.99 and 0.93, respetively. The high oeffiients indiate exellent agreement between the analytial and the experimental values. The umulative error e 2 over the 16 speimens used in the final analysis was yielding as average error of per speimen. The parameter Y φ, when heked for highly dutile olumn setions, was found to be almost unity for the average value of µ φ equal to Final form of design equation Based on the above, the amount of lateral steel in tied olumns may be alulated using the following expression The above proedure is applied to all those speimens tested during this program in whih longitudinal bars were effetively supported laterally. Comparison between the analytial and the experimental urvature dutility fators is shown in Fig. 13. The orrelation oeffiient is 0.94 with an average differene between the test and the predited values less than 10 perent. As mentioned above, minimization of the total umulative error was the only riterion used in the development of Eq. (14). No attempts were made to minimize the error in individual olumns. Fig. 11 and 12 also show simplified versions of equations for Y p and Y φ as given below Y p P P o (15) α P 5 ( µ + φ ) 1.15 P o A 29 sh, (14) Y φ µ φ 18 (16) Fator α is unity for Category III onfigurations and for Category II onfigurations as long as the presribed limiting onditions are met. However, for Category I onfigurations, the α value is greater than unity. 428 Eq. (15) provides a onservative estimate for Eq. (12) for most of the axial load range up to P/P o equal to It should be noted that the allowable axial load for tied olumns is 0.56P o (1). Eq. (16) gives a slightly onservative al- ACI Strutural Journal / July-August 1997

9 ternative to Eq. (13). Considering Eq. (15) and (16), Eq. (14) an be rewritten as: µ A φ 7.2 sh, (20) α P 1.4 P o µ φ A 18 sh, α µ φ A 18 sh, (17) Design for Category I onfigurations The parameter α may be estimated in this ase by using the experimental results. Values for α were alulated using Eq. (14) for all the speimens with Configuration E from Table 1 and are listed in Table 2. The average value of α is about 2.70 whih implies that the amount of lateral steel needed in setions with Configuration E to attain a speifi dutility demand may be two to three times that required for setions with Configuration A. The experimental M-φ relationships reported previously 8 onfirm this finding. The fator α for Category I onfigurations may also be estimated by adopting the onept of effetively onfined onrete ore area 5 as shown in Fig. 7. The ratio between the area of effetively onfined onrete and the total onrete area λ at tie level is given by n i 1 C i 2 λ A o (18) Based on Eq. (19) and (20), it an be stated that for axial load below the balane point, the urrent ACI Code steel may be suffiient to provide µ φ of about 7 to 8 for setions with Configuration E. However, for a moderately dutile olumn with µ φ 12, the required amount of lateral steel should be 50 perent higher than that required by the Code. Design hart On the basis of the proposed equations [Eq. (14) and (17)], a design hart is onstruted in Fig. 14 for olumns in whih a minimum of 3 longitudinal bars are effetively supported laterally in eah fae (Category III onfigurations). The amount of required lateral steel inreases with an inrease in the axial load level and an inrease in the dutility demand. Three dutility zones as disussed earlier are indiated in the figure whih shows that the Code presribed amount of tie steel may be adequate to provide high dutility olumns only if the applied axial load is less than 0.4P o, and moderate dutility olumns under higher axial loads as long as at least three longitudinal bars are effetively supported laterally on eah olumn fae. Under high levels of axial load, the Code required amount of lateral steel may not be suffiient to meet high dutility demand. The same figure an be used for Category II setions as long as the limiting onditions shown in Fig. 10 are satisfied. For olumns with Category I onfigura- where A o the ore area enlosed by the enter line of perimeter hoop; C i is the base of the urve representing the area whih is not effetively onfined; and n the number of these urves. It may be reasonably assumed here that the onfiguration parameter α is proportional to 1/λ. Sine α 1 for Category III onfigurations, α for Category I onfigurations (α I ) may be written as α I λ III /λ I where λ III and λ I an be alulated using Eq. (18). For the speimens in whih the longitudinal bars are uniformly distributed around the ore perimeter, the λ values for Configurations A and O (Fig. 9) are and 0.273, respetively. Hene, α I The dutility of Setion E with 8 longitudinal bars, 4 orner bars, and 4 unsupported middle bars was sometimes observed to be even worse than that of Setion O with only four orner bars. 20 It may be reasonable, therefore, to onlude that the fator α for Category I onfigurations may range from 2.3 to 2.7. An average value of 2.5 is thus assumed for all onfiguration types in this ategory. As suggested before, the use of Category I onfigurations may be reliable only for moderate dutility olumns under axial load level below the balane point. For this low axial load, (P/P o ) Taking α equal to 2.5, Eq. (14) and (17) redue to Eq. (19) and (20), respetively. ( µ φ ) A 11.5 sh, (19) Fig. 13 Comparison of experimental and predited urvature dutility fators Table 2 Calulated α values for speimens with Configuration E Speimen ES-13 E-13H E-13L E-2 E-8 E-10 E-13 Y p Y φ α ACI Strutural Journal / July-August

10 tions (α 2.5), the ode-provided amount of lateral steel will be insuffiient to provide even moderately dutile olumns under axial loads exeeding balaned load (P/P o 0.3). Effet of hoop/tie spaing Experimental and theoretial evidenes show that hoop spaing plays a signifiant role in the mehanism of onfinement. 4,5 Larger ratio of hoop spaing s to ore width B will result in smaller area of effetively onfined onrete in the ore (Fig. 7). The proedure presented here for the sake of simpliity does not inlude tie spaing as an ative parameter. However, it should be noted that the test data on whih the equations are based were obtained from speimens in whih tie spaing varied from 0.20B to 0.43B. In this pratial range of spaing, the onfinement mehanism has reasonably high effiieny. Another important reason to limit spaing is to avoid premature bukling of longitudinal bars when a olumn is subjeted to seismi exursions in the inelasti range. In the speimens onsidered here, tie spaings varied between 3.4d b and 7.2d b where d b is the bar diameter. In this range of s/d b, premature bukling of the longitudinal bars an generally be avoided. 2,13 The proposed proedure an be used to design the onfining steel for a given olumn performane as long as the tie spaing is less than 0.43B and 7d b. For a onservative design the limit to the tie spaing is suggested to be the smallest of B/3, 6d b and 200 mm (8 in.). Fig. 14 Lateral steel requirements APPLICATION OF THE PROPOSED DESIGN APPROACH The proposed equation is applied to a 700 mm (27.6 in.) square olumn previously reported by Park et al. 21 The results are presented graphially in Fig. 15 and are ompared with the ACI and NZS Code requirements as well as the lateral steel required aording to Park. 22 For omparative purposes, the analytial equation proposed here was onverted to be a funtion of (P/f A g ) instead of (P/P o ). Under high axial loads, the steel required for highly dutile olumns aording to Park is signifiantly less than that based on the proposed equation. However, for urvature dutility fator µ φ equal to 10, the requirements aording to Park are somewhat onservative ompared with the proposed urve. The amount of steel required aording to the ACI Code is inadequate to ahieve µ φ 10 under high axial loads even for well-onfigured olumns. The 1982 NZ ode requirements for lateral steel produed highly dutile to moderately dutile olumns for most of the axial load range. In the 1995 version of the NZ ode, the effet of axial load is more severe ompared with the 1982 version. The required amount of lateral steel, aording to the 1995 NZ ode, is similar to that propposed by Park 22 for µ φ 20. Eq. (14) is also applied to six speimens reported by Muguruma and Watanabe 23 and by Azizinamini et al. 24 Details of these speimens are given in Table 3 whih also ompares the analytial values of urvature dutility fators with the experimental values. The omparison shows exellent agreement. The only differene may be notied in Speimen AL- 2. It is believed that the atual value of µ φ for this speimen is greater than the experimental value listed in Table 3 sine the M-φ envelope urve for this speimen was reported only 430 Fig. 15 Appliation of the design proedures up to the maximum moment. The post-peak desending part of the urve was not provided. SUMMARY AND CONCLUSIONS The development over the years of the ACI Code provisions for the design of onfining steel in tied olumns is presented. It appears that some of the hanges made from one edition of the Code to the next are not suitable to provide dutile olumns. The urrent Code requirements are evaluated based on experimental evidenes, and the areas in whih the requirements need modifiation are explored. Although extensive experimental evidene indiates that dutile behavior of onfined onrete olumns depends signifiantly on the level of axial load as well as the distribution of steel and the lateral support provided to the longitudinal bars, these fators are not onsidered in the urrent Code equations for onfining steel. Dutility demand is also not given due importane in the Code design proedure. Therefore, olumns designed aording to the urrent Code may display brittle behavior under ertain irumstanes and may be overly onservative in terms of dutility in other ases. The required amount ACI Strutural Journal / July-August 1997

11 Table 3 Appliation of proposed equations Speimen f, MPa Size Lateral steel Longitudinal steel Axial load level Spaing, mm f yh, MPa No. Size f y1, MPa Speimens* reported by Mugurauma and Watanabe 26 BH φ13 mm AH φ13 mm BL φ13 mm AL φ13 mm Speimens reported by Azizinamini et al. 27 P P f A g P o NC # NC # * Column setion mm; ore setion mm; onfiguration Type D Column setion in.; ore setion in.; onfiguration Type A In Ref. 26, the M-φ envelope urve for this speimen was reported only up to the maximum moment. The post peak desending part of the urve was not given , µ φ, exp. µ φ, pred. of lateral steel should be a funtion of axial load level, steel onfiguration, and the expeted dutile performane. To aount for the fators disussed above, a proedure for the design of onfining steel in tied olumns is proposed. Three ategories of steel onfigurations are outlined. Limiting onditions under whih these ategories of steel onfigurations may reliably be used are suggested. A sample design hart is also presented whih an be used to determine the amount of lateral steel required for a speifi dutility level in a olumn that ontains a minimum of three laterallysupported longitudinal bars in eah fae and the steel is uniformly distributed. A omparison between the amount of lateral steel as suggested by the new approah and the Code requirements indiates that under moderate-to-high levels of axial loads, the Code requirements may not be suffiient even in well-onfigured olumns to meet the high dutility demand. However, at low axial load levels (P 0.4P o ), the ode requirements may be relaxed. For steel onfigurations in whih only four orner bars are adequately restrained laterally, the ACI Code design will produe olumns with inadequate dutility for most of the axial load range. The proposed equation when applied to realistially-sized speimens tested by different investigators yielded exellent agreement with the test data. ACKNOWLEDGEMENTS Researh reported here was supported by grants from the Natural Sienes and Engineering Researh Counil of Canada and the U.S. National Siene Foundation. REFERENCES 1. ACI Committee 318, Building Code Requirements for Reinfored Conrete (ACI ) and Commentary (ACI 318R-95), Amerian Conrete Institute, Detroit, Code of Pratie for the Design of Conrete Strutures (NZS 3101:1982 and NZS 3101:1995), Standards Assoiation of New Zealand, Wellington. 3. Code for the Design of Conrete Strutures for Building (CAN 3- A23.3M84), Canadian Standards Assoiation, Rexdale, Ontario, 1984, 281 pp. 4. Sheikh, S. A., and Uzumeri, S. M., Strength and Dutility of Tied Conrete Columns, Journal of the Strutural Division, ASCE, V. 106, ST5, May 1980, pp Sheikh, S. A., and Uzumeri, S. M., Analytial Model for Conrete Confinement in Tied Columns, Journal of the Strutural Division, ASCE, V. 108, ST12, De. 1982, pp Building Code Requirements for Reinfored Conrete, ACI Committee 318, Amerian Conrete Institute, Detroit, 1956, 1963, 1971, 1977, 1983, ACI Strutural Journal / July-August Sheikh, S. A., and Khoury, S., Confined Conrete Columns with Stubs, ACI Strutural Journal, V. 90, No. 4, July-Aug. 1993, pp Sheikh, S. A.; Shah, D. V.; and Khoury, S. S., Confinement of High- Strength Conrete Columns, ACI Strutural Journal, V. 91, No. 1, Jan.- Feb. 1994, pp Sheikh, S. A., and Yeh, C. C., Tied Conrete Columns Under Axial Load and Flexure, Journal of the Strutural Division, ASCE, Proeedings, V. 116, No. 10, Ot. 1990, pp Bertero, V. V., and Felippa, C., Disussion of Dutility of Conrete by H. E. H. Roy and M. A. Sozen, Proeedings of the International Symposium on Flexural Mehanis of Reinfored Conrete, ASCE-ACI, Miami, 1964, pp Iyengar, K. T. R. J.; Desayi, P.; and Reddy, K. 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