3 t World Conerence on Eartquake Engineering ancouver, B.C., Canada August -6, 24 Paper No. 397 SEISMIC DESIGN AND DETAILING OF EXTERIOR REINFORCED CONCRETE BEAM-COLUMN JOINTS Sy-Jiann Hwang, Hung-Jen Lee 2, and Kuo-Cou Wang 3 SUMMARY Te role o orizontal oop reinorcement in joint or seismic resistance is a subject o muc debate. Currently tere is little consensus witin te design and researc communities as to declare weter joint oops serve to conine te core concrete or to carry joint sear directly. Te ACI 38-2 Code provisions empasize te importance o te coninement o te joint core, wic results in congested joints and causes diiculty in construction. Moreover, te increasing use o ig-strengt concrete, resulting in larger amount o joint oops, poses an even worse situation. Te main objective o tis paper was to investigate te eect o joint oops on te sear strengt o exterior reinorced concrete beam-to-column connections subjected to eartquake loading. An attempt was made to relieve te congestion o steel in joints. A newly developed sotened strut-and-tie model postulates tat te unction o joint oop is to carry sear as a tension tie, to constrain te crack widt, and not to conine te concrete core. Te sotened strut-and-tie model suggests tat transverse steel is more important or resisting sear oter tan or conining concrete, tereore te required amount and spacing limits o te joint oops can be alleviated. Consequently, te oter objective was to evaluate te perormance o exterior joints wic conorm to te design pilosopy per te sotened strut-andtie model. Six exterior beam-to-column subassemblages were tested under reverse cyclic loading. All test specimens were designed to ave adequate sear strengt o joints according to te sotened strut-andtie model. Te parameters investigated include te amount and te detailing o joint oops. Te test results indicate tat a lesser amount o oop reinorcement wit wider spacing could be used witout signiicantly aecting te perormance o joints i te connections are provided wit adequate sear strengt according to te sotened strut-and-tie model INTRODUCTION Te role o orizontal oop reinorcement in joint or seismic resistance is a subject o muc debate. It as been argued tat oops carry a substantial portion o te joint sear directly wit te remainder being carried by te concrete core in te orm o a diagonal compression strut []. An alternative Proessor, Dept. o Construction Engineering, National Taiwan University o Science and Tecnology, Taipei, Taiwan 672, ROC 2 Assistant Proessor, Department o Construction Engineering, National Yunlin University o Science and Tecnology, Yunlin, Taiwan 6445, ROC 3 Master, Dept. o Construction Engineering, National Taiwan University o Science and Tecnology, Taipei, Taiwan 672, ROC
argument is tat oops contribute to te sear resistance o joints indirectly by conining te concrete core, tus enancing its diagonal compressive strengt [2]. Tese conlicting views about te unction o transverse reinorcement lead to dierent demands or oop as well as te disparity in detailing rules. Currently, te ACI 38-2 Code provisions [2] empasize te importance o te coninement o te joint core. In consequence, te closely spaced transverse reinorcement in te end regions o laterally loaded columns must be detailed witin joints unless a suitable coninement is provided by te surrounding beams [2]. Te use o crosstie is inevitable since te maximum spacing between legs o oops is limited to 35 mm on center [2]. Tese ACI requirements or adequate concrete coninement result in congested joints wic are very diicult to construct. Moreover, te increasing use o igstrengt concrete, resulting in larger amount o joint oops [2], poses an even worse situation or construction. It seems necessary to declare weter joint oops serve to conine or to carry sear in a more concise manner. A sotened strut-and-tie (SST) model, satisying equilibrium, compatibility, and constitutive laws o cracked reinorced concrete, as been developed or determining te sear strengt o beam-column joints [3, 4]. Joint oops play two roles in te sear-resisting mecanisms as postulated by te SST model. One is to orm tension tie and provide additional sear-transerring pat beside te main diagonal strut. Te oter is to control te crack widts and retard te sotening process o te cracked concrete. Te SST model suggests tat transverse reinorcement is more important or resisting sear tan or coninement, tereore te required amount and spacing limits o te joint oops can be alleviated. Te main objective o tis study was to investigate te eect o joint oops on te sear strengt o exterior reinorced concrete beam-to-column connections subjected to eartquake-type loading. Oter objective was to evaluate te perormance o exterior joints wic conorm to te SST design pilosopy. To acieve tese objectives, six exterior beam-to-column subassemblages were tested under reverse cyclic loading. RESEARCH SIGNIFICANCE Te study reported erein is intended to clariy te eect o joint oops on te sear-resisting beavior o exterior beam-column connections under large load reversals. An attempt was made to relieve te congestion o steel in joints. Te test results indicate tat a lesser amount o oop reinorcement wit wider spacing could be used witout signiicantly aecting te perormance o joints i te connections are provided wit adequate sear strengt according to te SST model. SOFTENED STRUT-AND-TIE MODEL Te simpliied version o te SST model [5] or te design o joints is briely introduced in tis section. Fig. sows te eartquake-induced orces acting on an exterior joint. Te orizontal joint sear orce is estimated as j j = T col () were T is te tensile orce resulting rom te steel o te beam; and col is te orizontal column sear above te joint. Te diagonal compression C d to be resisted according to te strut-and-tie model is ound to be (Fig. ) C d = j / cosθ (2) were θ is te angle o inclination o te diagonal compression wit respect to te orizontal axis. For estimating te design value o orizontal joint sear orce j, u, an overstrengt actor o.25 or te beam steel sould be included [2]. 2
col T C d θ Fig. Forces at exterior joint Based on te SST model [5], te nominal diagonal compression strengt C, can be deined as C were K and K v are te indexes o orizontal and vertical ties, respectively; ζ is te sotening coeicient and can be approximated as ζ 3.35/ c. 52 ; c is te compressive strengt o a standard concrete cylinder in unit o MPa; and A str is te eective area o te diagonal strut. Te orizontal tie index K is expressed as K d SST d, SST = ( K + Kv ) ζ c Astr (3) = + ( K ) A / F K (4) were A t is te area o orizontal tie; y is te yield strengt o joint oop reinorcement; K is te orizontal tie index wit suicient orizontal reinorcement and can be estimated as 2 K / [.2 ( γ + γ )] (5) were γ is te raction o diagonal compression carried by te orizontal tie in te absence o te vertical tie and is deined as [6] γ = ( 2 tanθ ) / 3 or γ (6) F is te balanced amount o te orizontal tie orce and can be calculated as F γ ( K ζ A ) cosθ (7) t y = c str Te related equations to te vertical tie are te same as Eqs. (4) to (7), except tat all te subscript are replaced by v and cos θ and sin θ are intercanged. TEST PROGRAM Six exterior reinorced concrete beam-column connections using concrete wit design compressive strengt o 7 and 28 MPa and Grade 6 steel were constructed and tested [7,8]. A typical beamcolumn subassemblage tested in tis study is sown in Fig. 2. Suicient sear reinorcement was provided in te beam and columns outside o te joint to prevent sear ailure in te beam or te column. All test specimens were designed to ave adequate sear strengt o joints according to te SST model. Te parameters investigated include te amount and te detailing o joint oops. Figure 3 presents te dimensions and te reinorcement details o joints. 3
Reaction wall Actuator (+) ( ) pull pus Column 8-# 24-#4 @ 9 Beam aried joint 9 3 96 kn axial load 2-#4 @ 97 2-#4 @ 97 5 35 35 5 NOTES: () All dimensions in mm (2) 4 mm cover to oops (3) mm =.39 in.; kn =.2248 kip Fig. 2 Specimen coniguration and test setup 42x42 36 32x45 394 45x45 8-# 7-3T44 7-3T4 8-# 45x45 394 32x45 394 45x45 8-# 7-2T5 7-T55 8-# 55x55 494 38x5 494 55x55 2-# 28-3T4 28 - T 2-# Fig. 3 Beam-column joint details All specimens were cast lat rater tan vertical as in actual construction. Te test day compressive strengt or te concrete cylinders and te average yield stress or te reinorcing steel are presented in Table. Te design values or te test parameters as well as te actual values or eac specimen are listed in Table 2. 4
Specimen Concrete c MPa Table Material properties Reinorcement Beam bars #8 y MPa u MPa Column bars # y MPa u MPa Joint oops size y MPa () (2) (3) (4) (5) (6) (7) (8) 7-3T44 [7] 76.8 43 65 42 659 #4 498 7-3T4 [8] 75.2 49 75 458 69 #4 436 7-2T5 [8] 76.6 49 75 458 69 #5 469 7-T55 [8] 69.7 49 75 458 69 #5 469 28-3T4 [8] 35 49 75 458 69 #4 436 28-T [8] 33 49 75 458 69 Note: MPa = 45 psi Specimen M R Table 2 Design parameters Joint strengt Joint oop u u ρ Spacing SST Amount ACI mm ρ, ACI A t γ y u () (2) (3) (4) (5) (6) (7) (8) 7-3T44 2.9 (3.).88 (.9).62 (.63) 3 layers 2-#4 97.9 (.).63 (.85) 7-3T4 3. (3.).76 (.89).54 (.63) 3 layers -#4 97.46 (.45). (.88) 7-2T5 3. (3.).76 (.88).54 (.63) 2 layers -#5 46.3 (.33).5 (.98) 7-T55 3. (3.).76 (.92).54 (.66) layers 2-#5 293.3 (.36).5 (.98) 28-3T4 5. (4.9).86.56 3 layers -#4 22.6 (.75).9 (.8) 28-T 5. (4.9).9.56 none --- Note: mm =.394 in.; Numbers outside parenteses are te design values; numbers inside are te actual values. In order to provide coninement troug te joint, Specimen 7-3T44 [7] was detailed wit te joint oops as per te ACI requirements. As sown in Fig. 3, te joint o Specimen 7-3T44 was reinorced wit tree layers o double #4 oops wit crossties. Te joint oop reinorcement ratio ρ o Specimen 7-3T44 was as ig as 2.44% and its spacing was 97 mm (Table 2). Te Specimens 7-3T4, 7-2T5, and 7-T55 [8] were intended or testing te eectiveness o oop detailing based on te concept o sear resistance. Tose specimens ad larger dimension tan tat o Specimen 7-3T44 (Fig. 3), but teir joint oop ratios were only about a tird o Specimen 7-3T44 [column (7) o Table 2]. Te oop details o Specimen 7-3T4 conormed to te ACI 38-2 Code [2]. Specimen 7-3T4 was constructed using tree layers o #4 oops wit crossties at te joint (Fig. 5
3). However, te strict detailing rules o joint oops wit te purpose o coninement were alleviated or Specimens 7-2T5 and 7-T55. Te joint o Specimen 7-2T5 was built using two layers o #5 oops witout crosstie (Fig. 3). Furtermore, two set o #5 oops, unctioning as a tension tie, were grouped into te middle o joint o Specimen 7-T55 (Fig. 3). It is commonly believed tat te elastic ties can maintain te integrity o te members under severe cyclic loading caused by eartquakes. Tereore, te amount o joint oops o te Specimens 7-3T4, 7-2T5, and 7-T55 was designed to remain in elastic range or tension tie during tests according to te SST model. Te required orizontal tie orce can be estimated as γ u, and tese specimens were provided wit barely enoug joint oops, i.e. A / γ, (Table 2). Specimen 28-3T4 [8] was constructed using tree layers o #4 oops witout crossties at te joint (Fig. 3). Te strict detailing rules o joint oops wit te purpose o coninement were alleviated, and te normal strengt concrete was used or Specimen 28-3T4. Tis is to ceck te applicability o te SST design pilosopy to te exterior joints using normal strengt concrete. Specimen 28-T [8] is a lower bound unit, wic ad barely enoug joint strengt ( u / SST. 9 ) and no joint oop (Table 2). From te perspective o te SST model, te ACI 38-2 Code [2] overestimates te sear strengt o exterior joints. It is noted tat te design joint sear orce is approximately a al o te ACI value ( u / ACI. 56 ; Table 2). Horizontal load was applied wit an actuator using displacement control as sown in Fig. 2. Figure 4 presents te loading istory o tis test program. t y j u Drit Angle (%) 8 6 4 2-2 -4-6 -8 - Pull.25.5 Pus 2 4 6 8 Cycle Fig. 4 Loading istory A complete description o te test program can be ound in te Reerence 9. DISCUSSION OF TEST RESULTS Plots o te applied load versus te drit ratio or all specimens are sown in Fig. 5, were te drit ratio is deined as te delection o te load point divided by te distance between te load point and te column center line. Te curves o te joint orce j versus te joint sear deormation γ j are also plotted in Fig. 5, were j was calculated using Eq. () and γ j was measured by gauges. 6
3 5 7-3T44-5 3 5 7-3T4 j γ j - j -5 3 5 7-2T5 γ j - j -5 3 5 7 -T55 γ j - j -5 4 2 28-3T4 γ j µ = 9 - j -2 4 2 µ = 9 28 - T γ j - j -2 - γ j -4-2 -8-4 4 8 2 DRIFT RATIO (%) Fig. 5 Load versus delection response o specimens Te test results on strengt and ductility are revealed in Table 3. Te measured joint strengt j, test was determined rom te peak applied load P max using Eq. (). Te displacement ductility µ is deined as max / y corresponding to te measured orizontal displacement at.75 strengt o te beam., were max is te orizontal displacement at te ree end o te beam P max. Te yield displacements y or all test units were calculated by extrapolating M n, linearly to M n, were M n is te nominal lexural 7
Table 3 Test results Test results Comparisons Strengt Ductility Dissipated Hoop Sear Strengt Specimen energy Failure P max test P n, calc µ y to 8% drit mode At y test test kn kn kn mm kj γ test SST ACI () (2) (3) (4) (5) (6) (7) (8) (9) () () 7-3T44 25 65 69 24 8.7 267 BF.69.99.69 7-3T4 24 9 24 7. 269 BF.88.9.63 7-2T5 224 62 9 24 7. 255 BF.94.92.66 7-T55 27 26 89 23 7.3 26 BF.97.93.67 28-3T4 33 29 27 8 9.2 32 BF.66..72 28-T 276 38 27 9 6.6 23 BF-JS.98.66 Note: kn =.2248 kip; mm =.394 in.; Failure mode BF means te lexural ailure o beam inging, and BF-JS means te joint sear ailure ater beam inging. Te ailure modes o te test specimens were classiied into BF and BF-JS (Table 3). Te term o BF designates te beam lexural ailures due to te buckling o te beam compression bars. Te classiication o BF-JS means te joint sear ailure ater te development o te beam lexural inge. Te occurrence o te beam bar buckling and te distortion o te joint sear deormation are sown in Fig. 5. Potograps o tese two dierent modes o damaged specimens at te conclusion o te tests are presented in Fig. 5. Importance o Sear Strengt Specimen 28-T was detailed witout any orizontal reinorcement in te joint (Fig. 3). However, suicient sear strengt was provided or te joint o Specimen 28-T according to te SST model. Altoug ailed in joint, satisactory ysteretic response was obtained or te Specimen 28-T (Fig. 5), and te displacement ductility µ can reac a value o 6.6 (Table 3). Tis observation indicates tat designing te joint wit suicient sear strengt will ensure a certain level o perormance even witout joint reinorcement. However, it sould be noted tat te axial compressive load on te columns during te tests was very small (Fig. 2). Wit a ig axial load present, buckling o te longitudinal column bars would ave been more likely. As sown in Table 3, te strengt ratios test / SST are close to one, and te ailure mode contained te type o BF-JS. Tis correlation gives evidence tat te joint sear strengt is crucial or seismic beavior o beam-column joint and tat te joint strengt can be accurately predicted by te SST model or te joints using normal or ig strengt concrete. On te oter and, te strengt ratios test / ACI are always less tan one despite te occurrence o joint ailure (Table 3). Tis indicates tat te ACI 38-2 Code [2] overestimates te sear strengt o te exterior beam-column joints. Eect o Coninement Te Specimens 7-3T4, 7-2T5, and 7-T55 sared te same properties except or te joint oops. Te detailing o te joint oops or Specimen 7-3T4 ollowed te ACI strict requirements. However in Specimen 7-T55, te crosstie was removed and te vertical oop spacing was increased to 3 mm or te joint (Fig. 3). In disregard o te breakdown on coninement eect, tese specimens possessed similar seismic beavior. Tis can be examined troug teir ysteretic curves in Fig. 5 and oter indexes, suc as strengt, ductility, energy dissipation and ailure mode, sown in Table 3. 8
Te similarities in seismic beavior among tese units imply tat te joint oop plays no role in conining concrete core. Te beneicial eect o coninement by transverse reinorcement on te seismic beavior o beamcolumn joint was not ound in tis study. Te increase in strengt and ductility o concrete conined by reinorcement is observed or te axially-loaded columns or te beams under lexure, were te concrete deorms under te plane-remaining-plane restriction. However, te beam-column joint is a region o ig sear, tus te joint deormation is govern by te Mor s compatibility in stead o te Bernoulli s compatibility. In consequence, te concrete strengt witin te joint sould be described by te sotening penomenon [, ]. Te joint oop sould be viewed as crack-controlled steel and not as concrete-conining reinorcement. Tereore te adding o joint oop is to retard te deterioration o concrete strengt and not to enance te concrete strengt. Te crack-controlled reinorcement requires less amount o steel and wider spacing or detailing. It is wortwile to point out tat Specimen 7-3T4 ad te same ailure mode o beam inging as Specimen 7-3T44 (Fig. 5). However, te amount o joint oop o Specimen 7-3T4 is only a al o tat witin Specimen 7-3T44. Te joint oop ratios ρ / ρ, ACI o Specimens 7-3T4 and 7-3T44 are.46 and.9, respectively (Table 2). Tis reveals tat te ACI requirement on te amount o joint oop is unnecessary. Eect o Tension Tie Altoug varied in joint oops, te Specimens 7-3T4, 7-2T5, and 7-T55 possessed similar ysteretic beavior as presented in Fig. 5. Among tose canges in joint oops, te eects o tension tie were careully maintained in te perspective o SST model, sown as A t y /γ u in Table 2. Altering te joint oops and not disturbing te eect o tension tie can preserve te seismic beavior o beam-column joints, wic means te eect o tension tie is te key role o joint oop in seismic resistance. Figure 6 presents te measured strains in te joint oops or Specimens 7-3T44, in wic gages and 2 measured te strains including eects o tension tie and gages 3 and 4 measured only te eect o crack control. In general, te strain readings o gages and 2 are larger tan tose o gages 3 and 4. As sown in Fig. 6, te readings o gages and 2 increase rapidly and in proportion wit te growt o joint sear j or drit angle less tan %. Aterwards gages and 2 gained strains slowly due to joint deormation and mild increase in j due to strain ardening o beam bars. Te readings o gages 3 and 4 increased gradually wit te expansion o joint [Fig. 6(b)]. 9
a a - 3 4 b b + Section a-a 2 Section b-b (a) Location o gages ε ε y -8-4 4 8 Drit Angle (%) (b) Specimen 7-3T44 Fig. 6 Measured strain in te joint oops or Specimens 7-3T44 2 3 4 Te joint oops o Specimens 7-3T4, 7-2T5, and 7-T55 were designed as tension tie according to SST model and kept in elastic range or sear transerring. As sown in Fig. 7, te strains in te joint oops o tese specimens were kept airly well in elastic range [(a)-(c)]. It sould be noted tat comparable strain readings were observed among specimens wit dierent detailing or tese specimens in Fig. 7. Tis is indicative tat te major caracteristic o joint oops can be captured by viewing tem as tension tie. It is also noted tat te SST model can predict te requirement o tension tie reasonably well using te equation o A t y = γ u, wic corresponds one tird o te ACI requirement or tese Specimens (Table 2). Drit angle (%).5 2 4 6 8 (a) 7-3T4 (b) 7-2T5 (c) 7-T55 Gage location 2 3 4 5 6 7 8 ε ε y Fig. 7 Measured strain in te joint oops Eect o Crack Control It was observed tat te Specimens 7-3T4, 7-2T5, and 7-T55 were ailed by te buckling o compression bars in beam inges (Fig. 5), and te yielding o joint oops o tese specimens was eectively delayed by adding suicient amount o transverse steel (Fig. 7). Te actor o joint oop yielding as a decisive inluence on te ailure modes o te beam-column joints. It is believed tat te early yielding o joint oop provides no reliable mecanism to restrain te deterioration o te joint
concrete and causes te joint ailure at larger displacement levels. To design te joints wit te elastic joint oops is appealing or te special moment resisting rames, because te elastic ties can maintain te integrity o te members under severe cyclic loading caused by eartquakes. Te dierent detailing in joint oops or Specimens 7-3T4, 7-2T5, and 7-T55 preserved te equivalent tie action but caused sligt deviation on te eect o crack control among specimens. Te crack-controlled reinorcement would be more eective wit smaller spacing. Among te tree specimens, Specimen 7-3T4 owned te best detailing in te aspect o crack control, ollowed by Specimen 7-2T5, wit Specimen 7-T55 olding te poorest detailing. By comparing te j versus γ j curves in Fig. 5, Specimen 7-3T4 possessed a straigt linear relationsip, and Specimen 7-T55 displayed a wider-banded linearity. As sown in Figs. 7(a) to 7(c), Specimen 7-3T4 experienced te least strains in te joint oops. Above argument can also be veriied troug te measurement o crack widt. Figure 8 presents te measurement o crack widts in te joint regions. As can be seen, Specimen 7-3T4 yields te smallest crack widt, ollowed by Specimen 7-2T5, wit Specimen 7-T55 giving te largest crack widt. Max. Widt o Diagonal Crack (mm)..5. 7-T55 7-2T5 7-3T4 2 4 6 8 Drit Angle (%) Fig. 8 Comparison o joint crack widt Altoug te crack-controlled ability o Specimen 7-T55 was sown up as inerior to tat o Specimen 7-3T4, but it is o interest to note tat Specimen 7-T55 is superior to Specimen 28-T (Fig. 5). Tis indicates tat te amount o joint oop is more important tan te joint oop spacing i te vertical spacing is limited witin 3 mm. Moreover as or seismic concern, Specimen 7-T55 sould be judged as eective as Specimen 7-3T4 troug comparison o teir strengt, ductility, energy dissipation, and ailure modes (Table 3). In te ligt o te test results, it is tus concluded tat te vertical spacing o joint oop up to 3 mm is an acceptable range. CONCLUSIONS Based on te cyclic load tests o 6 exterior beam-column joints, and witin te limitations o tose test data, te ollowing conclusions are made:. Te joint oops are ound to act as a tension tie as well as to constrain te crack widt. Te current ACI requirements, viewing te joint oop as conining te concrete core, are unnecessary and very diicult or construction. Te test results indicate tat a lesser amount o oop reinorcement wit wider vertical spacing up to 3 mm could be used witout signiicantly aecting te perormance o joints.
2. Witout ig axial load in te column, a beam-column joint witout oop can possess satisactory seismic beavior, as long as te joint is provided wit adequate sear strengt according to te SST model. 3. Te deterioration o beam-column joint under displacement reversals could be eectively restrained by te elastic joint oops. For beam-column joints, were tere is a need or sustained strengt under deormation reversals, it is recommended to design te joints wit adequate sear strengt and wit suicient amount o oops to remain in elastic range under eartquake loading. Te required amount o oops can be determined by viewing joint oops as tension tie and using te equation o A t y = γ u according to SST model. 4. Te SST design pilosopy is equally applicable to te seismic joints using bot te normal and te ig strengt concrete. ACKNOWLEDGMENTS Te autors are grateul to te National Science Council o te Republic o Cina or inancial support under Projects NSC 88-22-E--, NSC 89-22-E--, NSC 9-22-E--55, and NSC 9-28-E--3. REFERENCES. NZS 3:995, Concrete Structures Standard, NZS 3: Part, 256 pp.; Commentary NZS 3: part 2, 264 pp., Standards Association o New Zealand, Wellington, 995. 2. ACI Committee 38, Building Code Requirements or Structural Concrete (ACI 38-2) and Commentary (ACI 38R-2), American Concrete Institute, Farmington Hills, 22, 443 pp. 3. Hwang, S. J., and Lee, H. J., Analytical Model or Predicting Sear Strengts o Exterior Reinorced Concrete Beam-Column Joints or Seismic Resistance, ACI Structural Journal, ol. 96, No. 5, September-October 999, pp. 846-857. 4. Hwang, S. J., and Lee, H. J., Analytical Model or Predicting Sear Strengts o Interior Reinorced Concrete Beam-Column Joints or Seismic Resistance, ACI Structural Journal, ol. 97, No., January-February 2, pp. 35-44. 5. Hwang, S. J., and Lee, H. J., Strengt Prediction or Discontinuity Regions by Sotened Strutand-Tie Model, Journal o Structural Engineering, ASCE, ol. 28, No. 2, December, 22, pp. 59-526. 6. Comité Euro-International du Beton (CEB)-Fédération International de la Precontrainte (FIP). (993). Model Code 99, 993, (MC9), Tomas Telord, London. 7. Liao, D. F. Sear Strengt o Reinorced Concrete Beam-Column Joints or Seismic Resistance, Master Tesis, Department o Construction Engineering, National Taiwan University o Science and Tecnology, 999. (in Cinese) 8. Wang, K. C. Seismic Design and Detailing o Reinorced Concrete Exterior Beam- Column Joints, Master Tesis, Department o Construction Engineering, National Taiwan University o Science and Tecnology, 22. (in Cinese) 9. Hwang, S. J., Lee, H. J., Liao, D. F., Wang, K. C., and Tsai, S. H., Role o Hoops on Sear Strengt o Reinorced Concrete Beam-Column Joints or Seismic Resistance, submitted to ACI Structural Journal, 24.. eccio, F. J., and Collins, M. P., Compression Response o Cracked Reinorced Concrete, Journal o Structural Engineering, ASCE, ol. 9, No. 2, December 993, pp. 359-36.. Zang, L. X. B., and Hsu, T. T. C., Beavior and Analysis o MPa Concrete Membrane Elements, Journal o Structural Engineering, ASCE, ol. 24, No., January 998, pp. 24-34. 2