STRUCTURAL BEHAVIOR OF R/C DEEP BEAM WITH HEADED LONGITUDINAL REINFORCEMENTS

13 th World Conferene on Earthquake Engineering anouver, B.C., Canada August 1-6, 24 Paper No. 58 STRUCTURAL BEHAIOR OF R/C DEEP BEAM WITH HEADED LONGITUDINAL REINFORCEMENTS Soo-Yeon SEO 1, Seung-Joe YOON 1, Woo-Jin LEE 2 SUMMARY This study is aimed to investigate whether the standard hook anhorage designed aording to ACI 318-2 at the ends of the positive moment region an be replaed with mehanial anhorage using steel head and to estimate the shear behavior of deep beams. Eight deep beam speimens with headed reinforements for mehanial anhorage and two general deep beam speimens with standard hook are designed. Main variables onsidered in the test are the anhorage type and shear span-to-overall height ratio. Two point stati loads applied to the speimen and displaements are measured to ollapse of the speimen. From the study, it was found that the speimen with headed reinforements as a mehanial anhorage showed better load resistane apaity when it was designed to satisfy the development length requirement of the ACI ode. From this, it an be expeted that the headed reinforement has strutural apaity ompatible to the hooked bar when it is used as longitudinal reinforements in RC deep beam design. In prediting shear strength of deep beam, Strut-and-Tie Model of Appendix A in ACI 318-2 was onservative and showed lowest standard deviation among several design methods. INTRODUCTION Reinfored onrete deep beam is defined that members with lear spans in equal or less than four times the overall member depth or regions of beams that are loaded on one fae with onentrated loads within twie the member depth from the support and supported on the opposite fae so that ompression struts an be developed between the loads and supports. In ase of the building system omposed of bearing wall and moment frame as upper and lower part, respetively, the load of upper part is transferred to olumn of another lane through the transfer girder. Therefore, the transfer girder is to be under high shear stress so that the depth of it is to be deeper. For this kind of beam, reently, the importane regarding the bonding of reinforement and its anhor has been inreased beause high stress in aordane with the demand for the bulky and high-rise building is developed and transferred into onrete struture, whih maximizes the onentrated stress at anhorage. In the reinfored onrete, the standard hook used in exterior beam-olumn joint is onsidered as an effetive method for proper fabriation and onstrution to satisfy the requirement of design ode that 1 Professor, Department of Arhitetural Engineering at Cungju National University, Chungju, Korea 2 Researher, Institute of Industrial Siene/Tehnology at Cungju National University, Chungju, Korea

dutile tension failure instead of onrete failure should govern the over behavior of a member. However, standard hook tends to derease the onstrution and eonomi effiieny due to the ongestion of reinforements in an anhorage region. Reently the study on alternative mehanial anhorage for the standard hook in exterior beam-olumn joint and deep beam has been presented 1,2). This study is to investigate whether the standard hook anhorage designed aording to ACI 318-2 3) at the ends of the positive moment region an be replaed with mehanial anhorage using steel head and to estimate the shear behavior of deep beams. Based on the results from the monotoni loading test of deep beam, the shear design proedures ontained in the ACI 318-99 11.8 4), Strut-and-Tie model of ACI 318-2 and CSA A23.3-94 5) are evaluated. EXPERIMENTAL PROGRAM Test speimens Ten speimens are planned aording to experimental variables: anhorage type of longitudinal reinforement, shear span-to-overall height a/h, vertial shear reinforement ratios ρ v and horizontal shear reinforement ratios ρ h. Table 1 and Fig. 1 show the detail of all speimens that have retangular ross setion with size of 16mm 6mm 25mm. Speimens are lassified as two groups aording to the anhorage type of longitudinal reinforement. The first one (A) is the group designed to have longitudinal reinforements with 9-degree hooks and the seond group (M) is with mehanial anhorage. The steel head devie shown in Fig. 2 is applied to the speimen as a mehanial devie ompatible to the hook anhorage. In the speimen details, vertial shear reinforement is designed as losed stirrups type of 1mm deformed bars, while the horizontal shear reinforement is straight type of 1mm deformed bars. All speimens are planned to have same onrete ompressive of 4MPa. Speime n a/h Longitudinal Reinforement Anhorage ρ s Type (%) Table 1 Detail of speimens S h (mm) Shear reinforement ρ h (%) S v (mm) A5FF.5 A1FF 1. 9 hook M5FF.5 (a) standard 9-degree hook 11.8 M1FF 1. 11.8 M5NN.5.89 M1NN 1. Mehanial M5FN.5 anhorage M1FN 1... M5NF.5 M1NF 1... 11.8 (b) Mehanial anhorage * First letter states anhor type of reinforement (A; ACI standard hook, M; mehanial anhorage). Number is shear span-to-height ratio a/h. Letters after number means web reinforement detail type Test setup and instrumentation All beams were tested to failure under two-point symmetri top loading as shown in Fig. 3. ertial defletions were monitored by the LDTs. At eah load inrement, the test data were aptured by a data logger and automatially stored. The strains of reinforements were measured using 5mm strain gages. Until the first rak ourred, load was applied by keeping inrements of 2kN. Subsequently, the load ρ v (%)

inrements were inreased to 4kN eah after the rak. Applied loads and support reations were transmitted to the speimens by means of 15 16 3mm steel plates. A5FF, A1FF M5FF, M1FF M5NF, M1NF M5FN, M1FN M5NN, M1NN Fig. 1 Reinforement details of experimental deep beams Fig. 2 Details of mehanial anhorage Fig. 3 Speimen test setup

Name Measured shear strength (kn) Table 2 Failure modes and experimental results Measured Measured strain at Shear stress δ u δ r (N/mm 2 u ( 1-6) ) (mm) (mm) Slope of diagonal rak ( ) Failure Mode u, r v u v r ε s ε h ε v A5FF 591 171 6.16 1.78 5 21 866 48 292 64 Bearing failure A1FF 458 161 4.77 1.68 97 33 2929 9812 9521 43 Diagonal-splitting M5FF 629 23 6.55 2.4 69 22 1282 7259 1258 6 Bearing failure M1FF 58 161 5.29 1.68 131 44 327 2511 3276 48 Shear-ompression M5NN 376 132 3.92 1.38 44 17 172 - - 65 Bearing failure M1NN 329 141 3.43 1.47 65 31 175 - - 5 Diagonal-splitting M5FN 683 294 7.11 3.6 59 24 1589 8977-7 Shear-ompression M1FN 371 156 3.86 1.63 73 28 1794 2928-46 Shear-ompression M5NF 494 22 5.15 2.29 73 26 138-122 6 Diagonal-splitting M1NF 422 166 4.4 1.73 78 3 2262-8586 43 Diagonal-splitting Where u is shear strength at peak point and r is shear strength at initial diagonal rak; v u is shear stresses at peak point and v r is shear stress at initial diagonal rak; δ u, δ r are defletions at u and r, respetively; ε s, ε h, ε v are strains of main flexural reinforement, horizontal shear reinforement and vertial shear reinforement, respetively. BEHAIOR OF TEST SPECIMENS Load-displaement relationship Fig. 4 shows the mid-span defletions of speimens with different shear span-to-overall height ratio a/h. All speimens with the same a/h had a similar initial stiffness but different after diagonal rak. The initial diagonal raks were found at 32%-42% of ultimate shear strength in the speimen with a/h of.5, while at 34%~48% in speimen with a/h of 1.. The mid-span defletions dereased with an inreasing amount of web reinforement. On omparing dutility among all speimens, speimens M5FF and M1FF whih had both vertial and horizontal shear reinforement for rak-ontrol aording to ACI 318-2 Appendix A showed more dutile behavior after yield than others. After diagonal rak, the shear stiffness of the beams without web reinforement dropped signifiantly. 14 M5FF M5FN 12 M5NF M5NN 1 14 M1FF M1FN 12 M1NF M1NN 1 8 6 8 6 4 4 2 2 2 4 6 8 1 12 14 16 2 4 6 8 1 12 14 16 Mid- span defletion (m) Mid- span Defletion (m) (a) Speimen with a/h of.5 (b) Speimens with a/h of 1.

Fig. 4 Load-defletion urve of speimens with mehanial anhorage Load inrement patterns of eah speimen were similar until ultimate load without the influene of anhorage type. In ase of a/h of 1., however, speimens with mehanial anhorage showed more dutile behavior than speimen with ACI 9-degree standard hook after ultimate strength. At ultimate strength, speimen H5FF with mehanial anhorage showed 6.5% higher strength than speimen A5FF with 9-degree standard hook. In a/h of 1., similarly, the strength of speimen M1FF with mehanial anhorage was 1% higher than that of A1FF. On the viewpoint of initial shear rak formation, there were not severe differenes between speimens with mehanial and hook anhorage in a/h of 1.. In ase of a/d of.5, however, the formation of initial shear rak was delayed by using the mehanial anhorage. This result is supposed to be originated from the strong anhorage apaity of mehanial anhor. From this, it an be onluded that the mehanial anhorage has high anhorage apaity and an suffiiently be applied to deep beam when it satisfy the development length requirement of the ACI. 14 14 12 Wi t h mehani al anhor age 12 Wi th mehani al anhor age 1 1 8 6 4 wi t h 9- degr ee st andar d hook 8 6 4 Wi t h 9- degr ee st andar d hook 2 2 2 4 6 8 1 12 14 16 Mid- span defletion (m) 2 4 6 8 1 12 14 16 Mid- span defletion (m) (a) Speimen with a/h of.5 (b) Speimens with a/h of 1. Fig. 5 Comparison of load-defletion urve for speimens with different anhorage type Crak patterns and Failure modes Fig. 6 shows the rak patterns at failure for all 1 deep beams together as well as the loads at whih eah rak was first observed. Failure of all speimens took plae only after the primary diagonal rak developed fully between the load and support region, and after yielding of main tension reinforement. Primary diagonal rak parallel to the axis of the ompression struts was observed for all speimens. It was found that the speimen with both vertial and horizontal reinforements had more sattered rak pattern than the speimen with either horizontal or vertial reinforement. The speimen with mehanial anhorage showed on failure of onrete that is one of typial failure pattern of anhor around viinity of anhorage. The final failure mode in this experiment ould be lassified into three types of failure pattern; diagonal splitting failure, ompression strut failure and shear ompression failure. In the speimen M1NN, as a the diagonal splitting failure pattern, shear raks onneted with loading and supporting point ourred and expanded to failure making a booming sound. The ompression strut failure was found in the speimen M5FN in whih ompression struts were formed due to several diagonal raks and finally developed to the failure of at upper or lower part of strut. The speimen M5FF showed the loal ompression failure ausing ollapse of the speimen at around the loading point.

M5FF M1FF M5NN M1NN M5FN M1FN M5NF M1NF Fig. 6 Crak patterns at failure Effet of shear span-to-overall height ratio Fig. 7 shows the load-defletion urves and the load-strain urves of longitudinal reinforement for speimens with different a/h. The ultimate shear strength of tested speimen dereased when a/h inreased as shown Fig. 7. From the omparison of A-series (A5FF, A1FF) and M-series (M5FF, M1FF) with both horizontal and vertial shear reinforements, it was found that the defletion and strain inreased from 65 to 94% and from 136 to 24% with inrement of a/h, respetively. Speimens M5NN and M1NN without web reinforement showed inreased defletion and strain of 25% and 63%, respetively at a/h of 1.. In speimen M5FN and M1FN with horizontal shear reinforement only, however, the defletion was dereased about 2.4% and the strain of longitudinal reinforement inreased about 13% when a/h inreased. The omparison of speimen M5NF and M1NF speimen with vertial shear reinforement only showed that the defletion and the strain inreased about 5% and 118% with the

inrement of a/h, respetively In addition, with a/h inreasing, the tied-arh ation beomes less effetive beause of the redued angle. 14 A5 FF A1FF 14 A5 FF A1 FF 14 M5FF M1FF 14 M5FF M1FF 12 12 12 12 1 1 1 1 8 6 8 6 8 6 8 6 4 4 4 4 2 2 2 2 2 4 6 8 1 12 14 16 18 5 1 15 2 25 3 35 Mid- span defletion (mm ) Strain (x1-6 ) (a) Speimens with 9-degree hooks 2 4 6 8 1 12 14 16 18 5 1 15 2 25 3 35 Mid- span defletion (mm) Strain (x1-6 ) (b) Speimens with mehanial anhorages 14 M5NN M1NN 14 M5NN M1NN 14 M5FN M1FN 14 M5FN M1FN 12 12 12 12 1 1 1 1 8 6 8 6 8 6 8 6 4 4 4 4 2 2 2 2 2 4 6 8 1 12 14 16 18 5 1 15 2 25 3 35 2 4 6 8 1 12 14 16 18 5 1 15 2 25 3 35 Mid- span defletion (mm) Stra in (x1-6 ) Mid- span defletion (mm ) Strain (x1-6 ) () Speimens without web reinforements (d) Speimens with horizontal reinforements only 14 M5NF M1NF 14 M5NF M1NF 12 12 1 1 8 6 8 6 4 4 2 2 2 4 6 8 1 12 14 16 18 5 1 15 2 25 3 35 Strain (x1-6 ) Mid- span defletion (mm ) (e) Speimens with vertial reinforements only Fig. 7 Load-defletion and strain urves with variable a/h Strain in web reinforements Strains measured in the horizontal and vertial shear reinforements at the ritial setion were shown in from Fig. 8 to Fig. 11. From Fig. 8 and Fig. 1, it an be seen that there are not lear differenes of strains between horizontal and vertial shear reinforements before the diagonal rak. However, after the rak, the strain of horizontal reinforement rapidly inreased while vertial reinforement showed a little extension of strain. This means that the ontribution of horizontal reinforement is to be high in speimens with a/h of.5 after rak. In speimens A1FF, M1FF with a/h of 1, the serious differene of

strain between the horizontal and vertial reinforement was not found until failure. From this, it an be onluded that both two reinforements develop similar ontribution to the shear at a/h of 1. 12 12 1 1 8 6 4 8 6 4 2 Horizontal reinforement ertial reinforement 2 4 6 8 1 12 14 16 2 Horizontal reinforement ertial reinforement 2 4 6 8 1 12 14 16 Strain (x1-6 ) Strain (x1-6 ) Fig. 8 Load-strain urve of speimen A5FF Fig. 9 Load-strain urve of speimen A1FF 14 12 1 1 8 8 6 4 6 4 2 H o rizo ntal shear reinfor em ent ertial shear reinforement 2 4 6 8 1 12 14 16 2 Horizontal shear reinforement erti al shear reinfor em ent 2 4 6 8 1 12 14 16 Strain (x1-6 ) Stra in (x1-6 ) Fig. 1 Load-strain urve of speimen M5FF Fig. 11 Load-strain urve of speimen M1FF EALUATION ON CODE DESIGN FORMULAS FOR SHEAR ACI 318-99 Setion 11.8 4) In ACI 318-99 Code, the setional shear strength of deep flexural member is alulated by ombining the ontributions of both onrete and distributed shear reinforements. Ultimate shear strength by onrete and reinforement are shown in from Eq. (1) to Eq. (3). The onrete ontribution an be ounted by Eq. (1) or Eq. (2). = 2 f ' b d (psi, in.) (Eq. 11-28) (1) M u ud = 3.5 2.5 1.9 f ' 25 w bwd 6 f ' bwd ud + ρ M (psi, in.) (Eq. 11-29) (2) u w where 3.5-2.59(M u / u d) is to be kept less than or equal to 2.5; and f = speified ompressive strength of

onrete; b w = web width; A s = area of nonprestressed tension reinforement; d =distane from extreme ompression fiber to entroid of longitudinal tension reinforement; u =fatored shear fore at ritial setion; ρ = ratio of tension reinforement; l n = lear span; a = shear span; M u = fatored moment ourring simultaneously with u at the ritial setion. The use of shear reinforement is required whenever the fatored shear fore at the ritial setion exeeds the shear strength by onrete. The ontribution from the shear reinforement is omputed with Eq. (3). s A = s v l n 1 + d 12 + A s vh l n 11 d 12 f y d (psi, in.) (Eq. 11-3) (3) where A v = area of shear reinforement perpendiular to flexural tension reinforement within a distane s; A vh = area of shear reinforement parallel to flexural tension reinforement within a distane s 2. The ACI 318-99 Code defines an upper limit for the shear strength of deep flexural members as shown in Eq. (4). 8 f' bwd for ln / d < 2 = 2 l (Eq. 11-27) (4) n n 1 + f' bwd for 2 ln / d 5 3 d By virtue of study of Gerardo Aguilar 1) and Kang-Hai Tan 6,7), it has been found that the role of horizontal steel ontribution is overestimated in the formulas for deep beam design in ACI 318-99 Code. Fig. 12 Desription of Strut-and-Tie Model Fig. 13 Desription of Canadian Code Appendix A of ACI 318-2 Building Code 3) Appendix A of ACI 318-2 ode provides new approahes to the shear design of deep beam. In the Strut-and-Tie Model (STM) approah, the flow of fores or stresses within the member is represented by means of a truss like Fig. 12. STM onsist of the struts, ties and nodal zones. The permitted stress of all struts, ties and nodal zones shall not exeed the limited value.

The effetive ompressive strength of the onrete in strut and nodal zone shall be taken as Eq. (5) and Eq. (6). Strut : Nodal zone : f f u u =.85β f ' (psi) (Eq.(A-3)) (5) s.85β n f = ' (psi) (Eq.(A-8)) (6) where the value β s and β n range.4 1. and.6 1., respetively. In ase that onrete ompressive strength is less than 41MPa, the minimum steel quantity for preventing rak an be inreased 25%, if it is satisfied with a minimum amount of the grid reinforement rossing the strut, or required steel in same diretion as shown in Eq. (7). A bs si i sin γ.3 (Eq.(A-4)) (7) where A si is area of surfae reinforement in the i th layer rossing a strut and b is width of beam and S i is spaing of reinforement in the i th layer adjaent to the surfae of the member. Canadian CSA A23.3-94 5) In Canadian CSA Code, STM is reommended as a method for shear design of deep beam. Unlike the ACI Code, the 1984 CSA Code uses the onept of shear span-to-effetive depth ratio a/d rather than the effetive span-to-depth ratio l n /d for deep beam design. The CSA Code permits two alternative design methods for shear, the simplified method and the general method. The latter is based primarily on the Modified Compression Field (MCF) theory developed by Collins et. Al 8). The ompressive stress in the inlined onrete strut shall be based on Eq. (8). i f u = f.8 + 17ε ' 1.85 f ' (MPa) (CSA 11.3) (8) 2 ε1 = ε + ( ε +.2) ot α (CSA11.31) (9) s s s where ε 1 = the prinipal tensile strain in raked onrete due to fatored loads; α s = the angle between the strut and the adjoining tensile ties; ε s = the tensile strain in the tensile tie inlined at as to the ompressive strut. Comparison of test results with design formulas A omparison between the measured and alulated shear strength for the tested speimens was arried out. The odes onsidered for the omparison are the ACI 318-99, the Appendix A STM of ACI 318-2 and the CSA A23.3-94. The material safety fators for onrete and steel reinforement have been set to unity for omparison purpose. Table 3 and Fig. 14 show the omparison. The shear design proedures of the ACI 318-99 and STM of the ACI 318-2 underestimated the shear strength of deep beam, espeially showed lowest predited shear strength for the speimen with horizontal shear reinforement only. In the shear strength predition of deep beams, the ACI 318-99 has the lowest average mean of.65 among the three methods. Using the shear design method of CSA, it was shown that most lose predition ould be ahieved. In ase of the speimen without web reinforement, however, CSA Code overestimated shear

strength by inluding the effet of web reinforements that do not exist and onsidering maximized effetive stress of strut. The ratio between results of STM and test, STM / TEST is ranged at an average mean of.74 and the standard deviation of.1. This means that STM is reommended as a most desirable method beause it has lowest standard deviation although its predited shear strength is relatively higher than that of ACI 318-99. Speimen Table 3 Summary of preditions for ultimate shear strength of deep beams TEST (kn) ACI (kn) STM (kn) CSA (kn) ACI TEST STM TEST CSA TEST A5FF 591 348 431 569.59.73.96 A1FF 458 348 39 399.76.67.87 H5FF 629 348 431 569.55.69.9 H1FF 58 348 39 399.69.61.79 H5NN 376 221 345 521.59.92 1.39 H1NN 329 193 248 472.59.75 1.43 H5FN 683 348 431 569.51.63.83 H1FN 371 328 39 399.88.83 1.8 H5NF 494 39 431 569.63.87 1.15 H1NF 422 283 39 399.67.73.95 MEAN.65.74 1.4 STDE.11.1.23 CODE / test 1.5 1.25 1..75.5 Average Mean Standard Deviation Conservative Unonservative CODE / TEST 2. 1.5 1. ACI 318-99 ACI STM CSA 1994 without shear reinforement.5.25 with horizontal and vertial shear reinforement with vertial or horizontal shear reinforement only. ACI 318-99 ACI STM CSA. Fig. 14 Comparison of shear strength predition by different methods CONCLUSION 1. On omparing the ase with 9-degree hook anhorage, the speimen with headed reinforements as a mehanial anhorage showed better load resistane apaity when it was designed to satisfy the development length requirement of the ACI ode. 2. The deep beam with the shear reinforements satisfying the requirement of equation (A-4) of ACI 318-2 Code showed effetive behavior for rak ontrol and dutile behavior after yield. In ase of the speimen with only one diretional shear reinforement or nothing, however, it was shown that

shear strength rapidly dereased after the ultimate shear strength. 3. For most speimens, the load was supported by ompression strut onneting with loading point and bearing point at failure. And it was destroyed after the formation of diagonal rak paralleled with struts showing brittle frature when the diagonal splitting or ompression of strut governed the failure of speimen. 4. In ase of shear span-to-overall height ratio a/h=1, the strains of vertial and horizontal shear reinforement were similar after yield of longitudinal reinforement. But in ase of a/h=.5, horizontal shear reinforement showed higher strain than vertial shear reinforement after formation of initial diagonal raks. From this, it an be found that the horizontal reinforement has higher ontribution than vertial reinforement to the shear strength when the a/h is low. 5. In prediting shear strength of deep beam, Strut-and-Tie Model of Appendix A in ACI 318-2 was onservative and showed lowest standard deviation among several design methods. Therefore, it was judged that STM is a most desirable method for the design of deep beam. REFERENCES 1. Gerardo Aguilar, Adolfo B. Matamoros, Gustavo J. Parra-Montesinos, Julio A. Ramirez and James K. Wight, Experimental evaluation of design proedures for shear strength of deep reinfored onrete beams, ACI Strutural Journal,. 99, No. 4, July-August 22, pp. 539-548 2. John W. allae, Sott W. MConnell, Piush Gupta, and Paul A. Cote., "Use of Headed Reinforement in Beam-Column Joints Subjeted to Earthquake Loads.", ACI Strutural Journal,. 96, No. 5, September-Otober 1998, pp. 59-66 3. ACI Committee 318, Building Code Requirement for Strutural Conrete(318-2) and Commentary (318R-2), Amerian Conrete Institute, 22 4. ACI Committee 318, Building Code Requirement for Strutural Conrete(318-99) and Commentary (318R-99), Amerian Conrete Institute, 1999 5. Canadian Standards Assoiation, "Design of Conrete Strutures A23.3-94", Canadian Standards Assoiation, Rexdale, Ontario, 1994 6. Kang-Hai Tan, Fung-Kew Kong, and Li-Wei Weng, High-Strength Reinfored Conrete Deep and Short Beams: Shear Design Equations in North Amerian and UK Pratie," ACI Strutural Journal,. 95, No.3, May-June 1998, pp. 318~329 7. Kang-Hai Tan, Fung-Kew Kong, Susanto Teng, and Li-Wei Weng, "Effet of Web Reinforement on High-Strength Conrete Deep Beams," ACI Strutural Journal,. 94, No. 5, September-Otober 1997, pp. 572~582 8. ehio, F. J. and Collins, M. P., "Modified Compression-Field Theory for Reinfored Conrete Elements Subjeted to Shear," ACI Strutural Journal,. 83, No. 2, Marh-April 1986, pp. 219~231