BARC/2009/E/026 BARC/2009/E/026

Transcription

1 JOINT MODEL TO SIMULATE INELASTIC SHEAR BEHAVIOR OF POORLY DETAILED EXTERIOR AND INTERIOR BEAM-COLUMN CONNECTIONS REINFORCED WITH DEFORMED BARS UNDER SEISMIC EXCITATIONS by Akanshu Sharma, G.R. Reddy, K.K. Vaze, A.K. Ghosh, H.S. Kushwaha Reator Safety Division, HS&EG and BARC/2009/E/026 BARC/2009/E/026 Rolf Eligehausen Institut für Werkstoffe im Bauwesen, Universität Stuttgart, Germany 2009

2 BARC/2009/E/026 GOVERNMENT OF INDIA ATOMIC ENERGY COMMISSION BARC/2009/E/026 JOINT MODEL TO SIMULATE INELASTIC SHEAR BEHAVIOR OF POORLY DETAILED EXTERIOR AND INTERIOR BEAM-COLUMN CONNECTIONS REINFORCED WITH DEFORMED BARS UNDER SEISMIC EXCITATIONS by Akanshu Sharma, G.R. Reddy, K.K. Vaze, A.K. Ghosh, H.S. Kushwaha Reator Safety Division, HS&EG and Rolf Eligehausen Institut für Werkstoffe im Bauwesen, Universität Stuttgart, Germany BHABHA ATOMIC RESEARCH CENTRE MUMBAI, INDIA 2009

3 BARC/2009/E/026 BIBLIOGRAPHIC DESCRIPTION SHEET FOR TECHNICAL REPORT (as per IS : ) 01 Seurity lassifiation : Unlassified 02 Distribution : External 03 Report status : New 04 Series : BARC External 05 Report type : Tehnial Report 06 Report No. : BARC/2009/E/ Part No. or Volume No. : 08 Contrat No. : 10 Title and subtitle : Joint model to simulate inelasti shear behavior of poorly detailed exterior and interior beam-olumn onnetions reinfored with deformed bars under seismi exitations 11 Collation : 160 p., 6 figs., 1 ill.. 13 Projet No. : 20 Personal author(s) : 1) Akanshu Sharma; G.R. Reddy; K.K. Vaze; A.K. Ghosh; H.S. Kushwaha 2) Rolf Eligehausen 21 Affiliation of author(s) : 1) Reator Safety Division, Bhabha Atomi Researh Centre, Mumbai 2) Institut fuer Werkstoffe im Bauwesen, Universitaet Stuttgart, Germany 22 Corporate author(s) : Bhabha Atomi Researh Centre, Mumbai Originating unit : Reator Safety Division, BARC, Mumbai 24 Sponsor(s) Name : Department of Atomi Energy Type : Government Contd...

4 BARC/2009/E/ Date of submission : November Publiation/Issue date : Deember Publisher/Distributor : Head, Sientifi Information Resoure Division, Bhabha Atomi Researh Centre, Mumbai 42 Form of distribution : Hard opy 50 Language of text : English 51 Language of summary : English, Hindi 52 No. of referenes : 108 refs. 53 Gives data on : 60 Abstrat : A model for prediting the nonlinear shear behaviour of reinfored onrete beamolumn joints based on prinipal stresses reahing limits is proposed. The joint model proposes shear springs for the olumn region and rotational spring for the beam region of the joint. This is based on the atual displaement behaviour of the shear buildings. The spring harateristis are alulated based on well-known prinipal of mehanis using the prinipal stresses as the failure riteria. The model reasonably aurately predits the shear behaviour of the joint and also an onsider the effet of axial loads on the olumn. The model does not need any speial element or speial program for implementation and an be used for nonlinear stati pushover analysis of RC framed strutures giving due onsideration to joint deformations. The model is therefore extremely useful for pratial displaement based analysis of old RC buildings where the joints were not designed and detailed as per urrent odal requirements, invariably making them the weakest link in the struture. The bakground theory, assumptions followed and the omplete formulations for generating the joint harateristis are given in this report. The model is validated with experimental results of tests on exterior and interior beam-olumn onnetions given in the published literature having substandard detailing using deformed bars. 70 Keywords/Desriptors : EARTHQUAKES; REINFORCED CONCRETE; JOINTS; SEISMIC EFFECTS; SHEAR PROPERTIES; TENSILE PROPERTIES; DEFORMATION; FAILURE MODE ANALYSIS; STRUCTURAL BEAMS; NUCLEAR FACILITIES 71 INIS Subjet Category : S22 99 Supplementary elements :

5 JOINT MODEL TO SIMULATE INELASTIC SHEAR BEHAVIOR OF POORLY DETAILED EXTERIOR AND INTERIOR BEAM- COLUMN CONNECTIONS REINFORCED WITH DEFORMED BARS UNDER SEISMIC EXCITATIONS Akanshu Sharma, G.R. Reddy, K.K. Vaze, A.K. Ghosh, H.S. Kushwaha Reator Safety Division, HS&EG Rolf Eligehausen Institut für Werkstoffe im Bauwesen, Universität Stuttgart, Germany Bhabha Atomi Researh Centre Otober 2009

6 Abstrat A model for prediting the nonlinear shear behaviour of reinfored onrete beamolumn joints based on prinipal stresses reahing limits is proposed. The joint model proposes shear springs for the olumn region and rotational spring for the beam region of the joint. This is based on the atual displaement behaviour of the shear buildings. The spring harateristis are alulated based on well-known prinipal of mehanis using the prinipal stresses as the failure riteria. The model reasonably aurately predits the shear behaviour of the joint and also an onsider the effet of axial loads on the olumn. The model does not need any speial element or speial program for implementation and an be used for nonlinear stati pushover analysis of RC framed strutures giving due onsideration to joint deformations. The model is therefore extremely useful for pratial displaement based analysis of old RC buildings where the joints were not designed and detailed as per urrent odal requirements, invariably making them the weakest link in the struture. The bakground theory, assumptions followed and the omplete formulations for generating the joint harateristis are given in this report. The model is validated with experimental results of tests on exterior and interior beam-olumn onnetions given in the published literature having substandard detailing using deformed bars. 2

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8 Aknowledgements The authors would like to aknowledge the help and support of everyone who has diretly or indiretly helped in suessful ompletion of this work. Many thanks to Prof. Dr.-Ing. J. Ožbolt for sharing the bakground information on MASA and fruitful disussions regarding modelling aspets, and for Dr.-Ing. W. Fuhs for his support and enouragement. Speial thanks to Dipl.-Ings Christoph Mahrenholtz, Philipp Mahrenholtz, Josipa Bošnjak, Giovahino Genesio, Goran Periski, Khalil Jebara, Zlatko Bioi, Philipp Grosser, Georg Welz, Christian Kontzi, Anke Wildermuth, Ronald Blohwitz, Walter Berger, Martin Herzog and all other olleagues for their help, friendliness, kindness and support. Many thanks to Mrs. Monika Werner who ould provide almost every tehnial literature needed to arry out this work. A big thanks for the seretarial staff at the IWB, espeially Mrs. Silvia Choynaki, Mrs Bauer, Mrs Baur, Ms Stumpp and Mrs. Regina Jäger for making all the neessary arrangements to arry out the ollaborative researh programme suessfully. 4

9 CONTENTS Abstrat 2 Abstrat in Hindi (Saar) 3 Aknowledgements 4 Contents 5 List of Figures 9 1. Introdution General Objetives Sope Mehanis of RC Beam-Column Joints Introdution Classifiation of RC Beam-Column Joints Classifiation based on geometri onfiguration Classifiation based on strutural behaviour Classifiation based on detailing aspets Behavior of beam-olumn joints under load Failure modes of a beam-olumn joint Shear Fores in a Beam-Column Joint Exterior Joints Interior Joints Criteria for desirable performane of joints Codal and other reommendations Bond Requirements in RC Beam-olumn joints Bond in General Bond with Deformed Bars Bond under yli loading 40 5

10 3.4 Bond in RC Beam-Column Joints Literature Review of Beam-Column Joint Models Models based on experiments Townsend and Hanson (1973) Anderson and Townsend (1977) Soleimani et al (1979) Models based on analytial studies Rotational Hinge Models Otani (1974) Banon et al (1981) Fillipou et al (1983, 1988) El-Metwally and Chen (1988) Kunnath et al (1995) Alath and Kunnath (1995) Pampanin et al (2003) Comment on Rotational Hinge Models Multiple Spring Models Biddah and Ghobarah (1999) Elmorsi et al (2000) Youssef and Ghobarah (2001) Lowes et al (2003) Altoontash (2004) Shin and LaFave (2004) Comment on Multiple spring models Summary of Existing Models Formulations for the Proposed Model Contribution of Joint Shear Deformation to Storey Drift Modelling the Contribution of Joint Shear Deformation to 62 Storey Drift Results from experiments on beam-olumn joints tests 65 6

11 5.2.2 Results from detailed finite element analysis of joints Analytial omputation harateristis from mehanis 69 of the joints 5.3 Formulations for evaluating spring harateristis Joints without axial load on olumn Joints without axial load on olumn Prinipal tensile stress v/s shear deformation relations Exterior Joints Exterior Joints with beam bars bent in Exterior Joints with beam bars bent out Exterior Joints with straight beam bars with 83 full development length embedment Exterior Joints with straight beam bars 83 with 6 inh embedment Interior Joints Validation of Model with Experiments Tests by Clyde et al (2000) Test # Test # Test # Test # Tests by Pantelides et al (2002) Test unit Test unit Test unit Test unit Tests by El-Amoury and Ghobarah (2002) Tests by Dhakal et al (2005) Joint C Joint C

12 7. Conlusions and Disussion Advantages of the new model Limitations of the model Sope of further improvement of the model 113 Referenes 115 Appendix 128 8

13 List of Figures Fig 1.1 Major Failure Modes for a RC Beam-Column Joint 12 Fig 1.2 Typial beam-olumn joint failures 13 Fig 1.3 Damaged beam-olumn joint during earthquake 13 Fig 1.4 Joint Failures in 2007 West Sumatra Earthquake 14 Fig 1.5 Joint Failure ausing ollapse during 2004 Sumatra Earthquake 14 Fig 1.6 Joint Failures during May 2006, Mid Java Earthquake 15 Fig 2.1 Exterior beam-olumn joints in plane and spae frames 19 Fig 2.2 Interior beam-olumn joints in plane and spae frames 20 Fig 2.3 Load-defletion behavior of a flexural member 21 Fig 2.4 Typial non-dutile detailing presribed by older odes of pratie 22 Fig 2.5 Dutile detailing presribed by new odes of pratie 23 Fig 2.6 Reinfored Conrete Frame Struture under Lateral Loads 24 Fig 2.7 Ations and Fores on an Exterior Joint 25 Fig 2.8 Ations and Fores on an Interior Joint 29 Fig 2.9 Mehanis of interior joint under seismi ations 30 Fig 3.1 Simple onept of bond stresses 35 Fig 3.2 Bond Craking Mehanism 36 Fig 3.3 Components of Bearing Stresses on Ribs 37 Fig 3.4 Possible splitting rak failures 38 Fig 3.5 Mehanis of rib bearing on onrete 39 Fig 3.6 Bond-slip yli relationship for deformed bars 41 Fig 4.1 Takeda s hystereti rule 47 Fig 4.2 Beam-olumn joint subelement by Fillipou et al 48 Fig 4.3 Beam-Column Joint model by Alath and Kunnath 50 Fig 4.4 Model for RC beam-olumn joints by Pampanin et al 51 Fig 4.4 Beam-Column Joint model by Biddah and Ghobarah 52 Fig 4.5 Beam olumn joint model by Elmorsi et al 53 Fig 4.6 Beam-olumn joint model by Youssef and Ghobarah 54 Fig 4.7 Beam-olumn joint model by Lowes et al 55 Fig 4.8 Beam-olumn joint model by Altoontash 56 Fig 4.9 Beam-olumn joint model by Shin and LaFave 57 Fig 5.1 Typial deformed shape of framed strutures under earthquakes 60 9

14 Fig 5.2 Contribution of joint deformation to storey drift for exterior joints 61 Fig 5.3 Contribution of joint deformation to storey drift for interior joints 62 Fig 5.4 Modelling of joint deformational behaviour 63 Fig 5.5 Implementation of model in frame elements 64 Fig 5.6 Measuring joint shear deformations in tests 66 Fig 5.7 Typial measured joint shear stress v/s shear strain in tests 66 Fig 5.8 FE Model of the joint 68 Fig 5.9 Disrete bond element and harateristis for bond element 68 Fig 5.10 Suggested prinipal tensile stress v/s joint shear deformation 69 relationship Fig 5.11 Exterior joints with (a) beam bars bent out (b) beam bars bent in 70 Fig 5.12 Mehanis of exterior joint under seismi ations 71 Fig 5.13 Mehanis of interior joint under seismi ations 72 Fig 5.14 Flowhart for V v/s and M b v/s j relationships for no axial load ase 76 Fig 5.15 Flowhart for V v/s and M b v/s j relationships for with axial load 81 Fig 5.16 Assumed prinipal tensile stress-shear deformation relation for 82 exterior joints with bars bent in Fig 5.17 Assumed prinipal tensile stress-shear deformation relation for 82 exterior joints with bars bent out Fig 5.18 Assumed prinipal tensile stress-shear deformation relation for 83 exterior joints with top bars bent in and bottom bars bent out Fig 5.19 Assumed prinipal tensile stress-shear deformation relation for 84 exterior joints with top bars bent in and bottom bars straight with full development length Fig 5.20 Assumed prinipal tensile stress-shear deformation relation for 84 exterior joints with top bars bent in and bottom bars straight with 6" embedment Fig 5.21 Assumed prinipal tensile stress-shear deformation relation for 85 interior joints Fig 6.1 Details of joints tested by Clyde et al 87 Fig 6.2 Test setup of joints tested by Clyde et al 88 Fig 6.3 Experimental and analytial results for Test #2 91 Fig 6.4 Analytial hinge pattern obtained from analysis 91 Fig 6.5 Experimental and analytial results for Test #6 93 Fig 6.6 Experimental and analytial results for Test #

15 Fig 6.7 Experimental and analytial results for Test #5 96 Fig 6.8 Details of test units 1 and 2 97 Fig 6.9 Details of test units 5 and 6 98 Fig 6.10 Test setup used by Pantelides et al 99 Fig 6.11 Experimental and analytial results for test unit Fig 6.12 Experimental and analytial results for test unit Fig 6.13 Experimental and analytial results for test unit Fig 6.14 Experimental and analytial results for test unit Fig 6.15 Details of the joint tested by El-Amoury and Ghobarah 104 Fig 6.16 Test setup used by El-Amoury and Ghobarah 105 Fig 6.17 Experimental and analytial results for test by El-Amoury 106 and Ghobarah Fig 6.18 Details of speimens tested by Dhakal et al 107 Fig 6.19 Details of test setup used by Dhakal et al 108 Fig 6.20 Experimental and analytial results for speimen C1 by 109 Dhakal et al Fig 6.21 Experimental and analytial results for speimen C4 by 110 Dhakal et al Fig A.1 Theoretial moment-urvature determination 129 Fig A.2 Hognestad stress-strain model for onrete 132 Fig A.3 IS reommended stress-strain model for onrete 132 Fig A.4 Stress-strain urves for onrete onfined by retangular hoops 134 Fig A.5 Kent and Park (1971) model for Stress-strain urve for onfined 136 onrete Fig A.6 Transverse onfining steel in members 137 Fig A.7 Modified Kent and Park model for stress-strain urve for onfined 138 onrete Fig A.8 Stress bloks at different extreme ompression fiber strain 140 Fig A.9 Cantilever beam and its urvature distribution within elasti range 144 Fig A.10 Cantilever beam and its urvature distribution at ultimate moment 145 Fig A.11 Modeling of members and stress state of onrete element 149 Fig A.12 Strain state of raked onrete at the entroidal axis of setion A-A

16 1. INTRODUCTION 1.1 General Behavior of Reinfored Conrete (RC) beam-olumn joints under seismi exitations has generated lot of interest among researhers throughout the world in past few deades. Beam-olumn onnetions have drawn speial attention of researhers due to their highly omplex behavior under seismi loads, whih is a ombination of huge shear fores, diagonal tension and high bond stresses in the reinforement bars, all brittle modes of failure. In the analysis, generally the joint ore is onsidered as rigid and all the plasti rotations are assumed to take plae in the beams and/or olumns forming the joint ore. Although this assumption is reasonable for the struture subjeted to stati gravity loads, the same assumption may be highly misleading for the struture subjeted to dynami seismi loads. Under reversing dynami earthquake loads the joint ore is subjeted to tremendous shear fores, whih gradually softens the joint ore making it no more rigid. The two major failure modes for the failure at joints are (a) joint shear failure and (b) end anhorage failure (See Fig 1.1). (a) Joint Shear Failure (b) Inadequate Reinforement Anhorage Fig 1.1 Major Failure Modes for a RC Beam-Column Joint Thus, it an be said that defiienies of joints are mainly aused by inadequate transverse reinforement and insuffiient anhorage apaity in the joint (Liu, Pampanin and Dhakal, 2006). These problems have been highlighted, in reent past, by the damage observed in reent devastating earthquakes in different ountries. Fig 1.2 shows a typial example of a beam-olumn joint failure during the 1999 Turkey earthquake (Ghobarah and Said, 2002). 12

17 Another damaged struture after the Koaeli earthquake is shown in Fig 1.3 demonstrating a good example of the brittle joint shear failure mode (Liu, Pampanin and Dhakal, 2006). Most of suh joint brittle shear failures our due to non-dutile performane, either poor anhorage of the main reinforing bars or simply inadequate transverse reinforement in the joints, of reinfored onrete moment-resisting frames. Fig 1.2 Typial beam-olumn joint failures (Turkey Earthquake) Fig 1.3 Damaged beam-olumn joint during earthquake (1999 Koaeli, Turkey) 13

18 As per the 2007 West Sumatra earthquake reonnaissane report, the beam-to-olumn joints for the onrete moment frames that do not use dutile detailing, suffered great damages (Fig 1.4). In ertain ases, the reinforement steel did not extend suffiiently into the joint, nor did it have adequate development length. Furthermore, the joints were not onfined and hene were suseptible to shear failure. Fig 1.4 Joint Failures in 2007 West Sumatra Earthquake Fig 1.5 shows near omplete ollapse of strutures due to joint failures during the 2004 Sumatra Earthquake (Saatioglu, Ghobarah and Nistor Reonnaissane Report). Fig 1.5 Joint Failure ausing ollapse during 2004 Sumatra Earthquake Further reports on 2006 Mid Java earthquake onfirms the importane of beamolumn joints for the safety of the strutures. Fig 1.6 shows further examples of 14

19 strutural ollapse due to joint failures in reinfored onrete strutures (JSCE/AIJ Provisional Report on May 27,2006, Mid Java Earthquake). All the above-mentioned examples of joint failures during earthquakes highlight the importane of beam-olumn joints for the global safety of reinfored onrete strutures. These fats suggest that the attention to proper design of beam-olumn joint ores is not over emphasized. Fig 1.6 Joint Failures during May 2006, Mid Java Earthquake It is true that the new odes emphasize and provide guidane for designing and detailing the joint ores in a better way, but most of the existing strutures were designed and detailed aording to older standards and are in general having inherent defiienies. More and more emphasis is now laid on performing nonlinear displaement based seismi assessment of reinfored onrete strutures (ATC-40, FEMA 356, Priestley 1997, Priestley et al 2007). The two possibilities that arise are (i) (ii) Nonlinear Stati (Pushover) Analysis Nonlinear Dynami (Time History) Analysis Although nonlinear dynami analysis is more aurate and reliable, the omputation time, effort and osts are highly prohibitive for any pratial usage. Nonlinear stati analysis gives a good trade off between omputational effort and auray. 15

20 Determination of nonlinear load-displaement (Capaity) urve of the struture is entral to the analysis methodology. Conentrated plasti hinges (springs) are assigned at the ritial loations to apture the nonlinear behaviour of the struture. Therefore, the auray of the apaity urve depends strongly on the auray in determining the hinge harateristis. Determination of flexural, axial and shear hinge harateristis for the frame members, i.e. beams and olumns is well doumented in text (Park and Pauley 1975; Watanabe and Lee 1998) and ommerial softwares have apabilities to inorporate them (SAP2000 Nonlinear 2007; StaadPro 2007). However, in general for old strutures, the weakest link during earthquakes is the beam-olumn joint that undergoes brittle shear failure. Therefore just by onsidering inelasti behaviour of frame members is not enough to orretly apture the global behaviour of the struture. Rather, in many ases, suh an analysis an be very misleading and lead to dangerous results. Many researhers (Sharma et al 2008; Eligehausen et al. 2006; Lowes et al 2005; Pampanin et al 2003; Bing et al 2003; Youssef and Ghobarah 2001; Elmorsi et al 2000; Nagai et al 1996; Alath and Kunnath 1995; Filippou and Issa 1988; El- Metwally and Chen 1988;) have proposed various ways to model beam-olumn joints. Most of the approahes suggested ould be used for analyzing the joint behaviour quite niely. However, the models either require large omputational efforts so that they are not pratially useful for analyzing the global strutural behaviour or they need a speial element with various nodes and springs or a speial purpose program to implement the joint nonlinearity. This work is aimed at developing a lumped plastiity based model for the reinfored onrete beam-olumn onnetions that an reasonably aurately apture the shear behaviour of the joints and also is pratial enough to be used with existing ommerial software programs available. 16

21 1.2 Objetive The objetives of this work are: 1. To understand the nonlinear behaviour of beam-olumn onnetions 2. To develop a modelling tehnique for reinfored onrete beam-olumn onnetions in framed strutures that an reasonably aurately predit the nonlinear shear behaviour of the joints as well as ould be pratially implementable in ommerial software programs to perform the nonlinear analysis of the strutures. 3. To validate the model with the results of various experiments on different onfiguration of reinfored onrete beam-olumn onnetions available in literature. 1.3 Sope The sope of this work inludes: 1. Development of a rational, realisti and easily implementable model for reinfored onrete beam-olumn joints with old worked deformed bars as reinforement. 2. Validation of the model with experimental results. 17

22 2. MECHANICS OF RC BEAM-COLUMN JOINTS 2.1 Introdution A beam-olumn joint in a reinfored onrete struture is a zone formed by the intersetion of beam and olumn. A joint is defined as the portion of the olumn within the depth of the deepest beam that frames into the olumn (ACI 352 R 2002). The funtional requirement of a joint is to enable the adjoining members to develop and sustain their ultimate apaity. 2.2 Classifiation of RC Beam-Column Joints The reinfored onrete beam-olumn joints used in frames may be lassified in terms of geometri onfiguration, strutural behavior or detailing aspets Classifiation based on geometri onfiguration Based on the fundamental differenes in the mehanisms of beam bar anhorages, it is ustomary to differentiate between interior and exterior joints. a. Exterior beam-olumn joints Different types of exterior joints present in a building are shown in Fig 2.1. In a plane frame, the orner joints at roof (Fig 2.1(a)) and at intermediate floor (Fig 2.1(d)) fall under the ategory of exterior beam-olumn joints. In ase of a spae frame, the roof orner joint (Fig 2.1(b)), the roof edge joint (Fig 2.1()), the intermediate floor orner joint (Fig 2.1(e)) and the intermediate floor edge joint (Fig 2.1(f)) fall under the ategory of exterior beam-olumn joints. 18

23 (a) Plane frame roof orner joint (b) Spae frame roof orner joint () Spae frame roof edge joint (d) Plane frame floor orner joint (e) Spae frame floor orner joint (f) Spae frame floor edge joint Fig 2.1 Exterior beam-olumn joints in plane and spae frames b. Interior beam-olumn joints Different types of interior joints present in a building are shown in Fig 2.2. In a plane frame, the middle joints at roof (Fig 2.2 (a)) and at intermediate floor (Fig 2.2 (b)) fall under the ategory of interior beam-olumn joints. In ase of a spae frame, the roof middle joint (Fig 2.2 ()), and the intermediate floor middle joint (Fig 2.2 (d)) fall under the ategory of interior beam-olumn joints Classifiation based on strutural behavior Based on the rak propagation in the joint region and failure mehanism under loading, the joints an be lassified as 19

24 (a) Plane frame middle roof joint (b) Plane frame middle floor joint () Spae frame middle roof joint Fig 2.2 Interior beam-olumn joints in plane and spae frames (d) Spae frame middle floor joint a. Elasti beam-olumn joints It is preferable to ensure that joints remain essentially in the elasti range throughout the response of the struture. When inelasti deformations do not or annot our in the beams and olumns adjaent to a joint, the joint may be reinfored so as to remain elasti even after a very large number of displaement reversals (Pauley and Priestley, 1992). Under suh irumstanes, smaller amounts of joint reinforement generally suffie. Suh joints are lassified as elasti joints and they seldom our in pratie. b. Inelasti beam-olumn joints As a general rule, when subjeted to design earthquake, plasti hinges are expeted to develop at the ends of the beams, immediately adjaent to the joint. In suh ases, after a few yles of exursions into the inelasti range, it is not possible to prevent some inelasti deformation ourring also in parts of the joint (Pauley and Priestley, 1992). This is due primarily to the penetration of inelasti strains along the reinforing bars of the beams into the joint. These joints are lassified as inelasti joints. They require larger amounts of joint shear reinforement Classifiation based on detailing aspets Earthquake resistant design and detailing of reinfored onrete strutures was an unpopular and negleted area in the design odes of the past (IS 456:1964, IS 5525:1969). As earthquakes gained importane over a period of time, the seismi 20

25 design and detailing aspets were inluded in the more reent design odes (IS 4326:1976/1993, IS 1893:1984/2002, IS 13920:1993). As a requirement of urrent ode of pratie (IS 13920:1993), sine earthquake ours suddenly and without warning, it is very neessary in seismi design of strutures to avoid onstrution praties that ause brittle failure (sudden ollapse). The urrent seismi design philosophy relies heavily on the ation of members to absorb the vibrational energy resulting from strong ground motion by designing members to behave in a dutile manner. In this manner even if earthquake of greater intensity than foreseen ours, omplete ollapse of the struture may be avoided. Fig 2.3 shows the omparison of brittle and dutile load defletion behavior of a flexural member (Park and Pauley 1975). Load Dutile behaviour Load Brittle behaviour Defletion Fig 2.3 Load-defletion behavior of a flexural member Defletion Whether a joint will behave in a brittle or dutile manner depends largely on the reinforement details of the joint. Based on their behavior under loading, the beamolumn joints in a reinfored onrete struture an be lassified as a. Non-dutile joints Non-dutile or brittle joints are those, whih do not undergo large deformations beyond their yield point or elasti limit without a signifiant degradation in strength or abrupt failure. Suh joints typially have insuffiient development lengths, short lap splies, disontinuous reinforements, larger stirrup spaing, and no onfining reinforement in the joint ore. Fig 2.4 shows typial old non-dutile detailing of (a) beam-olumn joints of a reinfored onrete frame struture (ATC-40:1996, ACI 21

26 Detailing Manual, 1988) and (b) a antilever beam projeting from a beam over a olumn (SP34:1987). Disontinuous reinforement Widely spaed ties Short lap splie in high stress region Widely spaed ties No ties in joint ore No ties in joint ore (a) Beam-olumn joints in a frame Short lap splie in high stress region (b) Cantilever beam over a olumn Fig 2.4 Typial non-dutile detailing presribed by older odes of pratie b. Dutile joints Dutile joints have an ability to undergo large deformations and/or several yles of deformations beyond their yield point or elasti limit and maintain its strength without signifiant degradation or abrupt failure. Suh joints absorb muh of the energy through the hystereti behavior under a severe earthquake. Large anhorage lengths, long lap splies, ontinuous reinforements, loser stirrup spaing, and presene of onfining reinforement in the joint ore haraterize suh joints. Fig 2.5 shows typial dutile type reinforement detailing presribed by new odes of pratie (IS 13920:1993, ACI Detailing Manual 1988) for (a) beam-olumn joints of a frame, (b) anhorage of beam bars in external joint and () lap, splie in beam. Speial onfining reinforement is provided in the ruial zones suh as in lap splies, near eah joint fae, and on either side of any setion where flexural yielding may our under the effet of earthquake fores. 22

27 Continuous reinforement through joint Larger anhorage length Long lap splie with speial onfining reinforement Closely spaed ties as speial onfining reinforement (b) Anhorage of beam bars in external Confining reinforement in joint ore (a) Dutile detailing for joints in frame () Lap, Splie in beam Fig 2.5 Dutile detailing presribed by new odes of pratie 2.3 Behavior of beam-olumn joints under load Consider a frame of a reinfored onrete struture subjeted to lateral loads as shown in Fig 2.6 (a). The bending moment diagram (BMD) of the struture under suh lateral loading is shown in Fig 2.6 (b). Let us now onsider an interior beam-olumn joint of the frame. It an be seen from the BMD that the moments in olumns above and below the joint ore are of opposite signs. A similar inferene an be made about the beam moments aross the joint. Therefore, the joint region is subjeted to horizontal and vertial shear fores whose magnitude is typially muh higher than those observed in adjaent beams and 23

28 olumns. Therefore, if not properly designed, the joint ore may undergo shear failure. This issue will be further disussed in detail in the following subsetions. (a) Reinfored Conrete Frame (b) Bending Moment Diagram (BMD) Fig 2.6 Reinfored Conrete Frame Struture under Lateral Loads Failure modes of a beam-olumn joint As stated earlier, a beam-olumn joint is a region formed by the intersetion of a beam and a olumn. Therefore, it may be stated that, a beam-olumn joint primarily onsists of three elements viz. beam, olumn and the joint ore, generally onsidered as a part of olumn (ACI 352R-02). Eah of the three elements an undergo failure under different modes as enlisted below a. Flexural failure of beam. b. Flexural failure of olumn.. Shear failure of beam. d. Shear failure of olumn. e. Shear failure of joint ore. f. Bond failure of reinforement. g. Combinations of various modes listed above. A failure resulting from single mode is highly unommon and generally a ombination of two or more of the above modes is responsible for the omplete failure. Although, joint failure typially means the shear failure of the joint ore, but it 24

29 is quite unlikely that it serve as the weakest link. The failure (or rak propagation) usually initiates from beam or olumn, whihever is weaker, and then joint raking ours. This is primarily due to the penetration of inelasti strains along the reinforing bars of the beams or olumns into the joint. Therefore, if the joint ore is not designed for suh fores, it is very muh possible that ultimate failure results due to exessive shear raking in joint ore. The most favorable ondition from seismi design point of view is to have joint ore essentially in the elasti range and formation of plasti hinges shall our in beams. However, when the plasti hinges are developed at the ends of the beams immediately adjaent to a joint, it is not possible to prevent some inelasti deformation ourring in the parts of joint also. Therefore, the ideal situation is to have plasti hinge formation in beams at some distane away from the fae of the joint. But it is not possible to ahieve this ondition unless some speial treatment is done to beams, e.g., speial design and detailing (Pauley and Priestley, 1992, Pampanin and Christopoulos, 2003, Rao, Mahajan and Eligehausen, 2005), et. Suh treatment is out of sope of this report and will not be disussed further. Also the formation of flexural plasti hinges are preferred to those governed by shear. This is due to the fat that shear failure essentially is brittle in nature in ontrast to the flexural failure, whih is dutile Shear Fores in a Beam-Column Joint The behavior of a joint is haraterized by a omplex interation of shear, bond and onfinement mehanisms taking plae in a quite limited area (Costa, J.L.D., 2003). From Fig 2.6 above, it is lear that the lateral loading imposes suh a bending moment field in the beams and olumns that moments with the same magnitude but of opposite sign will take plae on parallel faes of the joint. As a onsequene, the joint region is subjeted to horizontal and vertial shear fores whose magnitude is L /h b times the maximum shear fore in the olumns and L b /h times the maximum shear fore in the beams, respetively, where L b and L are the lengths of beam and olumn with depths h b and h respetively, framing in the joint. 25

30 Exterior Joints When RC moment frames are subjeted to lateral seismi loading, high shear fores are generated in the joint ore. Fig 2.7 shows the mehanis of exterior joint when subjeted to seismi fores. The lateral seismi loading on a frame leads to bending moments and shear fores that an be simulated in the joint as shown in Fig 2.7 (a). Here the length of the beam L b is half of the bay width and L is the storey height. The other dimensions are explained in the figure. P C s2 C 2 V T 1 V T b V jv h V jh V b V jh V jv C b L C s2 C 2 Z T 1 T b Z b L b h b V b P M V C sb T 2 C 1 C s1 (b) Horizontal and vertial joint shear C b V C sb C s2 C 2 T 1 T 2 C 1 C s1 p T b M b p t C b C sb V b T 2 C 1 C s1 V V P P (a) External ations and fores in beams and olumns () Prinipal stresses in joint (a) Ation on an Exterior Joint (b) Fores Ating on Exterior Joint Fig 2.7 Ations and Fores on an Exterior Joint M Fig 2.7 (b) shows the joint shear fores generated due to these external ations. From equilibrium of the joint, as shown in Fig 2.7 (b), we get, V jh = T b V (2.1) 26

31 Now, we have T b = M b /Z b = V b L b /Z b (2.2) Also, from the equilibrium of external ations, we have, V = V b (L b +0.5h )/L (2.3) Substituting (2) and (3) in (1), we get, Lb Lb + 0.5h V jh = Vb Z b L (2.4) The horizontal joint shear stress an be obtained as V jh τ = h b (2.5) where, h' and b' are the length and width of joint ore respetively. In general, for suffiient auray, we an onsider, Z b = d b d' b (2.6) Where, d b = Effetive depth of the beam d' b = Effetive over to ompression reinforement Similarly, from equilibrium in vertial diretion, we an get vertial joint shear. However, it has been shown that (Park and Paulay, 1975; CEN 250; Paulay and Park, 1984; Tsonos, 2007) V V jv b = = α (2.7) jh h h 27

32 where, α is the joint aspet ratio. Now, vertial joint shear stress is given by, V jv σ = h b (2.8) Thus, (5), (7) and (8), we have, σ = ατ (2.9) The prinipal ompressive stress, p and tensile stress p t an be alulated as ( σ σ 4τ = ± + (2.10) 2 2 σ 2 p, t 1 2 These prinipal stresses are responsible for diagonal failure of the joint. In order to resist the prinipal diagonal tension fores, reinforement in the joint ore is required. As shown in Fig 2.4, the older odes of pratie did not reommend suh reinforement for the joint ore. Therefore, suh joints are more suseptible to joint shear failure than the joints detailed as per new odes and having reinforement in the joint ore (Fig 2.5) Interior Joints In ase of interior joints, the beam is running through the olumn (Fig 2.2). Therefore, the longitudinal reinforement of the beam that frames into the olumn either an terminate within the joint ore without bends (Fig 2.4) or an pass through and through the joint (Fig 2.5). Consider an interior joint ated upon by a set of ations (Pauley and Priestley, 1992) as shown in Fig 2.8 (a). The bending moment diagram (BMD) and shear fore diagram (SFD) are shown in Figs 2.8 (b) and () respetively. 28

33 (a) Interior joint under a set of ations (b) BMD () SFD Fig 2.8 Ations and Fores on an Interior Joint From Fig 2.8 (b), it an be notied that the bending moments just above and below the joint hange their nature with a steep gradient within the joint region thus ausing large shear fores in the joint ompared to that in the olumn. In order to alulate the horizontal shear fore in the joint ore, let us onsider the equilibrium of the joint. Let M h and M s be the hogging and sagging moments respetively ating on either side of the joint ore as shown in Fig 2.8 (a). T b and C b are the tensile and ompressive fores in the beam reinforements. V b is vertial beam shear and V ol is horizontal olumn shear. Fig 2.9 shows the mehanis of interior joints more learly. Similar to the expressions for exterior joints, we an obtain relations for joint shear and prinipal stresses for interior joint as shown in Fig 2.9. Lb Lb + 0.5h V jh = 2V b Z b L (2.11) 29

34 P C s2 C 2 V T 1 V C sb2 T b1 C b2 V jv h V jh V b V jh 0.5L - h b V jv C b1 C s2 C 2 Z T 1 L b T b2 V b T 2 V C 1 C s1 (b) Joint shear C sb1 C sb2 C b2 T b1 Z b h b P M C b1 V L b T b2 V b C sb1 C s2 C 2 T 1 V b T 2 C 1 C s1 M b C sb2 C b2 p T b1 M b 0.5L - h b V b T b2 p t C b1 C sb1 V b T 2 C 1 C s1 V P (a) External ations and fores in beams and olumns () Prinipal stresses in joint Fig 2.9 Mehanis of interior joint under seismi ations M V P In a similar way, the vertial joint shear fore an be obtained. In the above expressions, L b is always the distane from the fae of the olumn to the point of ontra-flexure of the beam. These shear fores are responsible for diagonal tension and hene raks in the joint. In order to resist suh diagonal tension fores, reinforement in the joint ore is required. As shown in Fig 2.4, the older odes of pratie did not reommend suh reinforement for the joint ore. Therefore, suh joints are more suseptible to joint shear failure than the joints detailed as per new odes and having reinforement in the joint ore (Fig 2.5). After a few yles of inelasti loading, the bond deterioration initiated at the olumn fae due to yield penetration and splitting raks, progresses towards the joint ore. 30

35 Repeated loading will aggravate the situation and a omplete loss of bond up to the beginning of the bent portion of the bar may take plae. The longitudinal reinforement bar, if terminating straight, will get pulled out due to progressive loss of bond. The pull out failure of the longitudinal bars of the beam results in omplete loss of flexural strength. This kind of failure is unaeptable at any stage. Hene, proper anhorage of the beam longitudinal reinforement bars in the joint ore is of utmost importane. More details on bond requirements are given in next hapter. The pull out failure of bars in exterior joints an be prevented by the provision of hooks or by some positive anhorage. Hooks are helpful in providing adequate anhorage when furnished with suffiient horizontal development length and a tail extension. Beause of the likelihood of yield penetration into the joint ore, the development length is to be onsidered effetive from the ritial setion beyond the zone of yield penetration. Thus, the size of the member should aommodate the development length onsidering the possibility of yield penetration. When the reinforement is subjeted to ompression, the tail end of hooks is not generally helpful to ater to the requirements of development length in ompression. However, the horizontal ties in the form of transverse reinforement in the joint provide effetive restraints against the hook when the beam bar is in ompression. 2.4 Criteria for desirable performane of joints In ase of dutile strutures designed for earthquake resistane may be formulated as follows (Pauley and Priestley, 1992, Pauley, Park, and Priestley, 1978, Uma and Prasad) a. The strength of the joint should not be less than the maximum demand orresponding to development of the strutural plasti hinge mehanism for the frame. This means that the joint should have suffiient strength to enable the maximum apaities to be mobilized in adjoining members. This will eliminate the need for repair in a relatively inaessible region and for energy dissipation by joint mehanisms. 31

36 b. The apaity of the olumn should not be jeopardized by possible strength degradation within the joint. The joint should also be onsidered as an integral part of the olumn.. During moderate seismi disturbanes, joint should preferably respond within the elasti range. d. Joint deformations should not signifiantly inrease story drift. e. The joint reinforement neessary to ensure satisfatory performane should not ause undue onstrution diffiulties. The seismi design philosophy relies on providing suffiient dutility to the struture by whih the struture an dissipate seismi energy. The strutural dutility essentially omes from the member dutility wherein the latter is ahieved in the form of inelasti rotations. In reinfored onrete members, the inelasti rotations spread over definite regions alled as plasti hinges. During inelasti deformations, the atual material properties are beyond elasti range and hene damages in these regions are obvious. The plasti hinges are expeted loations where the strutural damage an be allowed to our due to inelasti ations involving large deformations. Hene, in seismi design, the damages in the form of plasti hinges are aepted to be formed in beams rather than in olumns. Mehanism with beam yielding is harateristi of strong-olumn-weak beam behaviour in whih the imposed inelasti rotational demands an be ahieved reasonably well through proper detailing pratie in beams. Therefore, in this mode of behaviour, it is possible for the struture to attain the desired inelasti response and dutility. The funtional requirement of a joint, whih is the zone of intersetion of beams and olumns, is to enable the adjoining members to develop and sustain their ultimate apaity. The demand on this finite size element is always severe espeially under seismi loading. The joints should have adequate strength and stiffness to resist the internal fores indued by the framing members. 32

37 2.5 Codal and other reommendations As mentioned earlier, a system of diagonal ompression strut and tension tie is developed in the onrete ore to transmit the joint shear fores. Some of the internal fores, partiularly those generated in the onrete will ombine to develop a diagonal strut (Paulay and Priestley 1992; Hakuto et al 2000; Paulay et al 1978). Other fores transmitted to the joint ore from beam and olumn bars by means of bond, neessitate a truss mehanism. The strength of this diagonal strut ontrols the joint strength before raking. The transverse reinforement in the joint helps onfine the onrete diagonal strut in the joint ore thereby ontributing to inreased joint strength. If the joint shear fores are large, diagonal raking in the joint ore ours followed by the rushing of onrete in joint ore. The joint reinforement alone is not suffiient to avoid undesirable pinhing in hystereti loops at this stage (Murty et al 2003; ACI ; Stevens et al 1991). Standards suh as ACI 318 (2008) and NZS 3101 (1995) reommend to keep the stresses in the joint below permissible limits. ACI 318 speifies this limit based on the tensile strength of onrete by speifying the value of maximum permissible horizontal joint shear stress as k f, where, f' is the ylinder ompressive strength of onrete and k is a parameter that depends on the onfinement provided by the members framing into the joint. It is sometimes argued (Hakuto et al 2000) that the tension raking riteria may be too onservative and the joint ore may be apable of transferring signifiantly higher shear fores after diagonal tension raking also, by means of diagonal ompression strut mehanism. NZS 3101 reognizes this approah and speifies that to avoid diagonal ompression failure in the joints, the horizontal shear stress shall not exeed a value of 0.2 f'. It is now reognized that prinipal stresses that onsider the ontribution of axial fores also, provide better riteria for the damage in the joint (Priestley 1997; Pampanin et al 2003). The values are presribed as k f, where, f' is the ylinder ompressive strength of onrete and k is a parameter that depends on the type of joint, type of reinforement and end anhorage details. Priestley (1997) suggested the ritial prinipal tensile stress values for exterior and orner beam-olumn joints with 33

38 deformed bars with bent-in and bent-out type end anhorages and Pampanin (2003) has more reently suggested the same for exterior beam-olumn joints with plain round bars and end hooks. 34

39 3. BOND REQUIREMENTS OF BEAM-COLUMN JOINTS 3.1 Bond in General Bond refers to the interation between reinforing steel and the surrounding onrete that allows for transfer of tensile stress from the steel into the onrete. Bond is the mehanism that allows for anhorage of straight reinforing bars and influenes many other important features of strutural onrete suh as rak ontrol and setion stiffness. Fig 3.1 shows a straight bar embedded into a blok of onrete. When the bond stress is suffiient to resist design tensile loads in the bar, then the bar is developed and the embedment length neessary for anhorage of the fully stressed reinforing bar is referred to as its development length. The odes, e.g. IS 456:2000 presribe to embed the reinforement in onrete beyond the ritial setion, at least up to one development length. Fig 3.1 Simple onept of bond stresses (Thompson et al 2002) The omposite ation of onrete and steel is due to bond fores between these two materials. The bond plays a dominant role with respet to seismi behavior beause it affets stiffness and energy dissipation apaity. The relative slip between the plain bars and the surrounding onrete depends both on the steel strain, and the onrete strain. However, onrete strain is usually disregarded sine its value is negligible with respet to steel strain (Costa, J.L.D., 2003). The signifiant parameters that influene the bond performane of the reinforing bar are onfinement, lear distane between the bars and nature of the surfae of the bar (Uma and Prasad). Confinement of the embedded bar is very essential to improving 35

40 the bond performane in order to transfer the tensile fores. The relevant onfinement is obtained from axial ompression due to the olumn and with reinforement that helps in arresting the splitting raks. 3.2 Bond with Deformed Bars When a deformed reinforement bar is pulled out from a onrete blok, relative movements between steel and onrete (slip) our. Deformed reinforing bars develop bond stresses by means of transverse ribs that bear diretly on the onrete. As tensile fores develop in a reinforing bar, transverse raks propagate from the edges of the ribs as shown in Fig 3.2 (Goto 1971). The bond stress produed by the bearing of the ribs is not uniform and the loal bond stress an be even more than twie the average bond stress (Mains 1951). Bond stress peaks near raks and tapers off as the onrete arries more of the tensile load. The bond stress then reverses sign when another primary rak is formed. A bar does not uniformly yield in raked onrete when it is properly bonded and the yielding ours only loally near raks (Thompson et al 2002). Fig 3.2 Bond Craking Mehanism (Costa, J.L.D., 2003) Bearing stresses on the ribs at in a diretion roughly normal to the fae of the rib as shown in Fig 3.3a (Thompson et al 2002). These bearing fores an be split into parallel and perpendiular omponents (Fig 3.3b). The omponents parallel to the bar onstitute the bond responsible for resisting the tensile fore in the reinforement. The omponents perpendiular to the bar at outward from the bar surfae as splitting 36

41 stresses on the onrete. These radial splitting stresses are ounterated by ring tension stresses in the onrete surrounding the reinforing bar, (Fig 3.3). Ultimately, the radial splitting stresses exeed the tensile apaity of the surrounding onrete and splitting raks begin to propagate from the bar surfae. (a) Bearing stresses on ribs (b) Bearing stress omponents () Radial splitting and longitudinal bearing fores Fig 3.3 Components of Bearing Stresses on Ribs (Thompson et al 2002) The slip is mainly aused by the rushing of onrete in front of the lugs (Eligehausen, Popov and Bertero, 1983). At first, the bond resistane is made up by adhesion. On further loading, the mehanial interloking of ement paste on the marosopi irregularities of the bar surfae along with mehanial interloking between the lugs and onrete are mobilized. This high pressure on the onrete in front of the lugs auses tensile stresses in the onrete around the bar, whih in turn, reate internal inlined raks alled bond raks as shown in Fig 3.2. These bond raks modify the response of onrete to loading. The stiffness is redued and therefore for small inrement in bond stresses, larger slip inrements will result as ompared to the ase before raking. After the ourrene of bond raks, the stress transfer from steel to the surrounding onrete is ahieved by inlined ompressive fores spreading from the lugs into the onrete. The omponents of these fores parallel to the reinforement bar axis are proportional to bond stress,. The radial omponent, with respet to bar axis, loads the onrete like an internal pressure and indues tensile hoop stresses whih ause splitting raks. If the onrete 37

42 is unonfined, the bond stresses will fall to zero after this point (Eligehausen, Popov and Bertero, 1983). However, if the onrete is well onfined, the load an be inreased further. When approahing the peak bond resistane, shear raks in a part of the onrete keys between the ribs are initiated (Fig 3.3). With inreasing slip, an inreasing area of onrete between lugs is affeted by shear failure, and onsequently the bond is redued. After a ertain stage later on, the onrete between lugs is ompletely sheared off, and the only mehanism left is fritional resistane (Eligehausen, Popov and Bertero, 1983). Bond an fail in multiple ways. The longitudinal bond stresses an exeed the shear strength of the onrete keys between ribs and the bar an be pulled freely. More ommonly though, splitting raks will propagate from the bar to the surfae of the onrete and the over will spall off. Fig 3.4 (Thompson et al 2002) shows some of the many splitting raks that an our. The type of splitting failure that ours in unonfined onrete is governed by bar spaing and over dimensions. Limitless over does not provide limitless bond. Beyond a ertain level of splitting resistane, pullout failure will govern. Typially though, splitting resistane governs the level of bond stress that onrete an sustain. Fig 3.4 Possible splitting rak failures (Thompson et al 2002) As a rib begins to bear on the onrete a wedge of rushed paste is formed in front of the rib. This wedge ats to hange the effetive fae angle of the rib (Fig 3.5). Thus, the bond angle tends to hange as a reinforing bar aquires load. The effet of this is that radial splitting stresses tend to inrease at a rate greater than the longitudinal bond stresses as tensile load in the reinforing bar rises. 38

43 Initial Bearing of Rib on Conrete Initial Bearing of Rib on Conrete Fig 3.5 Mehanis of rib bearing on onrete In summary, the inlined raks initiate at relatively low bond stresses at the point of ontat between steel and onrete (Goto, 1971). The length and width of these raks are arrested by the restraint offered by seondary reinforement. With inreasing slip, the onrete in front of the lugs will get rushed. The bond fores that transfer the steel fore into the onrete are inlined with respet to longitudinal bar axis. On inreasing the stress in the bar further, more slip ours beause more loal rushing takes plae and later, shear raks in the onrete keys are initiated (Fig 3.2). This leads to a rapid derease in the slope of the bond stress-slip urve. At maximum bond resistane, a part of the onrete key between the lugs has been sheared off. When more slip is indued, an inreasingly larger part of the onrete is sheared off without muh drop in bond resistane. Lesser and lesser fore is needed to shear off the remaining bits of the onrete keys to smooth out the surfae of the shear rak. When the slip is equal to the lear lug distane, it means that the lugs have travelled into the position of the neighbouring rib before loading. At this stage, only the fritional resistane is left, whih is pratially independent of the deformation pattern or the related rib area. An important point of the above disussion is that the gradual shearing off of the onrete keys is possible only in the ase of well onfined (restrained) onrete. If the onfinement provided by the transverse reinforement annot prevent the exessive growth of eventually developing splitting raks, the bars will be pulled out before the onrete keys are sheared off. 39

44 3.3 Bond under yli loading As per Rehm and Eligehausen (1977), the influene of repeated loads on the slip and bond strength of deformed bars is similar to that on the deformation and failure behavior of un-reinfored onrete loaded in ompression. The bond strength dereases with inreasing number of yles between onstant bond stresses (fatigue strength of bond). The slip under peak load and the residual slip inrease onsiderably as the number of yles inreases. If no fatigue failure of bond ours during yling and the load is inreased afterwards, the monotoni envelope is reahed again and followed thereafter. Therefore, provided the peak load is smaller than the load orresponding to the fatigue strength of bond, a pre-applied repeated load influenes the behaviour of bond under servie load but does not adversely affet the bond behaviour near failure ompared to monotoni loading. Although many fators related to early onrete damage (miro-raking and mirorushing due to high loal stresses at the lugs) may be involved in this bond behaviour during repeated loads, the main ause of the slip inrease under onstant peak bond stress is reep of onrete between lugs (Rehm and Eligehausen 1977). In ase of yli loading, if the slip is reversed before the shear raks develop in the onrete keys, for the first loading yle, the response is exatly same as that of the monotoni urve. During unloading, at zero load a gap remains open with slip between the lug and the surrounding onrete, beause only a small fration of slip that is aused by elasti onrete deformations is reovered during unloading. When an additional slip in the reversed diretion is imposed, some fritional resistane is built up. This resistane is small and is represented by the bond stressslip urve almost parallel to the slip axis, lose to zero bond stress. The bar therefore slips in the opposite side and then the lug is again in ontat with onrete and a gap is opened on the other side of the lug. Due to onrete bloking any further movement of the bar lug, a sharp rise in the stiffness of hystereti urve ours and the bond 40

45 stress-slip relationship in the opposite diretion again follows the monotoni envelope losely. A different behaviour is followed if the slip is reversed after the initiation of shear raks in the onrete keys. In this ase, the bond resistane is redued ompared to the monotoni envelope. When loading in the reverse diretion, the lug presses against a key whose resistane is lowered by shear raks over a part of its length indued by the first half yle. Furthermore, the old relatively wide inlined raks will probably lose at higher loads than in the yle for the ase of slip reversal before shear rak initiation, thus ompliating the transfer of inlined bond fores into the surrounding onrete. Therefore, shear raks in the undamaged side of the onrete side might be initiated at lower loads and join the old shear raks. Therefore the bond resistane is redued ompared to the monotoni envelope. When reversing the slip again, only the remaining intat parts of the onrete between lugs must be sheared off, resulting in an even lower maximum resistane. Fig 3.6 shows the typial bond stress-slip urve for deformed bars under yli loading (Eligehausen et al 1983). Fig 3.6 Bond-slip yli relationship for deformed bars (Eligehausen et al. 1983) If a large slip is imposed during the first half yle, resulting in the shearing off of almost the total onrete key, when moving the bar bak, a higher fritional resistane must be overome than earlier two ases. This is beause the onrete surfae is rough 41

46 along the entire width of the lugs. In suh ase the maximum resistane offered s even lower. Thus, it follows that if the bar is yled between onstant peak values of slips on either side, the main damage is done during the first yle itself. During subsequent yles, the onrete at the ylindrial surfae where shear failure ourred is mainly ground off, dereasing its interloking and fritional resistane. 3.4 Bond in RC Beam-Column Joints The joint resistane mehanism depends on bond fores along its perimeter so that a truss mehanism an be mobilized and on a ompressed diagonal strut between orners. These are rather brittle modes of behaviour, whih explains the very limited apaity that joints have in dissipating energy and maintaining their strength. The flexural fores from the beams and olumns ause tension or ompression fores in the longitudinal reinforements passing through the joint. During plasti hinge formation, relatively large tensile fores are transferred through bond. When the longitudinal bars at the joint fae are stressed beyond yield splitting raks are initiated along the bar at the joint fae whih is referred to as yield penetration (Uma, Prasad). Adequate development length for the longitudinal bar is to be ensured within the joint taking yield penetration into onsideration. Therefore, the bond requirement has a diret impliation on the sizes of the beams and olumns framing into the joint. The ontribution of the diagonal ompression strut is signifiant during the first yle in the inelasti range. However it deteriorates with the inrease of the inelasti loading yles. This is due to the fat that yling at high levels of inelasti deformation auses permanent elongation on the beam bars and leads to full depth open raks at the beam-joint interfae (Costa, J.L.D., 2003). Under these onditions flexural ompression from the beams beomes negligible. The ompressive fores are then transmitted to the longitudinal bars of the beams, whih signifiantly inrease the bond stresses along the horizontal perimeters of the joint ore. This leads to a drasti 42

47 redution in the ontribution of the onrete strut to the transfer of horizontal joint shear and a onsequent inrease in the ontribution of the truss mehanism. The mobilization of the truss mehanism depends intimately on the effetiveness of bond between the steel bars and the surrounding onrete. The bond has a very poor response in terms of energy dissipation, stiffness and strength degradation under inelasti yling. Thus, it an be onluded that the development of plasti hinges in the end setions of the beams seriously affets the ability of the joint to resist in a stable manner the indued shear fores. Again, joints whose olumns are low axially loaded are the most sensitive to bond deterioration sine ompression helps to maintain the bond mehanism (Costa, J.L.D., 2003). Joint horizontal shear reinforement improves anhorage of beam bars (Ihinose, 1991). But, there is an upper bound to the benefiial effets of onfinement. At this limit, maximum bond strength is attained beyond whih the rushing of onrete in front of the rib portion of the deformed bar ours. Researh indiates better bond performane when the lear distane between the longitudinal bars is less than 5 times the diameter of the bar (Eligehausen, Popov and Bertero, 1983). As expeted, the deformed bars give better performane in bond. The behavior of the reinforing bar in bond also depends on the quality of onrete around the bar. In exterior joints the beam longitudinal reinforement that frames into the olumn terminates within the joint ore. After a few yles of inelasti loading, the bond deterioration initiated at the olumn fae due to yield penetration and splitting raks, progresses towards the joint ore. Repeated loading will aggravate the situation and a omplete loss of bond up to the beginning of the bent portion of the bar may take plae. The longitudinal reinforement bar, if terminating straight, will get pulled out due to progressive loss of bond. In an interior joint, the fore in a bar passing ontinuously through the joint hanges from ompression to tension. This auses a push-pull effet whih imposes severe demand on bond strength and neessitates adequate development length within the joint. The development length has to satisfy the requirements for ompression and for 43

48 tension fores in the same bar. Insuffiient development length and the spread of splitting raks into the joint ore may result in slippage of bars in the joint. Slippage of bar ours when the limiting bond stress is exeeded within the available development length. In the ase of interior joints, the olumn depth is the available development length for the straight longitudinal bars passing through the joint. Hene, for a given limiting bond stress, the ratio of development length to the bar diameter beomes a onstant value. Researh has shown that when the development length is greater than 28 bar diameters little or no bond degradation was observed with respet to various shear stress levels in the joint (Leon 1990). 44

49 4. LITERATURE REVIEW OF BEAM-COLUMN JOINT MODELS Many researhers have attempted to model the behaviour of RC beam-olumn joints following various approahes that inlude, lumped plastiity models, multi-spring models, finite element simulations and frature mehanis based approahes. A summary of the various approahes followed in the past is given here. In general the models proposed for RC beam-olumn joints an be lassified as 1. Models based on experiments 2. Models based on analytial studies These are disussed in details as under. 4.1 Models based on experiments Some of the earliest work to simulate the inelasti response of reinfored onrete frames relied on the alibration of the plasti-hinges within beam-olumn line elements to introdue the inelasti ation of the beam-olumn joint. These models are essentially based on experiments onduted on full or redued sale beam-olumn joints under yli exitations. Several geometri urves and rules defining the hystereti behaviour of the onnetions are proposed Townsend and Hanson (1973) Townsend and Hanson (1973) introdued a set of polynomial expressions whih represent the hystereti behaviour of beam-olumn onnetions and aount for the observed stiffness degradation Anderson and Townsend (1977) Anderson and Townsend (1977) proposed a degrading trilinear joint model whose parameters are determined to math a series of experimental results from exterior beam-olumn joint tests. 45

50 4.1.3 Soleimani et al (1979) Soleimani et al (1979) introdued the onept of effetive length by whih the urvature at the beam-olumn interfae if multiplied to yield the fixed end rotation. The parameters defining the hystereti behaviour of the onnetion were seleted to best fit the observed behaviour and were not derived from physial interpretation of the mehanisms ontributing to suh behaviour. Therefore, the generalization and objetivity of suh models so as to make them appliable for different onfigurations and loading onditions is doubtful. Suh models therefore remained rather unpopular and will not be disussed further here. 4.2 Models based on analytial studies Several models have been proposed in the past based on analytial studies by various researhers. These models an be further subdivided as 1. Rotational hinge models 2. Multiple spring models Rotational Hinge Models These models are typially omposed of a bilinear or trilinear monotoni envelope urve and an assoiated set of hystereti rules defining behaviour under yli load reversals. Several researhers proposed suh models Otani (1974) Otani (1974) used a bilinear idealization of the envelope urve and omputed the harateristi points of this bilinear envelope urve with an assumption that bond stresses are onstant along the development length of the reinforing bars and that the reinforing embedment length is long enough to develop steel fores of required magnitude. The fixed end rotation was found to be proportional to the square of the 46

51 moment ating at the beam-olumn interfae. Takeda (1970) rule (Fig 4.1) was used as the assoiated hystereti rule. Fig 4.1 Takeda s hystereti rule Banon et al (1981) Banon et al (1981) also followed basially the same assumptions as Otani and employed a bilinear envelope urve in onnetion with Takeda s hystereti rule. However, they inluded the observed pinhing effet due to bond slip and shear sliding. The model was used to represent the inelasti deformations due to slippage of the reinforement Fillipou et al (1983, 1988) The assumptions followed in the above two models do not agree with the experimental evidenes and they appear to be on unsafe side with respet to the strength and stiffness of the joint. Moreover they have one shortoming in ommon that the experimentally observed slip-through of reinforing bars in interior joints of ommonly used dimensions is not taken into aount. This leads to an interation between the two olumn ends so that no unique moment-rotation relationship an be derived for one end, unless the ations at the other end are aounted for. Moreover 47

52 they fail to provide an understanding and analytial desription of mehanisms leading to the observed signifiant stiffness degradation in RC beam-olumn joints. Fillipou et al (1983, 1988) proposed model that an give due onsideration to the effet of bond deterioration on hystereti behaviour of the joints. Fig 4.2 shows the analytial model of the joint subelement that aounts for the fixed-end rotations whih arise at the beam-olumn interfae of RC members due to bond deterioration and slippage of reinforement in the joint and in the girder region adjaent to the joint. Fig 4.2 Beam-olumn joint subelement by Fillipou et al (1983, 1988) The proposed model onsists of a onentrated rotational spring loated at eah girder end. The two springs are onneted by an infinitely rigid bar to form the joint subelement. The moment-rotation relation of the rotational springs is derived using the detailed model by Filippou et al. (1983) whih aounts for the geometry, material properties and reinforement layout of the onnetion. A different moment-rotation relation an be presribed at eah onnetion. The moment-rotation relation of the rotational springs of the joint subelement is based on a bilinear elasti-strain hardening envelope urve. The envelope urves are established with the aid of the joint model in Filippou et al. (1983) one the dimensions of a partiular joint and the arrangement of the reinforement are known. This proess takes plae as follows: the beam-olumn joint model whih represents a partiular onnetion of the frame under investigation is 48

53 subjeted to monotonially inreasing girder end moments. These give rise to onentrated rotations due to reinforing bar pull-out at the beam-olumn interfae. Thus, the model presented by Fillipou et al was the most detailed and was based on pure mehanis of the joints. The model was easier to implement and also, the results mathed reasonably well with the experiments. However, the biggest limitation was that the model did not give due onsideration to the joint shear and diagonal raking in the hystereti behaviour of beam-olumn joints El-Metwally and Chen (1988) El-Metwally and Chen (1988) modelled the joint mehanially as a onentrated rotational spring and utilized the thermodynamis of irreversible proesses to obtain spring stiffness. In the proposed model, the onnetion is assumed to be properly designed and have adequate shear strength. Thus, the joint is modelled mehanially as a onentrated rotational spring using the assumptions that (1) anhorage failure for longitudinal reinforement embedded in the joint ontrols inelasti joint ation under earthquake loading and (2) total energy dissipation due to anhorage failure is approximately onstant for all beam-olumn joints. The biggest disadvantage of the model is that it requires the moment rotation data from beam-olumn joint experiments to alulate the required parameters Kunnath et al (1995) Kunnath et al. (1995) modified the flexural apaities of the beams and olumns of gravity load designed RC frames to model insuffiient positive beam bar anhorage and inadequate joint shear apaity impliitly. To aount for insuffiient positive beam bar anhorage, the pullout moment apaity of the beam was approximated as the ratio of the embedment length to the required development length per ACI multiplied by the yield moment of the setion. This approximation required that the yield strength of the disontinuous steel be redued by the ratio of the atual to the required anhorage length. To model inadequate joint shear apaity, the flexural apaities of the beams and olumns framing into the joint were redued to a level that would indue shear failure of the joint. The proposed proedure was utilized in 49

54 inelasti dynami time history analyses of typial three-, six-, and nine-story gravity designed RC frames, whih revealed that they are suseptible to damage from joint shear failures and weak olumn-strong beam effets leading to soft-story ollapses Alath and Kunnath (1995) Alath and Kunnath (1995) modeled the joint shear deformation with a rotational spring model with degrading hysteresis. The finite size of the joint panel was taken into aount by introduing rigid links (Fig 4.3). The envelope to the shear stressstrain relationship was determined empirially, whereas the yli response was aptured with a hystereti model that was alibrated to experimental yli response. The model was validated through a omparison of simulated and experimental response of a typial GLD RC frame interior beam-olumn joint subassembly. Fig 4.3 Beam-Column Joint model by Alath and Kunnath (1995) Again, the biggest disadvantage of the above mentioned models is that they require the moment rotation data from beam-olumn joint experiments to alulate the required parameters Pampanin et al (2003) A simple model has been more reently proposed by Pampanin et al. (2002) that onsists of a non-linear rotational spring that permits to model the relative rotation between beams and olumns onverging into the node and to desribe the post- 50

55 raking shear deformation of the joint panel (Fig 4.4). Beam and olumn elements are modelled as one dimensional element with lumped plastiity in the end setions with an assoiated moment-urvature relationships defined by a setion analysis. The effet of moment-axial load interation is taken into aount for olumns. To represent the real geometri dimensions of the joint panel region, rigid elements are used to onnet the beam and olumn members to the rotational spring. Fig 4.4 Model for RC beam-olumn joints by Pampanin et al (2002) The definition of the moment-rotation relationship of the rotational spring is based on the results of experimental tests performed at the Department of Strutural Mehanis of the University of Pavia (Pampanin et al., 2002). A relation between the shear deformation and the prinipal tensile stress in the panel region was found and transformed into a moment-rotation relation to be assigned to the rotational spring. The shear deformation is assumed to be equal to the rotation of the spring and the moment is dedued as orresponding to the prinipal tensile stress evaluated on the basis of Mohr theory Comment on Rotational Hinge Models The rotational-hinge joint model provides a means of independently haraterizing inelasti joint ation with only a moderate inrease in omputational effort. But, this approah does not failitate the development of objetive and aurate alibration 51

56 proedures. It requires that data from experimental testing of beam-olumn joint subassemblages be used to develop a one-dimensional joint moment-rotation relationship. Developing suh a model that an be used to predit the response of joints with different design details requires either a large number of data sets and a sophistiated alibration proedure or multiple models for joints with different design details. Currently, there are not suffiient data in the literature to support the development of models that are appropriate for a broad range of joint designs Multiple Spring Models Multiple spring models is a more realisti and objetive extension of the rotational spring models. Instead of using a single rotational spring, this approah reommends to use various springs to model different mehanisms of the joints. A nie review of multiple spring models is given by Celik and Elingwood (2007) Biddah and Ghobarah (1999) Biddah and Ghobarah (1999) modeled the joint with separate rotational springs that modelled the joint shear and bond-slip deformations (Fig 4.4). Fig 4.4 Beam-Column Joint model by Biddah and Ghobarah (1999) 52

57 The shear stress-strain relationship of the joint was simulated using a tri-linear idealization based on a softening truss model (Hsu, 1988), while the yli response of the joint was aptured with a hystereti relationship with no pinhing effet. The bond-slip deformation was simulated with a bilinear model based on previous analytial and experimental data. The yli response of the bond-slip spring was aptured with a hystereti relationship that aounts for pinhing effets. They utilized this joint element in performing dynami analyses of three- and nine-story gravity load designed RC buildings. They ompared the dynami response of three and nine-story frames modelled with joint elements to the response of similar frames with rigid joints when subjeted to strong motion reords. The omparisons revealed that aounting for joint shear and bond-slip deformations in modelling results in signifiantly larger drifts, partiularly for the nine-story frame Elmorsi et al (2000) Elmorsi et al (2000) proposed an approah where beams and olumns are desribed by elasti elements and are onneted to the joint through the interposition of non-linear transitional elements. The effetive node panel region is modelled with another element onstituted by 10 joints (Fig 4.5). Fig 4.5 Beam olumn joint model by Elmorsi et al (2000) 53

58 This model allows to desribe the material behaviours with the introdution of the stressstrain relationships of steel and onrete. Conrete is defined by two different relationships defining the pre and post raking behaviour. Longitudinal reinforing steel bars are modeled with non-linear elements plaed along the upper and lower sides of the joint panel. Furthermore this model allows the introdution of a "bond-slip element" to represent the slipping of steel bars Youssef and Ghobarah (2001) Youssef and Ghobarah (2001) proposed a joint element (Fig 4.6) in whih two diagonal translational springs onneting the opposite orners of the panel zone simulate the joint shear deformation; 12 translational springs loated at the panel zone interfae simulate all other modes of inelasti behaviour (e.g., bond-slip, onrete rushing) elasti elements were used for the joining elements. The model was validated using experimental test results of dutile and nondutile exterior beamolumn joints. This model requires a large number of translational springs and a separate onstitutive model for eah spring, whih may not be available and restrits its appliability. Shear springs Rigid Members Elasti beam element Pin Joint Conrete and steel springs Fig 4.6 Beam-olumn joint model by Youssef and Ghobarah (2001) 54

59 Lowes et al (2003) Lowes and Altoontash [2003] proposed a 4-node 12-degree-of-freedom (DOF) joint element (Fig 4.7) that expliitly represents three types of inelasti mehanisms of beam-olumn joints under reversed yli loading. Eight zero-length translational springs simulate the bond-slip response of beam and olumn longitudinal reinforement; a panel zone omponent with a zero-length rotational spring simulates the shear deformation of the joint; and four zero-length shear springs simulate the interfae-shear deformations. Fig 4.7 Beam-olumn joint model by Lowes et al (2003) The envelope and yli response of the bar stress versus slip deformation relationship were developed from tests of anhorage-zone speimens and assumptions about the bond stress distribution within the joint. To define the envelope to the shear stress-strain relationship of the panel zone, the modified-ompression field theory (MCFT) (Vehio and Collins, 1986) was utilized. The yli response of the panel zone was modelled by a highly pinhed hysteresis relationship, dedued from experimental data provided by Stevens et al. (1991). A relatively stiff elasti loaddeformation response was assumed for the interfae-shear omponents. Lowes et al. [2004] later attempted to model the interfae-shear based on experimental data; this effort also predited a stiff elasti response for the interfae- 55

60 shear. Mitra and Lowes [2004] subsequently evaluated the model by omparing the simulated response with the experimental response of beam-olumn joint subassemblies. The experimental data inluded speimens with at least a minimal amount of transverse reinforement in the panel zone, whih is onsistent with the intended use of the model. Joints with no transverse reinforement, a reinforing detail typial in GLD RC frames, were exluded from this study. It was noted that in joints with low amounts of transverse reinforement, shear is transferred primarily through a ompression strut, a mehanism, whih is stronger and stiffer than predited by the MCFT. The model is therefore not suitable for the analysis of the joints of gravity load designed frames with no transverse reinforement Altoontash (2004) Altoontash (2004) simplified the model proposed by Lowes and Altoontash (2003) by introduing a model onsisting of four zero-length rotational springs loated at beamand olumn-joint interfaes, whih simulate the member-end rotations due to bondslip behaviour, while the panel zone omponent with a rotational spring remains to simulate the shear deformation of the joint (Fig 4.8). Fig 4.8 Beam-olumn joint model by Altoontash (2004) 56

61 The onstitutive relationship (i.e., the envelope and the yli response) for the panel zone from Lowes and Altoontash (2003) was retained, enabling the alulation of onstitutive parameters based on material properties, joint geometry, joint reinforing steel ratio, and axial load. However, alibration of onstitutive parameters was still required for joints with no transverse reinforement to overome the limitation of the MCFT for suh joints. He adapted the onstitutive model developed for the translational bond-slip springs in Lowes and Altoontash (2003) in a fiber setion analysis to derive the onstitutive model for the member- end rotational springs, but noted that detailed information on bond-slip response is needed. Furthermore, the development length was assumed to be adequate to prevent omplete pullout. The model is still not suitable for the analysis of the joints of gravity load designed frames with no transverse reinforement Shin and LaFave (2004) Shin and LaFave (2004) represented the joint by rigid elements loated along the edges of the panel zone and rotational springs embedded in one of the four hinges linking adjaent rigid elements (Fig 4.9). Fig 4.9 Beam-olumn joint model by Shin and LaFave (2004) 57

62 The envelope to the joint shear stress-strain response was approximated by the MCFT, whereas experimental data were used to alibrate the yli response. Two rotational springs (in series) loated at beam-joint interfaes simulate the member-end rotations due to bond-slip behaviour of the beam longitudinal reinforement and plasti hinge rotations due to inelasti behaviour of the beam separately. The proposed joint model is intended for RC beam-olumn joints of dutile moment frames designed and detailed following modern seismi ode requirements. LaFave and Shin (2005) disussed the use of the MCFT in defining the envelope to the shear stress-strain relationship of the panel zone. The authors olleted from the literature experimental joint shear stress and strain data of 50 RC interior joint subassemblies that failed in joint shear. The envelope responses to the experimental data typially follow a quad-linear urve that onnets three key points (orresponding to joint shear raking, reinforement yielding, and joint shear strength) starting from the origin and has a degrading slope one past the joint shear strength. For eah of the experimental subassemblies, the authors applied the MCFT as desribed by Lowes and Altoontash [2003] to determine the ordinates of the envelope points, partiularly the maximum joint shear stress (i.e., joint shear strength). Comparison of the ratio of analytial (MCFT) to experimental maximum joint shear stress versus the ratio of transverse joint shear reinforement provided to thatrequired by ACI [ACI Committee 318, 2002] revealed that the MCFT approah onsistently underestimates the joint shear strength for joints that do not satisfy the joint reinforement requirement per ACI Hene, the MCFT may be inappropriate for modeling GLD RC frames, whih have little or no joint transverse shear reinforement Comment on Multiple spring models The multiple spring models are in general more aurate and are based on mehanis of joints. However, in ertain ases, they also need large experimental data for alibration. The limitations of suh models are: 1. They need larger omputational effort as ompared to rotational hinge models. 2. Often need a speial element inorporated in software. 58

63 3. Most of the available models are not suitable for joints of gravity designed frames. 4.3 Summary of Existing Models Many researhers have proposed various models to apture the inelasti behaviour of reinfored onrete beam-olumn onnetions under seismi exitations. The first models begin with the experimental studies based models but they were found to be unobjetive. As the understanding of the behaviour of beam-olumn onnetions grew, more detailed and aurate models ould be proposed. Rotational spring models reommend modelling the joint as a rotational spring onneting beam and olumn elements, even though it is not so straightforward in reality. The moment-rotation harateristis determination in suh a ase needs large and areful alibration. The multiple spring models definitely reommend models that are muh loser to reality by modelling shear behaviour and slip behaviour by different springs but they need speial purpose programs or elements for implementation. Moreover, many of suh models are not suitable for the joints of gravity designed RC frames without any transverse reinforement, the ase that is most ritial and needs maximum onsideration. Therefore, there is still a large sope to develop realisti models that an not only predit the behaviour of even poor detailed beam-olumn onnetions well but are also are implementable in general purpose nonlinear analysis programs e.g. SAP2000, STAADPro, NISA ivil to name a few. At the same time, it is also needed that the model is loser to reality from the onsideration of deformation behaviour and load resisting mehanism. An attempt is made in this work to propose suh a model. 59

64 5. FORMULATIONS FOR PROPOSED MODEL As listed in previous hapter, several models are available in literature to model the reinfored onrete beam-olumn onnetions. However, there is still a need to develop, realisti, objetive and easily implementable models that an enable not only researhers but also the designers using general purpose programs to give due onsideration to the inelasti behaviour of RC beam-olumn onnetions. In this hapter, the basis and formulations for suh a model are proposed. 5.1 Contribution of Joint Shear Deformation to Storey Drift The typial deformed shape of a shear building under an earthquake is shown in Fig 5.1 below. The inter-storey drift is given as the differene in the deformation of two suessive stories Fig 5.1 Typial deformed shape of framed strutures under earthquakes At the joint level, the ontribution to joint shear deformation to storey drift is shown in Fig 5.2 for exterior joints and in Fig 5.3 for interior joints. As seen here, due to the joint shear deformation, γ, the olumn experienes a relative shear displaement of j b j γ h, where h b is the total depth of the beam. This deformation an be divided into two as = γ h / 2 for the olumn half above the beam entre line and = γ h / 2 for j b j b the olumn half below the beam entre line. This deformation is in addition to any shear deformations in the olumn due to external shear fores. 60

65 Again, as seen from Figs 5.2 and 5.3, due to joint shear deformation, the beam experienes a rotation of b j b γ j due to whih the beam tip displaement is equal to = γ L, where L b is the length of the beam tip (mid point of beam in ase of buildings) from the fae of the olumn. Again, this rotation is due only to the shear deformation of the joint and is in addition to any rotation in the beam that ours due to external bending moment. j h b /2 j h b j L b j L b j h b /2 Fig 5.2 Contribution of joint deformation to storey drift for exterior joints 61

66 j h b /2 j h b j L b j L b j h b /2 Fig 5.3 Contribution of joint deformation to storey drift for interior joints 5.2 Modelling the Contribution of Joint Shear Deformation to Storey Drift Based on the above disussed deformational behaviour of joint, the best way to model the ontribution of joint shear deformation to overall storey drift should be a model that an onsider the shear deformations in olumn and rotation in beam due to joint shear deformation. One reasonable way to model this behaviour is as shown in Fig

67 where shear springs in the olumn portion and the rotational springs in the beam region are assigned. j h b /2 j h b j L b j L b j h b /2 Fig 5.4 Modelling of joint deformational behaviour This kind of model an be, in a very straightforward manner, applied to general purpose programs where the beam and olumn members are modelled as frame 63

68 elements with 6 degrees of freedom at both ends and the springs are the regions of onentrated plastiity with user defined harateristis (Fig 5.5). V h b L V h /2 L b V Fig 5.5 Implementation of model in frame elements 64

69 Fig 5.5 shows the springs needed to apture only the joint behaviour. In order to apture the omplete deformational behaviour of beams, olumns and the joints, shear and rotational springs for beams and olumns must also be modelled. Formulations to alulate flexural and shear hinge harateristis for members is given in Appendix. Note that, although here, the modelling is shown only for exterior joints, the same model with another rotational spring for the beam on other side is valid for interior joints as well. Physially, the springs should have harateristis as moment in beam, M b v/s shear rotation of joint, γ j for the rotational spring and joint horizontal shear fore, V jh v/s shear deformation in olumn portion of joint, = γ h / 2. However, in programs j b based on matrix analysis using frame elements, it is not possible to model the reinforement details expliitly and therefore it is not possible to alulate horizontal joint shear fore that is given by equation (2.1). In order to make this model suitable for implementation in suh programs, we need to provide the harateristis for shear springs as shear fore in olumn, V v/s shear deformation in olumn portion of joint, = γ h / 2. j b One these harateristis are generated for the joints, the model an be implemented in the omputer model of the struture so that the joint behaviour an be taken into aount. There are different ways to generate these harateristis as desribed under: 1. Results from experiments on beam-olumn joints tests. 2. Results from detailed finite element analysis of joints. 3. Analytial omputation of harateristis from mehanis of the joints Results from experiments on beam-olumn joints tests The olumn shear fore an be diretly measured in the experiment using load ell. Also joint shear deformations an be alulated from the experiments using ross onfiguration of linear variable differential transformers (LVDTs) as shown in Fig 5.6. The joint shear deformation is given as 65

70 2 2 a + b γ j = ( δ d2 δ d1 ) (5.1) 2ab where, δ d 2 is the hange in length measured by LVDT, d2 δ d 1 is the hange in length measured by LVDT, d1 a is the horizontal distane between the end points of the LVDTs b is the vertial distane between the end points of the LVDTs a b d 2 Fig 5.6 Measuring joint shear deformations in tests Fig 5.7 shows a typial joint shear stress v/s joint shear stress plot obtained from the tests (Pantelides et al 2002). Fig 5.7 Typial measured joint shear stress v/s shear strain in tests 66

71 Using suh plots from experiments, the required harateristis of shear fore in olumn, V v/s shear deformation in olumn portion of joint, = γ h / 2 an be generated. j b Although, this method may be the most aurate and reliable one, it is highly prohibitive from the point of view of ost, time and resoures required. Moreover, onsidering the different types of joints that may be present in a struture, this method is highly impratial too. However, this is the only method that is available for alibration and also is needed to validate the results Results from detailed finite element analysis of joints Another method to obtain the harateristis is to perform detailed finite element analysis of the joints. One suh method is explored and reported by Eligehausen et al (2006) and Sharma et al (2008) where a finite element approah speially developed for detailed modelling of frature in quasi brittle materials has been proposed (Fig 5.8 and 5.9). MASA, a finite element program for 3D nonlinear analysis of onrete and reinfored onrete strutures, developed at the Institut für Werkstoffe im Bauwesen, Universität Stuttgart (IWB and Ožbolt, 2005, 2008) was used in these works. The miroplane material model with relaxed kinemati onstraint is used for modelling the onrete and a disrete one dimensional bond element model is used for modelling the bond behaviour of the reinforement bars. Quasi-brittle material (onrete) is in the program disretized by the eight node (hexa) or four node (tetra) solid finite elements. The disretization of the reinfored bars is performed by two-node truss elements or alternatively by beam elements. As the global solution strategy, three possibilities an be used: (1) Constant stiffness method (CSM), (2) tangent stiffness method (TSM) and (3) seant stiffness method (SSM). The analysis is inremental and therefore the total applied load has to be divided into a number of load or displaement inrements. 67

72 Fig 5.8 FE Model of the joint (Eligehausen et al 2006) Fig 5.9 Disrete bond element and harateristis for bond element To prepare input data as well as to analyze the results of the finite element analysis, ommerial pre- and post-proessing pakage FEMAP is used. The program generates nodes, nodal onnetivity, boundary onditions, material data and loads whih are required for the finite element ode of MASA. The link between FEMAP and MASA is realized through an input interfae program whih from FEMAP output data (neutral file) generates input data of the FE ode. To generate postproessing output results from the numerial results of the FE ode, an output interfae program an be used. The post-proessing output results an be read and graphially interpreted by FEMAP. 68

73 The auray and reliability of this method relies on the auray and reliability of the modelling tehniques. For the above mentioned model, it is shown that the model an predit the behaviour of the joints with high auray and an apture various failure modes. This method has muh less ost impliations but needs lot of modelling and omputational time and effort. Again, onsidering the fat that there may be several different kinds of joints existing in a struture, the omputational time and effort in this method beomes prohibitive Analytial omputation harateristis from mehanis of the joints The spring harateristis an also be generated analytially using the mehanis of the joint. As explained in hapter 2, a prinipal stress riterion provides a more rational basis of prediting joint failure. In this work, the same riterion is utilized. For joints with deformed bars as reinforement, Priestley (1997) suggested plots of prinipal tensile stress v/s joint shear deformation for interior and exterior joints (Fig 5.10). Pampanin (2002) suggested similar plots for exterior joints with smooth bars having end hooks (Fig 5.10). Fig 5.10 Suggested prinipal tensile stress v/s joint shear deformation relationship (Pampanin et al, 2002) 69

74 As per Priestley (1997), for joints with deformed bars, a lower limit of ritial prinipal tensile stress, p t of 0.29 f seems appropriate for both interior and exterior joints, where f ' is the ylindrial ompressive strength of the onrete. For exterior joints, when the beam reinforement is anhored by bending away from the joint (Fig 5.11 a), the diagonal struts in the joint annot be stabilized and the joint failure ours at an early stage. Thus, no further hardening is onsidered for suh joints. Fig 5.11 Exterior joints with (a) beam bars bent out (b) beam bars bent in For exterior joints with beam bars bent in a hardening behaviour with inrease of prinipal stress levels, up to 0.42 diagonal raking and damage in the joint panel zone. f is suggested that orresponds to more severe The formulations about generating the spring harateristis for the joints using the prinipal tensile stress riteria are provided in next setion. 5.3 Formulations for evaluating spring harateristis The fores ating on exterior joint due to seismi ations are shown in Fig 5.12 and that on interior joints are shown in Fig From plots of prinipal tensile stress and 70

75 joint shear deformation, we an generate the spring harateristis for the joint model proposed. The formulations are given here divided into two ases: 1. Joints without axial load on olumn 2. Joints with axial load on olumn P C s2 C 2 V T 1 V T b V jv h V jh V b V jh V jv C b L C s2 C 2 Z T 1 T b Z b L b h b V b P M V C sb T 2 C 1 C s1 (b) Horizontal and vertial joint shear C b V C sb C s2 C 2 T 1 T 2 C 1 C s1 p T b M b p t C b C sb V b T 2 C 1 C s1 V V P (a) External ations and fores in beams and olumns Fig 5.12 Mehanis of exterior joint under seismi ations M P () Prinipal stresses in joint Joints without axial load on olumn (P = 0) The prinipal tensile stress is given by (Tsonos 2007), p t 2 σ σ 4τ = 1+ (5.2) σ where, σ is the vertial joint shear stress given by, 71

76 V jv σ = (5.3) b h and τ is the horizontal joint shear stress given by, V jh τ = (5.4) b h P C s2 C 2 V T 1 V C sb2 T b1 C b2 V jv h V jh V b V jh 0.5L - h b V jv C b1 C s2 C 2 Z T 1 L b T b2 V b V T 2 C 1 C s1 (b) Joint shear C sb1 C sb2 C b2 T b1 Z b h b P M C b1 V L b T b2 V b C sb1 C s2 C 2 T 1 V b T 2 C 1 C s1 M b C sb2 C b2 p T b1 M b 0.5L - h b V b T b2 p t C b1 C sb1 V b T 2 C 1 C s1 V V P (a) External ations and fores in beams and olumns () Prinipal stresses in joint Fig 5.13 Mehanis of interior joint under seismi ations M P Here, b = breadth of the joint ore. h = depth of the joint ore. V jh = Horizontal joint shear fore. V jv = Vertial joint shear fore. 72

77 Thus, σ V jv = τ (5.5) V jh Also, it is shown that (Park and Paulay, 1975; CEN 250; Paulay and Park, 1984; Tsonos, 2007) V V jv jh h h b = = (5.6) α where, h b is the depth of the beam α is known as the aspet ratio of the joint Putting (5.6) in (5.5), we get, σ = ατ (5.7) Putting (5.7) in (5.2), we get, p t 2 ατ ατ 4τ = α τ or, p t ατ 4 = α Thus, (5.8) 2 p τ = t 4 α α (5.9) 73

78 Putting (5.9) into (5.4), we get, V jh 2 ptb h = 4 α α (5.10) Thus, for a given value of prinipal tensile stress, p t, we an alulate orresponding horizontal joint shear, V jh by using (5.10). Now, we have, shear fore in olumn, V = Tb V jh (for exterior joints, Fig 5.12), and (5.11 a) V = C + C + T V (for interior joints, Fig 5.13) (5.11 b) sb2 b2 b1 jh To alulate, V orresponding to V jh, we need to follow an iterative proedure as given below, 1. Calulate moment in beam, M b v/s tensile fore in the beam bar, T b urve for beam setion in ase of exterior joints and M b v/s C b + C sb + T b, for interior joints (Same proedure as followed for obtaining Moment v/s urvature diagram). Detailed proedure to obtain moment v/s urvature urve is given in appendix. 2. Assume a Value of T b or C b + C sb + T b, as appropriate. 3. Calulate olumn shear using equation 5.11 (a or b) as appropriate. 4. Calulate beam shear from statis of the joint e.g., V b V L = (for exterior joints without gravity load) (5.12) L + h / 2 b 74

79 5. Calulate moment in the beam, M b = Vb lb (5.13) 6. From M b v/s T b diagram or M b v/s C b + C sb + T b, find the value of T b or C b + C sb + T b. 7. If the value obtained in step 6 is lose to the orresponding assumed value in step 2, then the obtained value of M b orresponding to V jh is orret. Else, go to step 2. By this iterative proedure, we an obtain the values of V and M b orresponding to V jh (and in turn orresponding to p t ). Corresponding to a given value of j, we an alulate = j h b /2. Thus, we an have a V v/s relationship for shear hinge in olumn region of the joint and M b v/s j relationship for rotational hinge in beam region of the joint. A flowhart to derive V v/s and M b v/s j relationships from given p t v/s j for no axial load ase and exterior joints is given in Fig The same is appliable for interior joints with T b replaed by C b + C sb + T b Joints with axial load on olumn The prinipal tensile stress is given by (Tsonos 2007), p t 2 σ σ 4τ = 1+ (5.14) σ In this ase, σ is the vertial joint shear stress given by, σ V jv = (5.15) + P b h 75

80 Start Get the input values for the geometry and material properties for the joint and setion details for the beam. Calulate M b v/s T b relationship fort the beam setion Get the value of p t e.g. p = 0.29 f (for yield) and p = 0.42 f (for ultimate) t t Calulate V jh 2 ptbh = 4 α α Assume a value of T b = T i. Calulate Vi = Ti V jh Calulate V bi Vil = l + h / 2 b Calulate M bi = Vbi lb Read the value of T b (=T i+1 ) orresponding to M bi from M b v/s T b urve No Ti 1 i Is + T < 0.01 T i Yes Calulate V = T V Vl And Vb = l + h / 2 b jh Calulate = j h b /2 Read the value of j orresponding to the value of p t Draw V v/s and M b v/s j relationships. Stop Fig 5.14 Flowhart for V v/s and M b v/s j relationships for no axial load ase 76

81 and τ is the horizontal joint shear stress given by, V jh τ = (5.16) b h Also, it is shown that (Park and Paulay, 1975; CEN 250; Paulay and Park, 1984; Tsonos, 2007) V V jv jh h h b = = α (5.17) Putting (5.17) in (5.15), we get, V jv σ = + b h P b h αv P b h jh σ = + (5.18) b h Thus, σ = ατ + σ a (5.19) or, σ σ τ = a (5.20) α Putting (5.20) in (5.14), we get, p t 2 σ σ 4( σ σ a ) = 1+ (5.21) α σ 77

82 Rearranging equation (5.21), 2 2 pt 4( σ σ a ) 1 = 1+ (5.22) 2 2 σ α σ Squaring both the sides and simplifying, we get, σ (2 σ + α p ) σ + ( σ α p ) = 0 (5.23) a t a t Solving (5.23), we get, σ a + α pt + α α pt + 4 pt ( σ a + pt ) σ = (5.24) 2 Thus, for a given value of p t, a and, we an obtain the orresponding value of. Now, from eq (5.15), we an get, V = σb h P (5.25) jv By eq (5.17), we have, V V jv jh = (5.26) α Thus, for a given value of p t, we an alulate orresponding horizontal joint shear, V jh by using eqs (5.25) and (5.26). Now, we have, shear fore in olumn, V = Tb V jh (for exterior joints, Fig 5.12), and (5.27 a) 78

83 V = C + C + T V (for interior joints, Fig 5.13) (5.27 b) sb2 b2 b1 jh To alulate, V orresponding to V jh, we need to follow an iterative proedure as given below, 1. Calulate moment in beam, M b v/s tensile fore in the beam bar, T b urve for beam setion in ase of exterior joints and M b v/s C b + C sb + T b, for interior joints. 2. Assume a Value of T b or C b + C sb + T b, as appropriate. 3. Calulate olumn shear using equation 5.11 (a or b) as appropriate. 4. Calulate beam shear from statis of the joint e.g., V b V L = (for exterior joints without gravity load) (5.28) L + h / 2 b 5. Calulate moment in the beam, M b = Vb lb (5.29) 6. From M b v/s T b diagram or M b v/s C b + C sb + T b, find the value of T b or C b + C sb + T b. 7. If the value obtained in step 6 is lose to the orresponding assumed value in step 2, then the obtained value of M b orresponding to V jh is orret. Else, go to step 2. By this iterative proedure, we an obtain the values of V and M b orresponding to V jh (and in turn orresponding to p t ). Corresponding to a given value of j, we an alulate = j h b /2. Thus, we an have a V v/s relationship for shear hinge in olumn region of the joint and M b v/s j relationship for rotational hinge in beam region of the joint. 79

84 A flowhart to derive V v/s and M b v/s j relationships from given p t v/s j for with axial load ase and exterior joints is given in Fig The same is appliable for interior joints with T b replaed by C b + C sb + T b. One the V v/s and M b v/s j relationships are derived from given p t v/s j and details of the joint, the harateristis an be used as spring harateristis in the program to model the joint shear behaviour. 5.4 Prinipal tensile stress v/s shear deformation relations Various experiments have been performed by researhers in the past and have measured the joint shear deformations in the tests (Clyde 2000; Pantelides 2002; Pampanin 2002; Anderson 2008). Based on the data obtained on shear deformations in these tests and utilizing the reommendations made by Priestley (1997), the following plots of prinipal tensile stress v/s shear deformations were onsidered in this work to derive the spring harateristis. Only joints with deformed bars as reinforement are onsidered Exterior Joints Exterior Joints with beam bars bent in When the beam bars are bent into the joint (Fig 5.16), the diagonal struts in the joint are niely stabilized and therefore, even after a first raking (assumed to our at p = 0.29 f, the joint an offer further resistane and therefore a hardening t behaviour till the prinipal tensile stress reah a value of p = 0.42 f an be assumed (Priestley 1997). Based on these reommendations and using the experimental plots of shear deformations obtained by Clyde et al (2000), Pantelides et al (2002) and Anderson et al (2008) on similar joints, the plot of prinipal tensile stress v/s joint shear deformation, as shown in Fig 5.16 seems appropriate for alulating the spring harateristis. t 80

85 Start Get the input values for the geometry and material properties for the joint and setion details for the beam. Calulate M b v/s T b relationship fort the beam setion Get the value of p t e.g. p = 0.29 f (for yield) and p = 0.42 f (for ultimate) t t σ 4 ( ) Calulate a + α pt + α α pt + pt σ a + pt σ =, 2 V = σb h P and V = V / α jv jh jv Assume a value of T b = T i. Calulate Vi = Ti V jh Calulate V bi Vil = l + h / 2 b Calulate M bi = Vbi lb Read the value of T b (=T i+1 ) orresponding to M bi from M b v/s T urve No Ti 1 i Is + T < 0.01 T i Yes Calulate V = T V Vl And Vb = l + h / 2 b jh Calulate = j h b /2 Read the value of j orresponding to the value of p t Draw V v/s and M b v/s j relationships. Stop Fig 5.15 Flowhart for V v/s and M b v/s j relationships for with axial load 81

86 pt 0.42 f 0.29 f f f γ j 0.29 f 0.42 f Fig 5.16 Assumed prinipal tensile stress-shear deformation relation for exterior joints with bars bent in Exterior Joints with beam bars bent out When the beam bars are bent out of the joint (Fig 5.17), the diagonal struts in the joint annot be stabilized and therefore, the joint failure ours at early stage. No hardening an be assumed in suh ases after the first raking at p = 0.29 f. Further jointed resistane annot be relied upon in suh ases and therefore the prinipal tensile stress value of p = 0.29 f is assumed as the limiting value (Priestley 1997). Based on t these reommendations and using the experimental plots of shear deformations obtained for similar joints, the plot of prinipal tensile stress v/s joint shear deformation, as shown in Fig 5.17 seems appropriate for alulating the spring harateristis. t p t 0.29 f 0.19 f 0.10 f f γ j 0.19 f 0.29 f Fig 5.17 Assumed prinipal tensile stress-shear deformation relation for exterior joints with bars bent out 82

87 In many ases of gravity designed frames, the top beam bars are bent into the joint and the bottom beam bars are bent out of the joint. For suh ases, the plot of prinipal stress v/s shear deformation may be obtained by the superposition of Fig 5.16 and 5.17 as shown in Fig p t 0.42 f 0.29 f 0.10 f f γ j 0.19 f 0.29 f Fig 5.18 Assumed prinipal tensile stress-shear deformation relation for exterior joints with top bars bent in and bottom bars bent out Exterior Joints with straight beam bars with full development length embedment When the beam bars are not bent into the joint but kept straight, again the diagonal struts in the joint annot be stabilized and therefore, the joint failure ours at early stage. No hardening an be assumed in suh ases after the first raking at p = 0.29 f. In ases where the beam bars are embedded into the joint for full t development length, bond failure is unlikely and therefore, the same plot as shown in Fig 5.19 (same as for Fig 5.18) should apply Joints with straight beam bars with 6 inh embedment In most of pre 1970 s gravity designed buildings, the bottom bars of the joint were embedded only upto 6 inh inside the joint. In suh ases, the bond between onrete and rebars beomes the ritial parameter. Based on the tests by Pampanin (2002), the ritial prinipal tensile stress for smooth bars with end hooks is reommended as p = 0.19 f. t 83

88 pt 0.42 f 0.29 f f 0.08 f γ j 0.19 f 0.29 f Fig 5.19 Assumed prinipal tensile stress-shear deformation relation for exterior joints with top bars bent in and bottom bars straight with full development length Due to lak of test data on joints with deformed bars and 6 inh embedment, same value of prinipal tensile stress, i.e. p = 0.19 f is onsidered as limit for suh ases also. The plot proposed for suh joints is shown in Fig t pt 0.42 f 0.29 f 0.10 f " 0.06 f 0.13 f 0.19 f γ j Fig 5.20 Assumed prinipal tensile stress-shear deformation relation for exterior joints with top bars bent in and bottom bars straight with 6" embedment Interior Joints The prinipal tensile stress values that ould be resisted by an interior joint is generally muh higher than the exterior joints. Based on the test result data by Dhakal 84

89 et al (2005) and Hakuto et al (2000), the relationship between prinipal stress v/s shear deformation as shown in Fig 5.21 is reommended for the interior joints with deformed bars. p t 0.84 f 0.58 f 0.20 f f γ j 0.58 f 0.84 f Fig 5.21 Assumed prinipal tensile stress-shear deformation relation for interior joints The prinipal tensile stress-shear deformation relations proposed as above along with the formulations as given in this hapter were used for analysis of the joints. The validation of results with experiments is given in next hapter. 85

90 6. VALIDATION OF MODEL WITH TEST RESULTS Following the formulations and assumptions given in previous hapter, the analysis of joints tested by various researhers and given in literature was performed. The value of the raked modulus was onsidered as 0.45E, where E is the initial modulus of onrete taken as 4700(f') Tests by Clyde et al (2000) Clyde et al (2000) performed yli tests on exterior beam-olumn joints with varying axial loads. The beam bars were bent into the joint in all the ases and therefore plot as shown in Fig 5.15 was used to generate spring harateristis. The joints were designed in a way to have joint shear failure before the yielding of the beam bars. A typial exterior beam-olumn joint in a reinfored onrete frame building built in 1964 was hosen as a model for the projet. The overall dimensions of the original joint were redued by half, and reinforing details were redued based on shear stress alulations. The longitudinal reinforement in the beam was inreased to prevent early degradation of the beam, foring a shear mode of failure in the joint. There is no transverse reinforement within the joint ore, and the beam longitudinal bars are not adequately anhored in the onnetion. Four joints were tested under the program with an axial stress on the olumn as 0.1 f ' in two ases and 0.25f ' in other two ases. Typial reinforement details and dimensions of the joints tested are given in Fig 6.1 and the test setup is shown in Fig 6.2. The reinforement yield and ultimate strength values are given in Table below. Properties of reinforement bars used by Clyde et al (2000) Reinforement Type Bar Size No. (dia in mm) Yield strength, f y (MPa) Ultimate strength, f u (MPa) Beam longitudinal #9 (28.58) Column longitudinal #7 (22.23) Stirrups/ties #3 (9.53)

91 6.1.1 Test #2 Test #2 had an axial load on the joint orresponding to an axial stress on the olumn as 0.1 f '. The ylindrial onrete ompressive strength f ' was 46.2 MPa. Fig 6.1 Details of joints tested by Clyde et al (2000) For the given geometry, reinforement details and material properties, the beam and olumn flexural and shear harateristis were generated following the proedure given in Appendix. The joint spring harateristis were evaluated following the proedure explained in hapter 5. A sample alulation is given below. Let us onsider the point of p = 0.29 f. t p = 0.29 f = = 1.97 MPa t 87

92 and the axial stress is given as σ = 0.1 f = = 4.62 MPa a Fig 6.2 Test setup of joints tested by Clyde et al (2000) The aspet ratio, h 16 b α = = = 0.89 h 18 Substituting the values in eq (5.24), we get, ( ) σ = = 8.70 MPa 2 Thus, 88

93 V = ( σ σ ) b h = ( ) N jv a Or, V = kn jv From (5.26), we get, V jh V jv = = = kn α 0.89 Assume, T = 750 kn Thus, V = T V = = kn jh Thus, we have, V b Vl = = = kn l + h / / 2 b Moment in beam at the fae of the olumn, M b = V l = = kNm b b The orresponding tensile fore in the reinforement an be obtained as 780kN. Sine this is more than the assumed value of 750kN, another trial is required. Performing same alulations for a few times, we an onverge to a value of T = 745kN 89

94 Corresponding value of shear in olumn is V = T V = = kn jh and the bending moment in the beam is M b Vllb = Vblb = = = knm l + h / / 2 b Thus, orresponding to a prinipal tensile stress of p = 0.29 f, the values of shear fore in olumn and bending moment in the beam are V = kn and M b = knm respetively. t Similarly, the values of shear fore in olumn and bending moment in the beam orresponding to various levels of prinipal tensile stress an be alulated. In this ase these values were alulated for prinipal stress values of p = 0.29 f, p = 0.42 f and p = 0.10 f. t t t The omparison of experimental and analytial urves is given in Fig 6.3 below. To visualize the signifiane of joint modelling, a omparison is given with the analysis results when the model did not have springs to model the joint shear behaviour. It should be noted that in this ase also, the beam and olumn member had both flexural and shear spring harateristis assigned. Sine the test was performed under quasi yli loading, the envelope of the hystereti loops was onsidered for omparison with analytial results. The effet of modelling the joint is very lear from Fig 6.3. As per the test report (Clyde et al 2000), measurable flexural raks in the beam and shear raks in the joint appeared during the seventh load step orresponding to a lateral load of approximately 40 kips (178 kn). From the analysis, it an be seen that 90

95 the load at the beam end orresponding to a prinipal tensile stress of p = 0.29 f is kn, whih is extremely lose to the value of first signifiant raking in the experiment. t Load (kn) Experiment No joint model Joint Model -400 Displaement (mm) Fig 6.3 Experimental and analytial results for Test #2 (Clyde et al 2000) In the experiment, the subsequent loading steps produed only slight inrease in rak widths in the beam. Similar observations were made in the analysis. Fig 6.4 shows the deformed state and hinge pattern of the joint as obtained in the analysis. Fig 6.4 Analytial hinge pattern obtained from analysis 91

96 Pink olour hinge in the beam shows only a minor damage in the beam whereas red and yellow oloured hinges in the joint region depit extensive damage in the joint panel. The peak load was obtained as 267 kn in the experiment and 241 kn in the analysis, a value that orresponds to a prinipal tensile stress value of p = 0.42 f. t Thus, it an be onluded that not only the overall load defletion behaviour but also the failure modes were aptured very niely in the analysis using joint model. In the ase of model where the joint springs were not modelled, a large strain hardening behaviour after the first yield of beam bars was observed. The peak load in this ase was obtained as 370 kn and the ultimate displaement as 135 mm whih was found to be highly on the unsafe side Test #6 Similar to test #2, test #6 also had an axial load on the joint orresponding to an axial stress on the olumn as 0.1 f '. The ylindrial onrete ompressive strength, f ' was 40.1 MPa. For the given geometry, reinforement details and material properties, the beam and olumn flexural and shear harateristis were generated following the proedure given in Appendix. The joint spring harateristis were evaluated following the proedure explained in hapter 5. The omparison of experimental and analytial urves is given in Fig 6.5 below. To visualize the signifiane of joint modelling, a omparison is given with the analysis results when the model did not have springs to model the joint shear behaviour. As per the test report (Clyde et al 2000), measurable flexural raks in the beam and shear raks in the joint appeared during the sixh load step orresponding to a lateral load of approximately 156 kn. From the analysis, it an be seen that the load at the 92

97 beam end orresponding to a prinipal tensile stress of p = 0.29 f is kn, whih is extremely lose to the value of first signifiant raking in the experiment. t Load (kn) Displaement (mm) Experiment No joint model Joint Model Fig 6.5 Experimental and analytial results for Test #6 (Clyde et al 2000) The peak load was obtained as 262 kn in the experiment and 220 kn in the analysis, a value that orresponds to a prinipal tensile stress value of p = 0.42 f. t Thus, it an be again onluded that not only the overall load defletion behaviour but also the failure modes were aptured very niely in the analysis using joint model. In the ase of model where the joint springs were not modelled, a large strain hardening behaviour after the first yield of beam bars was observed. The peak load in this ase was obtained as 368 kn and the ultimate displaement as 170 mm whih was found to be highly on the unsafe side Test #4 Test #4 had an axial load on the joint orresponding to an axial stress on the olumn as 0.25 f '. The ylindrial onrete ompressive strength, f ' was 41.0 MPa. 93

98 For the given geometry, reinforement details and material properties, the beam and olumn flexural and shear harateristis were generated following the proedure given in Appendix. The joint spring harateristis were evaluated following the proedure explained in hapter 5. The omparison of experimental and analytial urves is given in Fig 6.6 below. To visualize the signifiane of joint modelling, a omparison is given with the analysis results when the model did not have springs to model the joint shear behaviour. As per the test report (Clyde et al 2000), major raking did not our until load step 10 following yielding whih orresponded to a lateral load of 60 kips (267 kn). From the analysis, it an be seen that the load at the beam end orresponding to a prinipal tensile stress of p = 0.29 f is 223 kn, whih is quite lose to the value of first t signifiant raking in the experiment Load (kn) Experiment No joint model Joint Model -400 Displaement (mm) Fig 6.6 Experimental and analytial results for Test #4 (Clyde et al 2000) 94

99 The peak load was obtained as 276 kn in the experiment and 286 kn in the analysis, a value that orresponds to a prinipal tensile stress value of p = 0.42 f. t Thus, it an be again onluded that even for a higher axial load, both the load defletion behaviour and the failure modes were aptured very niely in the analysis using joint model. The model without joint springs again yielded results on unsafe side Test #5 Similar to test #4, test #5 also had an axial load on the joint orresponding to an axial stress on the olumn as 0.25 f '. The ylindrial onrete ompressive strength, f ' was 37.0 MPa. For the given geometry, reinforement details and material properties, the beam and olumn flexural and shear harateristis were generated following the proedure given in Appendix. The joint spring harateristis were evaluated following the proedure explained in hapter 5. The omparison of experimental and analytial urves is given in Fig 6.7 below. To visualize the signifiane of joint modelling, a omparison is given with the analysis results when the model did not have springs to model the joint shear behaviour. The yield load in the tests was observed as 231 kn. From the analysis, it an be seen that the load at the beam end orresponding to a prinipal tensile stress of p = 0.29 f is 207 kn, whih is quite lose to the value of first signifiant raking t in the experiment. The peak load was obtained as 267 kn in the experiment and 268 kn in the analysis, a value that orresponds to a prinipal tensile stress value of p = 0.42 f, an extremely lose math. The model without joint springs again yielded results on unsafe side. t 95

100 Load (kn) Experiment No joint model Joint Model -400 Displaement (mm) Fig 6.7 Experimental and analytial results for Test #5 (Clyde et al 2000) 6.2 Tests by Pantelides et al (2002) Pantelides et al (2002) performed yli tests on exterior beam-olumn joints with varying axial loads. The six test units were full-sale models of typial exterior beamolumn joints in RC buildings found in the United States before The longitudinal and transverse reinforement in the beam and the olumn transverse steel was inreased to prevent early degradation of the beam and olumn, foring a shear mode of failure in the joint. There is no transverse reinforement within the joint ore, and the beam longitudinal bottom bars did not have adequate embedment into the joint. Analysis is performed for four units two of whih were tested with an axial stress on the olumn as 0.1 f ' and other two were tested with an axial stress of 0.25f ' on the olumn. The reinforement details and dimensions of the joints tested are given in Fig 6.8 and 6.9 and the test setup is shown in Fig The reinforement yield and ultimate strength values are given in Table below. 96

101 Properties of reinforement bars used by Pantelides et al (2002) Reinforement Type Bar Size No. (dia in mm) Yield strength, f y (MPa) Ultimate strength, f u (MPa) Beam longitudinal #9 (28.58) Column longitudinal #8 (25.4) Stirrups/ties #3 (9.53) Fig 6.8 Details of test units 1 and 2 (Pantelides et al 2002) 97

102 As seen in Fig 6.8, test units 1 and 2 had top beam bars bent into the joint in the form of a hook but overing full joint depth and the bottom bars were embedded only up to 6 inh inside the joint. Thus the plot shown in Fig 5.19 was followed to generate spring harateristis for the joint. Fig 6.9 Details of test units 5 and 6 (Pantelides et al 2002) Test units 5 and 6 (Fig 6.9) had both top and bottom beam bars bent into the joint in the form of a hook overing full joint depth. Thus the plot shown in Fig 5.15 was followed to generate spring harateristis for the joint. 98

103 Fig 6.10 Test setup used by Pantelides et al (2002) Test unit 1 Test unit 1 had an axial load on the joint orresponding to an axial stress on the olumn as 0.1 f '. The ylindrial onrete ompressive strength f ' was 33.1 MPa. For the given geometry, reinforement details and material properties, the beam and olumn flexural and shear harateristis were generated following the proedure given in Appendix. The joint spring harateristis were evaluated following the proedure explained in hapter 5. The omparison of experimental and analytial urves is given in Fig 6.11 below. To visualize the signifiane of joint modelling, a omparison is given with the analysis results when the model did not have springs to model the joint shear behaviour. 99

104 The effet of unsymmetri detailing of the joint is highly prominent in this ase. Note that a positive load indiates that the load was applied in the upward diretion. It is lear that the upward diretion resistane is defiient beause of the inadequate anhorage of the bottom beam bars of only 6 in. into the joint The peak load from the experiment was obtained as 93.8 kn for up diretion and kn for down diretion. In the analysis, the orresponding values were obtained as kn for up diretion and kn for down diretion that mathes losely the experimentally obtained values. The model without joint springs again yielded results on highly unsafe side for both the diretions Load (kn) Experiment No joint model Joint Model Down Joint Model Up -400 Displaement (mm) Fig 6.11 Experimental and analytial results for test unit 1 (Pantelides et al 2002) These results show that the model works perfetly well not only for joints with bent in bars but also for other poorer end anhorages as in this ase Test unit 2 Test unit 2 had an axial load on the joint orresponding to an axial stress on the olumn as 0.25 f '. The ylindrial onrete ompressive strength f ' was 30.2 MPa. 100

105 For the given geometry, reinforement details and material properties, the beam and olumn flexural and shear harateristis were generated following the proedure given in Appendix. The joint spring harateristis were evaluated following the proedure explained in hapter 5. The omparison of experimental and analytial urves is given in Fig 6.12 below. To visualize the signifiane of joint modelling, a omparison is given with the analysis results when the model did not have springs to model the joint shear behaviour. The effet of unsymmetri detailing of the joint is somewhat diminished due to the presene of higher axial load on the olumn whih was benefiial in preventing early bond slip of the bottom beam bars. The peak load from the experiment was obtained as kn for up diretion and kn for down diretion. In the analysis, the orresponding values were obtained as kn for up diretion and kn for down diretion that mathes niely with the experimentally obtained values. The model without joint springs again yielded results on highly unsafe side for both the diretions Load (kn) Experiment No joint model Joint Model Down Joint Model Up -400 Displaement (mm) Fig 6.12 Experimental and analytial results for test unit 2 (Pantelides et al 2002) 101

106 6.2.3 Test unit 5 Test unit 5 had an axial load on the joint orresponding to an axial stress on the olumn as 0.1 f '. The ylindrial onrete ompressive strength f ' was 31.7 MPa. For the given geometry, reinforement details and material properties, the beam and olumn flexural and shear harateristis were generated following the proedure given in Appendix. The joint spring harateristis were evaluated following the proedure explained in hapter 5. The omparison of experimental and analytial urves is given in Fig 6.13 below. To visualize the signifiane of joint modelling, a omparison is given with the analysis results when the model did not have springs to model the joint shear behaviour. The peak load from the experiment was obtained as kn for up diretion and kn for down diretion. In the analysis, the peak load was obtained as kn for both up and down diretions. The model without joint springs again yielded results on highly unsafe side for both the diretions Load (kn) Experiment No joint model Joint Model Down Joint Model Up -400 Displaement (mm) Fig 6.13 Experimental and analytial results for test unit 5 (Pantelides et al 2002) 102

107 6.2.4 Test unit 6 Test unit 6 had an axial load on the joint orresponding to an axial stress on the olumn as 0.25 f '. The ylindrial onrete ompressive strength f ' was 31.0 MPa. For the given geometry, reinforement details and material properties, the beam and olumn flexural and shear harateristis were generated following the proedure given in Appendix. The joint spring harateristis were evaluated following the proedure explained in hapter 5. The omparison of experimental and analytial urves is given in Fig 6.14 below. To visualize the signifiane of joint modelling, a omparison is given with the analysis results when the model did not have springs to model the joint shear behaviour. The peak load from the experiment was obtained as kn for up diretion and kn for down diretion. In the analysis, the peak load was obtained as kn for both up and down diretions. The model without joint springs again yielded results on highly unsafe side for both the diretions Load (kn) Experiment No joint model Joint Model Down Joint Model Up -400 Diaplaement (mm) Fig 6.14 Experimental and analytial results for test unit 6 (Pantelides et al 2002) 103

108 6.3 Tests by El-Amoury and Ghobarah (2002) El-Amoury and Ghobarah (2002) performed test on a greavity-designed exterior joint with details as shown in Fig 6.15 and test setup as shown in Fig The beam olumn joint was designed assuming that points of ontra-flexure our at the midheight of olumns and the mid-span of beams. The top longitudinal reinforements in the beam are bent down into the olumn, whereas the bottom reinforement was anhored 150 mm from the olumn fae. No transverse reinforement was installed in the joint region. The beam was reinfored using 4#20 as top and bottom longitudinal bars and #10 as transverse steel. The olumn was reinfored with 6#20 plus 2#15 as longitudinal bars and #10 ties spaed 200 mm. The onrete ompressive strength on the test day was 30.6 and The yield strength of the steel bars #10, #15 and #20 was 450, 408 and 425 MPa, respetively. Fig 6.15 Details of the joint tested by El-Amoury and Ghobarah (2002) 104

109 The speimen wase tested in the olumn vertial position, hinged at the top and bottom olumn ends and subjeted to a yli load applied at the beam tip as shown in Fig A onstant axial load of 600 kn was applied to the olumn, Fig 6.16 Test setup used by El-Amoury and Ghobarah (2002) For the given geometry, reinforement details and material properties, the beam and olumn flexural and shear harateristis were generated following the proedure given in Appendix. The joint spring harateristis were evaluated following the proedure explained in hapter 5. The omparison of experimental and analytial urves is given in Fig 6.17 below. To visualize the signifiane of joint modelling, a omparison is given with the analysis results when the model did not have springs to model the joint shear behaviour. The peak load from the experiment was obtained as 60 kn for up diretion and 86 kn for down diretion. In the analysis, the peak load was obtained as 64 kn for up and 105

110 102 kn for down diretions using joint model and 140 kn for both up and down diretions without using joint model. Thus, the model without joint springs again yielded results on highly unsafe side for both the diretions Load (kn) Experiment -100 No joint model Joint Model -150 Displaement (mm) Fig 6.17 Experimental and analytial results for test by El--Amoury and Ghobarah (2002) 6.4 Tests by Dhakal et al (2005) Dhakal et al (2005) performed experiments on gravity designed interior beam-olumn joints as shown in Fig 6.18, that are part of frames designed aording to the British standard BS8110. The speimens were full-sale reprodutions of a gravity designed frame between the points of ontra-flexure, whih are assumed to be the mid-heights of olumns in two suessive storeys and the entre-points of beams in two adjaent bays. The geometrial dimensions and reinforement details of the C1 and C4 type speimens are illustrated in Fig Speimens of both types had similar overall dimensions (3.7 m high olumn and 5.4 m long beam), and the ross-setion of the beam (300 mm width 550 mm depth) was the same in all speimens. The beam in C1 type speimens had seven 32 mm diameter bars, five at the top (2.7% reinforement ratio) and two at the bottom (1.1%), whereas C4 type speimens had 106

111 six bars at the top (3.3%) and three bars at the bottom (1.6%) of the beam. C1 type speimens had olumns with ross-setion mm, and two layers of four 25 mm diameter bars (2.4%) were laid parallel to the two longer sides. Similarly, in C4 type speimens, the mm olumn inluded eight 25mm diameter bars (2.5%) arranged symmetrially along the perimeter. The stirrups in the beam omprised of four legs of 10 mm diameter bars spaed at 200 mm apart, and the ties in the olumn had three legs of 10 mm diameter bars with 150 mm spaing. Both the speimens were without any vertial or lateral hoops inside the joint ore Fig 6.18 Details of speimens tested by Dhakal et al (2005) Standard ompression test results on ylinders showed that the average ompressive strength of onrete was 31.6MPa for the C1 type speimens and 32.7MPa for the C4 type speimens. Based on standard tension test results, the average yield strengths of the 32, 25 and 10 mm diameter bars were 538, and MPa respetively. Similarly, the average ultimate tensile strengths of these bars were 677.3, and 571.5MPa respetively. The test setup utilized by researhers is shown in Fig All speimens were subjeted to an axial ompression of 10% axial apaity at the olumn-top. 107

112 Fig 6.19 Details of test setup used by Dhakal et al (2005) Joint C1 For the given geometry, reinforement details and material properties, the beam and olumn flexural and shear harateristis were generated following the proedure given in Appendix. The joint spring harateristis were evaluated following the proedure explained in hapter 5. The omparison of experimental and analytial urves is given in Fig 6.20 below. To visualize the signifiane of joint modelling, a omparison is given with the analysis results when the model did not have springs to model the joint shear behaviour. The peak load from the experiment was obtained as 225 kn for both and down diretions. In the analysis, the peak load was obtained as 224 kn for both up and down diretions using joint model and 332 kn for both up and down diretions without using joint model. Thus, the model without joint springs again yielded results on highly unsafe side for both the diretions. 108