INVESTIGATION OF THE FAILURE MECHANISM AND MOMENT CAPACITY PREDICTION IN A TEN BOLT FLUSH END PLATE MOMENT CONNECTION. A Thesis.

Transcription

1 INVESTIGATION OF THE FAILURE MECHANISM AND MOMENT CAPACITY PREDICTION IN A TEN BOLT FLUSH END PLATE MOMENT CONNECTION A Thesis Presented to The Graduate Faculty o The University o Akron In Partial Fulillment O the Requirements or the Degree Master o Science Godwin Addiah Arthur August, 010

2 INVESTIGATION OF THE FAILURE MECHANISM AND MOMENT CAPACITY PREDICTION IN A TEN BOLT FLUSH END PLATE MOMENT CONNECTION Godwin Addiah Arthur Thesis Aroved: Acceted: Advisor Dr. Craig Menzemer Dean o the College Dr. George K. Haritos Faculty Reader Dr. Anil Patnaik Dean o the Graduate School Dr. George R. Newkome Faculty Reader Dr. Kallol Sett Date Deartment Chair Dr.Wieslaw Binienda ii

3 ABSTRACT Moment end late connections have ound their usage in a number o alications and extensive research has been done on smaller caacity connections o such tye. This study seeks to investigate the ailure mechanism and the subsequent rediction o the moment caacity o a ten bolt lush end late connection. The model under study is tyical o a lush end late connection resent in an existing steel arking deck. Yield line analysis methods have been emloyed in analyzing the various ailure mechanisms and have been used in develoing rediction equations or the design o the end-late. The modiied Kennedy method has also been used in the rediction o the bolt orces or all cases o the analysis with ailed bolts. A three dimensional inite element model using ABAQUS Standard has been emloyed to validate the results rom the analytical methods taking into consideration, the interactions between the connection comonents, boundary conditions and material non-linearities. The moment caacity and the corresonding ailure mechanism is redicted under two cases o bolt loss in rows o the connection. Limit state o end late yielding governs the design or the ten bolt connection and that with one row o bolt ailure at the to. Bolt racture governs the design when there are two rows o ailed bolts. iii

4 ACKNOWLEDGEMENTS My sincere thanks to all Faculty members o the Civil Engineering Deartment at the University o Akron or their immense contribution and hel esecially my advisor, Dr. Menzemer through whose guidance this work has been comleted succesully. To the other members o my thesis committee, Dr. Patnaik and Dr. Sett, or their hel, suggestions and contributions. To my riends, who through their encouragement saw me through the comletion o this research work. Finally, to my amily or the love, suort and encouragement throughout the entire duration o my study. To them I owe everything I have accomlished. iv

5 TABLE OF CONTENTS Page LIST OF TABLES. ix LIST OF FIGURES... x CHAPTER I. INTRODUCTION Background 1 1. Statement o Problem Justiication Objectives Scoe o Thesis Outline o Thesis...6 II. LITERATURE REVIEW Overview 7. End -Plate Moment Connections Moment Caacity Prediction and Moment rotation curves End Plate Design and erormance...17 v

6 .4 Flush End Plate Moment Connections.19.5 Finite Element Analysis....6 Need or Further Research...6 III. DEVELOPMENT OF MOMENT PREDICTION EQUATIONS Overview Yield Line Analysis o Steel End Plates Earlier Moment Prediction Equations Two Bolt Flush End Plate connection Four Bolt Flush End Plate Connection End Plate rediction Equations Case one ten bolt connection Case two eight bolts Case three six bolts Bolt Force Predictions Prying Action Determination o Plate Thickness Limits Modiied Kennedy Model Moment Caacity Prediction based on Bolt Forces.47 IV. RESULTS VERIFICATION AND FINITE ELEMENT ANALYSIS Overview Geometry o Structural comonents...51 vi

7 4.3 Moment Caacity Predictions Limit State o End Plate Yielding Limit State o Bolt Fracture Determination o Predicted Caacity Finite Element Analysis Model o the Connection Comonents Material Proerties Assembly Contact Interactions Boundary Conditions Loading and Analysis Stes Element Tye and Meshing Visualization o Results and Failure atterns Moment Caacity Prediction rom Finite Element Analysis Comarison and Summary o Results.69 V. SUMMARY, CONCLUSIONS AND RECOMMENDATIONS Summary Conclusions Recommendations...73 REFERENCES.74 APPENDICES..79 vii

8 APPENDIX A Assumed Yield Line Mechanisms...80 APPENDIX B Finite Element Analysis Outut Summary 88 viii

9 LIST OF TABLES Table Page 4.1 Section Proerties or End Plate and Beam Summary o Predicted Moment Caacities with Failure mechanisms Comarison o the Moment Caacity values 70 ix

10 LIST OF FIGURES Figure Page 1.1 Tyical Parking Deck with ailed tension bolts, (Courtesy: UA) End late moment connection tyes Virtual Dislacement in a two bolt lush unstiened end late Controlling Yield Mechanism or Four bolts Flush End Plate Controlling Yield Line Mechanism or Four Bolt (AISC) Equivalent orm o the 10 bolt Flush onto a Four Bolt Flush Coniguration Controlling Yield line Mechanism or the 10-bolt connection Controlling Yield line Mechanism or the 8-bolt connection Controlling Yield line Mechanism or the 6-bolt connection Stages o Plate Behavior based on the Kennedy Model Modiied Kennedy Model or cases o the lush end late connection Case One bolt orces with (a) No Prying Action (b) Prying Action Case Two bolt orces with (a) No Prying Action (b) Prying Action Case Three bolt orces with (a) No Prying Action (b) Prying Action...50 x

11 4. 1 Connection Details or End Plate with Adjoining Beam Comonents o the Flush End Plate connection in ABAQUS CAE (a) Stress Strain Relationshi or Beam, Endlate and Column Material (b) Stress Strain Relationshi or Bolts and Nut An Assembly o the 10-bolt Flush end late connection Connection Boundary Conditions Mesh o Connection Assembly Linear element, 8-node brick, C3D8 (ABAQUS Analysis Manual) Patterns in dierent cases o connection ailure Grah o alied moment against end late searation or case Grah o alied moment against endlate searation or case.69 xi

12 CHAPTER I INTRODUCTION 1.1 Background The study and research on structural connections has been a subject o interest in imroving the overall erormance o steel structures. Although some imrovements have been made to ensure economy and erormance, a number o connections in existing structures have been designed based on emirical methods and must be examined in evaluating or determining the structural soundness o older inrastructure. This has become necessary and evident due to the dilaidated state in which a good deal o inrastructure has been ound (ASCE Reort Card, 009). In this research, a ten bolt lush end late connection o an existing tyical steel arking deck is considered. Uon a routine maintenance check, it had been established that some bolts o the lush end late connections had ailed. Although the roblem might be due to causes other than over stressing, the structural adequacy o these connections is investigated and the moment caacity o the 10-bolt lush end late connection is examined using rediction equations derived rom existing methods and validated with results rom Finite Element Analysis (FEA). The redicted caacity is based on the number o ailed bolts, with the moment caacity o the connection determined at each 1

13 stage as a unction o the number o ailed bolts. Two cases o rows o ailed bolts have been considered. The neutral axis is directly aected by the loss o bolts and this directly aects the number o bolts in tension. The various ailure mechanisms that arise are also o interest. According to the AISC Seciication (005), the connection behavior o a semi-rigid connection requires a good knowledge o the moment caacity, rotational caacity and stiness o the connection. Though moment end late connections are normally classiied as tye one (rigid), study have shown that they exhibit semi-rigid roerties esecially in this case where there might be considerable rotation due to some ailed bolts in tension. (McGuire, 1988) A tyical lush end late bolted connection has a rectangular steel late o almost the same deth o beam section and welded to the end o the beam. The end late is bolted to the column lange with bolts both in the tension and comression side o the beam. Analysis o bolted end-late connections seem quite comlex due to the behavior o the individual comonents o the connection. The varying roerties which include material, geometry, and contact interactions between the various arts, bolt size, beam deth, grade o steel, web thickness and the column side arameters make the analysis comlicated. The eect o rying orces resulting rom the column and end-late interaces ater an extent o load alication comlicates the roblem. In order to investigate the ailure mechanism o the connection, an exerimental set-u usually needed to accurately redict the behavior and erormance o the structural comonents, will be a cost intensive otion since connection behavior results rom varied arameters o the various comonents.

14 It would be diicult to study the various interactions between the end late and column lange. A three dimensional inite element analysis rovides a convenient way to study the behavior and interaction o the various arts o the 10-bolt lush end late connection using ABAQUS Standard commercial code. (ABAQUS Manual, 006) 1. Statement o Problem The loss o structural caacity o older structures has been o major concern since the collase o the I-35 Bridge in Minneaolis. The situation is not isolated to bridges alone but to other structural systems which are either structurally deicient, due to inadequate technology or analysis at the time o design or as a result o atigue, corrosion or a combination o other actors. In steel structures, connections lay an imortant role and account or the overall structural rigidity and stability o the structure. Flush end late connections have ound use in a number o structures including arking decks rimarily due to the ease o erection and its added ability to resist lateral loads in light rames. Uon a routine insection, it was ound that some bolts at the lush end late connections o the beams had ailed, thus aecting the overall structural erormance and moment caacity o the connection. Though the ailed bolts have been relaced, the extent to which the moment caacity o the lush-end late connection was aected needs to be evaluated to ind out the imact on load carrying caacity and the robable ailure mechanisms which might result. 3

15 Figure Tyical Parking Deck with ailed tension bolts, (Courtesy: UA) 1.3 Justiication It is imortant thereore to have design equations or the rediction o the moment caacity o these lush end late connections. Murray and Shoemaker (AISC Design Guide 16) rovides a methodology or the design o extended and lush end late moment connections, but the conigurations are only u to our bolts in both the stiened and unstiened case. Extensive work has been carried out on the design o extended end late moment connections but very ew on large caacity connections. In studying the 10-bolt lush end late connection o the arking deck, an extraolation o the Design equations in AISC Design Guide 16 is emloyed and comared to a new set o design equations to be develoed rom yield line analysis and a modiied orm o the Kennedy method. The behavior o the connection would urther be validated using inite element analysis and comared with other design equations roosed. 4

16 1.4 Objectives In studying the robable ailure mechanisms resulting rom the ailed bolts and redicting the moment caacity, the ollowing will be examined: Identiying ossible ailure modes that could result due to a certain number o ailed bolts, analyzing the ailure mechanisms with the yield line method in evaluating end late yielding and the rediction o the bolt orces using a modiied orm o the Kennedy method. The controlling ailure mechanism will be o umost interest and will serve as a basis or the develoed equation. Accessing the eect o the various comonents o the connection on the overall structural caacity including moment caacity and rotational stiness, ater a certain number o ailed bolts. Prediction o the moment caacity o the 10-bolt Flush End late Connection and observation o various levels o ailure using Finite Element Analysis (ABAQUS Standard) Design methodology or the rediction o the moment caacity or a 10 bolt unstiened lush end late connection with a redetermined number o ailed bolts. 1.5 Scoe o Thesis The scoe o this research involves redicting the moment caacity o a 10-bolt lush end late connection based on available models and equations, develoment o rediction equations to be develoed as art o this study using the yield line method 5

17 and examining bolt orces using a modiied orm o the Kennedy method. The ailure mechanism in the 10 - bolt lush end late connection is to be investigated using inite element analysis with ABAQUS Standard, a commercial sotware code. 1.6 Outline o Thesis The thesis consists o ive chaters. The irst chater gives a descrition o the research, the scoe and the objectives. A review o existing work in the area o end late moment connections, the behavior o comonents, ailure modes, design methodology and inite element modeling with emhasis on lush end late connections is highlighted in the second chater. The assessment o the moment caacity o the connection based on existing models and the develoment o rediction equations based on the yield line analysis o the end-late and the rediction o bolt orces using the modiied Kennedy method is resented in the third chater. The inite element model o the connection, geometry, boundary conditions, material roerties and nonlinearity together with the modeling o the contact suraces, mesh generation and analysis is evaluated in chater our. It also resents a comarison o the rediction equations with veriication rom the analysis o the inite element results. The summary, major conclusions and recommendations derived rom the research are resented in the last chater. 6

18 CHAPTER II LITERATURE REVIEW.1 Overview The role that structural connections lay in the rigidity and erormance o a structure cannot be overemhasized, serving as oints or the transer o both service loads and in some instances lateral loads. Welded and bolted connections have been used in connecting structural members or decades ater riveting outlived its useulness. Structural bolts and welds lend themselves to abrication and erection o structures. End late connections have ound usage in various arts o steel buildings and rames but are mostly in beam column intersections. They are oten reerred or this urose. The behavior o the end-late connection will deend on variable arameters, including bolt diameters, number o bolt rows, bolt sacing, grade, endlate dimensions, stieners, column and beam sizes, bolt retension orce, yield strength o steel and the sli coeicient o contact suraces. According to the AISC Load and Resistance Factor Design seciication (005), moment connections based on the stiness may either be ully restrained (FR) or artially restrained (PR) based on the category o construction. Fully restrained connections must ossess suicient strength and stiness to transer 7

19 moment and still maintain an angle between connected members while a artially restrained moment connection are designed to transer moments but allow rotation between connected members as the loads are resisted. Due to the comlications involved in the design o artially restrained moment connections, AISC states that the resonse characteristics o a articular artially restrained connection must be documented or established by analytical or exerimental means. End late moment connections are made o several comonents involving a steel late welded to the end o a beam section and attached to a member with rows o high strength bolts. Two tyes o end late moment connections are commonly ound in ractice namely the Flush end late moment connection and the extended end late connection as shown in Figure.1 (a) Flush end late Tye (b) Extended End Plate Tye Figure.1 End late moment connection tyes 8

20 In a lush end late connection, the late does not extend beyond the beam langes and the bolt rows are thereore conined within the beam langes. Stieners might be resent to increase the overall strength rigidity. The lush end late connection has not been extensively used due to its lesser caacity to resist high lateral loads. It is thereore used mainly in rames subjected to light lateral loads. A number o exerimental tests have been done on both rigid and semi-rigid connections. Advances in structural analysis have allowed or the analysis o semirigid steel ramed structures so that, the real roerties o the connections are considered instead o tyical simle assumtions o either inned or ixed connections. In the simulation o end late connections, tee-stub models have long been used. The bolts are subjected to direct tensile loading and thus are requently used to transer load to the columns rom the suorting beams and girders. Accurate rediction o the structural behavior o steel beam-to column connections, by estimating the local deormations and induced stresses is necessary in assessing the caacity o the connections and reventing their ailure. There are actors aecting the study o these moment end late connections. Exerimental testing orms a major basis or research. It has its limitations due to increased cost and the inability to model certain testing conditions. Though inite element modeling only gives an aroximation o the actual solution, extensive research has shown that it gives result comarable to exerimental testing and thus suitable or this analysis. (Choi and Chang, 1996) 9

21 . End -Plate Moment Connections End late moment connections ound alication in the 1960 s ater develoment rom tee stub moment connections in the 1950 s. A great deal o work has been carried out on moment end-late connections ater a surge in usage dating back to the 1960s. Extensive work has been carried out in the ast and studies are still ongoing esecially on the erormance o these connections in seismic regions, (FEMA 00).Exerimental testing o various end late connections over time and the rogress that has been made and rojects ongoing currently is considered. End late connections have the advantage o being suitable or erection even in bad weather since only ield bolting is required. Sho welding o the lates eliminates those roblems that would have been encountered in the ield and the erection rocess is simliied. A major disadvantage is the resence o rying orces that may result due to bolts loaded in tension. Design rocedures have been available or both lush and extended moment end lates. Earlier methods only considered the use o statics and did not ully embrace the concet o the existence o rying orces. The design rocedure roosed resulted in both thick end lates and large bolt diameters. Various techniques have been emloyed in the analysis and the behavior o these connections. Yield line analysis theory has been used in analyzing the various ailure mechanisms that develo in the end-late and design equations have been roosed to better design end-lates. The tee-stub analogy has ound its use in redicting bolt orces. The major ailure modes occurring in end-late connections are late yielding and bolt racture. 10

22 More recently, inite element methods have been emloyed to study connection behavior and investigate various ailure mechanisms. Regression analysis results have been used in ormulating design equations or these connections. The behavior o connections can be established making a number o assumtions: The comonents o the connection can be studied individually and each contribution to the overall resonse o the connection under a given set o orces. The behavior o the connection on the overall stiness and strength o members joined. The structural behavior o the connection can best be described with its rotational stiness and moment resistance deicted in a moment rotation diagram. This behavior clearly dierentiates the various tyes o construction as resented in the AISC seciication (005). Connection stiness is taken as the sloe o the moment rotation curve. Earlier design rocedures, have roortioned connections so that joint deormation is revented or ket to a minimal level to simliy the analysis o the connection. However, it has been established that most connections are actually semirigid. Murray (1988) resents develoments based on research in the design o moment end-late connections. The various design methodologies and rocedures that had been roosed in the design o end late connections were considered. The rocedures used in most o this analysis involved the determination o the end late 11

23 using yield line analysis and the rediction o bolt orces using the modiied Kennedy method. Douty and McGuire (1965) erormed test on both tee-stub and end late moment connections. They investigated the orces induced in the bolts by the tension langes by testing both connection tyes. There was good correlation between theoretical and exerimental results and an increase in bolt tension in thinner lates was observed. Mann (1968) develoed rediction equations or end late strength based on exerimental testing. Nair et al (1974) urther investigated bolt rying orces by conducting tests on tee-stubs. The eect o rying orces in reducing the ultimate load carrying caacity and the atigue strength o bolts was clearly observed. A rediction equation or bolt orces including rying action was develoed. Zoetemeijer (1974) used the yield line theory in his analysis o the yielding o the end late. He roosed a design method based on two dierent collase mechanisms. Results rom series o tests were used to test his analytical model and there was good agreement. Packer and Morris (1977) also used yield line theory to redict end-late moment caacity. Their tests investigated ailure o the column lange. Straight and curved yield lines were considered in the yield line analysis o the late, though the work was not conclusive. Phillis and Packer (1981) continued the earlier work o Packer and Morris to establish the role that the end-late thickness had on momentrotation characteristics and on end-late ailure mechanisms. 1

24 Ater Mann and Morris (1979) had reviewed several research rograms and roosed design rocedures or extended end late moment connections, they suggested two very basic requirements that needed to be ulilled in lastic design: Connections must be strong enough to withstand hinge movements. Connections must rovide adequate hinge rotation while sustaining these moments. The design rocedure roosed included methods in determining bolt size and end late thickness. In the rediction o bolt orces, Kennedy et al (1981) derived a method using the tee-stub analogy. His method identiied three stages o tee-stub lange late behavior. The irst stage o loading occurred at lower loads and the behavior o the late was described as thick. Prying orces were absent at this stage. With an increase in the load, the second stage o behavior starts with the ormation o lastic hinges at the base o the stem o the tee. The rying orces at this stage o loading are between the two extremes, not being resent and the maximum. A subsequent lastic hinge orms through the bolt line in the third stage and the late is said to be thin, and rying orces are at a maximum. Kennedy develoed equations which set the various stages o late behavior with geometric roerties and yield stress values o the late and the alied lange orce. A modiied orm o the Kennedy method has been ound to be ideal or the rediction o bolt orces ater it had been tested to correlate well with exerimental results. 13

25 Tary and Cardinal (1981) discuss the eect o end-late thickness on the deormed shae and magnitude o dislacements o the column lange. Two tyes o end-lates are discussed and are described as thick when the end late thickness is about our times the thickness o the column langes and thin when about one and a hal times the thickness o the column lange...1 Moment Caacity Prediction and Moment rotation curves Sherbourne and Bahaari (1994) roosed a methodology which involved inite element modeling in establishing the moment-rotation relationshis or steel connections. As art o the indings, it was stated that one (beam) or two dimensional (late) models o connections do not accurately model the behavior when one o the lates is in contact, and either the column lange or end late is relatively thin. Prying orces in the rojected ortion o the end late increase with decrease o end-late thickness. The bolts in the rojected ortion o the thin end-late connection are under signiicant biaxial bending. Foley and Vinnakota (1994) simliied the develoment o moment-rotation curves or end late beam to column connections. They used a semi-analytical aroach to develo moment-rotation curves or unstiened extended end late connections. They used a modiied orm o the ower model roosed by Kishi and Chen (1990) which used a three arameter (M,K i,β) model based on initial stiness, moment caacity and an exerimentally based arameter. 14

26 M K i = θ 1 K i + M β 1/ β Where M and θ are the resisting moment o the connection and the rotation o the connection resectively, M is the lastic moment caacity o the connection and K i is the initial stiness o the connection. K i and M are determined analytically, while the decay arameter β is evaluated based on exerimental data. The lastic moment caacity o the connection was determined based on the ailure modes listed below: Failure o the bolts in the tension region. Failure o the end-late in the tension region. Failure o the column lange in the tension region Web yielding o the column in the comression zone Web criling o the column in the comression zone Their roosed method was suosed to lead to easier creation o adequate momentrotation curves or design oice use. Maggi et al (005) utilized arametric analyses to study the behavior o bolted extended end late connections using inite element analysis. T-stub ailure models were used or calculations o the lexural strength or the end late. Failure modes included ormation o yield-lines in the late and bolt tension ailure was well deined. Failure due to a combination o these mechanisms reresents levels o interaction between the end late and bolts which is diicult to redict accurately. 15

27 Hongxia, et al.(008) develoed a tee stub model or end late behavior at large deormations. He roosed a yield line model based on the virtual work rincile considering material hardening or both the T-stub and bolts ater yielding. His yield line model was comared to end late connections on the basis o equivalent yieldlines. The model reresented the behavior o endlate connections well. A single row o bolts in an end late connection was modeled as a tee stub. The eect o material roerties and varying end late thickness was highlighted in his inite element analysis. His model considered the yield strength and the hardening hase o the late and the bolt, as well as comatibility between them. Kukreti, Murray and Abolmaali (1987) develoed a methodology or establishing moment-rotation relationshis or bolted steel connections based on inite element modeling. The methodology was demonstrated or a lush end late connection. A ew secimens were exerimentally tested to veriy the inite element solution and comuter analysis. The data collected were regressed to develo a rediction equation characterizing the general behavior o the lush end late connection. Murray (1990) resented design rocedures or three conigurations namely our bolt unstiened, our bolt wide unstiened and the eight bolt extended stiened end-late moment connections. This was based on earlier methods o Krisnamurthy (1978), Ghassemieh et al (1983) and Murray and Kukreti (1988). Borgsmiller (1995) resented a simliied method or the design o our lush and ive bolt extended end late moment connection using the simliied version o 16

28 the modiied Kennedy method in redicting bolt orces and the yield line analysis method in the design o the end late. His studies established that rying orces in connections become signiicant when ninety ercent o the end late strength is achieved, establishing a threshold where rying orces can be ignored. Good correlation with ast results was obtained. Summer and Murray (001) investigated extended end late connections with tests on 6 multile row extended end late connections to investigate the validity o current design rocedures or gravity, wind and low seismic loading. The test also investigated the eects o the standard and large inner itch distances and the connections utilized in both A35 and A490 bolts. Kukreti & Biswas (1997) develoed a comuter rogram to analyze the moment-rotation behavior o end late connections subjected to seismic loading. The rogram had the caability o alying retension loads to bolts in the model. The redicted results were validated with exeriments conducted on three connection geometries in which the end late thickness is varied. The ailure modes in the analytical model comared well with that o the exerimental with a maximum dierence o about 18%..3 End Plate Design and erormance The underlying hilosohy in the design o end late connections lies in the yielding o the endlate, racture o the bolts and deormation in the column lange. The erormance o the endlate connection is aected by varying conditions notable 17

29 among them being seismic loading and in ire conditions. The erormance o the connections is reviewed with resect to these two conditions. The extended moment end late connection has been shown to rovide the required ductile behavior during earthquakes and thus erorms better than lush end late connections. Broderick and Thomson (001) studied the behavior and resonse o lush end late joints under earthquake loading. They erormed an exerimental investigation under monotonic and cyclic loading; they observed that individual connections dislayed the same ailure mode in both cyclic and monotonic loading. They concluded that secimens under cyclic loading dislayed large rotation ductility caacities and their modes o ailure were similar under monotonic loads. In many instances, ailure occurred due to thread striing on nuts and bolts. They stated that the Euroean codes aeared to identiy the ailure modes or analysis correctly, but under-redicted the moment caacity. They re-emhasized the low moment caacity ossessed by lush end-late connections and that its use must be restricted to areas o low to medium seismicity. Gang Shi et al (006) studied the behavior o end-late moment connections under earthquake loading. They erormed eight ull-scale tests in investigating endlate thickness, bolt diameter and end-late stieners, with both lush and extended end-lates. Their results showed that an extended end late rovided adequate strength, joint rotational stiness, ductility and energy dissiation caacity to erorm better in seismic rames than lush end-late connections. The lush end lates did not rovide enough structural rigidity and showed large rotations between the column lange and end late under such conditions. 18

30 Connection behavior during ires might indicate the extent to which damage or ailure occurs in the structure, since connections contribute to the overall structural stability o the rames. The erormance o connections in ire is o umost imortance in structures. Al-Jabri (005) investigated the behavior o unrotected lush end late connections at elevated temeratures using ABAQUS, commercial sotware code. A three dimensional model was used to establish the moment-rotation characteristics o the connections under load and in elevated temeratures. Hongxia,et al.(008) erormed tests at both ambient and elevated temeratures to investigate the behavior o connections at the end o unrotected beams in ire situations. At higher temeratures, ailure always occurred in the bolts. They emhasized the role o thicker end lates at elevated temeratures in enhancing eak resistance, but reducing the rotational caacity o the connection..4 Flush End Plate Moment Connections In the United States, lush end late connections ound widesread use in reengineered metal buildings until the early 1980 s. Alication o the lush end late ound extensive use in the United Kingdom. Flush end-late connections have been used in the structure under study that was built in Its usage has been limited and currently available research shows extended end late connections with stieners erorm better than lush end lates in rames and have the added advantage o resisting lateral loads. Nevertheless, lush end lates have been used in a number o 19

31 structures where geometry does not allow the usage o extended end lates and where lateral loads are minimal. Phillis and Parker (1981) studied the eect o the thickness o the end late on lush end late connections through exerimental testing. There were two rows o bolts in the tension region in order to study the inluence o the second row o bolts on the stiness o the connection. They concluded that lush end-lates with two rows o bolts in the tension region are suitable or semi-rigid construction, exlaining that the second row o tension bolts were eective to an extent than had earlier been under estimated. Zoetmeijer (1981) roosed a chart or aroximating the ultimate load caacity o a stiened column lange or lush-end late when the distance rom the bolt to the lange and web o the beam are known. Srouji(1983), ater a review o earlier work by Douty and McGuire(1965), Zoetmeijer(1981) and Kennedy et al(1981) develoed a methodology or the design o our conigurations o end late connections including two-bolt lush, our bolt lush, unstiened our-bolt extended and stiened our bolt extended. He used the yield line method to determine end late thickness, and a modiication o the Kennedy method to redict the bolt orces considering rying eects. Exerimental testing o the various conigurations roduced excellent agreement or both the end-late strength and bolt orce magnitudes. Hedrick (1985) extended the work o Srouji and resented a uniied yield-line based design rocedure or our tyes o lush end-late coniguration. 0

32 Li, et al.(1996) develoed a method or the rediction o the moment caacities o lush end late comosite connections. In as much as the tension side o the connection had to work in conjunction with reinorced concrete, much o their indings are alicable to this research. Possible ailure modes based on careul study o various exerimental data included yield or racture o bolts in tension, yield o the column lange in bending, weld ailure between the end-late and steel beam, yield or buckling o the lower beam lange in comression and shear, and yielding or buckling o the column web in transverse comression. They investigated the eect o the slab reinorcement on the lush end late connection and derived equations or redicting moment caacity o such connections. They roosed equations based on the number o bolts in both the tension and comression zones. It was also noted that the eect o the comosite section on the connection could be treated as a row o bolts and will give satisactory results. Bursi and Jasart (1997) studied the behavior o the lastic and ailure mechanism o a tee stub connection which was later extended to investigate the behavior o end late connections. They used brick as well as contact elements and based their conclusions on results rom the inite element model. Bose, Wang and Sarkar (1997) develoed a sohisticated three dimensional model to investigate the behavior o unstiened lush end-late steel bolted joints using LUSAS commercial code. They comared the results with exerimented data. The results conirmed the accuracy o their inite element method rediction model. 1

33 Olsen (1997) roosed design ormulae or bolted lush and extended end lates based on lasticity theory, His model equation did not consider the eect o rying orces or lush end lates. The design ormulae was written in a generalized set or both lush and extended end late connections. Murray and Shoemaker (00) resented a guide or the design o both extended and lush end late moment connections. Flush end late connections that could be designed was limited to our tyes, our bolt unstiened, two bolt unstiened, our bolt stiened with stieners between the tension langes and our bolt stiened with stieners inside the bolt rows. The rovisions in the design guide are limited to gravity and low lateral loads. A uniied design based on the Borgsmiller (1995) method was used..5 Finite Element Analysis Krishnamurthy and Graddy (1976), in their attemt to redict deormation in end lates or an extended our-bolt extended connection, were constrained by comuter size, seed and the comlexity o the mesh to better model connection behavior. Krisnamurthy (1979) used inite element techniques to model three dierent tyes o connection namely to-angle connections, tee stub connections and end lateconnections. D and 3D models were created o the various tyes o connections. Parametric studies were then erormed on each to establish a correlation between the two dierent models leading to the develoment o a set o rediction equations.

34 Kukreti et al (1987) in a comarison o two dimensional and three dimensional models considering comlexity and analysis accuracy, concluded that two dimensional models rovided adequate reliable modeling o moment end late connections at the time. Ahuja (198) used inite element analysis to investigate the elastic roerties o eightbolt stiened connections. The investigation was continued by Ghassemieh(1983) to include the non-linear behavior o the end-late and bolts. Abolmaali et al (1984) develoed correlation coeicients rom D and 3D inite analysis or two bolt lush end-late moment connection conigurations. Finite element D analysis served to generate regression equations or the design o the connections adjusting them by correlation coeicients to closely match exerimental results. Kukreti et al (1990) modeled an eight bolt connection and conducted arametric studies to redict end late dislacement and inner bolt orces. Regression analysis o the data was conducted ater comaring with exerimental data or correlation. Gebbeken, et al. (1994), Bahaari and Sherbourne (1994) used various inite element analysis codes in studying the behavior o our bolt unstiened end late moment connections. The non-linear material behaviors as well as the contact interactions between the comonent arts were modeled using dierent elements. Bahaari, et al. recommended that three dimensional models be used to generate analytical ormulations to redict the behavior and strength o the connection comonents. 3

35 Choi and Chung (1996) studied several techniques involved in inite element modeling o connections and ointed out laws involved in earlier methods. They develoed a reined three-dimensional inite element model or end-late connections using an elastolastic non conorming solid element with variable nodes. Eect o bolt retensioning and the shaes o bolt shank, head and nut were taken into consideration. An algorithm or contact with a new ga element was used to simulate the interaction between the end late and column lange. Their model clearly established in detail, moment-rotation relationshis, contact henomenon and eective stress distributions. Bursi and Jasart (1998) addressed some o the basic issues relating to inite element modeling o end late connections. According to their study, inite element models deending on constitutive relationshis, ste size, number o integration oints, kinematic descritions, element tyes and discretizations together with the non- linear behavior o the comonents makes the modeling rocess cumbersome. They roosed a suitable analysis methodology or end late moment resisting connections and roer three dimensional inite element models. The individual comonents o the connection were critically examined. Bahaari & Sherbourne (000) studied the behavior o eight-bolt large caacity endlate connections. They highlighted extensive work that had already been done on end-late connections, but those were limited to those with smaller caacity, thereby making it necessary to study large caacity connections, as been done in this research. They used ANSYS, a commercial inite element code in studying the structural behavior o unstiened eight bolt end late. The endlate, beam and column langes were modeled with late elements, and the bolt shank with six sar elements. They 4

36 roosed that an inelastic inite element model reviously used or common extended end late connections may be emloyed or modeling the end late with more bolts in the tension region. As an alternative to the two row eight bolt connection, a hybrid coniguration was suggested in which our bolt rows are above, and two rows o twobolt are under the beam lange. The latter, oers slightly more initial stiness, esecially or thick end lates, and the same ultimate strength. Olsen (00) roosed a new design method based on an easy to understand aroach or develoing the set o equations derived rom mechanics rinciles as resented in Eurocode 3. Abolmaali, et al. (005) develoed a three arameter ower model rediction equation or the moment-rotation behavior o lush end late connections with one row o bolt below the tension and comression langes. A inite element model o the connection region along with the connected beam and column was develoed or load deormation analysis. Shrih, et al. (008) studied the behavior o lush end late connections using a highly detailed three dimensional inite element model in ANSYS. The connection used in the analysis was tyical o what is resently used in steel ramed buildings. Good correlation between exerimental results and the inite element solution was established with a deviation o about 1%. Serving as a methodology towards the creation o inite element models, a sub-rame constructed with similar connection roerties was used to generate temerature rotation diagrams that described the behavior o the connection and redicts the ailure mechanism o such a rame in extremely high temeratures. 5

37 Ju, et al. (003) used three dimensional elastolastic inite element methods to study the structural behavior o butt-tye steel bolted joint. They observed that when steel reaches non-linear behavior, the nominal bolt orces obtained rom the inite element analysis were almost linearly roortional to the bolt number arranged in the connection. Bolt ailure deended marginally on late thickness that dominates the magnitude o the bending eect..6 Need or Further Research Extensive research work has been conducted in the area o end late moment connections. However, only a small ercentage has considered the investigation o the ailure mechanism in large caacity lush end late connections and moment caacity redictions. Available literature rovides or the design o lush end late connections o smaller caacity. There is thereore a need to investigate the behavior o lush end late connections with reduced caacities due to the ailure o some tension bolts. Corresonding ailure mechanisms resulting rom these ailures is also o major concern. Research indings illustrate the use o the yield line analysis in redicting moment caacity o the end lates and the modiied Kennedy method or the rediction o the bolt orces. Three dimensional inite element analyses can accurately redict the behavior o lush end late connections, and has been utilized in the analysis. Develoment o design equations rom both the yield-line analysis method and the modiied Kennedy method are resented. Details o the study have been resented in subsequent chater. 6

38 CHAPTER III DEVELOPMENT OF MOMENT PREDICTION EQUATIONS 3.1 Overview The develoment o a moment rediction equation or the 10-bolt lush end late connection involves the investigation o the various ailure mechanisms in the endlate and in the rediction o the maximum load that causes bolt racture. Thereore, two limit states have thereore been considered in the analysis namely end late yielding and bolt racture. Yield line theory has been used in the investigation o the steel end lates. The modiied Kennedy method is emloyed to redict bolt orces. Both methods have been used in revious studies and it has been shown to accurately redict the moment caacity o end late connections. (Sumner, 001) 3. Yield Line Analysis o Steel End Plates Local collase mechanisms have been investigated using yield line theory. Though originally designed or reinorced concrete, it has ound its useulness in the design and analysis o steel lates. Assumed yield line modes are normally based on exerimental observations but since exerimental testing has not been done in this study, extensions o assumed yield lines based on earlier work by Srouji (1983) and the AISC Design Guide 16 (AISC, 00) have been emloyed. 7

39 Two major comonents o the method include: (a) An assumed yield line mechanism model or all ossible ailure atterns based on the geometry o the end late. (b) Generation o work energy equations or both external and internal work and the subsequent determination o the moment caacity. Srouji, et al. (1983) set out guidelines or the location o yield lines in steel lates by making the ollowing assumtions: (a) Axes o rotation generally lie along lines o suort (b) Yield lines ass through the intersection o the axes o rotation o adjacent late elements (c) Along a yield line, the bending moment is assumed to be constant and equal to the lastic moment o the late Two methods o analysis are generally emloyed in yield line analysis namely the equilibrium method and the virtual work method. The latter has been shown to be more suitable or the analysis o steel lates and is thereore emloyed in the analysis. This involves a small arbitrary dislacement in the direction o the alied load and the external work generated. The internal work done by the late is estimated by the rotation o the late along the yield lines. By equating the internal and external work, the unknown moment caacity o the late can be redicted. It is an uer bound theory and thereore several ailure atterns need to be evaluated to get the least or smallest uer bound. The least uer bound solution is the attern that roduces the lowest ailure moment. 8

40 The internal work or a yield line analysis is the summation o the internal work stored in each o the yield lines orming the mechanism. The internal work er unit length is equal to the normal moment on the yield line multilied by the normal rotation o the yield line. Thereore the work o the nth yield line is as given by the exression: w i = m θ nds = m θ nl Ln n Total work or the entire mechanism is thereore given by W i = N n= 1 w i = N n= 1 m θ L n n Where m is the lastic moment caacity o the late, θ n is the normal rotation o yieldline n, and L n is the length o the yield line rojected to the axis o rotation. Comlicated atterns may be simliied by searating the internal work into its comonents, that is: W i N = n=1 ( m θ L + m θ L ) x nx x x ny y Where θ nx and θ ny are the x- and y- comonents o the relative rotation o the rigid late segments along the yield line, L x and L y are the x and y comonents o the yield line length, and m is the lastic moment strength o the late er unit length. 9

41 b g δ =1 t s h t w h θ M l Fig Virtual Dislacement in a two- bolt lush unstiened end late Considering the two bolt lush end late coniguration in Figure 3.1, the external work due to the unit virtual dislacement is given W e = M l 1 θ = M l For small angles, θ h M l is the yield moment or the connection and θ is the virtual rotation o the connection 3.3 Earlier Moment Prediction Equations Extensive work has been done or the rediction o moment caacity in a two bolt and our bolt lush end late coniguration. The work o Srouji (1983) and Murray (00) 30

42 31 as highlighted in the AISC Design guide rovide equations or the analysis o such connections Two Bolt Flush End Plate connection Srouji (1983) used yield line analysis to develo moment rediction equations or a two bolt lush unstiened end late. Analysis o the ossible ailure modes led to the choice o the controlling mechanism as shown in Figure 3., and is used in the derivation o the internal work as: ( ) ( ) = s g s b h h m W t i In the exression, s is an unknown exression that is ound by dierentiating the internal work equation leading to the value o s as: g b s 1 = Equating the external Energy to the Internal energy yields the ollowing exression or the redicted moment o the end late. ( ) ( ) = s g s b h h m h M t l ( ) ( ) = s g s b h m M t l The lastic moment er unit length o late (m ) or yield line analysis is given by

43 3 y F t m = 4 1 Where F y is the yield stress o the end late and t is the end late thickness. The design rocedure resented in the AISC Design Guide 16 on Flush and extended end late moment connection emloys the above moment rediction equation or the design o a two bolt lush end late coniguration. The redicted moment caacity o the lush end late is given by: ( ) ( ) = s g s b h t F M t y l Four Bolt Flush End Plate Connection Srouji (1983) develoed equations or the our bolt lush end late ater yield line analysis o several ossible ailure mechanisms. The controlling yield line mechanism is shown in Figure 3.. The total internal energy is ( ) = g h s u h h b h m W t b t t i 4 In the exression, u is an unknown exression that is ound by dierentiating the internal work equation leading to the value o u as: = t t h h g b u 1

44 33 h u g b t b t Figure 3. Controlling Yield Mechanism or Four bolts Flush End Plate (Srouji 1983) The resulting moment caacity redicted is given by; ( ) = g h s u h h b t F M t b t t y l The controlling mechanism or the our bolts unstiened lush end late in the AISC Design Guide Manual or Flush End Plate and Extended End Plate connection is dierent rom that resented by Srouji (1983). This mechanism was reached ater urther exerimental testing o the end late connection.

45 34 h g s t w t h 1 h t b b t Figure 3.3 Controlling Yield Line Mechanism or 4-Bolt (AISC Design Guide 16) The total internal energy is ( ) ( ) [ ] = g s h h g s h h b h m W b b i In the exression, s is an unknown exression that is ound by dierentiating the internal work equation leading to the value o s as: g b s 1 = The value o is set as equal to s, i the value o is greater than s. The redicted Moment Caacity is given by ( ) ( ) [ ] = g s h h g s h h b t F M b b y l

46 3.4 End Plate rediction Equations The moment carrying caacity o the connection deends on the resistance o the comonents in the tension region o the connection. The neutral axis o the bolt grou directly aects the behavior o the connection because it rovides a mechanism or determining the number o bolts in the grou that will be in tension. Dierent cases o the lush end late connection based on the number o rows o bolts are analyzed Case One Ten bolt connection. ( All rows o tension bolts resent) With the 10 bolt lush end late connection under consideration, it is assumed that the neutral axis lie directly in the third row o bolts. Two rows o bolts will be ound in the tension zone o the connection, and thereore will be synonymous to a our bolt lush end late coniguration. The rediction equations or a our bolt lush end late coniguration in the AISC Design Guide 16 can be emloyed. The equations dealt with in this reort do not include the saety actors emloyed in the rocess o design. The study involves a measure o the actual strength o the connections. A number o assumtions have been made in alying the equivalent orm o the roosed model below: The minimum distance, s is less than b (internal bolt sacing). Where s is greater than b, the value o b must be used. The bolts in comression only rovide resistance against shear. 35

47 b b b Tension Zone h Neutral Axis h Comression Zone Figure 3.4 Equivalent orm o the 10 bolt Flush onto a Four Bolt Flush Coniguration A yield analysis o the 10-bolt connection has been done as art o the study to investigate the ailure atterns. Dierent yield line atterns as resented in Aendix A have been evaluated to determine the controlling yield line mechanism. The controlling yield line attern is as shown in Figure 3.5. The total internal work o this mechanism is given by: 4m b h1 h + Wi + 1 h b g [ h ( + )] = b 36

48 b t t b b h h 1 g h h 3 Figure 3.5 Controlling Yield line Mechanism or the 10-bolt connection The redicted moment caacity is given by: b h1 h + M l Fyt + 1 b g [ h ( + )] = b 3.4. Case Two 8 bolts (One row o ailed bolts) An assessment o the connection strength o older structures makes it necessary to consider Case. The uer bolts o a connection might have ailed due to a number o actors. A careul evaluation o the structure when the bolt loss has occurred is imortant in investigating the overall eect on the moment caacity o the connection. In the research, the moment caacity o the connection is redicted when one row o 37

49 tension bolts has ailed. Dierent yield atterns have been investigated to determine the controlling collase mechanism. The controlling yield line mechanism is as shown in Figure 3.6 b t t b b h h 1 s g h h 3 Figure 3.6 Controlling Yield line Mechanism or the 8-bolt connection The total Internal Work o this mechanism is given by: 4m b h h + Wi + h + b s g [ h ( + s + )] = b The redicted moment caacity is given by: b h h M l Fyt b s g [ h ( + s + )] = b 38

50 In the exression, s is an unknown exression that is ound by dierentiating the internal work equation leading to the value o s as: s 1 = b g This value o s gives the minimum moment caacity o the late Case Three 6 bolts (Two rows o ailed bolts) The loss o two bolt rows changes the behavior o the connection and aects the overall caacity o the connection. The neutral axis dros urther downwards into the second row o bolts resent. The resulting model o the connection can thereore be comared to the two bolt lush end late in the AISC Design Guide 16, though with a ew modiications. As art o the research, a urther review o the yield line analysis o the connection with the two rows o bolt loss is investigated based on the assessment o a number o cases. The controlling yield line mechanism is as shown in Figure 3.7 The total internal Work o this mechanism is given by: W 4m b h3 h3 = + + s h s g i 3 [ h ( + )] In the exression, s is an unknown exression that is ound by dierentiating the internal work equation leading to the value o s as: s 1 = b g 39

51 b b h s g h 3 Figure Controlling Yield line Mechanism or the 6-bolt connection The redicted moment caacity is given by: M b h3 h3 = + Fyt + s s g l 3 [ h ( + )] When the value o is greater than s, its value should be set to s to give the least moment caacity o the connection. 3.5 Bolt Force Predictions The ultimate limit state o the connection deends on either the yielding o the end late or the ailure o the tension bolts. Moment caacity o the connection has earlier been redicted based on end late yielding. The rediction o orces in the bolts as a 40

52 result o loading on the connection is necessary in order to establish the overall caacity o the connection. When a connection is subjected to lexure, its bolts in tension are acted on by the tensile loads through the bending o the lates. Connection ailure occurs when the bolts in tension reach their tensile caacity. A major ste involved in the rediction o these orces is the determination o all the rying orces Prying Action The eect o rying action in end lates tends to increase the eective tensile load that is transerred to the bolts and thereore its eect needs to be evaluated. A modiied orm o the Kennedy model (1981) has been emloyed in dierent studies which involve end late moment connections such as that by Srouji (1983) and Borgsmiller (1995). Three stages o late behavior occur during the rocess o the alication o the load. The initial behavior o the late stage (Figure 3.8a) is reerred to as thick when the load as alied. At this stage, no rying orces are acting and thus the bolts exerience only direct tensile orces as a result o the alied load. As the load is increased, an initial lastic hinge is ormed in the late at the base o the tee stem; the behavior o the late is same to be intermediate. At this stage, rying orces are resent but not a maximum (Figure 3.8b). Another lastic hinge develos at the bolt line in addition to that initially occurring at the stem o the tee ater the load is urther increased. The end late behavior at this stage is reerred to as thin (Figure 3.8c) 41

53 F B B (a) Thick Plate Behavior ( Prying Forces Absent) F Q B+Q B+Q Q (b) Intermediate behavior ( Prying orces exist) 4

54 F Q max B+Q max B+Q max Q max (c) Thin Plate Behavior (Prying orces maximum) Figure 3.8 Stages o Plate Behavior based on the Kennedy Model A simliied method roosed by Borgsmiller (1995) has been used in this study which considers only two stages o the behavior o the late being the thick late limit where rying orces are absent and the thin late limit where maximum rying orces occur Determination o Plate Thickness Limits Srouji (1983) roosed several thicknesses limits equations uon which the behavior o the late might be described as thick, intermediate or thin. Ater the resulting lange orce, F, has been determined with a lange stress, σ, the thick late limit t thick is ound by a set o two equations given by: 43

55 44 y F t t σ.11 1 = Using the iterative equation below, the thick late limit is ound. 1 3 = t t F t t y thick σ σ I the actual late thickness, t is greater than t thick, then thick late behavior has been established and thus rying orces are absent, Q = 0. For the thin late limit, t hin, another set o two equations are involved given by : ( ) ' w b F F d t b t y yb b + = π σ Where w = width o end late er bolt at bolt line minus bolt hole diameter. F yb is the yield stress o the bolt. Then using the interactive equation 1 3 ' 3 ' = w t t b F w t t F b F d t b t y y yb b thin σ σ π σ I t is greater than t thin, then intermediate late behavior occurs and thus rying orces exist and should thereore be accounted or. In the same way, when t is less than t thin, maximum rying orces occur and is thereore considered in the estimation o the caacity.

56 Borgsmiller (1995) simliied the requirement or the determination o the limits or late behavior through urther exerimental testing. Only the thin late and thick late behavior is taking into consideration in his aroach. The eect o the rying orces becomes evident when 90% o the ull strength o the end late has been develoed as a result o the alication o load. Thereore no rying orces need to be considered or the rediction o the orces in the bolts when M n M l Modiied Kennedy Model A modiied orm o the Kennedy model has been used in the rediction o bolt orces by taking hal o the original Kennedy model to reresent a lush end late connection. A simliied orm o the Kennedy model had earlier been used by Srouji(1983) in the rediction o the bolt orces. The various models have been emloyed to hel redict the models or each case o bolt loss. F M b M b M1 M M 3 P P a b B 1 B Q (a) Case 1 10 bolts resent 45

57 F M b M b M1 M 3 M 4 P B P b B 3 a Q (b) Case -8 bolts resent ( one row o ailed bolts) F M b M1 M 4 P B a Q (c) Case 3-6 bolts resent ( rows o bolts missing) Figure Modiied Kennedy Model or cases o the lush end late connection. 46

58 3.5.4 Moment Caacity Prediction based on Bolt Forces The maximum rying orces, Q max, I is given in the AISC design manual o lush and extended moment end late connections as : Q max, i = w' t 4a i F y 3 F w' t ' i where b 1 t w ' = db +, a = i db 3 F ' i = t F y 3 b πd b Ft w' + 8 4, i I the radical in either exression or Q max,i is negative, combined lexural and shear yielding o the end late is the controlling limit state and the end-late is not adequate or the seciied moment. The last term in the numerator o the F i term reresents the contribution o the bolt shank bending. In determining the maximum moment leading to maximum orces in the bolts, the static moment o the bolts about the centerline o the comression lange is taken. Moment caacity equations have thereore being derived or the three dierent cases considered with or without rying orces. Case One Ten bolts Taking moments about the comression lange (Figure 3.10) gives the exression i. Without Prying Action 47

59 M ( h1 ) Pt = P h n t + M ( h ) n = Pt 1 + h b (a) (b) t t Pt (P - Q max ) t b P t (P - Q t max) b h h 1 g h h 3 M n M n Figure Case One bolt orces with (a) No Prying Action (b) Prying Action ii. With Prying Action The bolt tension is increased by the maximum rying, Q max. The exression or the moment is given by the maximum o either one o the two equations. M n ( Pt Q max ) h 1 + ( Pt Q max ) = h M ( P Q )( h ) n = t max 1 + h This exression is written in terms o the retension Force, T b as M ( h ) n = Tb 1 + h 48

60 Case Two Eight bolts b (a) (b) t b t P t (P - Q t max) b h h s 1 P t (P - Q max ) t g h h 3 M n M n Figure Case two bolt orces with (a) No Prying Action (b) Prying Action Taking moments about the comression lange (Figure 3.11) gives the exression: i. Without Prying Action M ( h ) n = Pt + h ii. With Prying Action The exression or the moment is given by the maximum o either one o the two equations. M ( P Q )( h ) n = t max + h 3 3 This exression is written in terms o the retension Force, T b as M ( h ) n = Tb + h 3 49

61 Case Three Six bolts b (a) (b) h s b P t (P - Q max ) g h 3 M n M n Figure Case three bolt orces with (a) No Prying Action (b) Prying Action Taking moments about the centre line o the comression lange gives the exression i. Without Prying Action M n = ( ) Pt h 3 ii. With Prying Action The exression or the moment is given by the maximum o either one o the two equations. M n 3 ( P ) = h Q t max This exression is written in terms o the retension Force, T b as M n = ( ) Tb h 3 T b = seciied bolt retension 50

62 CHAPTER IV RESULTS VERIFICATION AND FINITE ELEMENT ANALYSIS 4.1 Overview The behavior o the lush end lates with 10-bolts and the two cases o the connection with ailed bolts have been evaluated and consequently veriied with results rom an investigation using a inite element analysis. Though there has not been exerimental testing o the connection, earlier studies (Choi and Chang, 1996) have shown that inite element analysis can accurately redict the behavior o such connections. A inite element model has been develoed or the ten bolt lush end late connection, and the two cases o ailed bolts which occur in the tension regions o the connection. The detail o the roosed structure used in the study is a ten bolt lush end late connection o an existing steel arking deck. 4. Geometry o Structural comonents The structure is a steel rame structure with re-tensioned concrete decking. The beams between both sides o column along the san are castellated. The castellated beam, which is a built u section using a W1 x 6 as the to chord and a W4 x 76 as the bottom chord has been modeled as a combined section with roerties as shown in 51

63 Figure 4.1. The beam is connected to a W10 x 39 column. The steel used or all sections is Grade 60. The end-late which has been welded to the end o the beam has a thickness o 0.5 inches. The beam with the welded end late is bolted to the column lange with A35 high strength bolts o ¾ diameter. Details o the geometry o the beam and end late is shown in Figure 4.1 with dimensions resented in Table 4.1 b t t b b h h 1 g h h 3 Figure 4.1- Connection Details or End Plate with Adjoining Beam 5

64 Table 4.1 Section Proerties or End Plate and Beam Comonent Beam End Plate Dimensions h = in. b = 8.4 in t = in. t w = 0.4 in. b = 8.4 in. g = 4.1 in. =.585 in. b = 3.9 in. t = 0.5 in 4.3 Moment Caacity Predictions Moment caacity rediction equations develoed in the earlier chater have been used to redict the moment caacity o the connection described above. This involved rediction based on the yielding o the end late and the ruture o the bolts Limit State o End Plate Yielding Yield strength o end late, F y = 60ksi 1 1 s = b g = =. 91in 53

65 AISC Design Guide 16 nominal connection strength M l M l = F b h h + s + g [ h ( ) + h ( s )] + 1 g yt 1 b b = [ ( ) ] + M l = 197 ki-in Using Derived Prediction Equations Case One nominal connection strength b h1 h + M l Fyt + 1 b g [ h ( + )] = b M l = [ 18.8( )] M l = 106 ki-in Case Two nominal connection strength b h h M l Fyt b s g [ h ( + s + )] = b M l = [ 14.9( )] M l = 180 ki-in 54

66 Case Three nominal connection strength M b h3 h3 = + Fyt + s s g l 3 [ h ( + )] M l = [ 11( )] M l = 937 ki-in 4.3. Limit State o Bolt Fracture Bolt Data Diameter, d b = 3/4in Tensile strength or A35 Bolts, F t = 90ksi Bolt Force, P t db = π Ft = kis 4 Yield strength o End Plate, F y = 60ksi Without Prying Action Case One - nominal connection strength ( ) ( ) M = P h + h = =, 680 Ki-in n t 1 Case Two nominal connection strength ( ) ( ) M = P h + h = =, 060 Ki-in n t 3 55

67 Case Three nominal connection strength M n ( ) ( ) = P h = = 875 Ki-in t 3 With Prying Action Q max, i = w' t 4a i F y 3 F w' t ' i Where b w ' = db + = + = a i t = 3.68 d b = = F ' i = t F y 3 b πd b Ft w' = Ksi Qmax, i = 60 3 = Case One nominal connection strength ( )( ) ( ) ( ) max Kis M = P Q h + h = =,510 Ki-in n t Case Two nominal connection strength ( )( ) ( ) ( ) M = P Q h + h = = 1930 Ki-in n t max 3 56

68 Case Three Nominal connection strength ( )( ) ( ) M = P Q h = = 80 Ki-in n t max Determination o the Predicted Caacity The ailure mode with the minimum redicted value is chosen as the controlling ailure mechanism and its moment is taken as the redicted moment caacity o the connection. The controlling ailure mechanism can thus be determined based on these moment caacity values. Exerimentally, the redicted yield moment caacity is determined rom a moment end searation resonse curve using a bilinear aroximation i there are no clearly deined yield oints. This method can be used in determining the yield moment rom a Finite element analysis (FEA). The redicted moment caacity values with their corresonding controlling yield mechanisms have been summarized in Table 4. Table 4. Summary o Predicted Moment Caacities with Failure mechanisms Cases M l -End Plate M n - Bolt Fracture (ki-in) Controlling Yielding.(ki-in) Without With Mechanism Prying Prying 1 (10 bolts) End-late yielding (8 bolts) End-late yielding 3(6 bolts) Bolt Fracture 57

69 4.4 Finite Element Analysis ABAQUS Standard commercial sotware (a inite element code) has been used in creating a three dimensional inite element model o the 10 bolt lush end late connection. In order to use the model to redict the moment caacity o the connection, comonents o the connection including beam, column, end late and bolts have been modeled to reresent their erormance in service. Simliied modeling techniques have been adoted to reduce analysis time and imrove the accuracy o the inite element solution. Symmetry about a vertical lane through the beam web and lange and that o the column was emloyed and thus only hal o the ull model was analyzed Model o the Connection Comonents The comonents o the connection were modeled in ABAQUS CAE, using its grahic building tools. For a simliied model, a tyical connection in the structure was modeled to include the column side, beam, end late, bolts and nuts. A section o the column which sans rom loor to loor in the actual structure was modeled and the necessary boundary conditions alied. The beam o the structure which is castellated and directly suorts the loor deck was modeled as a cantilever without the erorations with movement restricted in the horizontal direction to reresent a continuous condition. The end late was modeled to be in contact with the beam to avoid comlications which would arise in modeling the welds. 58

70 (b) Beam with End Plate Model (a) Column Model (c) Bolt and Nut Model Figure 4.- Comonents o the Flush End Plate connection in ABAQUS CAE 4.4. Material Proerties Structural Steel was used as the material or the comonents o the model, but with dierent stress -strain relationshis. The modulus o elasticity or steel, E, was taken as 9,000ksi with a Poisson s ratio, v, o 0.3. A bilinear stress strain curve was used in modeling the material in the beam, end late and column langes, all having yield strengths, F y o 60ksi. The lastic behavior was considered to be linear ater yield (Figure 4.3a). A trilinear stress strain curve was used in modeling the bolts and nuts with yield strengths, F y o 90ksi and ultimate strengths o 100ksi (Figure 4.3b) 59

71 Stress (σ) F y E ε y 11ε y Strain(ε) Figure 4.3 (a) Stress Strain Relationshi or Beam, End late and Column Material Stress (σ) F ub F yb E ε y 3.5ε y 8ε y Strain(ε) Figure 4.3 (b) Stress Strain Relationshi or Bolt and Nut (Sumner, 001) 60

72 4.4.3 Assembly The individual comonents o the connection were modeled as art instances in ABAQUS as solid 3D deormable bodies. Each art instance was thereore resented in its own coordinate system. The Assembly module in ABAQUS made it ossible to arrange the individual comonents in a single unit by assembling them using the relevant osition constraints and translations. Figure 4.3 shows an assembly o the connection with the individual comonents. Figure 4.4 An Assembly o the 10-bolt Flush end late connection 61

73 4.4.4 Contact Interactions The assembly module simly ositions each comonent relative to each other under a global coordinate system, but does not establish contact between aces even i the suraces are together. The contact between the various interaces o the connection was deined and established through the creation o both master and slave suraces. Normal and tangential behavior has been deined to reresent the contact between adjoining suraces with or without riction. Contact was established between column and beam interaces as well as bolt and nut contact on both the beam and column sides arising as a result o retension. This was achieved in the irst ste o the analysis and the results showed that there were no strains or deormations in the model beore loading. Penetration error between the interaces was ket to a minimum and was within the accetable tolerance Boundary Conditions The rescribed boundary conditions deine states that various art o the assembly exhibit both at the initial stage and within other stages in the analysis. It also describes their behavior in terms o dislacement and rotations during analysis stes. Two major orms o boundary conditions including dislacement and symmetry boundary conditions were used. For an easy and economic analysis, only hal o the connection was modeled and a symmetric boundary condition alied to simulate the behavior o the actual connection. The column ends were restrained in all the directions. The same was alied to the bolts and the nuts in their initial state with movement in the 6

74 horizontal direction only when the load was alied. The ree end o the beam was restrained rom movement in the horizontal direction. These conditions closely reresent the actual state in which the comonents undergo in an actual exerimental setu (Srouji, 1983). Fig 4.5 Connection Boundary Conditions Loading and Analysis Stes Dierent analysis stes were emloyed to establish contact and to aly the loads. General static analysis was conducted without linear erturbation. Loading on the connection was induced by alying two vertical loads (a coule) to the beam ti at the ree end. These loads were increased until the model had shown signs o instability. Bolt Pretension was achieved by the alication o a tensile load to simulate the tightened condition o the bolt and nut with the code seciied minimum bolt tension. (AISC, 005). Three dierent cases was simulated including the ten bolt case, one row o ailed bolts and inally, two rows o ailed bolts. 63

75 4.4.7 Element Tye and Meshing Proer meshing in a inite element model leads to an economic analysis with higher accuracy, both o which cannot be overemhasized. In order not to unnecessarily increase the degrees o reedom o the various art instances, the mesh was created with varying densities, being denser only around regions o interest and bolt holes where stress concentrations and suraces o contact between individual comonents make u the model. Figure Mesh o Connection Assembly An 8 node brick (C3D8) solid continuum element was chosen rom the ABAQUS element library and used on all comonents o the connection. This element has nodes only at their corners as shown in Figure 4.6, uses linear interolation in each direction 64

76 and is oten called a linear element or a irst order-element. There is a constant volumetric strain in the element which revents shear locking when the material resonse is incomressible. Full integration elements are deined to control hour glass. Figure 4.7 Linear element, 8-node brick-c3d8 (ABAQUS Analysis Manual) Visualization o Results and Failure atterns Visualization results or the three cases analyzed using ABAQUS is shown in Figure 4.7 or the three cases o the analysis with (a) being the undeormed shae and (b) the deormed shae. It clearly indicates the likely ailure atterns that would orm in the connection. Thick late behavior could be inerred rom the Von mises stress distribution by examining the deormed shae in each analysis case. Areas in tension showed high stresses in the tension zones and occurred along aths where yield lines were likely to occur as outlined in the develoment o the yield line mechanism models or the rediction o the moment caacity. 65

77 Case 1-10 bolts (a) Undeormed (b) Deormed Case 1 row o bolt missing (a) Undeormed (b) Deormed 66

78 Case 3 rows o bolts missing (a) Undeormed (b) Deormed Figure 4.8 Failure Patterns in dierent cases o connection ailure 4.5 Moment Caacity Prediction rom Finite Element Analysis Nodal dislacements rom the end late and column lange were used to calculate endlate searation. The values were recorded at each analysis ste and used in lotting a moment end late searation curve or the various cases, with Case one (Figure 4.8) and Case two (Figure 4.9) as examles in this reort. The end late yield moment was then determined rom these lots using bilinear aroximation as shown in Figure 4.8. There was a loss in stiness in the connection when the alied moment was increased. The ten bolt lush end late connection had the highest stiness in its elastic region ollowed by the eight bolts and then the six bolts. 67