Effect of prying action forces on design method of rigid bolted connections with circular end plate. *Mohammad Reza Farajpour 1

Transcription

1 Effec of prying acion forces on design mehod of rigid boled connecions wih circular end plae *Mohammad Reza arajpour 1 1 eparmen of civil engineering, Tabriz branch, Islamic Azad Universiy, Tabriz, Iran 1 Su.farajpour@iau.ac.ir ASTRACT This paper presens an exac way for compuaion prying acion forces in boled rigid connecions wih circular end plae by sudying he behavior of his ype of connecions. esides, finie elemen models of boled connecions wih circular end plae is made in various geomery. rying acion effec in hese models is regarded and collapse mechanism of T connecions is used o compuaion siffness. Also, deformaion and disribuion of surface press which resul from prying acion phenomena is used. ih using he resul from parameric analyses of connecions, an improved mehod is presened o compuaion prying acion. Then, an improved mehod is proposed o design boled rigid connecions wih circular end plae in regard wih prying acion effec. Accuracy assessmen of proposed mehod, will display efficiency and favor accuracy in designing boled connecions wih circular end plae. Keywords: boled rigid connecions, circular end plae, finie elemen model, prying acion forces, design mehod, failure models, and collapse mechanism. 1. INTRUCTIN ell-designed connecions can paricipae in non-linear behavior of srucures and improve is seismic behavior. eam-column join is he mos alened poin o form a plasic hinge. Suiable roaional capaciy of oled connecions allow hem o preven more laeral frame dislocaion and reduce he need for duciliy in beams and columns wih non-elasic deformaion and energy absorpion, insead of merely cracking. This highlighs he need for an analyical approach and deailed design of connecions. efore 1994 Norhridge earhquake, i was assumed ha he frame wih welded connecions is he bes sysem o bear graviy and laeral loads. I was expeced ha he failure of hese frames would be limied o local submission and buckling in beams and also persisen small relaive displacemen beween levels. Norhridge earhquake caused devasaion in weld joins and cracks in he heaed seel secion of connecion pars. Since hen, due o he possibiliy of building boled connecions facory, high safey and low cos of implemenaion, his ype of connecion is increasingly drawing he aenion of he designers. (Krishnamuri 198), heading research group of AISC Insiue along wih Meal uildings Manufacurers Associaion MMA, have conduced 1) h candidae

2 he firs sudies done on he behavior and design of boled connecions. His research progressed in boh heoreical and experimenal areas, resuling in dozens of repors, essays and hesis. The resuls of his research were insered in he (AISC Regulaions 198) as design crieria of boled connecions. ih he increasing abiliy of compuers, (Sherbourne and ahaari ) designed a fla wo-dimensional ension model for boled connecions using ANSYS Sofware and hen creaed is 3 model. Using AAUS sofware, iller modeled beam-o-column connecions o find designing formulas (heeler ). (aniunas and Urbonas 6) conduced some research in he area of boled connecions a he Universiy of Salkoekia in Lihuania. Their research was based on Europe componen model and hey evaluaed heir modeling accuracy based on experimenal resuls of da Silva of he Universiy of rague (asilva 1). ue o he fac ha designing mehods of oled connecions are based on (Krishnamuri 198) fla wo-dimensional model, Recen advances in finie elemen sofware and accurae measuremen ools have made i possible o improve analysis and designing mehods providing a beer undersanding of he disribuion of ension, srain and join behavior. This paper sudies he behavior of endplae boled rigid connecions in wo cases of skimmers and elbow (Huihuan 16). inie elemen models of he connecions made by classificaion of Europe Regulaions (EC3), have been considered full rigid (Huu Tai 16). Afer checking and evaluaing he accuracy of finie elemen models, wih parameric analysis of rigid connecions and T, imporan facors have been idenified in connecion behavior (Chakhari 7). Then finie elemen models of T Connecions wih circle plae were creaed in differen saes and compared o simple T connecions. ne of he imporan parameers influencing he behavior of connecions is prying acion phenomenon. esigning regulaions haven offered any exac mehod for calculaing prying acion power, and only ried o reduce is effecs wih increasing he reliabiliy of design mehods. In some cases his causes uneconomical design, unreal prediced behavior and a change of behavior of he srucure (Smiha 13). This paper sudies he impac of prying acion forces on he behavior of circular endplae rigid connecions and he laws governing were developed as a mahemaical model. The resul of his survey is presening an improved mehod for applying he effec of hese forces on he behavior of his ype of connecions. Aferwards, mehods of analysis and designing connecions were sudied and accuracy of each was evaluaed by finie elemen analysis resuls (ANSI/AISC 1, AISC 5). inally, a modified proposal for he designing boled rigid connecions was offered and he accuracy of he mehod was evaluaed using finie elemen models.. INITE ELEMENT MELIN To deermine he behavior of boled connecions, hree groups of finie elemen model were developed using AAUS sofware (Abaqus elemen reference 16). In order o idenify facors conribuing o he phenomenon of prying acion, parameric analysis and calculaion of he prying acion forces, a group of finie elemen models of T connecions has been creaed wih variable endplae hickness. To compare he behavior of connecions wih circulaed endplae, some models of T connecions wih circulaed endplae were creaed and compared wih simple T connecions. Tables 1 and show he geomery of models creaed. The simple connecion models were used

3 o convergence analysis of member and evaluae he accuracy of finie elemen models compared wih experimenal resuls (a silva 1). eween finie elemen models, nonlinear geomeric behavior, nonlinear maerials and large deformaions have been considered. The srucure used for modeling conneciviy componens is solid and mechanical properies of bol maerials are of high srengh A49 in hree linear form wih pre sressing force 15 KN and seel ip beams, columns and plaes have been inroduced in he sofware in seven linear form (Crocei 16). elding in finie elemen models has been defined as coninuous connecion wih TIE and reliance beween connecing plae and column flange (HAR) wih he separaing propery afer unloading. In order o mesh conneciviy componens, he low-order erahedral mesh is used in hree-dimensional sress sae. Suiable dimensions of elemens have been defined using analysis of convergence among componens. Each conneciviy componen has been loaded and analyzed independenly under differen mesh and assessing he accuracy of he resuls of he analysis, he mesh size has been se properly. The resuls of bol convergence analysis are provided in Table 3 and beam in Table 4. ig.1 shows ypical beam o beam connecion models wih circular endplae, ig. shows circular endplae T connecions and ig.3 shows T connecions wih simple recangular endplae. ig.4 shows he finie elemen mesh model of samples. Tensional loading is applied in 18 sages. In model analysis sage, he non-linear geomeric properies of models have been considered. To evaluae he accuracy of finie elemen models, a Silva experimenal daa has been used (a silva 1). L S S L cl 1.9 r R cl 1.9 r R ig. 1 oled connecion model wih circular endplae The comparison beween experimenal resuls and finie elemen of simple T connecion shows accurae modeling connecions. Comparing dislocaion of a paricular node caused by ension loading of finie elemen model of connecion wih a Silva experimenal resuls has shown he error of abou 8%.(a silva 1)

4 r L S S L cl ig. T connecion model wih circular plae R 5 L S S L X X 5 Sec x-x 5 ig. 3 Simple T Model connecion ig. 4 Typical finie elemen model of sample coupling connecion wih circular endplae and T connecion wih circular

5 Table 1. The geomery of finie elemen models of simple T Connecion Model Connecion ase plae Hole ol ol plae hickness dimension diameer diameer ype () M mm 5X5mm mm mm A49 35.M 35.mm 5X5mm mm mm A49 M mm 5X5mm mm mm A49 λ Model M 35.M M Table. The geomery of finie elemen models of circular plae Connecion ase plae Hole ol ol plae dimension diameer diameer ype hickness () mm R=5mm mm m A49 m 35.mm R=5mm mm m A49 m mm R=5mm mm m A49 m λ Model Model no 1 seed :.3 size Model no seed :.1 size Model no 3 chosen ( )model seed :.5 size Table 3. The resuls of boled convergence Change he Maximum ol in Node lengh of bol misses sress ension (N) number (mm) (pa) in bol 9 3 =5 Sp =1 =5 =1 = 5 =1 Sp1-65 Sp1-65 Sp1-65 Sp1-65 Sp Lengh difference % 16.7% 5.6% 5.7% 3. RYIN ACTIN RCES In he design of boled connecions, regardless of lever forces causes errors in he design. In his sudy, o undersand he behavior of lever forces, he iner planar pressure caused by he disribuion of he forces in T connecions, in boh simple and circular, have been checked. acors affecing he prying acion phenomenon include hickness and rigidiy of he connecion plae, diameer and lengh of he bol, posiion and geomery of he hole, he mechanical properies of maerials and he ype of connecion load. This paper sudies he effec of rigidiy of connecion plae. λ coefficien is used o deermine rigidiy of connecing plae. In foundaion engineering his coefficien is used o calculae foundaion rigidiy on elasic foundaion.

6 Table 4. The resuls of convergence analysis of he beam ube conneced o a circular plae model eam in Node Maximum shif in he Shif N.m bending number end of beam(mm) difference Model no 1 M= / seed :/5 M= / size Model no 1 M= / %8 seed :/ M= /4 1 9 %8 size Model no 1 M= / %6 (chosen M= %6 model) seed :/1 size (1) K 4 s 4EI () K K s s (3) E K s.4 In he above equaion, λ is he rigidiy facor of connecing plae, is he connecing plae widh along he incoming anchor, is he hickness of connecing plae and E is elasiciy modulus of plae maerials. To deermine he forces of prying acion, he analysis of finie elemen models of T connecion has been done wih variable hickness of connecing plae. Simple T connecion failure mechanism is shown as figure 5-A for simple T connecions and 5- for circular endplae T connecions. Sudying curve 6-A and 6- ha show changes of prying acion forces and he shif of maximum gusse plae on he exernal force of T connecion wih semi-rigid plae in boh simple and round form, four disinc phases can be deeced in he load-prying acion curve and load-displacemen curve. In hese curves, he firs elasic pars have been formed on he web plae connecion. Secion A- shows he diagram of linear deformaion and elasic gusse plae. In A- and -C phase, a sharp change in slope of he curve can be seen. This secion of loading is indicaor of mechanism of connecing. A poin of he curve, plasic hinge of web connecion is expanded and a sharp rise in ension of bol line ( line of gusse plae) can be seen. A poin C, plasic hinges are formed in line of bol on gusse plae and limied poins of bol web are yielded bu he plasic hinge is no formed compleely. hen he ension in he bol increases, relaive bol deformaion will be also added and separaion of gusse plae of rigid foundaion increases and he secion relaed o he impac of forces resulan of prying acion will be ransmied o he ouer edge of he plae and he raio of he slope of load-prying acion diagram will be duly added. This connecion is broken because of plae yield a he poin of web T profile. Sudying finie elemen models indicaes ha he failure

7 mechanism of mos T connecions wih semi-rigid endplae (> λ> 1.5) looks like figure 5-C. Sudying 7-A and 7- curves relaed o rigid plae T connecions (.5> λ>.3), hree disinc phases are recognizable in he load-displacemen and Load-prying acion curves. In -A1 phase, he curve is linear and elasic and a he poin of A1 he firs plasic hinges are creaed on gusse plae a web T. A he poin of 1 he plasic hinge of he web is complee and a seep slope can be observed in order o increase he ension in he bol axis. Also a his sage due o he formaion of plasic T profile base and reducion of prying axis and he exernal load ransmission o he web cener, he slope of he load-prying acion will change. A he poin of C1 he gusse plae is separaed from web base and limied poins of he bol axis become plasic bu a complee plasic hinge is no formed here. Sudying he finie elemen models and load-displacemen and load-prying acion curves of rigid plae connecion of which is (.5> λ>.3), his resul is ha figure 5 (a) is he form of failure of mos of hese connecions and sysem failure is originaed from web base connecion. In he connecions ha are high in rigidiy plae (λ <.3) he failure is originaed from he bol base and no failure happens in he gusse plae. y examining 8-A and 8- curves which are relaed o he sof plae connecion (4 <λ), hree disinc phases in load-prying acion and wo phases in load-displacemen diagram have been observed. In hese diagrams, he -A phase is linear and elasic sage while A- and -C are he connecion mechanizaion sage. The connecion failure happens a he gusse plae bol line. ue o he sofness and high duciliy of he upper side of he plae, connecion deformaion caused by loading in he non-elasic phase, is in he form of second level curve. Examining he finie elemen models, figure 5- is he form of mos connecion failure mechanisms wih sof plaes. y examining he resuls of parameric T connecions, i is considered ha he amoun of prying acion forces creaed in he connecions has direc relaionship wih he rigidiy of gusse plae. In connecion wih rigid plaes of (.5> λ) he amoun of prying acion forces is iny and negligible. y reducing he rigidiy of gusse plaes, prying acion forces increase. (λ - / ) Curve shows ha he slope of he curve of connecions wih super sof gusse plaes (4 <λ) leans oward zero and prying acion forces creaed in hese connecions are consan coefficien of exernal loads applied o he connecion. Also (1.67 = λ) is urning poin of his graph and can be considered as sof and rigid plae boundary (ig. 8). recangula r C Table 5. Comparison beween models A racure mechanism /+ /+ /+ /+ /+ /+

8 Connecion plae yield lines lasic hinges Connecion plae momen disribuion A C Circular racure mechanism Connecion plae yield lines lasic hinges Connecion plae momen disribuion cl 1.9 cl 1.9 cl 1.9 /+ /+ /+ /+ M /+ /+ /+ /+ M /+ /+ r /+ /+ r /+ /+ r M M /+ /+ M M /+ /+

9 5 (KN) A C (KN) 5 A C U3(mm) -CURVE -U MEL M A-CURVE - MEL M (KN) ig. 5 ailure mechanism of T connecions (a simple and circular endplae mode) 5 (KN) A C (KN) 5 A C U3(mm) -CURVE -U MEL M A-CURVE - MEL M (KN) ig. 6 The resuls of parameric analysis of semi-rigid T connecion Also changes in prying acion forces are proporional wih failure mechanism of gusse plae. In connecions wih rigid plae, reducion of λ value and prying acion forces caused A ype failure mechanism, in sof plae connecions, ype failure mechanism and in connecions wih semi rigid plae C ype failure mechanism have occurred (ig. 5). Examining circular endplae T connecions i was observed ha all he resuls of he sudying simple T connecion is rue for his ype of he connecions. The resuls of examining circular endplae T connecion failure mechanisms are

10 provided in ig.5 (b). Also he failure mechanism of circular endplae beam o beam connecions was quie consisen wih he foregoing and one way connecion o he rigid foundaion or anoher endplae beam has no impac on he process of failure mechanism of connecion poin and endplae. ig.1 shows he sress disribuion in he endplae connecions and also deformaion of bol and endplae in finie elemen models creaed. Sharp focus of ension in creaed yield line of endplaes is quie eviden. ig.11 shows he disribuion of ension and deformaions of connecions of wo circular endplae beams. 5 (KN) C1 5 (KN) C A1 A (KN) U3(mm) -CURVE -U MEL 35.M C1 (KN) A-CURVE - MEL 35.M C1 (KN) A1 3 A U3(mm) CURVE -U A-CURVE - MEL 35.M MEL 35.M ig. 7 The resuls of parameric analysis of rigid T connecion (KN)

11 / 1 8 λ= CURVE / - λ (=N) ig. 8 The impac of gusse plae rigidiy on he prying acion forces curve - Simple T connecion.. Circular plae T connecion (KN) C (KN) λ C A U3(mm) (KN) -CURVE -U MEL M C (KN).5 A-CURVE - MEL M C (KN) A U3(mm) CURVE -U A-CURVE - MEL M MEL M ig. 9 he resuls of parameric analysis of super sof T connecion (KN)

12 C A ig.1 A: Circular endplae T connecions finie elemen model failure : Endplae deformaion under loading C: eformaion and failure mechanism of he bol under loading ig. 11 inie elemen model failure of circular endplae couple T connecions 4. THE CALCULATIN THE RYIN ACTIN RCE N SIMLE T CNNECTINS (aella, 1999) conduced exensive sudies in he field of calculaion of he prying acion forces resuled in providing approximaion mehods in a cerain ype of T connecions (Cavdar 9). Smih e al., provided and approximaion formula o calculae prying acion force (Smih 1991). In his formula ha is presened o calculae prying acion forces in T connecions under ensile loading, he connecion plaes are assumed quie rigid. The applied bols are ype A49 and he connecion loading is pure ensile and in he web of he profile T. Eq. 4 presens he Smih approximaion formula. (4) 1.b. 14.L. [ 6.a. 1.L. f f ]

13 In he above equaion is he nominal diameer of he bol, is he exernal ension of a bol, f is he connecion plae hickness, b is he disance of he bol axis o he cener of he profile T web, a is he disance beween he bol axis o he edge of he plae and L is he lengh of he connecion plae heigh ha includes a bol (L= h/n). y evaluaing he accuracy of his formula on finie elemen models of connecion T an error abou 8-16% is resuled in he calculaion of he prying acion force. ue o he high error of his formula, he use of his mehod o calculae he prying acion forces in T connecions. In he Code AISC-LR an approximaion mehods is presened for he calculaion of prying acion forces (AISI 1). In his mehod he prying acion forces in T connecions are calculaed by he Eq.5. (5)....( ) c In his equaion, is he prying acion forces of a bol, β is he design ension of he bol, ρ is he bol axis disance from he web edge o bol axis disance from he plae edge raio, δ is he plae widh coefficien or he plae ne widh o is nominal widh raio in he rows of bol holes, α is he connecion plae momen in bol row () o plae momen in bol row (M) raio in he uni widh, is he plae hickness and c is he hickness needed o wihsand he anchor of he exernal loading (ig.1). This compuaional mehod is provided for cerain scenarios of he T-shaped connecions and is error in he connecions wih semi-rigid plae (λ= 1.67) is abou 4% and by reducing he hickness and rigidiy of he connecion plae and increasing he prying acion forces, is error is increased. This error has increased o 8 percen in he quie sof connecions. T+ T+ a b b a M T ig. 1 The geomery of AISC compuaional mehod

14 ig. 13 The iner planar pressure caused by prying acion forces 5. THE CALCULATIN RYIN ACTIN RCE IN T CNNECTINS ITH CIRCULAR ENLATE or he accurae calculaion of prying acion force in T connecions wih circular endplae, he geomeric facors ha affec he empirical relaion 4 should be modified. rying acion forces are calculaed by iner planar compressive sress caused by hese forces based on igure 13.ased on he difference in he sress disribuion in circular plaes wih riangular plaes due o he border cleaning of he bols on he four sides of he connecion plae and by is fiing he numerical informaion of he models wih ren geomeric condiions, he geomeric facors of he plaes in which he bol hole is a he cener of he disance beween he edge of he beam conneced o he endplae and he free end of he plae is defined as follows (arajpour 13). (6) a. 886 b In his equaion b is he disance beween he bol edge and he ensile flange wing and a is he disance beween he bol edge and he iner planar pressure area. a is he maximum possible lengh o exend he conac pressure by he prying acion phenomenon in he ensile bols of he connecions wih he circular endplae. ig.13 shows he sress disribuion in hese connecions. y calculaing he geomeric facor he following process is recommended for calculaing he prying acion forces a each bol. (6) r M 1 u h n (8) b a (9) d 1 p

15 (1) 1 rn ( 1) ru (11) 1 ru c [( ) ( ) 1] rn (1) c b rn (13) rn[...( c ) ] p. y In he above equaions, ru is he exernal ension of he bol, M is he exernal momen, h is he heigh of he beam, n is he number of ensile bols, is he raio of he geomeric coefficiens ha have been obained from he Eq.6, is he facor ha is deermined by Eq.9, d is he hole diameer, is he share of each bol in he widh of he connecion obained by dividing he widh of he plae by he number of bols, rn is he nominal ension of he bol design, is he conac sress disribuion coefficien of connecion prying acion wih he circular endplae, is he hickness of he connecion plae, c is he iniial hickness of he connecion plae obained by he Eq.1, y is he yield sress of he plae maerials and is he prying acion force of a bol a he end of he connecion. 6. CNCLUSINS In his sudy, he behavior of boled connecions wih circular endplae is examined. Afer creaing finie elemen models of he connecions he accuracy of he compuer models is assessed. The maximum error of finie elemen models is abou 8 percen. ih parameric analysis of hese connecions he imporan facors affecing he connecions behavior are deeced. ne of he mos imporan parameers in connecions behavior is prying acion phenomenon, he ignorance of ha in design sage could causes errors in calculaions. To calculae he prying acion forces in T connecions here are wo experimenal mehods. y sudying compuaional approaches of Smih and AISC he compuaional error in Smih mehod in comparison wih finie elemen mehod is 8 o 16% ha depends on he rigidiy of he connecion plae. In he second mehod in he connecions wih semi-rigid plaes he error is esimaed4 percen. To find ou how o adjus he AISC formulaion models of T connecions wih variable hicknesses are creaed and analyzed paramerically. y analyzing he failure mechanism of hese connecions and he effec of prying acion forces, i is concluded ha he prying acion forces is direcly relaed wih he rigidiy of he connecion and prying acion is increased by reducing rigidiy. Also in connecions wih very sof plaes, he prying acion force is a consan coefficien of he exernal

16 forces applied o he connecion. In rigid connecions, i is possible o ignore prying acion forces under cerain condiions. y comparing he disribuion of conac sress obained by prying acion phenomenon in connecions wih simple and circular endplae and he fiing of he numerical daa obained from finie elemen models, he geomeric facor of.886 is proposed for he connecions wih circular endplae if he bol hole is in he middle of he beam edge and he free edge of he plae. In calculaing he prying acion forces wih he improved mehod, he maximum error is esimaed o be 5% in he anicipaion of hese forces a connecions. Also using he improved mehod i is possible o anicipae he need o calculae prying acion force in semi-rigid connecions. y calculaing he prying acion forces and heir inclusion in he process of designing, i is possible o reduce his compuaional and design error significanly. REERENCES Krishnamurhy, N. (198) "Modeling and predicion of seel boled connecion behavior." Journal of Compuers & Srucures, 11(), pp ahaari, M. R. Sherburne, Archibald, N. () "ehavior of eigh-bol large capaciy endplae connecions." Journal of Compuers & Srucures, 77, pp heeler, A. T., Clarke, M. J. and Hancock,. J. () "E Modeling of four-bol, ubular momen end-plae connecions." Journal of Srucural Engineering, ASCE, 16(7), pp Urbonas, K., aniunas, A. (6). "ehavior of semi-rigid seel beam-o-beam joins under bending and axial forces." Journal of consrucion seel research, 6, pp Simoes-da-Silva, L., lima, L., Vellasco,. and e Andrade, S. (1). "Experimenal behavior of end-plae beam o column joins under bending and axial force." Eccs echnical commiee 1, wg1., eparmen of civil engineering, Universiy of Coimbra. Huihuan Ma, Shan Ren and eng an, A. (16). " Experimenal and numerical research on a new semi-rigid join for single-layer reiculaed srucures." Journal of Engineering Srucures, 16, pp Huu-Tai Thai and rian Uy. (16). " Roaional siffness and momen resisance of boled endplae joins wih hollow or CST columns." Journal of Consrucional Seel Research, 16, pp Chakhari and Zghal, A. (7). Numerical model for boled T-subs wih wo bol rows. Journal of Srucural Engineering and Mechanics, 6(3). Smiha, M. S. and Saish Kumar S. R. (13). " Seel concree composie flange plae connecions, finie elemen modeling and parameric sudies." Journal of Consrucional Seel Research, 8, pp American insiue of seel consrucion, ANSI/AISC. (1). "Specificaion for srucural seel building." American Insiue of Seel Consrucion. (5) "Manual of seel consrucion, Load and resisance facor design." connecions, Chicago. Abaqus Elemen Reference. (16). "Abaqus documenaion." nline help. Crocei, R. usafsson. J. irhammar, U. A., Cosa, L. and Asimakidis, A. (16). "Nailed Seel lae Connecions: Srengh and ucile ailure Modes." Journal of Srucures, 8(1), pp

17 Cavdar,., ayrakar, A. Cavdar, A. and Karal, M. E. (9) "Sochasic finie elemen analysis of srucural sysems wih parially resrained connecions subjeced o seismic loads." Seel and Composie Srucures, 9(), pp Smih, J.C. (1991). "Srucural seel design lrfd approach." Norh Carolina Sae Universiy, iley Inc. arajpour, M. R. (13). "Effec of beam o column connecions on saic and seismic response of seel frames" M.Sc. hesis, Azad universiy, Maraghe branch, Iran. arajpour, M. R., Hosseinzadeh, Y. and Lofollahiyaghin, M. A.(13). "Effec of prying acion forces on rigid end plae connecions" journal of Sharif, 4, pp