Towards Systems Behavior Factors for Composite Frames: Experimental and Analytical Studies

Transcription

1 Toward Sytem Behavior Fator for Compoite Frame: Experimental and Analytial Studie A Summary Final Report to the Amerian Intitute of Steel Contrution by Roberto T. Leon and Tiziano Perea Shool of Civil and Environmental Engineering Georgia Teh, Atlanta, GA Jerome F. Hajjar Department of Civil and Environmental Engineering Northeatern Univerity, Boton, MA Mark D. Denavit Department of Civil and Environmental Engineering Univerity of Illinoi at Urbana-Champaign, Urbana, IL February 11

2 I. Introdution Compoite teel-onrete trutural ytem ontitute a valuable and growing etor of the ontrution market, often being adopted for ome of the more hallenging ontrution onfiguration beaue of the high trength and tiffne offered by thee ytem. At the preent time, it remain diffiult to predit the maximum trutural repone of a frame ytem that inlude ompoite beam-olumn baed on typial frame analyi and deign trategie. Fiber Analyi (FA) or Finite Element Analyi (FEA) may be ued to obtain an improved aement of the repone; however, their appliation in onventional deign of low- to moderate- height building i neither pratial nor ommon. The development of tability deign proedure and eimi deign parameter or behavior fator appliable olely to ompoite ytem inorporating teel reinfored onrete (SRC) or onrete-filled teel tube (CFT) olumn, a oppoed to uing thoe for imilar teel or RC trutural ytem, i alo needed. To reah thee goal, a multi-intitution ombined experimental/omputational reearh program wa undertaken, inluding: (a) experiment of lender, full-ale onrete-filled teel tube beamolumn that inluded lender ro-etion to fill the gap in the experimental databae; (b) development of new finite element formulation that enable aurate repreentation of the eimi repone of three-dimenional ompoite braed and unbraed frame truture; and, () reommendation for deign of ompoite truture within the ontext of the Amerian Intitute of Steel Contrution Speifiation for Strutural Steel Building, inluding interation effet, effetive rigiditie, bond proviion, ontrution onideration, and analyi reommendation. Thi work erve a the foundation for the eond part of the tudy, in whih a large number of nonlinear dynami analye have been arried out to evaluate the performane of thi ytem and to develop the ytem behavior fator. The main objetive of the experimental omponent of thi reearh are: To obtain experimentally the ritial load of lender ompoite irular CFT (CCFT) and retangular CFT (RCFT) full-ale beam-olumn with different boundary ondition. There i a dearth of data on lender ompoite olumn and the poible interation between the tability and trength of the etion, a well a the ability of lender CFT ro etion to onfine the onrete. To obtain experimentally a large number of data point on or near the axial load-moment (P-M) interation diagram of ompoite CFT beam-olumn. There i very little data on the ultimate trength of ompoite etion under different ombination of axial load and moment, partiularly when oupled with large lateral deformation and three-dimenional loading. To obtain experimental repone of CFT beam-olumn under yli lateral fore, and from thi, evaluate the trength and dutility of lender CFT beam-olumn for eimi loading. In addition, thi reearh provide ome of the mot detailed data in the literature regarding the evolution of tiffne, trength, and damage in ompoite member. To evaluate the effet of the wet onrete in teel tube during the pouring, while ating under hydrotati preure, while in the tranition to a hardening tate, and when the element i loaded ompoitely during the experiment. Page

3 To evaluate the effet of the tability, onrete onfinement, teel loal bukling, and the interrelation among thee on the behavior of CFT. To refine material ontitutive model and trutural model to have an analytial predition that follow the experimental repone. To provide reommendation for the ontrution and the deign of irular and retangular ompoite CFT beam-olumn in frame truture. The main objetive of the analytial omponent of thi reearh are: To develop a omprehenive et of experimental data from the worldwide literature on SRC and CFT ompoite member and frame. To formulate and validate advaned nonlinear model for the analyi of teel and onrete ompoite frame through the development of ditributed platiity fiber-baed beam finite element formulation. To provide reommendation for the aement of load tranfer via natural bond trength for retangular and irular CFT olumn. To deign a erie of arhetype frame uitable for the parametri tudie to etablih eimi repone fator, diret analyi parameter for tability deign, and to provide related analyi/deign reommendation. The purpoe of thi report i to provide brief highlight of the reearh. Complete detail of thi reearh are reported in Leon et al. (9), Denavit and Hajjar (1), Denavit et al. (1), Perea et al. (1) and Perea (1). Together thee report ummarize the prior literature on experimental teting of ompoite beam-olumn, omputational formulation for ompoite ontrution, and behavioral aement of ompoite member. The report alo preent a omprehenive et of data obtained from the experimental program, detailed analyi of experimental reult, and a omplete deription of the formulation and validation of the omputational model. II. Experimental Methodology The experimental program onited in teting 18 full-ale onrete-filled teel tube beamolumn ubjeted to omplex three-dimenional load protool. Thee omplex full-ale tet were poible due to the apabilitie of the Multi-Axial Sub-aemblage Teting laboratory (MAST), a part of the NEES Collaboratory (Hajjar et al. ). At the time thi program wa onduted, thee CFT peimen were the lenderet and the longet CFT olumn and beamolumn teted in the world. Tet Speimen The tet matrix i ummarized in Table 1. An extenive databae (Leon et al. 5, Goode 7) wa ued to identify gap in exiting knowledge; thee gap were partiularly lear for very lender olumn and for beam-olumn with high-trength onrete. Thu the tet matrix onit of a mix of three irular CFT and one retangular CFT peimen with length of 18 ft. Page 3

4 and 6 ft. and onrete infill with nominal trength of 5 ki and 1 ki. The retangular CFT were teted both in their trong () and weak (w) axi diretion. Speimen with the mot lender wall ommonly available were ued. Typial detail of thee peimen are hown in Figure 1 through 4. Table 1 Tet matrix of the CFT peimen with nominal value Speimen L Steel etion Fy f D/t name (ft) HSS D x t (ki) (ki) C HSS5.563x C HSS1.75X C HSSx Rw HSSx1x R HSSx1x C HSS1.75X C HSSx Rw HSSx1x R HSSx1x C HSS1.75X C HSSx Rw HSSx1x R HSSx1x C HSS1.75X C HSSx Rw HSSx1x R HSSx1x C HSS5.563x Page 4

5 Figure 1 Cirular CFT peimen with an HSS5.563x & 6 18 & 6 Figure Cirular CFT peimen with an HSS1.75x.5 Page 5

6 18 & 6 18 & 6 Figure 3 Cirular CFT peimen with an HSSx.5 18 & 6 18 & 6 Figure 4 Retangular CFT peimen with an HSSx1x.315 Page 6

7 III. Intrumentation Plan The intrumentation of the peimen onited of: Strain gage for meauring both longitudinal and tranvere train. The train gage were plaed in three (and in ome ae four) fae of the exterior teel wall. At leat three meaurement at the ame level of the olumn allow the omplete alulation of train within the ro-etion auming plane etion remain plane. LVDT for meauring relative diplaement (elongation of hortening) along the peimen. A with the train gage, LVDT were plaed on three fae to allow the alulation of the relative diplaement at any point within the ro-etion auming plane etion remain plane. LVDT were attahed to the peimen through a et of braket bolted and tud welded to the teel. String-pot for meauring lateral diplaement and getting the diplaed profile in both horizontal axe. LED for meauring the poition hange of a et of point. Thee meaurement are aptured by the Krypton ytem (Metri K6 Dynami Meauring Mahine, DMM), whih meaured detailed three-dimenional poition of the target point plaed on the peimen.. Additional alulated hannel were obtained from the meaured data. Some of thee alulation inlude, but are not limited to: Moment at the bae, and at different point along the peimen Rotation and urvature at different ro-etion Evolution of the diplaed hape or deformation in ome egment. Stree at different poition through the ro-etion and the peimen length. IV. Loading Hitorie The Multi-Axial Sub-aemblage Teting (MAST) ytem, a hown in Figure 5, onit of a tiff teel rohead onneted to 4 vertial atuator (eah with a apaity of 33 kip and ± in. troke) and atuator in eah horizontal axi (eah with a apaity of 44 kip and ±16 in. troke). The MAST ytem ha the apability of ontrolling the 6 DOF independently with a maximum apaity of P z = 13 kip of vertial fore and V x =V y =88 kip of horizontal fore. The MAST faility ha permitted the ue of very omplex load hitorie, whih were needed for the alibration of the analyi model and to validate omplex behavior of ompoite beamolumn. Eah tet onited of everal load ae, with eah ae having one or more yle. A typial et of load yle i hown in Table. Load ae wa ued to get rid of fore and moment indued during the peimen-rohead onnetion and adjut the initial poition of the peimen to aount for initial imperfetion, a key fator in the tability tudy. Load ae 1 onited of a bukling tet with the olumn ubjeted to axial load and idealized a pinned-free, a hown in Figure 6. Load ae onited of applying an axial load, followed by a erie of Page 7

8 uniaxial lateral diplaement. Load ae 3 i imilar to load ae, but the diplaement are biaxial. Loal ae 4 orrepond to torional loading. Figure 7 how typial reult for load ae 1, with fore meaured from the load ell in the teting mahine. For omparion, the ro-etional trength and a implified P-M interation diagram inluding length effet are alo hown. A an example of the omplexity of the poible load hitorie, Figure 8 how a ombination of Load Cae and 3, in whih the deformation in the X and Y diretion were impoed while maintaining the moment at the top at zero. The graph how the moment at the bottom a given by equilibrium alulation from external load. Load ae i a uniaxial bending ae, while ae 3 i a biaxial ae. In load ae 3, the reulting moment at the bottom are affeted by the initial imperfetion, reulting in the piral pattern hown. Figure 5 Overall view of MAST faility. Page 8

9 Figure 6 Load hitorie. Page 9

10 Table Typial Load Hitory Load Cae 1a Degree of Freedom Step Ation Δ x /F x Δ y /F y Δ z /F z R x /M x R y /M y R z /M z F 1 Set zero F x = F y = z = M x = M y = M z = Δ z = R x = R y = R z = Adjutment Δ F Δ y = x = y F ontrolled z = M x = M y = R z = Conentri Δ 1 F Loading x = Δ y = z M ontrolled x = M y = R z = a 1 b 1 3a 1 3b a 4b 1 1 Conentri Unloading Uniaxial Loading Uniaxial Loading Biaxial Loading Biaxial Loading Biaxial Loading Pure Torion Torion & axial load Conentri Loading Biaxial Loading F x = Δ y = Δ x ontrolled Δ x Δ z ontrolled M x = M y = R z = Δ y = F z =.5 P C M x = M y = R z = ontrolled Δ y = F z = 1. P C M x = M y = R z = Δ x & Δ y ontrolled y F z =.5 P C M x = M y = R z = F z =.75 P C M x = M y = R z = x F z = 1.5 P C M x = M y = R z = Δ x = Δ y = F z = M x = M y = Δ x = Δ y = F z =. P o M x = M y = Δ x = Δ y = Δ x & Δ y ontrolled y x Δ z ontrolled Δ z ontrolled Δ z ontrolled M x = M y = R z = F z = 1.5 P C M x = M y = R z = Page 1

11 15 1 P (kip) Cro-etion Beam-olumn Experimental P (kip) Cro-etion Beam-olumn Experimental M (kip-ft) M (kip-ft) (a) Speimen 4-Rw-18-5 (b) Speimen 8- Rw-18-1 Figure 7 Typial reult of bukling tet with moment baed on rohead fore Figure 8 Load ae (uniaxial bending at three axial load level how by irle) and 3 (biaxial bending at three load level) Page 11

12 V. Experimental Reult Wet Conrete Sine thi reearh intended to tet very long CFT peimen, initial deformation on the teel tube indued by the onrete during ating were onidered in advane of the ontrution proe and the data analyi. The tree and deformation in the teel tube under hydrotati preure were evaluated with loed-form analytial olution and omplemented with finite element analyi. Thee analytial reult indiated that problem would arie in the RCFT peimen, unle tree and deformation were limited to reaonable value. For thi reaon, tiffener were ued during ating of mot of the RCFT peimen to ontrol the initial deformation due to the hydrotati preure of wet onrete. During the teting of the RCFT, advere effet were lear in thoe peimen that were not tiffened, a the teting tarted with oniderable initial outward deformation on the plate. Thee deformation led to an earlier initiation of the teel loal bukling at the elevation where the maximum outward defletion initially ourred a a onequene of the wet onrete preure. In ontrat, there were very low initial deformation on the plate of thoe peimen that were tiffened properly, and in thee ae the loal bukling developed a expeted at the ritial etion (near the bae) and only a a onequene of interation of high train and the lender wall. Reommendation to minimize the effet of the wet onrete preure inlude implified equation to etimate the maximum tranvere tre and the maximum outward expanion that may our in a RCFT member at the ating proe. The limit are: σ max h p h b h t F = max 1 3b 4h p h Ω + 3 b + 4h t + 4 y (1) δ 1 5b + 4h p h L = max 3 b + h E t () where, h and b are, repetively, the longer and the horter inner width of the retangular ro-etion ( h = h - t ; b = b - t ), t i the thikne, b and h are the overall outide dimenion, L i the preure length, and p i the hydrotati preure. If either the orreponding tree or deformation in retangular CFT ro etion exeed the limit above, it i reommended that external upport be added during ating. Member trength may then be aeed uing urrent proedure. Page 1

13 Bukling Tet Reult for Load Cae 1 are hown, in their unorreted form, in Figure 9. In Table 3, the P n value are omputed following the 1 AISC Speifiation, but uing atual material value and imperfetion, K=, and no reitane fator. It hould be noted that everal tet (open ymbol), did not ahieve the expeted bukling load due to lak of axial load apaity. For a orret aement of the data, thee reult needed to be orreted for the following reaon: In everal ae, a the true bukling load wa approahed, the horizontal fore at the top of the olumn, whih theoretially hould be zero, began to inreae and thu K<. The tet ontroller did not take into aount the ompliane of the loading ytem. The levi pin in the atuator ontributed ome fritional fore. The initial imperfetion were different from thoe aumed in the AISC deign equation. The orreted data i hown in both Figure 1 and Table 3. Overall, the reult how very good orrelation to the expeted value, indiating that the urrent AISC deign proedure are aurate for lender etion and that the effet of onfinement dereae a the lenderne inreae. Table 3 Load Cae 1 reult Speimen f F y L Δ o /L δ o /L Κ λ P n P exp (ki) (ki) (ft, in) (%) (%) - - (kip) (kip) 1C /..711 * C / * C / C / C C / C / C / C / C Rw Rw / Rw / Rw / R R / R / R / (*) The value tated in thi table orrepond to the out-of-traightne at the beginning of the load ae. The initial out-of-traightne (δ o /L) before teting were.45% and.74% for the peimen 1 and 18, repetively. Page 13

14 P P o AISC (1) Euler urve CCFT C5 C1 C RCFT Rw R Bukling not met Figure 9 Unorreted data for bukling load. P P o AISC (1) Euler urve CCFT C5 C1 C 1 1 RCFT Rw R Figure 1 Correted data for bukling load. Page 14

15 Interation diagram To develop interation (P-M) urfae, loading ae LC and LC3 were ued. Thee load ae onited of a ontant ompreion fore in load ontrol, while the top i driven laterally in diplaement ontrol (Figure 11(a)). The methodology ued for the extration of experimental P- M value of interation ha been previouly ued for the alibration of the interation equation for teel member in the AISC Speifiation and Euroode, uing data obtained from eondorder inelati analyi of benhmark teel frame. The maximum table apaity of a beam olumn i defined by it maximum lateral trength (F max ) at whih the inipient intability ondition arie (Figure 11(b)). The total eond order moment onit of the firt order moment (FL) and the eond order moment (P-Δ), a hown in Figure 11(). Beyond F max, the beam-olumn i in an untable ondition even when the ritial ro-etion till ha ome remaining apaity. A et of axial load (P) and bae moment (M) point related to the intant when the peimen reahed the maximum table apaity (F max ) are extrated and ompiled a the total beam-olumn apaity. The total apaity a defined above doe not inorporate the effet of the initial imperfetion. Initial imperfetion tend to inreae the demand from eond-order effet, and a a reult, the available firt-order moment apaity i redued. The initial imperfetion an be inluded a the differene between the total apaity and that apaity onumed by the imperfetion. The reultant P-M point from the previou proe are ompiled a the net beam-olumn apaity. The experimental reult inluded in Figure 1(d) inlude: (a) the pure ompreion loading (LC1) up to a given level of gravity fore (yan line and quare); (b) the path from the uniaxial bending loading (LC) up to a total eond order moment at inipient bukling (M total, blank quare); and () the net eond-order moment (M net, blak quare). Figure 11 Extration of P-M interation value from experimental data Page 15

16 The net moment extrated from the tet peimen are then ompared with the implified interation diagram propoed in the AISC (1) Speifiation for ompoite beam-olumn. The following obervation were noted from thee omparion (Figure 1): In the horter peimen, the net P-M apaitie extrated from the tet drop outide of the bilinear implified diagram of the AISC for beam-olumn, whih underetimate the P-M apaitie of the horter peimen around the point C λ -B. The purpoe of negleting the bulge with thi vertial line in the AISC Simplified diagram intended to be onervative through a lower bound, and thi implifiation wa upported by the available experimental data at the time. The hape of the bilinear implified diagram turned out to be le onervative in beamolumn with intermediate lenderne; however, for beam-olumn with high lenderne, the AISC implified diagram wa unonervative with overetimated net apaitie. It mut be noted that the net moment apaitie obtained from the experiment ha a ubtantial amount of flexural trength lot due to the large imperfetion. Neverthele, many of thee point are till unonervative even if the imperfetion are negleted. Thi unonervative behavior in lender beam-olumn ugget a hange in the deign equation for the alulation of P-M interation diagram that erve both hort and lender beam olumn. Similar onluion were oberved in both uniaxial and biaxial bending, a well a in the omputational analye. New propoed equation to eliminate thi problem are given in a later etion. Flexural Rigidity for CFT Member Little well-doumented data i available on the effetive moment of inertia for ompoite member. In the urrent AISC Speifiation, the effetive tiffne i given a: A C3 =.1+ <.3 for SRC A + A EIeff = EI + C3EI A C3 =.6 + <.9 for CFT A + A (3) The evaluation of the flexural rigiditie extrated from the tet reult during the entire load protool exhibited ome variability, mainly a the damage in the onrete ore and the teel tube progreed through the load protool. Figure 1 how the two main method ued to extrat EI value: (a) from the moment-urvature data omputed from train gage, and (b) from loaddefletion data. In both ae the value are taken at the beginning of the unloading proe. Although diperion wa large, intereting reult were extrated from the analyi of thi data. A brief ummary of the obervation inlude: The averaged value of the flexural rigiditie extrated from the repone during the pure ompreion loading ae (LC1) were very loe to the value predited by the AISC (5, 1) Speifiation. However, for the lender etion in thi work, the averaged value do not how proportionality with the teel ratio in the ro etion (i.e., ρ = A /A), a indiated by the C 3 oeffiient in the equation. Page 16

17 P/P n AISC C1 C Rw R M/M B (a) Normalized P-M interation diagram 1. P/P n.8.6 AISC.4 C1 C. Rw. R M/M B () Shorter peimen (λ<1.7) 1. P/P n.8 P A /P n P Cλ /P M net /M AISC C1 C Rw R λ (b) Slenderne v. the normalized net moment P/P n AISC.4 C1. C. Rw λ (d) Slender peimen (λ>1.7) 1. P/P n.8 M AISC =M B P<P C <M AISC <M B P>P C.6 AISC.6 AISC.4 C1.4 C1 C C. Rw. Rw. R. R M/M B λ (e) M net /M AISC 1. (f) M net /M AISC >1. Figure 1 Experimental net moment normalized to the AISC trength Page 17

18 In addition, the lenderne parameter of the olumn (λ) doe not how proportional variation with the tet data. Intead, a ontant averaged oeffiient of C 3 =.8 wa obtained for the determination of the bukling trength of a CFT olumn: EI = E I +.8E I (4) eff Figure 13 Extration of average tiffne value. Similarly, averaged value of the flexural rigiditie were alo extrated from the repone during the uniaxial and biaxial loading ae (LC and LC3). Thi i a unique et of data ine thi intend to give a implified equation that approahe the expeted rigidity for a beam-olumn under eimi loading (i.e., ombined ontant axial load and yli uniaxial or biaxial lateral load). A expeted, the atter of the data inreaed a the damage progreed on the peimen; even with ome diperion i exhibited in the averaged tet data, the following equation are propoed for the determination of the effetive tiffne of a CFT beam-olumn under eimi loading, and for the evaluation of lateral and flexural apaity baed on frame analyi. When loal bukling i not expeted (a in ompat ro etion):: EI = E I +.4E I (5) eff On the other hand, when the teel tube i ueptible to loal bukling: ( ) EI =.85 E I +.4E I (6) eff Page 18

19 Steel Loal Bukling in CFT Member Extration of the firt ourrene of loal bukling in the 18 peimen teted for thi projet wa baed on multiple meaurement from the intrumentation (Figure 13). Baed on the data extrated from thee tet, an update of the urrent AISC empirial equation for the longitudinal train in the teel tube at the initiation of loal bukling i propoed for both CCFT and RCFT. The propoed equation are: For irular onrete filled tube (CCFT): y y.9 lb.9 D F F ε = t E = (7) E λ ε y For retangular onrete filled tube (RCFT): F y Fy 9 εlb = 9 h = (8) t E E λ From the empirial equation hown above, an update of limit for lender (λ r ) and nonompat (λ p ) filled tube are propoed a follow: For irular onrete filled tube (CCFT) with lender teel etion E λ.3 r = (9) F y For irular onrete filled tube (CCFT) with non ompat teel etion E λ.15 p = (1) F y For retangular onrete filled tube (RCFT) with lender teel etion E λ r = 3. (11) F y For retangular onrete filled tube (RCFT) with non ompat teel etion E λ p =.1 (1) F y Plati Hinge Length in CFT Member An analyi of the plati hinge length wa made, baed on the maximum urvature within the olumn length, throughout the load protool. Baed on thi data analyi, the equation below propoed for teel etion preent a reaonable predition of the plati hinge length. L p M y S 1 = L 1 = L 1 = L 1 M p Z k (13) Page 19

20 (a) CCFT (b) RCFT Figure 13 Comparion between loal bukling from thi tudy and data ued to alibrate urrent AISC Equation Torional Strength and Stiffne of CFT Member The experimental torional repone obtained from the tet of the CFT peimen point out the following behavior: The reult indiate a partial ontribution of the onrete to both the torional trength and the torional rigidity. Both the trength and the tiffne ontribution were alibrated with the tet data and deign equation developed for torion. The trength repone under torion and ombined axial load wa lightly higher than the trength obtained in pure torion only in CCFT; due to high damage aumulation, the torion trength with and without ompreion wa very imilar to the pure torion trength. The torional tiffne i lightly higher in CCFT due to better performane of irular ro etion hape; and earlier loal bukling damage in RCFT, whih i le evere in CCFT. Auming full ontribution of the teel omponent and partial ontribution of the onrete omponent, deign equation are propoed to etimate both the torional trength trength and the torional rigidity for non-yli and yli loading. Thee deign equation predit reaonable value of the torion trength and torion rigidity. The equation are a follow: 1 Tn = T + T 4 (14) 1 GJ + GJ for CCFT GJeff = 1 GJ + GJ for RCFT 6 (15) Page

21 VI. Analytial Studie Evolution of Interation Strength The hange in ize, hape, and loation of the beam-olumn interation urfae with the progreion of yli loading wa invetigated. One peimen, 9R-18-1, wa ubjeted to a unique loading hitory in it latter load ae that onited of a erie of probe and ubprobe. After the ompletion of the firt three load ae, the peimen wa moved to zero diplaement and a ompreive axial load of 3,56 kn (8 kip), whih wa held ontant for the remainder of the tet, wa applied. A probe wa ompleted by inreaing the lateral diplaement with a fixed ratio of X to Y diplaement until a deired diplaement pat the limit urfae wa reahed (tability wa maintained beaue the lateral degree-of-freedom were in diplaement ontrol). From thi poition a erie of ubprobe were ompleted by inreaing the diplaement in a different fixed ratio of X to Y diplaement until the ritial flexural trength wa reahed, at whih point the lateral diplaement were revered to the termination point of the original probe. The proe wa then repeated for everal additional X/Y diplaement ombination. Thi an about the termination point of the probe determine the urrent limit urfae of the beam-olumn. The proe wa repeated ix time, obtaining information about the interation urfae at ix different point during the loading. The reulting interation diagram are hown in Figure 13, where eah diagram repreent a lie of the threedimenional (P-M x,bae -M y,bae ) interation urfae at ontant the applied axial load. Thi behavior ould ignifiantly impat the auray of ommon nonlinear frame analyi approahe uh a tre-reultant platiity model that do not aount for hange in the limit urfae. 4 3 X Moment (kn-m) Load Cae 4 Load Cae 5 Load Cae 6 Load Cae 7 Load Cae 8 Load Cae Y Moment (kn-m) Figure 14 Experimental Interation Surfae, Speimen 9-R-18-1 Page 1

22 VII. Analytial Studie The primary fou of the analytial reearh ha been the development of aurate nonlinear model for the analyi of ompoite truture. The new formulation will enable future reearher to ondut tudie inluding large-ale parametri invetigation of ompoite frame ytem ubjeted to eimi and non-eimi loading, a well a, doumentation of behavioral repone uitable for performane-baed deign proviion. Additional omplementary apet of the analytial work have inluded experimental databae development, arhetype frame deign, and aement of bond trength. Databae Development A detailed databae of experimental reult of retangular CFT, irular CFT, and SRC uitable for the alibration and validation of nonlinear finite element formulation ha been reated. Tet with a broad range of material and geometri harateriti have been ought o that the unique harateriti of ompoite beam-olumn an be integrated into the formulation. Thee model aount for key harateriti uh a, in the teel, gradual redution of modulu, gradual redution of the elati zone, ratheting, overhooting, and oftening due to loal bukling; and in the onrete, nonlinear repone up until the peak tre, variation in the peak tre with onfinement, pot-peak oftening, pot-peak dutility due to onfinement, tenion tiffening, and rak opening and loure via yling into tenion and bak into ompreion. A new verion of a ynopi of experimental and omputational tudie of CFT olumn, beamolumn, onnetion, and frame ha been publihed (Gourley et al. 8). Thi i the fourth edition of a detailed ynopi that wa firt publihed in The ynopi inlude ummarie of all well-doumented reearh on CFT in the literature, and inlude extenive table that highlight the key parameter tudied in the experimental reearh. Thi work alo ontributed diretly to the databae development that etablihed the CFT tet matrix in thi work. Advaned Nonlinear Model A omprehenive finite element formulation for the analyi of teel and onrete ompoite frame truture ha been developed. The model i apable of aurately modeling frame ytem oniting of any ombination of CFT, SRC, or wide flange teel olumn, wide flange teel beam, and HSS teel brae. The model are implemented in the OpenSee framework. Two- and three-dimenional mixed ditributed platiity fiber beam element provide the bae for the model. The element tiffne and internal fore wa derived in the orotational frame, allowing rigid body mode of deformation to be aounted for olely in a geometri tranformation. Cubi-Hermitian and linear interpolation funtion were ued for the tranvere and axial deformation field, while linear and ontant interpolation funtion were ued for the bending moment and axial load field. The Green-Lagrange train meaure wa adopted to define the axial train, while urvature wa aumed to be the eond derivative of the tranvere deformation field. The axial train at eah of the fiber in the etion i determined utilizing a Page

23 kinemati aumption (i.e., initially plane etion remain plane), negleting any lip ourring between the teel and onrete. In the mixed formulation, element ompatibility and etion equilibrium are atified with two equation beyond element equilibrium. The imultaneou olution of all three governing equation add to the omplexity of the tate determination algorithm. The unbalane from the additional equation i onverted to an unbalaned fore at the global level and eliminated through the global olution iteration. Different fiber ro etion diretization aigned to the element allow for the modeling of the variou teel and ompoite member. The fiber etion are an aumulation of many intane of the teel and onrete material model in a onfiguration reembling the ro etion of the member to be analyzed. The propertie aigned to the material model are baed given material propertie (e.g., F y, F u, or f ), the type of etion being analyzed, and the loation of the material within the etion. Example fiber etion are hown in Figure 15, where eah irle repreent a fiber and the different olor repreent material model with different propertie (a) CCFT Setion (b) RCFT Setion () Wide Flange Steel Setion (d) SRC Setion Figure 15 Example Fiber Setion New yli uniaxial material model have been implemented in the OpenSee framework. Thee model are baed on well-etablihed exiting teel and onrete model with modifiation to Page

24 allow for modeling of behavior peifi to ompoite member. The ame bai teel model and onrete model are ued for all of the different etion, however, different parameter and different option built into the model, the variety of behavior oberved in teel and ompoite member i apable of being modeled. The teel model i baed on the bounding-urfae platiity model of Shen et al. (1995). In thi model, the inremental relation between tre and train i etablihed baed on a et of hardening and flow rule. The yli harateriti of teel, uh a train hardening, elati unloading, dereaing elati zone and gradual tiffne redution a a reult of yli loading, Bauhinger effet, bounding tiffne, ratheting, are repreented by introduing internal variable and inorporating them with the ontitutive relation. Additional harateriti were deired and thu, the following modifiation were made: To model the built-in reidual tre from old-forming of teel tube, an option wa implemented to eliminate the yield plateau and inlude an initial plati train. Thi initial plati train an be obtained through omparion with tenile oupon tet of oldformed teel tube. Initial plati train value of.6 for CCFT member and.6 and.4 for the orner and flat region, repetively, of RCFT member are found to produe aurate reult. To model the built-in reidual tre from hot-rolling of teel wide flange hape, an option wa implemented to define an initial tre. The value initial tre varie throughout the ro etion o it i neeary to define multiple material with different value of initial tre (e.g. Figure 15). To model loal bukling in the teel tube or the flange or web of a wide flange teel hape everal optional modifiation were made to the ompreion region of the teel model. When ative, loal bukling i aumed to initiate when a ertain ritial train, ε lb, ha been reahed. For train higher than the loal bukling train, the repone i aumed to be a linear deending branh, with lope K, followed by a ontant reidual tre branh, with tre F re. The ontitutive relation for the onrete ore are adapted from the rule-baed model of Chang and Mander (1994). The tre-train behavior i modeled with a family of loe form equation in term of train and a et of rule whih identifie the proper equation to be ued for any arbitrary train inrement. Multiaxial tre ondition are aounted for impliitly by eleting the peak tre and train at peak tre that reflet the level of onfinement. It allow for omprehenive modeling of yli oftening, yling into tenion and then bak into ompreion, and other omplex onrete phenomena. The level of onfinement experiened by the onrete ha a ignifiant impat on the behavior of CFT member. For irular member the onfinement erve to inreae both the trength and dutility of the onrete ore, wherea, for retangular member only the dutility i affeted. The ompreive bakbone tre-train urve for the onrete i baed on the model of Tai, whih i defined by the initial lope E, peak oordinate (ε, f ), and r fator. The initial lope and train at peak tre for unonfined onrete, ε, are defined uing expreion from the literature. The peak tre and train at peak tre are taken a the unonfined value for RCFT member, wherea for CCFT member they are omputed uing a onfinement model and an Page 4

25 etimation of the onfinement preure. The r fator, whih ontrol the nonlinear deending branh, wa alibrated to the pot-peak behavior of hort onentrially loaded CFT olumn, and alo differ between CCFT and RCFT. Thee parameter were alibrated to a et of welldoumented experiment on onentrially load hort olumn. Thee tet were eleted to have ombination of high and low value of teel yield tre, F y, onrete ompreive trength, f, and ratio of teel tube diameter or depth the thikne, D/t ratio. The wide flange teel etion utilize only the teel uniaxial material model. The ame material propertie are ued throughout the etion, but the initial tre and loal bukling behavior vary. Initial tre i defined baed on the Lehigh reidual tre pattern (Galambo and Ketter 1959). Loal buking of the flange ha been alibrated to experimental tet. The SRC model inorporate the wide flange model a deribed above; with the exeption that loal bukling i inhibited by the onrete etion that urround it. The onrete i eparated into three region baed on onfinement (Figure 15d). The over onrete, whih lie outide the lateral reinforing, i aumed to have zero onfinement and i apable of palling. The onrete within the lateral reinforing i labeled moderately onfined. An enhanement in trength and dutility i omputed baed on the onfinement preure provided by the lateral reinforement. Additional enhanement in trength and dutility i omputed for the highly onfined onrete within the flange of the teel hape. Extenive verifiation tudie have been performed to verify the auray of the model (Denavit et al. 1). The formulation wa verified againt a wide range of monotoni and yli experiment, inluding hort olumn, beam, and proportionally and non-proportionally loaded beam olumn. Several elati and dynami problem were alo analyzed to validate the geometrially nonlinear and dynami formulation. The tudie howed that aurate reult an be obtained for ompoite member and frame ubjeted to a variety of loading ondition. Figure 16a how verifiation reult for yli pure bending of irular onrete-filled teel tube and Figure 16b how verifiation reult for yli non-proportional loading of teel reinfored onrete antilever olumn. Thee reult how the ability of the model to apture the initial tiffne, peak trength, and unloading tiffne, the CFT alo how the ability of the model to apture loal bukling of the teel tube. Page 5

26 8 Tet #3; Elhalakani & Zhao 8; Speimen: F4I1 8 Tet #7; Elhalakani & Zhao 8; Speimen: F14I Moment (kn-m) - Moment (kn-m) Stre (MPa) -6 Experiment Analyi End Rotation (rad) Repone of Extreme Steel Fiber Repone of Extreme Conrete Fiber 4 - Analyi Strain (mm/mm) Stre (MPa) -1 - Analyi Strain (mm/mm) x 1-3 D = 11 mm; t = 1.5 mm; D/t = 88. f = 3.1 MPa; F y = 43 Mpa; L = 8 mm (a) Cyli Pure Bending of Cirular Conrete-Filled Steel Tube Speimen 6; Rile and Paboojian 1993 Speimen 8; Rile and Paboojian 1993 Horizontal Fore (kn) Experiment Analyi Tip Defletion (mm) Horizontal Fore (kn) (b) Cyli Non-Proportional Loading of Steel Reinfored Conrete Cantilever Column Figure 16 Cyli Verifiation Reult Stre (MPa) -6 Experiment Analyi End Rotation (rad) Repone of Extreme Steel Fiber Repone of Extreme Conrete Fiber 5 Analyi Strain (mm/mm) Stre (MPa) Analyi Strain (mm/mm) D = 89.3 mm; t =.5 mm; D/t = 35.4 f = 3.1 MPa; F y = 378 Mpa; L = 8 mm P -3-4 Experiment Analyi Tip Defletion (mm) Speimen H (mm) B (mm) f' (MPa) Steel Setion Fy (MPa) db (mm) Fyr (MPa) L (mm) P (kn) W8x ,93 1, W8x ,93 1,49 Page 6

27 Thi formulation ha been ueful in apturing the behavior exhibited by the peimen teted the MAST faility even in the more omplex three-dimenional load ae. Figure 17 how a omparion of reult for peimen 11 in load ae 3a. Figure 17 Verifiation Reult for Speimen 11C-6-5 Load Cae 3a In addition to validation of the model, omparion have been made to diplaement-baed and fore-baed beam element uing uniaxial material model baed on ontitutive relation from the literature. The reult of thee omparion have hown that epeially for the latter load ae, the urrent model i better apable of prediting thi behavior than the exiting model. Arhetype Frame Deign A omplete et of twenty arhetype truture have been deigned uing RCFT and CCFT beamolumn and teel girder and brae, ranging in height from three to eighteen torie, inluding both braed and unbraed frame. Parameter of the frame are hown in Table 4. Thee frame were eleted and deigned in aordane with FEMA P695 and are intended to be ued for large ale parametri-tudie to ae the ytem behavior fator (e.g., R, Cd, Ωo) for ompoite braed and unbraed frame and to aid in enhaning the non-eimi and eimi deign proviion for thee ytem. Page 7

28 Table 4 Arhetype Frame Lateral Fore Column Bay Width Seimi Deign Frame Reiting Sytem Type Storie Gravity Loading (ft) Category A1 C-SMF RCFT 3 Interior/Warehoue D max A C-SMF RCFT 3 Interior/Warehoue D max A3 C-SMF RCFT 3 Perimeter/Offie D max A4 C-SMF RCFT 3 Interior/Warehoue D min A5 C-SMF RCFT 3 Perimeter/Offie D min A6 C-SMF RCFT 3 Perimeter/Offie 3 D max A7 C-SMF RCFT 3 Interior/Warehoue 3 D max A8 C-SMF RCFT 9 Interior/Warehoue D max A9 C-SMF RCFT 9 Perimeter/Offie D max A1 C-SMF RCFT 18 Interior/Warehoue D max A11 C-SMF RCFT 18 Perimeter/Offie D max B1 C-SCBF CCFT 3 Interior/Warehoue D max B C-SCBF CCFT 3 Interior/Warehoue D max B3 C-SCBF CCFT 3 Perimeter/Offie D max B4 C-SCBF CCFT 3 Interior/Warehoue D min B5 C-SCBF CCFT 3 Perimeter/Offie D min B6 C-SCBF CCFT 3 Perimeter/Offie 3 D max B7 C-SCBF CCFT 3 Interior/Warehoue 3 D max B8 C-SCBF CCFT 9 Interior/Warehoue D max B9 C-SCBF CCFT 9 Perimeter/Offie D max CFT member deigned with lower D/t ratio, CFT member deigned with higher D/t ratio Bond Strength for CFT Column Work ha been ompleted to improve the aement of the bond trength of CFT. A new approah for aeing the nominal bond trength for both retangular and irular onretefilled teel tube (CFT) ha been propoed. Baed on omparion to puh-out tet of onretefilled teel tube, an equation wa developed to ompute the nominal bond tre a a funtion of tube dimenion. Thi equation i onervative, in that it neglet experiment in whih the load i introdued via hear tab, whih exhibit mall rotation and bear againt the onrete, thu inreaing the bond tre; future reearh will invetigate inorporation of thee tet. The longitudinal bond tranfer length wa derived by examining the ditribution of bond tre along the height of the olumn a well a experimental data from CFT onnetion tet. The irumferential bond tranfer width wa identified for CFT a the entire perimeter of the interfae, aounting for the bond ontribution from the interfae on the ide that do not have girder or brae framing in. Page 8

29 The urrent deign proviion (AISC 5, 1) are thu found to be onervative for mot of the ae examined (exept for very large diameter tube). A new formula for nominal bond trength of CFT truture i propoed a: where R = pdc F (16) n in in p = entire perimeter of the teel-onrete interfae D = diameter or width of the teel tube C in = if the CFT extend to one ide of the point of fore tranfer = 4 if the CFT extend to both ide of the point of fore tranfer F in = bond tre = 11 (t/d ) for RCFT (unit: lb, inhe) = 36 (t/d ) for CCFT (unit: lb, inhe) For implementation in deign proviion, both minimum and maximum ap on the bond tre hould be onidered. One-dimenional analye, auming uniform behavior around the perimeter of the interfae, were performed to ae the nonlinear ditribution of bond and jutify the ue of a uniform bond tre in deign alulation. The teel tube and onrete ore are modeled with tru element and the interfae i modeled with zero length pring loated at the node. The uniaxial teel and onrete material model deribed above were ued for the teel tube and onrete ore. A bilinear, elati-perfetly plati model i ued to deribe the load-lip relationhip. The reult inluding etion fore ditribution, lip, and bond tre along the length of the olumn for one of thee analye i hown in Figure Height (in) 15 1 Steel Load Con Load Fore (kip) 1 Slip (in) x Bond Stre (pi) Figure 18 Reult of Bond Analyi at Deign Bond Strength Page 9

30 VIII. Future Work The experimental and analytial work ompleted a part of thi projet ha made poible a wide variety of poible future tudie that will further advane the knowledge of behavior of teel and onrete ompoite frame ytem. Thee tudie inlude: Development of diret analyi reommendation for tability deign of ompoite frame. Diret analyi reommendation an be developed and validated againt omputational reult from the tati analye of mall enitive benhmark frame. Development of equivalent tiffne reommendation for elati analye of ompoite frame. Equivalent tiffne value for ompoite olumn are ued in elati analye to determine the fundamental frequenie of vibration of a truture, a well a eimi fore and deformation demand. Suh reommendation hould aount for the effet of material nonlinearity, mot notable onrete raking, on the average frame behavior. Reommendation ould be developed through omparion between omputational reult from tati and dynami analye of the arhetype frame and elati frame analye utilizing equivalent tiffne value. Development of eimi performane fator for ompoite peial moment reiting frame and ompoite peial onentrially braed frame ytem. A methodology ha been developed reently for the development of eimi performane fator (FEMA 9). The methodology ha a trong dependene on the nonlinear tati and dynami analye. Stati puhover analye are ued to determine the ytem overtrength fator (Ω o ), while inremental dynami analye are ued to determine the repone modifiation fator and the defletion amplifiation fator (R and C d ). Invetigation of eimi tability for ompoite frame. Prior reearh ha indiated that the diret analyi method ha limited appliability for eimi deign. Stability iue relevant to the eimi performane of ompoite frame ould be tudied utilizing fully nonlinear frame analye a a point of omparion. Refinement of propoed bond trength equation to aount for additional experiment that inlude loading on hear-tab to indue lip in CFT. IX. Deign Reommendation A a reult of the experimental and analytial tudie reported herein, a number of propoal will be made to AISC TC5 for the 15 ode yle. Beyond the propoal for proviion for wet onrete fore, loal bukling and torional fore deribed above, new interation equation will be propoed. Thee take the form hown in Table 5 and 6 for the determination of the P-M interation diagram of CFT ro-etion. For impliity, the plati tre ditribution method wa adopted in the derivation of the ro-etion trength; however, If deired or poible, the ro-etion trength obtained in thi implified fahion an be replaed by the more exat apaity obtained with the train ompatibility method. Page 3

31 A propoed methodology for the determination of the P-M λ interation diagram of CFT beamolumn i illutrated in Figure 19, where the beam-olumn apaity i obtained a the roetion trength redued by the lot apaity due to tability and imperfetion effet. Table 5 Equation for the P-M interation diagram of RCFT ro-etion Geometri propertie: h = h t b = b t r t r = r t = t ( 4 π ).8584 ( 4 π ).575 A = bh r = bh t A = bh r A = bh b h t bh Z = 4 bh Z = Z 4 3 bh I = 1 3 bh I = I 1 Material propertie: F =.85 f ' Anhor point: P A F P = AF = y Po = P + P To = P P 1 P b = M = ZF + ZF P / M o = M( yo) yo = 4tF + b F M = M( y ) ; P( y ) = o o o b y y P-M ontinuou funtion: h h < y < h P( y) = y b F 4 ytf ( ) = Z y Z b y y Page 31

32 M = M( y ) ; P( y ) = P o o o P / Pi yi = 4tF + b F y M = M( y ) ; P( y ) = P n n n n y n P / Pn = 4tF + b F y ( ) = Z y Z ty 1 M ( y) = Z ( y) F + Z ( y) F y Table 6 Equation for the P-M interation diagram of CCFT ro-etion Geometri propertie: π D D = D t A = 4 A π D 4 A A = π D t t = or ( ) 3 D Z = 6 π D I = D Z = Z 6 4 π D I = I 64 Material propertie: 1.558Fyt F =.85 f =.85 f' + or D 7.94 f1 f l F =.85 f' f' f' D Fy fl = t D/ t D D D K = F K = Fy 8 Anhor point: P A F P = AF = y Po = P + P To = P P 1 P b = M = ZF + ZF D M o = M( y θ o o) yo = o b y ( ).K. 3.4 K K + K + KK θ o +.68K.68K P-M ontinuou funtion: D D < y < θ y = D 1 ( y) o ( ) = ( θ( ) π) + ( θ( ) in θ( )) P y y K y y K Page 3

33 θ K 1 o e + 1 or K M = M( y ) ; P( y ) = o o o M = M( y ) ; P( y ) = P o o o M = M( y ) ; P( y ) = P n n n n θo 5π K K 1/4 θ Z( y) = Zin θ Z( y) = Z in 1 M ( y) = Z ( y) F + Z ( y) F 3 y P o P ro-etion trength (P, M) P P n P n, M n P / beam-olumn trength (P, M λ ) M o M b M P ( n Pe) ( ) P P Mλ = M Mn P n P P e Figure 19 Determination of the P-M λ interation diagram of CFT beam-olumn aounting the redution by tability and imperfetion to the ro-etion trength. Page 33

34 Aknowledgement The work deribed in thi report i part of a NEESR projet upported by the National Siene Foundation under Grant No. CMMI-61947, the Amerian Intitute of Steel Contrution, the Network for Earthquake Engineering Simulation, the Georgia Intitute of Tehnology, and the Univerity of Illinoi at Urbana-Champaign. In-kind material and labor wa provided by Atla Tube In. and LeJeune Steel Co. Any opinion, finding, and onluion expreed in thi doument are thoe of the author and do not neearily reflet the view of the National Siene Foundation or other ponor. Referene Amerian Intitute of Steel Contrution (AISC) (5). ANSI/AISC36-5: Speifiation for Strutural Steel Building, AISC, Chiago, Illinoi. Amerian Intitute of Steel Contrution (AISC) (1). ANSI/AISC36-1: Speifiation for Strutural Steel Building, AISC, Chiago, Illinoi. Chang, G. A. and Mander, J. B. (1994). Seimi Energy Baed Fatigue Damage Analyi of Bridge Column: Part I - Evaluation of Seimi Capaity, Report No. NCEER-94-6, National Center for Earthquake Engineering Reearh, State Univerity of New York, Buffalo, NY. Denavit, M. D., Hajjar, J. F., Perea, T., and Leon, R. T. (1). Cyli evolution of damage and beam-olumn interation trength of onrete-filled teel tube beam-olumn, 9th US National and 1th Canadian Conferene on Earthquake Engineering, Toronto, Canada. Denavit, M. D. and Hajjar, J. F. (1). Nonlinear eimi analyi of irular onrete-filled teel tube member and frame, Report No. NSEL-3, Newmark Strutural Laboratory Report Serie (ISSN ), Department of Civil and Environmental Engineering, Univerity of Illinoi at Urbana-Champaign, Urbana, Illinoi. FEMA (9). Quantifiation of Building Seimi Performane Fator, FEMA P695, Federal Emergeny Management Ageny, Wahington, D.C. Galambo, T. V., and Ketter, R. L. (1959). Column under ombined bending and thrut, Journal of Engineering Mehani Diviion, ASCE, Vol 8, No., pp Goode, C. D. (7). ASCCS Databae of Conrete-Filled Steel Tube Column. ASCCS. Gourley, B. C., Tort, C., Denavit, M. D., Shiller, P. H., and Hajjar, J. F. (8). A Synopi of Studie of the Monotoni and Cyli Behavior of Conrete-Filled Steel Tube Beam-Column, Report No. NSEL-8, Newmark Strutural Laboratory Report Serie (ISSN ), Department of Civil and Environmental Engineering, Univerity of Illinoi at Urbana- Champaign, Urbana, Illinoi, April. Page 34