Experimental and Numerical Study on Bar-Reinforced Concrete Filled Steel Tubular Columns Under Axial Compression

Transcription

1 The Open Civil Engineering Journal, 211, 5, Open Acce Experimental and Numerical Study on Bar-Reinforced Concrete Filled Steel Tubular Column Under Axial Compreion Jinheng Han * and Shuping Cong School of Civil Engineering and Architecture, Shandong Univerity of Science and Technology, Qingdao 26651, China Abtract: The behavior of bar-reinforced concrete filled teel tubular column ubjected to axial load were tudied. One plain concrete filled teel tubular column and three bar-reinforced concrete filled teel tubular column were teted. The deformation of pecimen and the train of teel tube were meaured. Baed on experimental reearche, a imple numerical analyi method wa preented to imulate the full load-deformation proce of bar-reinforced concrete filled teel tubular hort column ubjected to axial compreion. Firtly, the interaction proce of teel tube and concrete wa analyzed, and then, the implified contitutive model of teel tube and concrete were etablihed on the bae of previou analyi reult. Secondly, the relation between lateral and longitudinal train of teel tube wa analyzed baed on experimental reult, and a imple method wa preented to calculate the lateral train of teel tube. Thi method wa ued a the upplement to the contitutive model. Finally, a program wa worked out to imulate the full load-deformation proce of bar-reinforced concrete filled teel tubular hort column. The program imulation reult of both ultimate bearing capacity and load-deformation curve are in good agreement with the experimental reult. Keyword: Bar-reinforced concrete filled teel tubular column, tet, Interaction, Contitutive model, Load-deformation proce, Numerical imulation. 1. INTROUCTION Bar-reinforced concrete filled teel tubular (CFST) column have a good advantage that they can atify the practical need of fire reitance depending on the firereitant ability of themelve, o the external fire-proof protection layer are not neceary. A a reult, a lot of invetigation have been carried out to reearch the fire reitance and ultimate bearing capacity of bar-reinforced CFST column [1-3]. However, reearche on the full proce of force-deformation of CFST column are relatively carce. Bar-reinforced CFST column i a typical confined concrete becaue the core concrete i confined by teel tube. Many of the previou reearch work on confined concrete have been mainly focued on the concrete confined by tranvere reinforcement [4-7] or FRP [8-1]. It i very eay to determine the confinement preure which i correponding to the yield trength of tranvere reinforcement or FRP. But it i very different for barreinforced CFST hort column which are confined by teel tube. Firtly, the confinement effect doen t exit at the early tage of loading jut a dicued a follow. Secondly, after the appearance of the interaction between concrete and teel tube, the lateral train of teel tube need to be previouly known to determine the tre of teel tube. The lateral train of teel tube i determined by the lateral dilatational train of core concrete, in turn, the dilatational *Addre correpondence to thi author at the School of Civil Engineering and Architecture, Shandong Univerity of Science and Technology, Qingdao 26651, China; Tel: ; Fax: ; hjheng28@163.com train of core concrete i influenced by the confinement preure from teel tube. So the core concrete and teel tube interact and affect each other, and it very difficult and complex to determine the lateral train of teel tube and calculate the tre tate of teel tube and core concrete. Baed on experimental reearche, the relation between lateral and longitudinal train of teel tube wa analyzed, and a imple method wa preented to calculate the lateral train of teel tube and imulate the full load-deformation proce of bar-reinforced CFST hort column ubjected to axial compreion. 2. EXPERIMENTAL STUY In order to tudy the behavior of CFST column ubjected to axial load, one plain concrete filled teel tubular column and three bar-reinforced concrete filled teel tubular column were teted. The diameter of longitudinal reinforcing bar i 2mm. The meaured yield trength of longitudinal reinforcing bar i 493MPa and that of hear reinforcement i about 23MPa. The parameter of the tet pecimen are lited in Table 1, and the detail of the pecimen are hown in Fig. (1). A erie of train roette were pated at the upper, middle and lower part of the teel tube a hown in Fig. (1) to meaure the longitudinal and lateral train of teel tube. At each part, there were four train roette called a A B C repectively. For convenience, the lateral train meaured by each train roette i labeled a 1 and the longitudinal train i labeled a 2. For example, A1 indicate the lateral train meaured by the train roette A / Bentham Open

2 11 The Open Civil Engineering Journal, 211, Volume 5 Han and Cong Table 1. Parameter of Tet Specimen Number Height H/mm Outer iameter /mm Thickne of t/mm Concrete f ck /MPa f k /MPa Longitudinal Reinforcement Thickne- of Quantity Concrete Cover c/mm Shear Reinforcement Ultimate Bearing Capacity N ue/kn A A @ A @ A @ H Strain roette A1 A2 A3 A A B C C 2 A2 B2 C2 2 A1 B1 C1 1 Specimen A2 Strain /% Fig. (1). etail of pecimen. B The relation curve for pecimen between axial load and axial average train meaured by diplacement gauge are hown in Fig. (2). Two typical tet reult of longitudinal and lateral train of teel tube correponding to axial load are hown in Fig. (3). Furthermore, the lateral-axial train curve for teel tube are hown in Fig. (5). Fig. (2). Axial load-axial average train curve for pecimen. A4 Specimen A1 Specimen A2 2 Specimen A3 Specimen A4 Axial average train /% LOA-EFORMATION PROCESS ANALYSIS The load-deformation proce of CFST column ubjected to axial compreion i an interacting proce among teel tube and core concrete, which can be implified a three tage a below. A B C 2 A2 B2 C2 2 (a) A1 B1 C1 1 Strain /% (b) Specimen A3 Fig. (3). Meaured train of teel tube for (a) Specimen A2 and (b) Specimen A3. The firt tage i that the teel tube and core concrete work independently. At the beginning, the tranveral train of teel tube i bigger than that of core concrete becaue the teel tube ha no effect on core concrete owing to the fact that the Poion ratio of teel tube i alo higher than that of core concrete. There i no confinement effect between concrete and teel tube at the initial loading tage. However, the Poion ratio of core concrete increae greatly due to the increae of the load. Therefore, the Poion ratio of concrete will be finally equal to that of teel tube at the tate I a, when the interaction between concrete and teel tube jut i occurring. At thi time, the axial deformation of the column i normally maller than the peak train c of unconfined concrete, and both the teel tube and the concrete till remain in elatic condition. After tate I a, the teel tube i in lateral and longitudinal plane tre tate, and the core concrete i in compreion treed condition in tripdirection.

3 Experimental and Numerical Study on Bar-Reinforced Concrete Filled The Open Civil Engineering Journal, 211, Volume The econd tage i before the peak train of core concrete confined by teel tube. At thi tage, the tre of teel tube pae from elatic tate to platic tate. In platic tate, the lateral tre of teel tube will teadily increae while the longitudinal tre decreae. At the ame time, the axial compreive trength and deformation capability of core concrete, correponding to the peak tre and peak train, increae gradually becaue of the ignificant confinement of teel tube. Since the lateral tre of teel tube i variable in the compre proce, the peak tre and peak train of core concrete i alo in the proce of dynamic growth. But the increae peed of the peak train of core concrete i maller than the axial compreive train of the column. Ultimately, the peak train of core concrete confined by teel tube i equal to the axial compreive train of the column, and the critical tate II a arrive. At thi tage, the longitudinal tre of teel tube increae before platic condition and decreae after platic condition, while the lateral tre of teel tube and the tre of core concrete increae continuouly. In a certain tate before core concrete reache it peak train, the um of the bearing capacity of core concrete and teel tube reache maximum, which i the ultimate trength of the column. The third tage i after the peak train of core concrete confined by the teel tube. After the econd tage, the tre of core concrete decreae with the train increae even though the confinement preure till increae. At thi tage, the longitudinal tre of teel tube and core concrete decreae continuouly. Therefore, the trength of the column i decreaing until the column i cruhed. 4. THEORY OF NUMERICAL ANALYSIS 4.1. Baic Aumption (1) At the initial loading tage, both core concrete and teel tube are compreed independently. There i no teelconcrete interaction. (2) After core concrete begin to be confined by teel tube, the teel tube i in plane tre tate and Mie yield rule can be ued to determine the tre-train relationhip. At the ame time, the core concrete i in triaxial compreive tre tate owing to the confinement of teel tube. The tre in the column ection i uniformly ditributed. (3) Becaue the confinement effect applied to core concrete by teel tube i uniform in any direction, the radial train and hoop train of core concrete are equal, and the lateral train of teel tube and the hoop train of core concrete are alo equal. (4) Superpoition method i ued to conider the effect of longitudinal reinforcement for the ultimate bearing capacity of the column. But the effect of the tirrup i ignored Simplified Stre-Strain Relationhip of Core Concrete and Core Concrete The tre-train relationhip of unconfined concrete and confined concrete are hown in Fig. (4) [11]. The expreion for the tre-train curve of confined concrete i defined a uggeted by Popovic (1973), which i later modified by Mander (1984) and i given by the following expreion 4: Fig. (4). General tre-train curve for unconfined and confined concrete. f f c = cc xr r 1+ x r (1) cc = c [1+ 5( f cc / f c 1)] (2) Where f c and c denote the longitudinal compreive tre and train, repectively; f cc and cc are the peak tre and peak train of confined concrete repectively; x = c / cc ; r = E c /(E c E ec ) ; E ec = f cc / cc ; E c = f c MPa; c and f c tand for the peak train and peak tre of unconfined concrete. Baed on the William-Warnke failure criterion, the peak tre of confined concrete with uniform lateral retraint can be derived a follow: f cc = f c ( f l / f c 2 f l / f c ) (3) Where f l denote the hoop tre (confinement preure) caued by teel tube, correponding to the peak train of confined concrete. The pot-peak region of equation (1) i not ued and diplaced by the expreion uggeted by Montoya (24) [5], which i given by f f c = cc (4) A( c / f cc ) 2 B( c / f cc )+ C +1. Where A =.25( f cc /( c8 cc )) 2 ; B = 2A / E ec ; C = A / E 2 ec ; c8 tand for the train in pot-peak region correponding with.8 f cc, which can be given by c8 = c (1.5 + ( f c ) f l / f c ) (5) The tre-train relationhip of teel tube in pre-yield tate can be given by z L f c f / cc f / c Eec c Mander Model cc Montoya Model = E 1 2 z 1 1 L Confined concrete Unconfined concrete c (6)

4 112 The Open Civil Engineering Journal, 211, Volume 5 Han and Cong The incremental tre-train relationhip of teel tube in pot yield tate can be given by d z d L = E t z t z t L d z (7) S t z t L t L d L where ubcript z and L tand for the longitudinal and lateral direction repectively; E and are the elatic modulu and Poion ratio of teel tube repectively; z and L are the longitudinal and lateral tre deviator of teel tube repectively; S = t z z + t L L ; tz = E 1 (2 2 z L ) ; 3 3 t L = E 1 (2 2 L z ) 3 3 It can be een from the implified tre-train relationhip that the tre of teel tube and the confinement preure of core concrete can be determined if the longitudinal and lateral deformation have been known. Then, the tre-train relationhip of core concrete can be alo determined. So the key quetion i how to determine the deformation proce of teel tube Analyi and Simplified Treatment for the eformation of A dicued above, the core concrete and teel tube interact and affect each other, and it very difficult to determine the lateral train of teel tube and calculate the tre tate of teel tube and core concrete. In order to implify the analytical proce, four bar-reinforced CFST hort column were experimented to tudy the tre-train relationhip of teel tube and core concrete. The experimental reult, a lot of lateral-axial train curve for teel tube, are hown in Fig. (5). If the longitudinal and lateral train of teel tube, correponding to the tage I a and tage II a, are z, L and cc, Lc repectively, the lateralaxial train curve can be claified into three ection repectively correponding to the three tage analyzed above. Thee three ection can be imply treated baed on the experimental reult. At tage I, there i no interaction between core concrete and teel tube. The teel tube i in elatic tate and it lateral train i given by L = z (8) And L = z At tage III, the tre-train relationhip of core concrete i in pot-peak region. The relation between lateral and longitudinal train of teel tube can be conidered a linear relation with a contant lope of k approximately. So the expreion can be given a L = k( z cc )+ Lc (9) At tage II, the train of teel tube increae quickly. Refer to the tet reult, the train of teel tube can be expreed a cubic equation a follow, L = a z 3 + b z 2 + c z + d (1) Where, a, b, c and d are four coefficient which can be determined by two eparation point, tangent lope at the tart point and at the end point of thi cubic curve. It i needed to notice that the coordinate value and the tangent lope of the tart and end point are variable correponding to the pecific contructional condition of the CFST column. Therefore, the relationhip curve are not contant but are needed to be determined in calculating proce Lateral train /%.2 L = z Longitudinal train /% (b) Fig. (5). Lateral-axial train curve of teel tube for (a) Specimen A2 and (b) Specimen A3. Moreover, three pecial value mut be determined primarily in order to etablih the tre-train relationhip of teel tube completely. (1) The longitudinal train z when the interaction between core concrete and teel tube i jut occurring. The train i correponding to the tage I a, when the ecant Poion ratio c of concrete i equal to the Poion ratio of teel tube. According to Ottoen model, the ecant Poion ratio of concrete i given by v c = v i ;.8 (11) c = v f (v f v i ) 1 (5 4) 2 ;.8 < 1. Where, = f c / L = z tet3 tet4 tet5 tet6 (a) pecimen A tet3 tet4.9 tet5 tet6.6 pecimen A3 L = z.3 L = z Longitudinal train /% Lateral train /% f cc ; f i the peak Poion ratio of concrete; i i the original Poion ratio of concrete, which i preented by Candappa (21) and i given by the following expreion [12]:

5 Experimental and Numerical Study on Bar-Reinforced Concrete Filled The Open Civil Engineering Journal, 211, Volume v i = ( f c ) f c (12) If c =, the ratio between the tre of confined concrete and unconfined concrete can be derived from equation (11). In turn, z can be determined by the uniaxial tre-train relationhip of unconfined concrete. (2) The peak train cc of confined concrete. The train cc, correponding to the tage II a, can be derived byf cc from equation (2). While the peak tre f cc of confined concrete can be determined by the hoop preure f l, which i given by 2t f l = 2t f (13) k Where and t are the outer diameter and thickne of teel tube repectively; f k i the uniaxial yield trength of teel tube; i the coefficient of hoop preure correponding to the peak train of concrete. The calculating equation for, in [13], wa given by = v e v (14) But, the hoop preure f l derived from equation (13) and equation (14) i only an initial approximate value and the accurate value mut be determined in the numerical iterative proce. (3) The lateral train Lc correponding to the peak train of confined concrete. The relation between the lateral train and peak train of confined concrete, given by Lokuge (24) [14], i Lc =.5 cc. But thi reult i baed on the tet of confined concrete with contant triaxial preure. In fact, the hoop preure of core concrete in CFST column i gradually increaing. Therefore, the lateral train correponding to the peak train of core concrete hould be a little larger. The following expreion i ued in thi paper to determine the lateral train Lc. Lc =.65 cc (15) 5. NUMERICAL SIMULATION FOR THE WHOLE LOA-EFORMATION PROCESS The concrete trength i taken a.85 f c in order to take into account the trength difference between concrete tet cube and tet pecimen [13]. And the trength of teel tube i taken a.85f k in order to take into account the effect of non-uniform tre ditribution and local buckling. Furthermore, other parameter ued in the numerical imulation are taken a E =2.1 5 MPa c =.2 =.28 f =.5 k=1.1. In the numerical calculation proce, the axial train of the column increae gradually from zero in order to determine the tre-train relationhip of core concrete and teel tube. Furthermore, the axial force of the column can be worked out and the whole load-deformation proce can be obtained. A key tep in the calculation procedure i to determine the hoop preure correponding to the peak train of confined core concrete to etablih the tre-train relationhip of core concrete and teel tube. Baed on the foregoing analyi reult, one program ha been developed to imulate the full load-deformation proce of bar-reinforced CFST hort column under axial compreion. The imulation reult of the longitudinal and lateral train of teel tube, and the comparion between the imulation reult and tet reult, are hown in Fig. (5). The deformation comparion of two bar-reinforced CFST column between calculating reult and experimental reult are hown in Fig. (6). Furthermore, ome calculating and experimental reult of the ultimate bearing capacity of CFST column, including the ratio of calculating data to teting data, are lited in Table 2. tet3 pecimen A2 tet4 2 Axial train /% (a) tet3 tet4 Specimen A3 Axial train /% (b) Fig. (6). Comparion of deformation between imulation and tet for (a) Specimen A2 and (b) Specimen A3. It can been clearly een from the comparion of calculating reult with experimental reult that the method preented to analyze the longitudinal and lateral train of teel tube i feaible and practicable. Moreover, the program alo ha a good accuracy to imulate the load-deformation proce and calculate the ultimate bearing capacity of CFST column.

6 114 The Open Civil Engineering Journal, 211, Volume 5 Han and Cong Table 2. Comparion of Ultimate CFST Column Between Experimental Reult and Simulation Reult Source Number Outer iameter of /mm Thickne of t/mm f k/mpa Concrete f ck /MPa Height of Specimen H/mm Tet Strength N ue/kn Prediction Strength N uc/kn Ratio of Strength N uc/ N ue SB SB SB SB [15] SB SB SB SB SB [16] CFST A Thi paper A A A SUMMARY In order to tudy the behavior of CFST column ubjected to axial load, one plain concrete filled teel tubular column and three bar-reinforced concrete filled teel tubular column were teted. The deformation of pecimen and the train of teel tube were meaured. A imple numerical analyi method ha been preented to imulate the full loaddeformation proce of bar-reinforced CFST hort column ubjected to axial compreion. The interaction proce of teel tube and core concrete i analyzed, and it i obviou that it very difficult and complex to determine the train and tre of teel tube and core concrete becaue they are independent and influence each other. For implicity, a imple method i preented baed on experimental reearche to calculate the train of teel tube, and further to calculate the tre of core concrete and teel tube. A program i worked out to analyze the full load-deformation proce of bar-reinforced CFST hort column baed on above reearching reult. The reult of the program for both ultimate bearing capacity and load-deformation curve how good agreement with different tet reult. ACKNOWLEGMENTS Thi work wa financially upported by the Promotive Reearch Fund for Excellent Young and Middle-aged Scientit of Shandong Province (BS21SF22). REFERENCES [1] G. Georgio, and L. enni, "Axial capacity of circular concretefilled tube column", J. Contr. Steel Re., vol. 6, pp , July 24. [2] Q. X. Wang,. Z. Zhao, and P. Guan, "Experimental tudy on the trength and ductility of teel tubular column filled with teel-reinforced concrete", Eng. Struct., vol. 26, pp , June 24. [3] P. K. Gupta, S. M. Sarda, and M. S. Kumar, "Experimental and computational tudy of concrete filled teel tubular column under axial load", J. Contr. Steel. Re., vol. 63, pp , February 27. [4] J. B. Mander, M. J. N. Prietley, and R. Park, "Theoretical tretain model for confined concrete", J. Struct. Eng., vol. 114, pp , [5] E. Montoya, F. J. Vecchio, and S. A. Sheikh, "Numerical evaluation of the behaviour of teel- and FRP-confined concrete column uing compreion filed modeling", Eng. Struct., vol. 26, pp , September 24. [6] C. aniel, and P. Patrick, "Stre-train model for confined high - trength concrete", J. Struct. Eng., vol. 121, pp , [7] G. Campione, and L. L. Mendola, "Behavior in compreion of lightweight fiber reinforced concrete confined with tranvere teel reinforcement", Cement Concr. Comp., vol. 26, pp , Augut 24. [8] L. Lam, and J. G. Teng, "Stre train model for FRP-confined concrete under cyclic axial compreion", Eng. Struct., vol. 31, pp , February 29. [9] E. Vintzileou, and E. Panagiotidou, "An empirical model for predicting the mechanical propertie of FRP-confined concrete", Contr. Build. Mater., vol. 22, pp , May 28. [1] T. Jiang, and J. G. Teng, "Analyi-oriented tre train model for FRP confined concrete", Eng. Struct., vol.29, pp , November 27. [11] G.. Hatzigeorgiou, "Numerical model for the behavior and capacity of circular CFT column, Part I: Theory", Eng. Struct., vol. 3, pp , June 28. [12]. P. Candappa, J. G. Sanjayan, S. Setunge, and J. Mater, "Complete triaxial tre-train curve of high-trength concrete", J. Mater. Civil Eng., vol. 13, pp , 21. [13] K. A. S. Suantha, G. Hanbin, and U. Tutomu, "Uniaxial tre-train relationhip of concrete confined by variou haped teel tube", Eng. Struct., vol. 23, pp , October 21.

7 Experimental and Numerical Study on Bar-Reinforced Concrete Filled The Open Civil Engineering Journal, 211, Volume [14] W. P. Lokuge, J. G. Sanjayan, and S. Setunge, "Contitutive model for confined high trength concrete ubjected to cyclic loading", J. Mater. Civil Eng., vol. 16, pp , 24. [15] C.. Goode, "Concrete filled teel tubular column-tate of the art", Indu. Con., vol. 26, pp , 1996 (in Chinee). [16] C. M. Zhang, L. C. Wang, and Y. Yin, "Studie on axial compreive experiment of everal kind of teel and high-trength concrete column", J. Harbin Int. Tech., vol. 36, pp , 24 (in Chinee). Received: September 9, 21 Revied: November 21, 21 Accepted: January 26, 211 Han and Cong; Licenee Bentham Open. Thi i an open acce article licened under the term of the Creative Common Attribution Non-Commercial Licene ( by-nc/3./) which permit unretricted, non-commercial ue, ditribution and reproduction in any medium, provided the work i properly cited.