Analyses of Steel Bridge Circular Columns using Fiber Model considering Local Buckling

Transcription

1 Civil Engineering Dimenion, Vol. 6, No., March 4, -7 ISSN print / ISSN X online CED 3, 6(), DOI:.9744/CED Analye of Steel Bridge Circular Column uing Fiber Model conidering Local Buckling Kinohita, K. Abtract: One of the mot concerned problem for analytical etimation of ultimate trength and ductility of teel bridge column i the conideration of local buckling. Stre-train curve with oftening behavior to include local buckling in fiber model analyi method were propoed by everal reearcher. However, accuracy of thoe model i till relatively low. A a conequence, mot teel bridge deign have been done uing fiber model analyi method without conideration of local buckling. In order to improve the analytical repone etimation of teel bridge column, a fiber model analyi method conidering local buckling i propoed in thi tudy. In thi method, multi-fiber element were ued to model the local buckling length to imulate local buckling deformation. The propoed method how good reult not only for etimating peak trength but alo pot-peak trength compared to previou experimental reult. However, further reearch hould be directed to improve the accuracy of the deformation mode. Keyword: Fiber model, local buckling, teel bridge circular column. Introduction Buckling Conideration of local buckling on analytical etimation of ultimate trength and ductility of teel bridge column i one of the important leon learned from evere bridge damage in pat earthquake (Figure ). Thi local buckling wa found in many different form including variation from different column ection. In general, fiber model analyi i ued for eimic evaluation of not only reinforced concrete column, but alo teel bridge column. The earliet tudy by Park et al. [] ued the fiber model analyi for a reinforced concrete member. Following thi tudy, the fiber model analyi wa ued and developed [,3]. A recent tudy on the eimic performance of a reinforced concrete bridge column teted on the E- Defene, which i a full-ize, three-dimenional hake table in Japan, wa reported by Kawahima et al. [4]. The tudy confirmed the accuracy of the fiber model analyi. For teel bridge column, analytical tudie uing the fiber model analyi were reported by Watanabe and Sakimoto [5], Tokunaga et al. [6]. Moreover, for teel bridge column with the conideration of local buckling, there are modeling technique that include local buckling effect in the tre-train curve of the platic hinge zone, where local buckling i occurred. Aitant Profeor, Dept. of Civil Engineering, Gifu Univerity, JAPAN. kinoita@gifu-u.ac.jp Note: Dicuion i expected before June, t 4, and will be publihed in the Civil Engineering Dimenion volume 6, number, September 4. Received 7 May 3; revied June 3; accepted 4 Augut 3. (a) Circular Column Buckling (b) Box Column Figure. Damaged Steel Bridge Column, Kobe Earthquake, 995 Although the modeling technique are not new and many uggetion have been made in previou tudie [7-8], in practice, a common aumption in the analyi of teel bridge column uing fiber model i to ignore the local buckling. The Japanee Standard Specification for Seimic Deign of Steel and Compoite Structure [9] permit thee

2 Kinohita, K. / Analye of Steel Bridge Circular Column / CED, Vol. 6, No., March 4, pp. 7 tructure to be evaluated uing the average train of the platic hinge zone a an alternative to evaluate peak trength without conideration of local buckling. However, Kakiuchi et al. [] concluded that thi approach cannot capture the actual behavior and would reult to overly conervative evaluation. The common aumption may be baed on two major reaon. Firt, ome of the uggeted model do not have hard evidence that they can capture actual behavior becaue of lack of agreement with experimental reult, and econd, there are many different form of local buckling a mentioned above. It i therefore neceary to develop new modeling technique that can provide not only a better repreentation for local buckling, but alo have good agreement with the experimental reult. A recent tudy on a fiber modeling technique to etimate local buckling of longitudinal bar in reinforced concrete (RC) column wa reported by Ichikawa et al. []. The tudy aimed to directly capture non-linear deformation of local buckling by uing fiber element to model longitudinal bar individually. The tudy how a poibility of further extenion of the fiber modeling technique. However, there ha been no further tudy to develop fiber modeling technique for teel bridge column. The main objective of thi tudy i to propoe a fiber model analyi method conidering local buckling of teel bridge circular column. In thi method, to imulate local buckling deformation, multi-fiber element are ued to model the local buckling length in the platic hinge zone. Thi concept i different from previou tudie that conider effect of local buckling in the tre-train curve of the platic hinge zone. Thi paper dicue analyi reult uing the propoed method compared to the previou experimental work. Overview of Previou Steel Bridge Circular Column [] The geometry and ection propertie of the teel bridge circular column ued in the analye are hown in Figure and ummarized in Table. Thi experimental work wa carried out by Public Work Reearch Intitute (PWRI) []. The column wa 9 mm in diameter with 9 mm thickne. The boundary condition were: a) Fixed column bae that wa fixed by high tenion bolt or pre-treed teel bar. The bae wa built-up ection coniting of thick teel plate, and hence wa aumed to be rigid. b) Pin connection between the top of the column and loading jack of each direction. Figure. Steel Bridge Circular Column Model [] Table. Propertie of the Column Model al Model Steel Grade SS4 Height h (m) 3.43 Thickne t (mm) 9 Diameter D (mm) 9.68 Rt.3 H (kn) 4.8 y (mm).5 P/y A.99 A diplacement-controlled teting on the horizontal direction with an axial load wa conducted with the loading hitory, hown in Figure 3, which wa applied to the column. The ratio of the axial force, P, to the value of the yield trength of teel plate, σy, multiplied by the ection area, A, wa approximately %. The lenderne parameter,, the radiu thickne parameter, Rt, the yield horizontal trength, H, and the yield horizontal diplacement, δy, in Table are given a follow: h I A E y () R A 6 P 9 y t 3 δ A 9 ing Plate Diaphragm 9 5 Diaphragm Section A-A (Unit: mm) Plate R () t E 9

3 Kinohita, K. / Analye of Steel Bridge Circular Column / CED, Vol. 6, No., March 4, pp. 7 H y P Z A h (3) H h 3 (4) 3E I where i the Poion' ratio of the teel plate, E i the modulu of elaticity of teel, I i the moment of inertia and Z i the ection modulu. The experiment howed that the peak-trength wa about 553 kn, and local buckling occurred at the bottom platic hinge zone of the column, which i known a elephant foot bulge. Fiber Modeling of Steel Bridge Circular Column In general, the circular column i modeled a a ingle fiber element that ha fine fiber diviion in the ection (Figure 4). In the circular column, local outof-plane bending deformation i created due to local buckling, however, the local out-of-plane deformation cannot be obtained from ingle fiber element, becaue each fiber diviion calculate only the axial deformation. Becaue of thi, thi modeling doe not give reult for out-of-plane deformation uch a local buckling Cycle Figure 3. Diplacement Controlled Teting Protocol (a) D/ (b) D/3 Figure 5. Propoed Fiber Model Previou tudie tried to conider oftening for potpeak behavior in order to aume local buckling in the tre-train curve of teel plate. However, a mentioned above, thi approach may not be able to capture the actual behavior of every teel bridge column becaue of lack of agreement with experimental reult. Moreover, additional calculation baed on experimental tet or finite element analye are required to conider more accurate tre-train curve. In fact, ome of calculation are complicated. In the propoed model (Figure 5), the platic-hinge zone i modeled a multi-fiber element while the general region i modeled a ingle fiber element. Thi way the out-of-plane bending deformation can be captured directly. Thu, the propoed model take advantage of the modeling technique that doe not need any additional calculation. A bi-linear tre-train curve with pot yield tiffne, which i aumed a % of the Young Modulu of teel plate, wa ued to model the teel plate. The yield trength of teel plate, σy, i aumed a 38 N/mm, which correpond to the experimental tet. The effect of element diviion on the ingle fiber model (ee Figure 4(a), (b), (c)) wa invetigated. Effect of Modeling Strength Z Y D/(.5D) D/(.5D) X D/3 (.33D) Z Y X.5D (a).5d (b) (b).5d (c).5d Figure Figure 44. Single Single Fiber Fiber Model Model.5D.5D Different analyi reult from the ingle fiber model cae and multi-fiber model cae are preented in term of trength and deformation. The effect of modeling wa determined by comparing with the experimental reult a the baeline. In addition, the reult are alo compared with the previou analyi reult by Goto et al. [3] that ued finite element model. Figure 6 to 9 how the relationhip between load and diplacement at the loading. Figure 6 3

4 Kinohita, K. / Analye of Steel Bridge Circular Column / CED, Vol. 6, No., March 4, pp. 7 indicate that the effect of element diviion (ee Figure 4(a), (b), (c)) on the ingle fiber model i not ignificant. Therefore, the reult uing.5 D element diviion ued for a comparion with the experiment reult. A hown in Figure 7, the dicrepancy in thi relationhip i oberved. The ingle fiber model overetimate not only the peak trength, but alo pot-peak trength. The peak trength obtained from the ingle fiber model can be about.5 time greater than in the peak trength from the experimental reult. Thi i due to the ue of the bi-linear tre-train curve in the teel plate without conideration of local buckling, which tiffen the platic hinge zone cauing it to allow more load to be carried. Thi overetimation can have a ignificant effect during eimic performance evaluation. H/H - Fiber Analyi.5D Fiber Analyi.5D Fiber Analyi.5D H/H Figure 8. Comparion of Relationhip between H/H and δ/δy in and Propoed Fiber Analyi H/H - - Propoed Fiber Analyi D/ Propoed Fiber Analyi D/3-5 diviion Figure 6. Effect of Element Diviion on Single Fiber Model H/H - Fiber Analyi.5D Analyi (Goto et al. (9)) Figure 7. Comparion of Relationhip between H/H and δ/δy in and Single Fiber Analyi Figure 9. Comparion of Relationhip between H/H and δ/δy in and Propoed Fiber Analyi with Fine Element Diviion in the Axial Direction On the other hand, a hown in Figure 8, the propoed multi-fiber model etimate well the peak trength, and lightly overetimate the pot-peak trength, but agree well with the experimental reult compared to the ingle fiber model. A light overetimation of the pot-peak trength i due to the ue of rough fiber element diviion on the platic hinge zone. A a follow up, a parametric tudy ha been conducted to tudy the enitivity of the diviion of the fiber element ued on the platic hinge zone to the reult. More pecifically, the diviion of the fiber element in the axial direction i invetigated a hown in Figure 5(a), (b). The diviion in the circumferential direction i kept the ame while the diviion in the axial direction i varied. Goto et al. [3] alo reported that the FEM analyi uing hell element i excellent in 4

5 Kinohita, K. / Analye of Steel Bridge Circular Column / CED, Vol. 6, No., March 4, pp. 7 etimating the repone of teel bridge frame pier with the circular column ubjected to cyclic loading when a mall element diviion or fine meh i utilized. Yamaguchi et al. [4] indicated that the element diviion on the platic hinge zone in the axial direction hould be le than D/3 and the apect ratio of the hell element length in the axial direction to the circumferential direction hould be le than /3 to accurately capture the peak trength when an error of le than % i deired. In thi tudy the element diviion of the platic hinge zone in the axial direction i under D/3, and the apect ratio of the length in the axial direction to the circumferential direction in the platic hinge zone i le than /3 (Figure 5(b)). Figure 9 how that a the element diviion in the axial direction increae, the pot-peak trength decreae and become cloer to the experiment, but not for the entire hitory. Therefore, an additional analyi i performed to determine the effect of diviion of fiber ection on the pot-peak trength. The diviion of fiber ection wa varied from 4-, 9-, 5-, to -diviion a hown in Figure. Figure how, that a the diviion of fiber ection in the axial direction decreae, the accuracy of the etimated repone in term of peak trength and pot-peak trength improve. More pecifically, peak trength of 4-, 9-, 5- and - diviion i.3,.4,.48 and.46, repectively, and therefore peak trength with fine diviion agree well with the experiment reult, which i about.3. Axial direction 4 diviion Thu, it can be concluded that the diviion of fiber ection in the axial direction ha ignificant effect on the peak trength and pot-peak trength. Similarly, the diviion of the fiber ection in the circumferential direction i invetigated. A hown in Figure, both the peak trength and pot-peak trength are imilar regardle of the diviion of the fiber ection in the circumferential direction. Therefore, it can be argued that the propoed method, with adequate diviion of both fiber element and fiber ection in the axial direction, give good reult in etimating not only the peak trength, but alo the pot peak trength. H/H - Propoed Fiber Analyi D/3-4 diviion Propoed Fiber Analyi D/3-9 diviion (a) 4- and 9-Diviion 9 diviion 5 diviion diviion Propoed Fiber Analyi D/3-5 diviion Propoed Fiber Analyi D/3- diviion Circumferential direction 4 diviion 4 diviion H/H (b) 5- and -Diviion Figure. Diviion of Fiber Section in both the Axial Direction and the Circumferential Direction Figure. Effect of Diviion of the Fiber Section in the Axial Direction 5

6 Kinohita, K. / Analye of Steel Bridge Circular Column / CED, Vol. 6, No., March 4, pp. 7 H/H - Propoed Fiber Analyi D/3-4 diviion Propoed Fiber Analyi D/3-4 diviion However, ingle fiber model i hown to be prone of large error. The effect of propoed modeling on out-of-plane bending deformation i determined by comparing the deformation from analyi reult uing the propoed model to the previou experimental reult. It i hown that propoed model can be improved to better capture the out-of-plane bending deformation in the platic hinge zone, where the local buckling occurred. Reference Figure. Effect of Diviion of the Fiber Section in the Circumferential Direction Buckling Figure 3. Deformation at Platic Hinge Zone Out-of-Plane Bending Deformation Figure 3 how the out-of-plane bending deformation of the platic hinge zone obtained from the propoed method. A hown, out-of-plane bending deformation due to local bucking occur in the propoed model. The multi-fiber element in the platic hinge zone allow thi deformation mode. However, it i alo oberved that there i a difference in the deformation mode at the platic hinge zone if compared to the experiment. The propoed model tend to deform toward the inide of the column a oppoed to the real deformation oberved in experiment. Thi ugget that ome improvement hould be made to the modeling of the platic hinge zone, although etimation of the peak trength and the pot-peak trength are good a decribed a mentioned above. Concluion Fiber model analyi technique ued in the analyi of teel bridge circular column have been dicued in thi paper. The effect of modeling on trength wa determined by comparing reult from ingle fiber model with multi-fiber model propoed in thi tudy. It i hown that peak trength and potpeak trength of the propoed model are comparable to thoe of the previou experimental work.. Park, R., Kent, D.C., and Nielen, N.N., Reinforced Concrete Member with Cyclic ing, Journal of the Structural Diviion, American Society of Civil Engineer, 98(7), 97, pp Sakai, J. and Kawahima, K., Nonlinear Seimic Repone Analyi of a Reinforced Concrete Bridge Column by the Fiber Element, Journal of Structural Engineering, Japan Society of Civil Engineer, 55A, 9, pp (In Japanee) 3. Sakai, J. and Unjoh, S., Earthquake Simulation Tet of Circular Reinforced Concrete Bridge Column under Multidirectional Seimic Excitation, Earthquake Engineering and Engineering Vibration, 5(), 6, pp Kawahima, K., Saaki, T., Kajiwara, K., Ukon, H., Unjoh, S., Sakai, J., Takahahi, Y., Koa, K., and Yabe, M., Seimic Performance of a Flexural Failure Type Reinforced Concrete Bridge Column baed on E-Defene Excitation, Doboku Gakkai Ronbunhuu A, Japan Society of Civil Engineer, 65(), 9, pp Watanabe, H. and Sakimoto, T., Seimic Repone Analyi of Concrete-Filled Steel Box Pier conidered on Local Buckling, Journal of Structural Mechanic and Earthquake Engineering, Japan Society of Civil Engineer, 647/I- 5,, pp (In Japanee) 6. Tokunaga, M., Ono, K., Hahimoto, A., Nihimura, N., and Taniue, H., Seimic Evaluation Method for Steel Member with Fiber Model in conideration of Hyterei, Doboku Gakkai Ronbunhuu A, Japan Society of Civil Engineer, 65(4), 9 pp (In Japanee) 7. Ihizawa, T., and Iura, M., Analyi of Tubular Steel Bridge Pier, Earthquake Engineering and Structural Dynamic, 34, 5, pp Kodama, N., and Yoda, T., Dynamic Repone Analyi of Box Section Steel Frame conidering Local Buckling, Journal of Structural Mechanic and Earthquake Engineering, Japan Society of Civil Engineer, 73/I-63, 3, pp (In Japanee) 6

7 Kinohita, K. / Analye of Steel Bridge Circular Column / CED, Vol. 6, No., March 4, pp Japan Society of Civil Engineer (JSCE), The Japanee Standard Specification for Seimic Deign of Steel and Compoite tructure, JSCE, 8. (In Japanee). Kakiuchi, T., Kaai, A., Inagaki, S., Fujiwara, Y., and Uami, T., Seimic Performance Evaluation of Steel Continuou Bridge with Rigid Supertructure-Pier Connection, Journal of Structural Engineering, Japan Society of Civil Engineer, 55A, 9, pp (In Japanee). Ichikawa, S., Saaki, T., and Kawahima, K., Analytical Idealization of Local Buckling of Longitudinal Bar for Analyzing the Seimic Performance of RC Column, Proc. 3 th Japan Earthquake Engineering Sympoium, Japan Aociation for Earthquake Engineering, 3,, pp Public Work Reearch Intitute (PWRI), Summary of the Cooperation Reearch on the Seimic Limit State Deign of Highway Bridge Pier, 999. (In Japanee) 3. Goto, Y., Kumar, P.G., and Kawanihi, N., FEM Analyi for Hyteretic Behavior of CFT Bridge Pier conidering Interaction between Steel Tube and Infilled Concrete, Doboku Gakkai Ronbunhuu A, Japan Society of Civil Engineer, 65(), 9 pp (In Japanee) 4. Yamaguchi, E., Oniki, K., Nagamatu, H., and Nannno, Y., On Finite Element Meh in Nonlinear Analyi of a Steel Circular-Section Bridge Pier, Journal of Structural Engineering, Japan Society of Civil Engineer, 5A, 5, pp (In Japanee). 7