SEISMIC BEHAVIOR OF STEEL RIGID FRAME WITH IMPERFECT BRACE MEMBERS

Transcription

1 INTERNATIONAL JOURNAL OF CIVIL ENGINEERING AND TECHNOLOGY (IJCIET) International Journal of Civil Engineering and Technology (IJCIET), ISSN (Print), ISSN (Online), Volume 6, Issue 1, January (21), pp IAEME ISSN (Print) ISSN (Online) Volume 6, Issue 1, January (21), pp IAEME: Journal Impact Factor (21): (Calculated by GISI) IJCIET IAEME SEISMIC BEHAVIOR OF STEEL RIGID FRAME WITH IMPERFECT BRACE MEMBERS Hamid Afzali 1, Toshitaka Yamao 2 1, 2 Graduate School of Science and Technology, Kumamoto University, Japan ABSTRACT Model of a steel rigid frame made of thin-walled box section with existence of I-section brace member with initial overall and local imperfection adopted to investigate buckling effects on steel structural behavior as it was subjected to earthquake excitation. In order to take into account of the influence of local deflections on structural response, shell elements were employed to model brace member as well as base columns. Cross sections components with relatively high amplitude of buckling parameters were considered in different case studies to make it susceptible to develop local deflection. Beam elements were also utilized to develop models with the same specification. FEM method applied to conduct nonlinear time history analysis using earthquake record in in-plane and out-of-plane direction. Seismic response of both shell element model and beam element model were obtained and compared to investigate the effect of local deformation on seismic behavior of the structure. It was found that in case of applying earthquake record in longitudinal direction of the structural frame, due to ignoring local deflections beam element model is not sufficient to present maximum response for structural case studies made of components with higher buckling parameters. Buckling deformations were observed and discussed based on obtained results in case of applying earthquake records in transverse direction. Keywords: Steel rigid frame, seismic behavior, time history analysis, initial imperfection, buckling effect I. INTRODUCTION Studying seismic behavior of rigid frames with bracings composed of structural members with relatively thin-walled cross sections members is important since it may be used as part of steel arch bridges which are frequently subjected to ground motions. When faced with the risk of instability in thin component plates during severe earthquakes, conventional approach of applying FEM method using beam elements in analysis procedure and designing of earthquake resistant steel structures seems to be inadequate to show seismic behavior of the structure [1] [2] [3]. Development of a model using shell finite element for structures made of built-up cross section with thin plate 113

2 International Journal of Civil Engineering and Technology (IJCIET), ISSN (Print), ISSN (Online), Volume 6, Issue 1, January (21), pp IAEME components helps to consider the effects of local behavior in seismic response. Buckling of a structural compressive member has encouraged many researches to work on this subject up to now. Employing shell elements enables us to observe local deformations and its effect on structural resistance deterioration. Investigating buckling effects in members of civil structures is an extensive research field. However, in most of previous works the main concern was buckling behavior of a specimen under compressive loading such as axial force or bending moment. Many researchers were interested in discussing compressive structural members alone rather than its influence on whole structure and other members. For instance, potential interaction between different buckling modes have considered as important research subject as well as efforts to present a theoretical design equations for buckling ultimate load. Closed formed prediction of elastic local buckling and distortional buckling based on interaction of connected elements is presented and examined for lipped channel and Z sections [4]. Sensitivity of compressive capacity of plates with geometric imperfections [] and sensitivity of buckling collapse depending on type of shell elements employed in making a model as well as the density of mesh generation were also examined by researchers. Different software packages used to make finite element model and finally results obtained by different solvers were compared [6]. Ductility of different cross sections such as steel box section and I-beam sections when they are subjected to axial load were explored [7] [8]. It is necessary to explore how buckling zones may grow through structural members under regular loading, and how it affects failure mechanism. In this paper the numerical finite element model of total structure was provided to study effect of buckling behavior of more than one member on structural response. This enables us to observe how buckling effects in a particular part of structure may affect resistance degradation in whole structural system. Obviously structural member specifications play a major role in forming local deflections; therefore there is a necessity to explain how variation on a specific parameter in a structural member contributes to total behavior of the structure. Here target structure was steel rigid frame with inverted V shape bracing. Effect of slenderness of brace member on behavior of structure was investigated as well. This structure may be a part of an arch steel bridge. In order to take account of local behavior in braces and base columns, finite element model was adopted employing shell elements in targeted zones. II. LAYOUT OF ANALYSIS 2.1 Analytical model Target structure was rigid frame with inverted "V" shape brace as illustrated in Fig. 1(a). Fig. 1(b) and Fig. 1(c) are box section for rigid frame, and I-section beam used for brace members. In Fig. 1(b), W=.3 m denotes side length of the box section, and the thickness of the component plate is t=.64 m. W B W H t B t w H w B f t f (a) Rigid frame with brace (b) Sec. 1-1 (c) Sec. 2-2 Figure 1: Geometry and cross sections in structure of rigid frame with brace member 114

3 International Journal of Civil Engineering and Technology (IJCIET), ISSN (Print), ISSN (Online), Volume 6, Issue 1, January (21), pp IAEME B represents total width and height of the I-section. The parameters t w, t f and denote the thickness of the web and flange, respectively. Constant vertical load of percent of axial yield capacity of column section imposed on two top corners of the rigid frame in order to consider super structural load. The material is assumed to be SM4 steel (JIS). The yield stress σ y is 23MPa; Young s modulus E is 2GPa, and Poisson s ratio is ν =.3. Other specifications are explained in Table 1. Plot of strain-stress curve is shown in Fig SM4 σ (N/mm²) Figure 2: Strain-stress curve of material Aiming to study buckling effects in structures with members made of thin plate components, width-to-thickness parameter of cross sections was considered and defined as following equations. ε Bf Rf = t R w R = f H = t H t w w σ y 12(1 ν 2 E kπ 2 ) σ y 12(1 ν 2 E kπ σ y 12(1 ν 2 E kπ 2 ) 2 ) (1) (2) (3) Equations (1)-(3) show width-to-thickness ratio for flange, web in I-shape beam, and for side plate in box section, respectively. Members with higher values of width-to-thickness parameter are deemed thin-walled sections. σ y is yield stress and E is modulus of elasticity. Buckling coefficient "k" is assumed equal to 4. for double-sided stiffened plates such as web in I-shape section and side plates of the square shape section. This parameter is set to.4 for flanges in I-beam sections. Rigid frame section properties are the same in all case studies. For plates of box-section R=.8 based on Equation (3). Aiming to consider probable local deformations in rigid frame, cross section with relatively slender plates determined for box section. According to JSHB [9], allowable design compressive stress is decreased for component plates of this section due to considering local buckling effects under service loading. Buckling parameter amplitude for plates of I-beam section ranged between.6,.8, and 1. to represent sections made of normal, relatively thin, and thin plates. Nine specimens with I-beam sections are explained in Table 1. L stands for length of the brace member and r is radius of gyration of the section. 11

4 International Journal of Civil Engineering and Technology (IJCIET), ISSN (Print), ISSN (Online), Volume 6, Issue 1, January (21), pp IAEME Table 1: Nine specimen of brace members with I-section Specimen of brace member B (m) t f (m) t w (m) L/r R f R w Numerical model Finite element software package of ABAQUS program [1] were employed to develop a model and demonstrating the seismic behavior of the structure. For the purpose of approximation of local deformations, as depicted in Fig. 3(a) shell model were employed in base columns and 83% of brace member length as regions with large internal forces rather than other parts of the structure, and most susceptible to local buckling effects. Super-structural load Super-structural load Super-structural load Super-structural load Shell element Beam element Fixed support Fixed support Fixed support Fixed support (a) (b) (c) Connecting beam element to the shell zone using rigid plates Figure 3: Numerical model 116

5 International Journal of Civil Engineering and Technology (IJCIET), ISSN (Print), ISSN (Online), Volume 6, Issue 1, January (21), pp IAEME Fig. 3(b) depicts the model made of all beam models. Responses of beam model were compared with that of shell model. In order to provide connectivity between beam elements and shell elements, end side of the shell element zone and beam zone were connected by rigid plates as shown in Fig. 3(c). Four node shell element S4R with reduced integration scheme were applied to model cross sections in base column and brace member. This element is robust and avoids shear locking that makes it appropriate for wide range of applications. The rigid frame members excluding base column were made of beam elements B31. These elements are also capable of taking account of shear deflections. Brace members are assumed to join to rigid frame using pin connections. Translational degrees of freedom are fixed at the base. Time history analyses were conducted in longitudinal and transverse direction proportional to the structure. 2.3 Applying initial Crookedness Thin plate components of built-up sections are not completely flat. Applying loading system may result in local deformations. Small initial crookedness and slenderness of the plates could lead in transverse deformations under compression. The axial load may generated by compression or bending moment. Crookedness influence local buckling behavior while the structure is subjected to external pressure also has been concerned in many researches. Imperfections may appear in two different types: geometric and stress. There is no verified theoretical approach to implement the shape and size of the initial geometrical imperfections. However, conventional methods assume that imperfections should be obtained through the form of classical linear eigen modes of the perfect structures. This research considers the effects of crookedness and global initial deflection in brace member on behavior of the structure. A computer program developed to generate crookedness as well as initial deflection along the brace member. Applied overall initial deflection is plotted in Fig. 4(a). It was approximated in shape of circular arc along the longitudinal axis of the brace member. Imperfection amplitude of L/1 (L is length of the brace member) was prescribed in middle of the brace. As shown in Fig. 4(b), Initial crookedness in flange and web plates applied in form of sinusoidal wave. As seen for I-beam section, initial local imperfection amplitude is B/2 for flange plate, and B/1 for web plate. L L/1 (a) Initial deflection (b) Initial crookedness of component plates Figure 4: Initial imperfections in brace member 117

6 International Journal of Civil Engineering and Technology (IJCIET), ISSN (Print), ISSN (Online), Volume 6, Issue 1, January (21), pp IAEME (a) Type II-I-1 (Kobe N-S) (b) Type II-I-2 (Kobe E-W) Figure : Input seismic waves III. ANALYSIS RESULTS Nonlinear time history analysis conducted to investigate seismic structural response of previously mentioned 9 specimens using ABAQUS software package. Von Mises yield criteria with isoperimetric hardening is employed in this study. Two seismic waves provided by JSHB [9] at Level II caused by inland faults in region with ground Type I [N-S and E-W components of Kobe earthquake (199)] were input in dynamic response analysis. Ground acceleration data of Type II-I-1 and Type II-I-2 waves which are applied in this paper are shown in Fig. (). As seen in Fig. (6), Kobe N-S component wave was applied in-plane direction and Kobe E-W component wave was applied in out-of-plane direction. Dynamic analysis performed for both shell and beam model types. Results are obtained and plotted to compare between various structural models. Displacement response Displacement response Type II-I-1 (Kobe N-S) Type II-I-2 (Kobe E-W) (a) In-plane seismic wave (b) Out-of-plane seismic wave Figure 6: Seismic wave conditions 118

7 International Journal of Civil Engineering and Technology (IJCIET), ISSN (Print), ISSN (Online), Volume 6, Issue 1, January (21), pp IAEME Table 2: Eigenvalue analysis results () Mode Frequency Period No. Effective mass ratio (%) (Hz) (s) X Y Z Table 3: Eigenvalue analysis results (beam model) Mode Frequency Period No. Effective mass ratio (%) (Hz) (s) X Y Z Eigen value analysis Before conducting time history analysis, structural dynamic characteristics should be determined to compute essential parameters used for dynamic analysis. In order to show natural mode shapes and frequencies of structures with each specimen, eigenvalue analysis was performed. Lumped masses equal to super-structural load were considered in corners of the rigid frame. Analysis results of the specimen up to 1th mode shape for both shell and beam model are shown in Table 2 and Table 3, respectively. According to effective mass ratio and mode shapes illustrated in Fig. 7, it was found that for this case study, in both model types the structure naturally tends to vibrate at mode shapes with lower frequencies in out-of-plane and in-plane directions. These two mode shapes were prominent for all cases as well. Comparison of modal frequencies between two types of shell model and beam one is illustrated in Fig. 8. It revealed good correlation in first three lowest frequencies. In shell model some frequencies were higher than corresponding values in beam model. However, these modes do not play a major role in vibration of the structure under dynamic load conditions. As seen prominent frequencies (mode 1 and mode 3) were almost the same in both model types. (a) Mode1(prominent) (b) Mode 2 (c) Mode 3(prominent) (d) Mode 4 Figure 7: Mode shapes of the model made of shell elements (Specimen 1-6-6) 119

8 International Journal of Civil Engineering and Technology (IJCIET), ISSN (Print), ISSN (Online), Volume 6, Issue 1, January (21), pp IAEME (a) Specimen (b) Specimen (c) Specimen (d) Specimen (e) Specimen (f) Specimen (g) Specimen (h) Specimen (i) Specimen Figure 8: Comparison of frequency results between shell model and beam model Time history response for in-plane seismic wave Above described analytical models were subjected to Type II-I-1 (Kobe N-S component- 199) in in-plane direction as it shown in Fig. 6(a). Structural damping was considered based on commonly used Rayleigh damping method. The damping matrix C is assumed to be proportional to the Mass M and stiffness K matrices, as C=α.M+β.K. α and β factors were calculated using the following formula. 4 f i α = π hi f β = π i f j ( h j f i hi f j ) 2 2 ( f f ) 2 2 ( f f ) i i h j f j j j f i and f j denotes major modal frequencies. h i and h j are damping coefficients of prominent modes. In order to compare structural responses and observing buckling effects on seismic behavior of the models, displacement response of the top point as shown in Fig. 6 and base shear force response are plotted in Fig. 9 to Fig. 11. As mentioned in Table 1 brace member s slenderness ratio and width-to-thickness ratio of cross section plate components varied between different specimens. Fig. 9 shows time history responses for brace member with slenderness ratio of L/r=1. Fig. 1 plots the results for the case of brace member with L/r=9, and Fig. 11 indicates seismic responses for L/r=8. (4) () 12

9 Base shear (x16 N) International Journal of Civil Engineering and Technology (IJCIET), ISSN (Print), ISSN (Online), Volume 6, Issue 1, January (21), pp IAEME (b) Base shear response (1-6-6) Base shear (x16 N) (a) Displacement response (1-6-6) (c) Displacement response (1-8-8) (d) Base shear response (1-8-8) Base shear (x16 N) (e) Displacement response (1-1-1) (f) Base shear response (1-1-1) Figure 9: Seismic response to Kobe N-S component earthquake record, R= Base shear (x16 N) (a) Displacement response (9-6-6) (b) Base shear response (9-6-6) 121 3

10 Base shear (x16 N) International Journal of Civil Engineering and Technology (IJCIET), ISSN (Print), ISSN (Online), Volume 6, Issue 1, January (21), pp IAEME (c) Displacement response (9-8-8) 2 3 (d) Base shear response (9-8-8) Base shear (x16 N) (e) Displacement response (9-1-1) (f) Base shear response (9-1-1) Base shear (x16 N) Figure 1: Seismic response to Kobe N-S component earthquake record, R= (a) Displacement response (8-6-6) 2 3 (b) Base shear response (8-6-6) Base shear (x16 N) (c) Displacement response (8-8-8) (d) Base shear response (8-8-8) 122 3

11 International Journal of Civil Engineering and Technology (IJCIET), ISSN (Print), ISSN (Online), Volume 6, Issue 1, January (21), pp IAEME Base shear (x16 N) (e) Displacement response (8-1-1) (f) Base shear response (8-1-1) Figure 11: Seismic response to Kobe N-S component earthquake record, R=.8 According to Fig.9 to Fig.11 history responses for the same seismic wave were different between shell model and beam model. As illustrated in Figs (e,f) peak responses belonged to shell model. Fig.12 also shows history of base force versus displacement for in-plane base excitation. As clearly seen in Figs. 12(c,f,i) when Rf=1. and Rw=1. larger maximum displacement responses were observed in case of shell model. It was found that regardless of slenderness ratio of brace member, beam model is not reliable in case of applying brace member made of component plate with high width-to-thickness ratio. For specimen 8-6-6, almost no instabilities were found in history responses (a) (d) (g) (f) (e) Base shear (x16) Base shear (x16) Base shear (x16) Base shear (x16) Base shear (x16) (c) (b) Base shear (x16) Base shear (x16).3 Base shear (x16) Base shear (x16) (h) (i) Figure 12: Time history base shear versus displacement [in-plane seismic wave (Kobe N-S)] 123

12 International Journal of Civil Engineering and Technology (IJCIET), ISSN (Print), ISSN (Online), Volume 6, Issue 1, January (21), pp IAEME 3.3 Time history response for out-of-plane seismic wave Type II-I-2 (Kobe E-W component) in out-of-plane direction as it shown in Fig. 6(b) was used to perform nonlinear time history analysis. Since the ground motion wave direction is perpendicular to the rigid frame plane, using various brace members had less effect on structural response. Results for specimen are plotted in Fig. 13. Plastic residual displacement was observed due to nonlinear instabilities. Significant buckling effects in base columns caused sudden drop of displacement response as shown in Fig. 13 (a). Opposite to in-plane seismic wave, as seen in Fig. 13(b) base shear response did not decreased severely during the second half of the history (a) Displacement response (1-6-6) (b) Base shear response (1-6-6) Figure 13: Seismic response to Kobe E-W component earthquake record, R=.8 Base shear (x1 6 N) Local deformation caused by out-of-plane seismic wave Severe local buckling effects in base column caused difference in vertical surface strain in shell elements. Significant local deflection confirmed by obtaining vertical stress-strain curve in outside and inside face of the elements El:1 and El:2 in base column as shown in Fig. 1. El:1 El:2 Figure 14: Local deflection in base column for models subjected to out-of-plane seismic wave In Fig. 1 σ Y and σ V denote yield stress and vertical stress respectively. ε V presents vertical strain and the term ε y points out to yield strain. The position of El:1 and El:2 are illustrated in Fig. 14. Based on output results not any residual strain occurred in case of in-plane excitation using Kobe E- 124

13 International Journal of Civil Engineering and Technology (IJCIET), ISSN (Print), ISSN (Online), Volume 6, Issue 1, January (21), pp IAEME W component earthquake record. As seen compression strain observed in outside surface of the element El:1 and tension strain developed in outside face of the element El:2. In both elements the compression strain is larger than the tension strain. It is because of existence of vertical loads assumed to represent super structural weight. In El:2 the strain grew steadily. However in El:1 more loops were observed since it directly affected by internal compressive forces generated by ground motion. Based on output results not any residual strain occurred in case of in-plane excitation using Kobe E-W component earthquake record. 2 Outside Inside 2 Outside σ v /σ y 1 σ v /σ y 1 Inside ε v /ε y (a) Hysteresis stress-strain in El: ε v /ε y (b) Hysteresis stress-strain in El:2 Figure 1: Local deflections in base column, R=.8, In case of applying out-of-plane seismic wave of Kobe E-W component IV. CONCLUSION Model of steel rigid frame with converted V shape brace member with various slenderness ratio and different width-to-thickness ratio studied to investigate the effect of local deflections on history response of the structure. In order to obtain better understanding of local buckling effects shell model adopted as well as beam model. Two results were compared to draw following conclusions. 1- Regardless of slenderness ratio, larger maximum displacement responses were observed in case of shell model with higher width-to-thickness ratios R f =1., R w = No instabilities observed in history responses for model with lowest slenderness ratio L/r=8 and lowest buckling parameter R f =.6, R w =.6. However, effects of local deflections caused instabilities for models with slenderness ratio of larger than L/r=8. 3- Since the brace members are not very effective in perpendicular stiffness of the structure, sever buckling deformation accrued as the model subjected to out-of-plane ground motions which lead in residual plastic displacement response. 4- Buckling effects may be confirmed through outside and inside surface strain. In this study maximum case amounted to 3 time larger than yield strain. 1

14 International Journal of Civil Engineering and Technology (IJCIET), ISSN (Print), ISSN (Online), Volume 6, Issue 1, January (21), pp IAEME REFERENCES [1] T. Yamao, S. Takaji. and S Atavit, 3 Dimensional Seismic Behavior of Deck Type Arch Bridges with Curved Pair Ribs, Proceedings of 8th International Conference on STEEL, SPACE & COMPOSITE STRUCTURES, 26, K. Lumpur, Malaysia, pp [2] T. Yamao, S. Atavit and Chandra F, Seismic Behavior and a performance Evaluation of Deck-Type Steel Arch Bridges under the Strong Earthquakes, th International Symposium on Steel Structures ISSS 9, 29, Seoul, Korea. [3] O. Mohamed, Y Nakamura, T. Yamao and T. Sakimoto, Performance Evaluation Method for a Seismic Design of Deck-type Steel Arch Bridges, Journal of Construction Steel, 26, Vol.14, pp [4] B. W. Schafer, Local, Distortional, and Euler Buckling of Thin-Walled Columns, Journal of Structural Engineering/ March 22. p [] Tetsuya Yabuki, Janice J. Chambers, Yasunori Arizumi, Tetsuhiro Shimozato, Hiroaki Matsushita, Buckling capacity of welded stainless steel flanges by finite element analysis, Engineering Structures 49 (213) [6] B. W. Schafer, Z. Li, C.D. Moen, Computational modeling of cold form steel, Thin-walled structures 48 (21) [7] O. Mohamed, T. Sakimoto, T. Yamao, Ductility of stiffened steel box member, Advanced steel structure,. [8] T. Yamao, A. Sujaritpong, Yoshie Tsujino, Evalustion of ultimate strength and strain of I- section steel members, The 4th International conference on advances in structural engineering and mechanics (ASEM 8), Jeju, Korea, May 26-28, 28. [9] Japan Road Association, Specifications for Highway Bridges, Part I - Steel Bridge and Part V - Seismic Design, Japan, 22. [1] Dassault Systèmes Simulia Corp., ABAQUS 6.11, Abaqus/CAE User s Manual. Providence, RI, USA,