Seismic Response of Infilled Framed Buildings Using Pushover Analysis

Transcription

1 ARI The Bulletin of the Istanbul Technical University VOLUME 54, NUMBER 5 Communicated by Zekai Celep Seismic Response of Infilled Framed Buildings Using Pushover Analysis Konuralp Girgin and Kutlu Darılmaz Department of Civil Engineering, Istanbul Technical University, 34469, Maslak, Istanbul, Turkey Structural frames are often filled with infilled walls serving as partitions. Although the infills usually are not considered in the structural analysis and design, their influence on the seismic behaviour of the infilled frame structures is considerable. In the present study, a parametric study of certain infilled frames, using the strut model to capture the global effects of the infills was carried out. Three concrete planar frames of five-stories and three-bays are considered which have been designed in accordance with Turkish Codes. Pushover analysis is adopted for the evaluation of the seismic response of the frames. Each frame is subjected to four different loading cases. The results of the cases are briefly presented and compared. The effect of infill walls on seismic behavior of two sample frames with different infill arrangements was investigated. The results yield that it is essential to consider the effect of masonry infills for the seismic evaluation of moment-resisting RC frames, especially for the prediction of its ultimate state, infills having no irregularity in elevation have beneficial effect on buildings and infills appear to have a significant effect on the reduction of global lateral displacements. Keywords: Infilled frame, pushover analysis, infill walls, seismic response, capacity spectrum, plastic hinge. 1. Introduction Infills have been generally considered as nonstructural elements, although there are codes such as the Eurocode-8 that include rather detailed procedures for designing infilled R/C frames, presence of infills has been ignored in most of the current seismic codes except their weight. However, even though they are considered non-structural elements the presence of infills in the reinforced concrete frames can substantially change the seismic response of buildings in certain cases producing undesirable effects (torsional effects, dangerous collapse mechanisms, soft storey, variations in the vibration period, etc.) or favourable effects of increasing the seismic resistance capacity of the building. The behavior of masonry-infilled RC frames has been examined by Fiorato et al. [1], Klingner and Bertero [2], Bertero and Brokken [3], Saneinejad and Hobbs [4], Madan et al. [5], Chaker and Cherifati [6], Karadogan and Yuksel [7]. To perform a step-by-step force displacement response analysis of buildings with infilled frames, a model for infills is required. Generalized macromodels seem more suitable for representing the global behavior of components in the analysis of such structures. For analyses where the emphasis is on evaluating the overall structural response, macromodels can be substituted for micromodels without substantial loss in accuracy and with significant gains in computational efficiency. Recent interests in the development of performance based codes for design or rehabilitation of buildings in seismic regions show that the pushover analysis is used widely to evaluate the acceptability of any proposed design, or to asses the seismic vulnerability of existing buildings (ATC-40 [8], FEMA-356 [9]). This analysis has been developed and investigated by many researchers; Saidii and Sozen [10], Fajfar and Fischinger [11], Fajfar and Gaspersic [12], Krawinkler and Seneveritna [13], and used for evaluation of infilled frames, Kappos et al. [14], Lee and Woo [15], Al-Chaar [16]. The pushover analysis can be considered as a series of incremental static analyses carried out to examine the non-linear behaviour of structure, including the deformation and damage pattern. The procedure consists of two parts. First, a target displacement for the structure is established. The target displacement is an estimate of the seismic top displacement of the building, when it is exposed to the design earthquake excitation. Then, a pushover analysis is carried out on the structure until the displacement at the top of the building reaches the target displacement. The extent of damage experienced by the building at the target displacement is considered to be representative of the damage experienced by the building when subjected to design level ground shaking. A judgment is formed as to the acceptability of the structural behavior for the design of the new building, or the level of damage of an existing

2 Konuralp Girgin and Kutlu Darılmaz Figure 1. Mechanical behavior and geometric properties of strut model. Figure 2. Distance to column and beam hinge. building for evaluation purposes. 2. Procedure In the presented procedure a mathematical model directly incorporating the nonlinear loaddeformation characteristics of individual elements of the structure is formed. The model uses the assumptions for the infills proposed by Klingner and Bertero [2], which adopts concentrated plasticity elements. A brief description of the formulations for predicting the lateral strength and stiffness parameters of the infill is given here. Details of the model and underlying theory can be found in the original reference. The infills are modelled as struts having a bilinear force-displacement relation. The bilinear law is characterized by an elastic branch defined by the stiffness of the connecting strut. This strut represents the secant stiffness up to the ultimate strength and by a second exponential degradation branch defined by the compressive strength which represents the envelope of the maximum strengths reached over the succession of loading cycles. In fact, there is also a third perfectly plastic branch, defined by a possible tensile strength typical in the case of reinforced masonry. In this study only unreinforced infill is considered, consequently this third branch is not taken into account. The initial elastic behavior of the struts which represent infills is defined by R = E inf Av/L, A = wt (1) where R denotes the axial force of the strut; E inf, Young s modulus of infill; v, the axial elongation in the strut; L, the length of the strut, (the distance between diagonally opposite nodes), w, the effective width related to the length of contact (λh) proposed by Mainstone [17], t, the thickness of the infill, Fig. 1(a). Strength envelope curve of the strut is defined by R = Af inf e γv (2) where f inf, compressive strength of the infill, γ, the empirical degradation parameter. Equivalent strut widths have been determined by many investigators to depend principally on the panel aspect ratio and the ratio of panel stiffness to frame stiffness E inf tsin2θ λh = 4 (3) 4EI c h inf and W L = 0.175(γh) 0.4 ; units in inches (4) in which h, h inf, θ and L refer to Fig. 1(b); E, the frame modulus, I c, the column moment of inertia The equivalent strut is to be connected to the frame members as depicted in Fig. 2(a). The infill forces are assumed to be mainly resisted by the columns, and the struts are placed accordingly. The strut is pin-connected to the columns at a distance l hc from the face of the beam. Plastic hinge property in columns can capture the interaction between axial load and moment capacity. These hinges are located at a distance 2

3 Seismic Response of Infilled Framed Buildings Using Pushover Analysis Table 1 Sections of the columns and their reinforcement Column b/h [mm] Reinforcement Stirrup S5E 250/300 6D14 (924mm 2 ) D10@150 S4E 250/300 8D14 (1232mm 2 ) D10@150 S3E 250/300 10D14 (1539mm 2 ) D10@120 S2E 250/400 10D14 (1539 mm 2 ) D10@100 S1E 250/400 10D14 (1539mm 2 ) D10@100 S5M 250/300 6D14 (924 mm 2 ) D10@150 S4M 250/300 8D14 (1232 mm 2 ) D10@150 S3M 250/300 10D14 (1539 mm 2 ) D10@120 S2M 300/400 10D14 (1539 mm 2 ) D10@100 S1M 300/500 10D14 (1539 mm 2 ) D10@100 l hc from the face of the beam. Hinges in beams characterize the bending behavior of the member. These hinges are placed at a distance l hb from the face of the column and at the midspan of the beam. Shear hinges are also incorporated in both columns and beams. The hinge in equivalent strut represents the axial load hinge. This hinge is placed at the midspan of the member. Rigid end offsets are placed on the column and beam members surrounding the infilled panel. For beams surrounding infilled panels, rigid end offsets are used from the beam/column joint to a distance of lhb from the face of the column. For columns surrounding infilled panels, rigid end offsets are placed from the beam/column joint to a distance of l hc from the face of the beam. These distances also correspond to the locations of the beam and column plastic hinges. The beam or column is therefore assumed to be rigid up to the point of the plastic hinge ensuring that the maximum Table 2 Sections of the beams and their reinforcement Beam Top Bottom Midspan 3D12 (339 mm 2 ) 5D12 (565 mm 2 ) Support 3D12+5D14 (1109 mm 2 ) 5D12 (565 mm 2 ) b w [mm] b [mm] t [mm] h [mm] internal forces computed are located at the defined plastic hinges (Al-Chaar [16]). The distances l hc and l hb can be defined by using Eqn. 5 and with refering to Fig. 2(a) and Fig. 2(b). w cosθ c l hc = w, tanθ c = h inf (5) cosθ c l b l hb = w sinθ b, tanθ b = l b h inf w (6) sinθ b The frames are assumed to be subjected to a monotonically increasing lateral load. The component gravity loads are also included in the mathematical model and combined with the lateral loads. The lateral load variation is assumed to represent the distribution of inertia forces in an elastic design earthquake. The distribution of the inertia forces will vary with the severity of the earthquake and as an extent of inelastic deformations and with time. The fact that no single load pattern can capture the variations, the lateral load pattern is important in pushover analysis. In this study static lateral loads are applied to the mathematical models in the following four patterns: 1) A vertical distribution proportional Figure 3. Elavation of the sample frames. Figure 4. Column and beam sections. 3

4 Konuralp Girgin and Kutlu Darılmaz Table 3 Number of reinforcement bars for columns Reinforcement n (A s1) n (A sg) 6D14 3-8D D to Equivalent Seismic Load distribution as defined in TEC (Turkish Earthquake Code) [18] satisfying the mass participation %75 in the first mode (L1), 2) a vertical distribution which yield a story shear forces proportional to the story shear forces obtained by combining modal responses from a response spectrum analysis of the frames (L2), 3) a distribution consisting of lateral forces proportional to the story mass at each level (L3) and 4) a vertical distribution proportional to the first mode shape loading (L4). The push-over analyses of the frames are carried out using the SAP [18] series program and stopped when a frame element of the system reaches its ultimate rotational capacity. 3. Examples The pushover analysis of three, five-storey, three-bay reinforced concrete planar frames are carried out. First frame is the bare framed structure (B1) which is considered as a reference frame, second frame has infilled walls in every span (B2) and third frame is filled with infilled walls in every span except the first storey (B3). The frames are designed according to the TEC, assuming effective peak ground acceleration of 0.40g(A o = 0.40), building importance factor I=1.0, normalized spectral acceleration S(T)=2.5, behavior factor R=8 (high ductility level). The value of base shear used for design is 278 kn. The design shear forces of beams and columns are taken to be compatible with the probable moment capacities of the sections. During the design process, the infills are considered as nonstructural members as it is done in usual practice. The geometry of the frames is shown in Fig. 3. The material characteristics, the section properties and the reinforcement of the elements are given in Table 1, Table 2, Fig. 4 and longitudinal reinforcement details of columns are given in Table 3. In the present numerical analysis for the infills E inf = 3000 MPa, t=140 mm, f inf =6 MPa,γ = 1.0 is assumed. Figure 5. Normalized lateral force-lateral dispalacement relataionships for the frame B1. Figure 6. Normalized lateral force-lateral dispalacement relataionships for the frame B2. Figure 7. Normalized lateral force-lateral dispalacement relataionships for the frame B3. Figure 8. Comparison of the normalized lateral and B3 frame for Loading L1. 4

5 Seismic Response of Infilled Framed Buildings Using Pushover Analysis Results of the pushover analyses that SAP[19] was used are presented as Base Shear/Total Weight (P/W) vs Top Displacement/Total Height ( /H) diagrams in Fig. 5, Fig. 6 and Fig. 7. For the infill configuration patterns given above, global response comparisons of the selected frames can be done for these different load patterns. It can be observed that in all loading patterns, the lateral load carrying capacity of the frames appears to be above the design base shear due to the safety factors in concrete and steel, minimum reinforcement, redundancy of structural system and overstrength arising from the design. Furthermore, the loading pattern effects the post-yield response and the ultimate lateral load capacity. For example loading L3 results in higher strength but lower ductility then the other loadings due to the disparateness of story shear forces. To determine the influence of infill arrangement on the structural behavior, the pushover curves are given for the same loading patterns in Fig. 8, Fig. 9, Fig. 10 and Fig. 11 comparatively. As it is seen infills increases lateral resistance and initial stiffness of the frames, and the increase depends on the infill arrangement. An irregularity of infill configuration in elevation yields a non-uniform stiffness distribution and effect significantly the storey drifts which can be accepted as damage indicators. The distribution of plastic hinges over the frames at the ultimate stage are given in Fig. 12. The number 1 indicates the first occurence of plastic hinge formation. As it is seen, collapse of the frame B1 is reached after numerous plastic hinges at several frame members. Collapse of the frame B2 which has regular infill arrangement is reached after numerous plastic hinges at several frame members and walls. Although the frame B3 is designed as high ductility level frame, the irregular infill arrangement restrict the spreading of plastic hinges, changes the sequence of plastic hinge formation, causes soft story mechanism and forces the behavior to be a non ductile one. To validate the ability of frames to satisfy the collapse prevention performance level for the design earthquake, the capacity spectrum method (ATC40) is carried out for load patterns L4 and L3, assuming the structural behavior type A and the local site as hard rock. Although a performance point (point A and B) can be found for B1 and B2 frames in Fig. 13 and Fig. 14, B3 building can not satisfy to resist the design earthquake Figure 9. Comparison of the normalized lateral and B3 frame for Loading L2. Figure 10. Comparison of the normalized lateral and B3 frame for Loading L3. Figure 11. Comparison of the normalized lateral and B3 frame for Loading L4. Figure 12. Formation of the plastic hinges. 5

6 Konuralp Girgin and Kutlu Darılmaz Figure 13. Seismic demand and structural capacity curves for L3. Figure 14. Seisismic demand and structural capacity curves for L4. within the collapse prevention performance level based on the acceptance criteria for plastic rotation limits given in ATC40. The design earthquake is defined probabilistically as the level of ground shaking that has a 10 percent chance of being exceeded in a 50 year period. 4. Conclusions The effect of infill walls on seismic behavior of a two sample frames with different infill arrangements was investigated. The results yields the following conclusions. 1- It is essential to consider the effect of masonry infills for the seismic evaluation of momentresisting RC frames, especially for the prediction of its ultimate state. 2- Infills having no irregularity in elevation have beneficial effect on buildings. In infilled frames with irregularities, such as soft story, damage was found to concentrate in the levels where the discontinuity occurs. 3- Since infills increases lateral resistance and initial stiffness of the frames they appear to have a significant effect on the reduction of the global lateral displacement. 4- Arrangement of infills may effect the post yield behavior and has an influence on distribution and sequence of damage formation. To generalize this, more infill arrangements should be investigated. 5- A carefully performed pushover analysis can provide insight into structural aspects that control performance of the structure during a severe earthquake 6- The choice of the static load distribution used in pushover analysis can affect the accuracy of the response estimates. The macro modeling approach used here considers the entire infill as a strut and takes into account only the equivalent global behavior of the infill in the analysis. The approach does not permit study of local effects such as frame-infill interaction within the individual infilled frame subassemblies. More detailed micromodeling approaches such as the finite element models need to be used to capture the spatial and temporal variations of local conditions within the infilled. 5. Appendix Equivalent strut width for the interior span of story 1. For column S1M I = 3.125x10 3 m 4 E=28000Mpa, E inf =3000Mpa, h inf =2.4m, t=0.14m, h=3.0m, θ =0.411rad L = =6.01m By using Eq.3, Eq.4 λh=59.3mm (2.33 in) so that the w=0.748 m Plastic hinge location distances By using Eq.5, Eq.6 θ c=0.286rad (16.4 o ) l hc =0.78m By using Eq.5, Eq.6 θ b =0.536rad (30.7 o ) l hc =1.46m References [1] A. E. Fiorato, M. A. Sozen, and W. L. Gamble, Structural Research Series No. 370, University of Illinois, Urbana, Ill, Nov. (1970). [2] R. E. Klingner and V. V. Bertero, J. Struct. Div. ASCE 104, 973 (1978). [3] V. V. Bertero and S. Brokken, J. Struct. Eng. ASCE, 109, 1337, (1983). 6

7 Seismic Response of Infilled Framed Buildings Using Pushover Analysis [4] A. Saneinejad and B. Hobbs, J. Struct. Engnrg. ASCE, 121, 634, (1995). [5] A. Madan et al., J. Struct. Eng. ASCE, 123, 1295 (1997). [6] A. Chaker and A. Cherifati, Earthquake Eng. Struc., 28, 1061 (1999). [7] F. Karadogan and E. Yuksel, European Association of Earthquake Engineering Task Group 8, Asymmetric and Irregular Structures, September 2002, Florence-Italy, (2002). [8] ATC, Seismic evaluation and retrofit of concrete buildings, Rep. ATC-40, Applied Technology Council, Redwood City, California (1996). [9] FEMA-356, Prestandard and commentary for seismic rehabilitation of buildings, Federal Emergency Management Agency, Washington (1997). [10] M. Saidii and M. Sozen, J. Struct. Div., ASCE, 107, 937 (1981). [11] P. Fajfar and M. Fischinger, Proc. 9th World Conf. Earthquake Engng., Vol. V, Tokyo, Kyoto, Maruzen, pp. 111 (1989). [12] P. Fajfar and P. Gaspersic, Earthquake Eng. Struc., 25, 23 (1996). [13] H. Krawinkler and G. D. P. K. Seneviratna, Eng. Struct., 20, 452 (1998). [14] A. J. Kappos, G. G. Penelis, and C. G. Drakopoulos, J. Struct. Eng., ASCE, 128, 890 (2002). [15] H. Lee and S. Woo, Earthquake Eng. Struc., 31, 353 (2002). [16] G. Al-Chaar, U.S. Army Engineer Research and Development Center, Construction Engineering Research Laboratory (ERDC/CERL) TR-02-1/ADA407072, January (2002). [17] R. J. Mainstone, Proceedings of the Institution of Civil Engineers, Supplement IV, pp 57 (1971). [18] 1998 Turkish Earthquake Code. [19] E.L. Wilson and A. Habibullah, Structural analysis program: SAP2000, Computers and Structures Inc., California, (2002). 7