PERFORMANCE STUDY OF RETROFITTED GRAVITY LOAD DESIGNED WALL FRAME STRUCTURES (SC-140) *A. Ahmed 1, K. H. Tan 1 1 Department of Civil and Environmental Engineering National University of Singapore, Singapore, Singapore ceeaziza@nus.edu.sg ABSTRACT Buildings designed primarily for gravity loads are prone to shear failures in walls, columns and beams when subjected to far field effects of earthquakes. Previously, pushover analyses carried out on these buildings were terminated when a local shear capacity was reached. However, in a recent study by considering shear yielding, ductile shear hinges were used to model the ultimate seismic behaviour of such buildings. This study suggested that for some cases, high-rise buildings in Singapore may incur some shear damage at the performance point. Also, experimental studies on typical components such as shear walls, wide columns and T-beam-wide-column-joints have suggested that FRP retrofit can be used to improve the seismic behaviour of such components. Based on these studies, macro-models are proposed to simulate the FRP retrofitted shear walls, wide columns and T-beam-wide-column joints. Using these models, the performance of the FRP retrofitted structures was studied against the seismic demand due to long distant earthquakes affecting Singapore using a previously proposed damage index for this type of buildings. Keywords: Concrete structure, damage index, ductile shear hinge, FRP retrofit, macro model, pushover analysis. 1. INTRODUCTION Since Singapore is located on a stable part of the Eurasian Plate, with the nearest earthquake fault 400km away in Sumatra, buildings in Singapore are gravity-load designed (GLD) structures designed according to BS8110 [1] which does not have any seismic provision. However, they are occasionally subjected to tremors due to the far-field effects of earthquakes in Sumatra [2]. The research on seismic performance including capacity of GLD reinforced concrete structures has been carried out in Singapore context [2, 3]. A macroscopic model for capacity evaluation of shear wall-frame structures was presented in Balendra et al. [2]; pushover analysis was terminated at the onset of shear failure at the base of the shear wall. Next, Tan et al. [4] focused on ductile shear failure and used nonlinear hinges available in SAP2000 software to model the post elastic shear behavior in columns and walls. This allowed the analysis to go beyond the initial shear yielding and simulate the global shear failure. However, shear yielding was detected near the base of the shear walls at the performance point. On the other hand, some researches on FRP retrofitting for GLD structures in Singapore have been carried out [3, 5-7]. Kong [3] and Li [5] focused on FRP retrofitting to address shear failure of shear wall structures, and Bhowmik [6] applied FRP retrofit to address shear and flexural failure of wide columns. Furthermore, Ahmed [7] studied the seismic behavior of the T-beam-wide-column joints and the effectiveness of FRP retrofit on such joints. In this current study, macro models in the form of nonlinear hinges are developed for retrofitted columns, shear walls and joints based on previous experiments and utilized in SAP2000 to realistically model and compare the performance of retrofitted buildings. A robust FRP scheme is applied on the buildings which involved the retrofitting of shear walls, wide columns and T-beam-wide-column joints. A damage index [7] is used to estimate the effectiveness of proposed FRP retrofit methods in improving the performance of such structures by comparing against the seismic demand curve of a critical soil site for an earthquake of M W = 9.5 at 600 km from Singapore. 2. MODELING OF STRUCTURE 2.1. Building under Study and Simplified Model Layout A typical 25-story building with plan view shown in Figure 1 is considered. The plan dimension of the building is 25 m by 20 m and the total height is 65 m (each story of height being 2.6 m). Slab thickness is 100 mm and the typical dimensions of beams and columns are 230 mm x 450 mm and 300 mm x 1200 mm, respectively. The structure comprises of moment resisting frames, two I-shaped shear walls located in the center and four L-shaped shear walls located at corners. There is no masonry infill present at the ground storey.
The building has been designed according to BS8110 [1], with no seismic provisions. High yield deformed bars (yield strength 460 MPa) were used as longitudinal reinforcement and low yield smooth bars (yield strength 250 MPa) were used as transverse reinforcement for all the components. The cube compressive strength of concrete was taken as 25 MPa. The unfactored dead loads (DL) calculated for the typical floors and the roof floor were 4.6 kn/m 2 and 3.6 kn/m 2, respectively. Unfactored live load (LL) was taken as 1.5 kn/m 2, and the load combination of 1.0 DL + 0.4 LL was used. Details regarding the basic modeling were presented by Tan et al. [4]. (a) Plan view (b) SAP2000 model Figure 1: Typical 25-storey building (a) Non-retrofitted (b) Retrofitted Figure 2: Locations of nonlinear hinges in beams, columns and braces 2.2. Modeling of Nonlinear Hinges Five types of nonlinear hinges were used in modeling this building. The orientations of the hinges can be found in SAP2000 manual [8]. Locations of theses hinges on non-retrofitted and retrofitted frame are presented in Figure 2a and 2b respectively. P-M2-M3 hinge simulates nonlinear behavior of a column under axial load and biaxial moment and are located at each end of the column. Shear hinges V2 and V3 were used simultaneously in each column to model the shear failure mechanism in two orthogonal directions and located at 0.4L and 0.6L of the columns. For beams, only V2 hinge was used at each end of the beam. Axial hinge P was used in masonry struts to simulate the post compressive failure behavior. M3 hinge was used to simulate the nonlinear flexural behavior of the beam. This approach is based on the fact that moment is highest at the ends of the column and shear force is constant throughout the length of the column. Of these five nonlinear hinges, P-M2-M3 hinges were automatically modeled by SAP2000 using the yield moment and ultimate rotation capacity for non-conforming components as per FEMA-356 [9] Tables 6-7, the flexural hinges P-M2-M3 for column is defined as in Figures 3d. 2.3. Flexural Hinge on Beams (M3) In Singapore, in particular, columns in residential buildings often have a cross-section with a large aspect ratio. As a result, beam-column joints are typically in the form of a T-beam wide column joint. Ahmed [7]
examined the lateral load capacity of such T-beam-wide column joints. Both interior and exterior joints with and without FRP retrofit were tested. (a) Shear hinge for shear wall (b) Shear hinge for columns (c) Axial hinge in braces (d) Flexural hinge in column (e) Flexural hinge in beam: M3 Figure 3: Constitutive relations of nonlinear hinges (non-retrofitted structure) Tests on T-beam-wide-column-joints demonstrated that the joint core incurred minimal damage and the joints displayed very limited ductility after yielding of beam. Thus the complete joint core is considered as rigid and modeled by means of rigid end offsets measuring half column and beam depth from the centerline. Flexural hinges (M3) are inserted at the offset location to simulate the nonlinear beam behavior. Flexural capacities of the tested beams were found to be close to the values obtained from sectional analysis as detailed by Ahmed [7]. So, the yield moment of the hinge is based on sectional analysis and rotational capacity is based on tests and the resultant M3 hinge is presented in Figure 3e. Again, the tests detailed in Ahmed [7] demonstrate that although the yield curvature remained similar to the non-retrofitted joints for the retrofitted joints, the ultimate flexural capacity increased by about 40%. Hence an enhancement factor β ( 1.40) was used to simulate the enhanced retrofit system presented by Ahmed [7]. 2.4. Shear Hinge Shear walls and wide columns are likely to fail in shear with a certain degree of ductility, especially with flexural yielding of the longitudinal reinforcement [4, 7]. Considering these facts and based on experimental data [7], models for ductile shear hinges (that is, displacement-controlled hinges) were proposed [4, 7]. The constitutive relation for the shear behavior of the shear walls without flexural yielding was modeled as a bilinear relationship with yield shear strain of 0.0015 and ultimate shear strain of 0.0023 as shown in Figure 3a. Also, based on tests on three wide columns similar to those in the building considered, an idealized shear stress-shear strain curve was proposed as shown in Figure 3b. That is, a yield shear strain of 0.003, ultimate shear strain of 0.0075 and a post elastic strength of 14% were assumed. The shear strain at initial flexural yield (γ y ) was calculated as [4]: γ y = 2M y LGA V where, M y = column moment at yielding of the longitudinal reinforcement, L is the length of column, G = shear modulus, E = Young s modulus, and A V = 5/6 A G is the shear area of the column cross section. For both shear wall and wide column, the elastic shear strength of each member ( V) is calculated according to Equation 2, based on ACI 318 [10]: N V = V c + V s = (1 + u ) ( f c ) b 14A g 6 wd + A vf y d s where, V c = contribution from concrete, V s = contribution from transverse steel, Nu = axial compression force; Ag = area of the cross section; f c = cylinder compressive strength of concrete, in MPa; b w = width of the web; Av = area of horizontal shear reinforcement at a vertical spacing s; d = effective depth, taken as (1) (2)
Base shear, kn 5h/6; h being the dimension of member in direction of loading, and f y = yield strength of steel. Also, the ultimate shear strength u is taken equal to V/Av. Retrofitted shear walls were tested by Kong [3] and Li [5]. They showed that the retrofitted shear wall also failed in shear. The effect of confinement was found to be negligible [5]. Thus the effect of confinement is not accounted for in calculating the flexural capacity of shear walls. The enhancement in shear strength was due to the increase in shear capacity due to the contribution of FRP which can be calculated following the formula proposed by ACI committee 440 [11] V f = E f ε f ρ f ( 5 6 h) t where, Ef = Young s modulus of fibre (69 GPa for GFRP and 240 GPa for CFRP), ρf = FRP shear reinforcement ratio is 2tf/t for continuously bonded shear reinforcement of thickness tf, εf = effective FRP strain at failure which is 0.0025 for GFRP [3] and 0.004 for CFRP [7], t = thickness of retrofitted section and h = height of the retrofitted section. The shear yield strength for the shear hinge simulating retrofitted shear wall is calculated by adding Equations (1) and (3). The shear strain is kept the same as non-retrofitted wall to be conservative. Bhowmik [6] presented the lateral load-deflection relationship of the wide column with and without FRP retrofit. FRP wrap prevented the column from failing in shear; however, flexural capacity did not increase significantly. The retrofitted wide column is modeled using a force controlled shear hinge where shear strength follows the same procedure as for shear wall. 2.5. Axial Hinge The stress strain curve shown in Figure 3c is used to model the nonlinear behavior of the axial hinge as described by Ahmed [7]. 250 (3) 200 150 Top displacement, mm (a) Plan view and dimensions (b) Comparison between test and SAP2000 results Figure 4: Shear wall tested by Kong [3] 2.6. Definition of Performance States Various performance states are defined on the proposed non-linear hinges. Here yielding of the member is denoted as the starting point. Individual performance state of each member has been divided as Immediate Occupancy (IO), Life Safety (LS), Collapse Prevention (CP) and Collapse (C). The IO, LS and CP states correspond to 30%, 60%, 80% and 100% of ultimate plastic rotation and plastic shear strain respectively following the general practice by FEMA-356 [9]. Details can be found in Ahmed [7] 2.7. Verification of Nonlinear Hinges Verification studies were performed to justify the accuracy of shear hinges in columns. Scaled models of a shear wall, which were tested under pushover loading by Kong [3] was considered. The dimensions are shown in Figure 4a. Pushover analysis was carried out as per the test. Figure 4b shows that result from SAP2000 compare very well with experimental results. Again, the same procedure was followed to verify the shear hinges proposed for retrofitted shear walls. Figure 4b shows the effect of the proposed shear hinge for retrofitted shear walls. The model is able to predict the base shear capacity of the shear wall; however it underestimates the top displacement capacity as expected. Verification studies on columns and beam column joints modeled using SAP2000 were also performed and have been detailed by Ahmed [7] 100 50 0 SAP2000 (Non-retrofitted) retrofitted) Test Shear (Non-retrofitted) wall Test [3] (Kong 2004) Test Retrofitted (Retrofitted) Shear [3] Wall (Kong 2004) SAP2000 (Retrofitted) (Retrofitted) 0 2 4 6 8
Damage index Spectral acceleration, Sa, g 3. APPLIED RETROFIT SCHEME Kong [3] and Li [5] studied retrofit scheme for typical shear walls in Singapore. Bhowmik [6] studied retrofitting of wide columns and retrofit scheme for T-beam-wide-column joint was studied by Ahmed [7]. The robust retrofit scheme applied in this study involves retrofitting of all three vulnerable components i.e. shear wall, wide column and T-beam-wide-column joints while keeping their proportion identical to the reference studies. (a) Retrofitted 25 storey frame (b) Retrofitted 25 storey shear wall Retrofitted first three storey Retrofitted bottom storey Figure 5: Constitutive relations of nonlinear hinges (retrofitted structure) For shear wall, Kong [3] and Li [5] applied one layer of GFRP (Glass Fibre Reinforced Polymer) sheet on a 2.6 storey 1/5 th scaled model. In this study the retrofit is applied on shear walls up to 3 rd storey and the contribution of FRP to the shear strength is calculated using a thickness five times the applied GFRP to account for scale effect. The proposed retrofit scheme for shear walls can be visualized as Figure 5a. Next, retrofit scheme is imposed on wide columns. Only the columns in ground storey are retrofitted. Based on the study by Bhowmik [6], only one layer of CFRP is used to wrap the columns to prevent shear failure. Again, the CFRP layer thickness was doubled while calculating the shear strength contribution of CFRP wrap to account for scale effect. Figure 5b presents the retrofit scheme for wide columns. Finally, a retrofit scheme is applied on the T-beam-wide-column-joints based on Ahmed [7]. In full scale model the proposed scheme is equivalent to a 0.44 mm CFRP layer applied trough out the length of the beam and another layer of same thickness terminated about 0.2 l (l = centre-centre distance of the columns) from the contra-flexure point of the beam. Figure 5b presents the retrofit scheme for T-beamwide-column joints. 0.4 0.35 0.3 0.25 0.2 0.15 0.1 0.05 10 0.8 0.6 0.4 Demand Mw 9.5 Capacity non retrofitted Capacity retrofitted Damage Index 1st Storey retrofitted Damage index 1st storey non retrofitted 0.2 0 0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 Spectral displacement, Sd, m Figure 6: Performance comparison of the structure (before and after retrofitting)
4. PERFORMANCE OF THE STRUCTURE Ahmed [7] proposed a new damage index which appropriately takes into account the contribution of shear wall, column and beam as well as non-structural elements i.e. masonry infills. This damage index considers the shear failure in addition to the flexural failure of the elements. Furthermore, the role of frame and wall in a structure in providing the overall stability of the structure is taken into consideration in the proposed damage index. Thus the procedure described by Ahmed [7] is used in this study. To obtain the capacity curve of the structure, nonlinear pushover analysis was carried out following the procedure applied by previous researchers [4, 7]. Figure 6 superimposes the demand curve of a critical soil site for an earthquake of M W = 9.5 at 600 km from Singapore on the capacity curves obtained for both non-retrofitted and non-retrofitted structures while being loaded along Y direction. This is because, this direction was found to be critical in previous studies [4, 5]. Additionally, the lower portion of Figure 6 plots the damage indices at the first storey against spectral displacement for both cases. The ultimate lateral load capacity of the retrofitted structure increases from 28% of self weight to 35% of self weight. The spectral displacement at global failure increases slightly from 164 mm to 170 mm. Both structures possess sufficient capacity to withstand the worst case scenario earthquake. However, at performance point, for the non-retrofitted structure the damage propagated up to 5 th storey [7]. While for the retrofitted structure no damage was observed. The damage index for the non- retrofitted structure is 6.3% and 0% for the retrofitted structure. Thus the performance state of the non-retrofitted structure is IO and retrofitted structure is undamaged (indicating that it will not experience yielding at the performance point). However, minor non-structural damage is expected. Although, near the ultimate capacity, the damage indices for retrofitted and non-retrofitted structure become similar, indicating a soft storey failure mechanism, which the proposed retrofit scheme, was not able to prevent. 5. CONCLUSION The proposed FEA model, which incorporates macro models to simulate retrofitted shear walls, wide columns and T-beam-wide-column joints, along with previously proposed damage index is a reliable and elegant tool to determine the seismic performance of full-scale retrofitted buildings. Using this model, the seismic performance of a typical GLD shear wall-frame building was evaluated for an earthquake scenario of M W = 9.5 at 600 km from Singapore on a critical soil site, before and after retrofitting. The proposed retrofit was able to delay the initiation of damage resulting in no structural damage at performance point due to this expected worst possible earthquake case scenario for Singapore. 6. REFERENCES [1] BS8110, (1985). Structural Use of Concrete: Parts 1, 2 and 3, British Standards Institution, UK. [2] Balendra, T., Li, Z. J., Tan, K. H., and Koh, C. G. (2007). Vulnerability of Buildings to Long Distance Earthquakes from Sumatra. J. Earthquake and Tsunami 1(1), 71-85. [3] Kong, K. H., 2004. Overstrength and Ductility of Reinforced Concrete Shear-Wall Frame Buildings Not Designed for Seismic Loads. Ph.D. Thesis, National University of Singapore, Singapore. [4] Tan, K.H., Balendra, T. and Ahmed, A. (2012). Seismic Vulnerability of Gravity-Load Designed Buildings, Invited Paper, 11 th International Symposium on New Technologies for Urban Safety of Mega-Cities in Asia, Ulaanbaatar, Mongolia. [5] Li, Z. (2006). Seismic Vulnerability of RC Frame and Shear Wall Structures in Singapore. Ph.D. Thesis, National University of Singapore, Singapore. [6] Bhowmik, T. (2011). FRP-confined capsule-shaped columns under axial and lateral loading. Ph.D. Thesis. National University of Singapore, Singapore. [7] Ahmed, A. (2012). Seismic Vulnerability and Retrofitting of Gravity Load Designed RC Buildings. Ph.D. Thesis. National University of Singapore, Singapore. [8] SAP 2000, (2009). CSI Analysis Reference Manual. Computers and Structures, Inc, Berkeley, California. [9] FEMA356, (2000). Prestandard and Commentary for the Seismic Rehabilitation of Buildings. Federal Emergency Management Agency, Washington, D.C. [10] ACI318, (2011). Building Code Requirements for Structural Concrete and Commentary. American Concrete Institute, Farmington Hills, Michigan, USA [11] ACI Committee 440 code (2002). Guide for the design and construction of externally bonded FRP systems for strengthening concrete structures, Detroit.