THE DEGREE OF ACCURACY OF MODAL PUSHOVER ANALYSIS ON DUAL SYSTEM STRUCTURE INCORPORATING SHEAR WALL INELASTICITY

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1 10NCEE Tenth U.S. National Conference on Earthquake Engineering Frontiers of Earthquake Engineering July 21-25, 2014 Anchorage, Alaska THE DEGREE OF ACCURACY OF MODAL PUSHOVER ANALYSIS ON DUAL SYSTEM STRUCTURE INCORPORATING SHEAR WALL INELASTICITY B. Budiono 1 and A.A. Suselo 2 ABSTRACT Modal pushover analysis procedure is applied on 10 floor reinforced concrete space structure (medium-rise building) with dual system (shear wall on building s parameter) as lateral resisting system. Structure design is based on Indonesian earthquake resistant building code namely SNI 1726:2012 and element detail design is based on RSNI3. Shear wall inelasticity is represented in concentrated hinge and distributed (fiber) inelasticity. Shear wall element, which dominates 60% structure s elastic stiffness, also contributes to overall structure s inelastic stiffness significantly. Lateral dominated structures undergo 50-60% average stiffness degradation in hinge model relative to fiber model; whereas torsion dominated structures undergo 70% stiffness degradation. The degree of accuracy for modal pushover analysis result compared to non linear time history analysis is determined for symmetric-plan, U1 (torsionally stiff), U2 (torsionally similarly stiff), and U3 (torsionally flexible) with fiber element model (100%DL). Error given by the modal pushover analysis is within ± 30% in displacement, ± 60% in story drift, and ± 10% in bending moment using CQC modal combination rule. Anomaly behavior is detected in U2 structure which has coupled modal characteristic. For design purpose, this anomaly can be estimated with ABSSUM modal combination rule (error ± 15%). Keywords: Fiber Element Model, 3D Structure, Modal Pushover Analysis, The Degree of Accuracy for Regular-Plan Structure & Irregular-Plan Structure (U1, U2, U3) 1 Professor, Dept. of Civil Engineering, Institute of Technology Bandung, Bandung, Indonesia Graduate Student Researcher, Institute of Technology Bandung, Bandung, Indonesia B. Budiono, A.A. Suselo. The Degree of Accuracy of Modal Pushover Analysis on Dual System Structure Incorporating Shear Wall Inelasticity. Proceedings of the 10 th National Conference in Earthquake Engineering, Earthquake Engineering Research Institute, Anchorage, AK, 2014.

2 The Degree of Accuracy of Modal Pushover Analysis on Dual System Structure Incorporating Shear Wall Inelasticity B. Budiono 1 and A.A. Suselo 2 ABSTRACT Modal pushover analysis procedure is applied on 10 floor reinforced concrete space structure (medium-rise building) with dual system (shear wall on building s parameter) as lateral resisting system. Structure design is based on Indonesian earthquake resistant building code namely SNI 1726:2012 and element detail design is based on RSNI3. Shear wall inelasticity is represented in concentrated hinge and distributed (fiber) inelasticity. Shear wall element, which dominates 60% structure s elastic stiffness, also contributes to overall structure s inelastic stiffness significantly. Lateral dominated structures undergo 50-60% average stiffness degradation in hinge model relative to fiber model; whereas torsion dominated structures undergo 70% stiffness degradation. The degree of accuracy for modal pushover analysis result compared to non linear time history analysis is determined for symmetric-plan, U1 (torsionally stiff), U2 (torsionally similarly stiff), and U3 (torsionally flexible) with fiber element model (100%DL). Error given by the modal pushover analysis is within ± 30% in displacement, ± 60% in story drift, and ± 10% in bending moment using CQC modal combination rule. Anomaly behavior is detected in U2 structure which has coupled modal characteristic. For design purpose, this anomaly can be estimated with ABSSUM modal combination rule (error ± 15%). Keywords: Fiber Element Model, 3D Structure, Modal Pushover Analysis, The Degree Of Accuracy For Regular-Plan Structure & Irregular-Plan Structure (U1, U2, U3). Introduction Indonesian archipelagos are mostly located at the intersection of tectonic plate (Indo- Australian & Pacific Plate). This geographical condition requires its human resources to understand the (inelastic) behavior of infrastructure, especially building, under strong earthquake. Non linear analysis and performance-based design has been developed (and still under continuous research) as a tool to modeling structural (inelastic) behavior under earthquake ground motions. Modal Pushover (static) Analysis (MPA) procedure [1] simplifies dynamic time history analysis with characterizes its analysis through building s modal properties. Further improvement for MPA procedure is presented with P-Δ effect [2], unsymmetric-plan structure [3], and extension to compute member forces [4]. This modified MPA procedure may be useful 1 Professor, Dept. of Civil Engineering, Institute of Technology Bandung, Bandung, Indonesia Graduate Student Researcher, Institute of Technology Bandung, Bandung, Indonesia B. Budiono, A.A. Suselo. The Degree of Accuracy of Modal Pushover Analysis on Dual System Structure Incorporating Shear Wall Inelasticity. Proceedings of the 10 th National Conference in Earthquake Engineering, Earthquake Engineering Research Institute, Anchorage, AK, 2014.

3 to estimate building s responses in which dominated by higher mode [4]. Fiber element model was introduced in 2010 [6]. This model divides structural section into concrete and steel fibers. Each fiber could develop its inelasticity through its material level behavior. Fiber element is mainly used for modeling shear wall as 4-node (in plane) panel with 8 degree of freedom (Perform 3D [7] element). This study will focus on the accuracy of MPA (static) procedure to dynamic time history analysis. Each of procedure will be applied on 10 floor RC space structure which could develop inelastic behavior, especially on shear wall, through distributed (fibers) and concentrated (hinges) inelasticity. Structural System Description Structural Design Properties Hypothetical office building is designed to have dual system (RC shear wall & open frame) as lateral-gravity resisting structure. Overall structure has 10 typical (25 x 35 m) floor with total height (30 m). Planar shear wall is located at building perimeter (0/C-D, 7/C-D, A/3-4, F/3-4) as shown in Fig. 1 (left). Figure 1. Typical floor framing plan (left), typical framing elevation at axis A and F (right). Gravity & Earthquake Load Demand Gravity load is adapted from building function as office building. Dead loads consist of self weight, super imposed (architectural load), mechanical, and electrical. Live load (include room furnishing and light partition walls) is defined at 250 kg/m 2 for first-ninth floors and 100 kg/m 2 for tenth (roof) floor. Building mass (W) source for dynamic (earthquake) analysis consists of combination from 1.0 dead load live load and is estimated at 84,091 kn (8,409 ton). Earthquake demand is adapted from Indonesian local code [8] which is in accordance with FEMA P-750 (2009), IBC 2009, and ASCE/SEI Importance factor is taken at 1.0 (office building) and reduction factor 7.0 (special RC shear wall and frame resisting system). Earthquake demand is assumed for Jakarta with medium soil condition. PGA is estimated

4 at 0.36 g with MCER (T: 0.2 s) at 0.63 g and MCER (T: 1 s) at 0.28 g. Maximum considered earthquake-mce (2,475 years) is estimated: S MS = 0.81 g, S M1 = 0.51 g, S M0 = 0.21 g. Design earthquake spectrum (475 years) is estimated at two-third from MCE. Static and Dynamic Analysis for Earthquake Demand Static (equivalent) and dynamic (response spectrum) analysis procedure is based on Indonesian local code [8]. Both analyses include accidental eccentricity and torsion 5% on building dimension perpendicular to earthquake forces. Static analysis requires design base shear 4,631 kn (0.055W), whereas dynamic analysis only produces 2,134 kn (0.025W). In this case, dynamic analysis will be used for ultimate load combination (gravity & earthquake), but with scale factor (1.84) which requires dynamic analysis to have design base shear no less than 85% static base shear (0.047W). Ultimate load combinations (gravity & earthquake) are checked against each element stress capacity and code-permitted story drift (2% story height). Furthermore, P-Δ effect is insignificant because stability coefficient in each story is less than 0.1. In this case, P-Δ effect is automatically considered in analysis software. Element Detailing Design Longitudinal and transversal rebar area for flexural component (beams) and axial-flexural component (columns and shear walls) could be automatically calculated from available software based on ultimate load combinations. Detailing process, which include rounding-off design rebar area into actual rebar area (diameter) and detailing checking (shear capacity design, beam-column joint shear ratio, strong column-weak beam, etc.) is conducted manually based on Chapter 21 Indonesian local code [9] which in accordance with ACI 318M-11. Horizontal Irregularities Irregular-plan structures are obtained from regular/symmetric-plan structure with additional eccentricities from structural centre of rigidity (CR) to floor s centre of mass (CM). This modification represents un-balanced loads in each floor. Irregularities in this study are defined from Chopra, et al [3], which use both lateral and torsion dominant modes to represent coupling behavior between them. Torsionally stiff structure (U1) is obtained at 7% eccentricities at the longest plan width (35 m), which has 69.8% lateral mode & 46.8% torsion mode. Torsionally similarly stiff (U2) is obtained at 36% eccentricities, which has 60.8% lateral mode & 60.9% torsion mode. Torsionally flexible (U3) is obtained at 36% eccentricities and additional 4 times rotational inertia mass in each floor, which has 30.1% lateral mode & 60.2% torsion mode. Element Modeling & Acceptance Criteria Beam & column element is modeled as quasi-static element, which only could develop its inelastic behavior on both hinge length at end of element. In other hand, (shear) wall is modeled by both beam-column element and fiber model. In this case, beam-column model is similar with quasi-static element, whereas fiber model could develop its inelastic behavior through each of its

5 panel partition. Hinges and Fibers Model Force-deformation (F-D) relation is used to define each hinge behavior (at different element s end) of beam & column model. Backbone (F-D) curves for beam & column element are derived from couple reference: empirical (experimental data) value from Chapter 3 ATC-72 [6], section finite element (FE) with Response-2000 [10], and code-based value from FEMA-356 [11]. In beam hinges model, empirical estimation seems to be in accordance with FE analysis in counter-clockwise moment, whereas code-based estimation rather under-estimates FE analysis. In clockwise moment, code-based estimation is preferable. Therefore, beam hinge models use empirical value for counter-clockwise moment and code-based value in clockwise moment. Column hinge model is derived from interaction between nominal working axial forces (P) with biaxial moment capacity (M-M). Hinge with P-MM interaction needs yield surface interaction to define yielding and post-yielding occurrences. The P-M and M-M yield surface is based on Perform-3D plasticity theory equation (Eq. 2.1 & Eq. 2.2 on Chapter 2 [7]). Empirical estimation, section FE, and code-based value are also conducted to verify the results. (Shear) Wall fiber model is based from Perform-3D shear wall element model on Chapter 9 [7]. This element uses both inelastic behavior from its material (concrete and rebar steel). Each element has 4 nodal and 24 degrees of freedom, which only 8 DOFs are incorporated with element in plane important deformations (stiffness). This element doesn t have rotational stiffness, so imbedded beams are needed to transfer rotational deformations (moments) from structural beams or coupling beams connected to it. Therefore, Perform-3D shear element model could be in accordance to rectangular plate element with plane stress distribution (practical application for wall with relatively small thickness compared to its length and height). Acceptance Criteria Acceptance criteria for hinges are defined mainly from FEMA-356 [11] and ATC-72 [6]. ATC-72 only defines Service and MCE criteria, while FEMA-356 defines acceptance criteria as Immediate Occupancy (IO), Life Safety (LS), and Collapse Prevention (CP). ATC-72, which is the newer code, almost has larger acceptance criteria for MCE rather than CP (FEMA) criteria. But in other hand, ATC has more strict criteria for Service rather than IO (FEMA). Fibers acceptance criteria are determined from its material strain-stress relationship. These limitations are based on material standard specification, experimental test, or field adaptation. Code-based limitations for material strain [12] define for unconfined concrete compression strain and for other conditions. Strain limitations for rebar steel are defined at 0.02 (compression) and 0.05 (tension). These values are believed to be maximum strain considered for each material (without over-strength consideration). Therefore, acceptance criteria for Service condition (assumed to be still in elastic region) are considered to be half from maximum condition for concrete and 4% for rebar tension capacity.

6 Results Lateral Stiffness Degradation (Beam-Column & Fiber Element Model) Shear wall inelastic behavior is represented as hinges (beam-column element) and fibers. In this case, shear wall hinges are modeled with SAP v.15 whereas fibers are modeled with Perform-3D v.5. Fig. 2 (left) shows space structural model for beam-column model and (right) fiber model. Figure 2. Space structure with beam-column element (left) and fiber element to represent shear wall inelasticity (right). Lateral stiffness degradation is calculated from first mode pushover analysis for both models. Each step in pushover analysis represents inelastic occurrence for both hinges and fibers (beam, column, or shear wall). Thus, overall post-yield strength for fiber element is greater than beam-column model, especially on torsion dominated structure. This condition is represented as lateral stiffness degradation. First 3-modes dynamic properties for each model are shown in Table 1. Table 1. Structure first 3-modes dynamic properties for SAP and Perform-3D symmetric models. Modes Period (s) Modal Mass Participation Factor (%) Perform-3D SAP* Vibration Direction Y-dir X-dir Torsion** *The elastic period (stiffness) which is slightly different for SAP model is mainly caused by beam insertion point **Torsion direction MMPF information could not provided by Perform-3D

7 In this study, direction interest is chosen at the weaker/more flexible mode (Y-dir). In symmetric structure, elastic shear wall section has to resist about 61.4% design earthquake base shear in Y-direction. Each other structure (U1, U2, and U3) resist the same value at elastic condition. After first yielding occurs at shear wall element, the shear capacity for hinges model are greatly reduced, because of limited inelastic capacity provided by hinges relative to fibers. These conditions are shown in Fig. 3. Reduction ratios are relatively compared to fiber models. Symmetric Reduction for: Max. Shear capacity = 13% Av. Inelastic stiffness = 54% U2 Reduction for: Max. Shear capacity = 30% Av. Inelastic stiffness = 51% Figure 3. U1 Reduction for: Max. Shear capacity = 10% Av. Inelastic stiffness = 60% U3 Reduction for: Max. Shear capacity = 51% Av. Inelastic stiffness = 69% Lateral stiffness degradation curve for symmetric structure (top left), U1 (top right), U2 (bottom left), and U3 (bottom right). These curves show that building mass eccentricities (torsion) in structure with perimeter shear wall will cause its capacity and stiffness significantly reduced (hinges relatively to fiber). This condition is probably caused by perimeter shear wall in torsion dominated structure undergoes severe damage (flexural) so the hinges reach its maximum rotation before it could redistribute forces to frames. In this case, fiber element is recommended to be used, especially for torsion dominated structure, for further modal pushover and time history analysis. Modal Pushover & Time History Analysis Modal pushover is applied to both symmetric and unsymmetrical structures (U1, U2, & U3). Differential equation which represents multi-story building to horizontal earthquake, u

8 excitation is shown below. mu cu f u, sign u m u t (1) Where u, u, and u correspond to structural lateral displacement, velocity, and acceleration. Lateral force, f s at n th floor depends on lateral displacement history. Spatial distribution for effective force at floor s height is defined by vector s = ml and earthquake history u t. Complete MPA procedure is provided in original paper [1] by Chopra, et al. Peak/maximum responses given by pushover analysis for each characterized (SDF) structure should be modally combined to obtain total structure responses. In this study, modal combination CQC and ABSSUM is used to compare total responses obtained by MPA. SRSS is proven to have typical value with CQC combination rule at well-separated frequencies and has poor estimation for coupled/close-spaced frequencies. One (1) scaled earthquake history excitation is used for time history analysis. El-Centro 1940 N-S direction with 1.3 scale factor is used as benchmark to compare MPA responses results to exact responses from dynamic analysis. The Degree of Accuracy of MPA The degree of accuracy of MPA is determined for structural level (story deflections and drifts) and member/element level (flexural forces) with additional procedures [4] suggested by Chopra, et al. Fig. 4-6 show MPA accuracy in each story (with upper-lower bound error suggested by this study). Beams frame 5/C-D is chosen for MPA accuracy on member/element level. Structural Level Symmetric U1 Figure 4a. MPA accuracy on story deflection for symmetric (left) and U1 (right) structure.

9 U3 U2 Figure 4b. MPA accuracy on story deflection for U2 (left) and U3 (right) structure. Figure 5. Symmetric U1 U2 U3 MPA accuracy on story drift for symmetric (top left), U1 (top right), U2 (bottom left) and U3 (bottom right) structure.

10 Member/Element Level Figure 6. Symmetric U1 U2 U3 MPA accuracy on story drift for symmetric (top left), U1 (top right), U2 (bottom left) and U3 (bottom right) structure. Conclusions Fiber element model is proven to have better inelastic behavior than hinges and also contributes to overall structure stiffness degradation. This study recommends the use of fiber element for shear wall structure, especially for non linear analysis. MPA accuracy in this study is proven to have moderate error (up to 30%) on story deflection, large error (up to 60%) on story drift, small error (up to 10%) on beam flexural force. This error decreases simultaneously with additional plan-eccentricity on structure. However, this condition also means that structure lateral movement begins to be replaced with rotational movement. In this case, shear and torsion behavior is assumed to be elastic, so this phenomenon is needed to be added as design consideration, especially on torsion-dominated structure. Coupled behavior on U2 (torsionally similarly stiff) structure is against the principle of MPA theory. MPA require each modal to be well-separated in order to get each mode s characterized behavior and combined by modal combination rules. In this case, CQC rule couldn t give

11 structural response for this coupled condition. In other hand, ABSSUM rule, which usually give over-estimated response, could give reasonable responses because it gives absolute value (not considering response s vector). This study is only conducted in medium-rise building (10 floors), which has about 70% modal mass participation factor on its first mode. This means that there is no significant difference in lower story drift compared to upper story, which usually observed in high-rise buildings. Acknowledgement This study is partially funded by IMHERE Project B.2C FTSL-ITB RGR Program Contribution of Research Outcomes to Courses. This financial support is greatly acknowledged, especially on purchasing the Perform-3D software. CSI Perform-3D v.5 S/N: C1FB FBY21526JER licensed to Prof. Bambang Budiono (ITB). References 1. Chopra AK, Goel RK. A Modal Pushover Analysis Procedure for Estimating Seismic Demands for Buildings. Earthquake Eng. Struct. Dyn. 2002; 31 (3): Goel RK, Chopra AK. Evaluation of Modal and FEMA Pushover analyses: SAC Buildings. Earthquake Spectra 2004; 20 (1): Chopra AK, Goel RK. A Modal Pushover Analysis Procedure for Estimating Seismic Demands for Unsymmetric-Plan Buildings. Earthquake Eng. Struct. Dyn. 2005; 33 (1): Goel RK, Chopra AK. Extension of Modal Pushover Analysis to Compute Member Forces. Earthquake Spectra 2005; 21 (1): Applied Technology Council (ATC-55 Project). FEMA 440 Improvement of Nonlinear Static Seismic Analysis Procedures. Federal Emergency Management Agency: Washington, Applied Technology Council, BSSC, NIBS, FEMA. PEER/ATC-72-1 Modeling and Acceptance Criteria for Seismic Design and Analysis of Tall Buildings. ATC: California, Computer and Structure Inc. (CSI). Component and Elements for Perform-3D TM and Perform-Collapse. CSI: California, Sub Panitia Teknis S4 Bahan, Sains, Struktur, dan Konstruksi Bangunan. SNI 1726:2012 Tata Cara Perencanaan Ketahanan Gempa untuk Struktur Bangunan Gedung dan Non Gedung. Badan Standardisasi Nasional: Jakarta, Sub Panitia Teknis (SPT) Bahan, Sains, Struktur, dan Konstruksi Bangunan. RSNI3 Persyaratan Beton Struktural untuk Bangunan Gedung. Badan Standardisasi Nasional: Jakarta, Bentz E, Collins MP. User Manual for Response-2000, Shell-2000, Triax-2000, Membrane University of Toronto: Toronto, American Society of Civil Engineer. FEMA 356 Prestandard and Commentary for The Seismic Rehabilitation of Buildings. Federal Emergency Management Agency: Washington, ASCE Seismic Rehabilitation of Existing Buildings. American Society of Civil Engineer: Virginia, 2006.