1

Amongst all the natural hazards, earthquakes have been the biggest potential for causing the greatest damages. Since earthquake actions are random and unpredictable, engineering com-munity need tools for the evaluation and design of structures that takes into account the action of these forces. Performance based seismic design is gaining a new dimension in the seismic design philosophy. Earthquake loads have to be carefully modelled so as to assess the real be-haviour of structures with a clear understanding that damage is expected but it should be lim-ited. In this context, pushover analysis which is an iterative procedure shall be looked upon and studied.

From the effects of significant earthquakes for the past decades it is concluded that the seismic risks in urban areas and rural areas alike are increasing. Special attention should be put on this aspect, and it can be done through: (1) the development of more reliable seismic standards and code provisions than those currently available and (2) their stringent implementation for the complete engineering of new engineering facilities. Performance-based design is aimed at con-trolling the structural damage based on precise estimations of proper response parameters. Performance-based seismic design explicitly evaluates how a building is likely to perform, given the potential hazard, considering uncertainties inherent in the quantification of potential hazard and uncertainties in assessment of the actual building response. It is an iterative process that begins with the selection of performance objectives, followed by the development of a prelimin-ary design, an assessment as to whether or not the design meets the performance objectives, and finally redesign and reassessment, if required, until the desired performance level is achieved.

In this paper, a regular RC building structure will be analysed using Pushover Analysis provi-sions of the following codes, International Building Code (IBC), National Structural Code of the Philippines (NSCP) and the EUROCODE8 (EC8). Sap2000 software package, developed by Computer and Structures International, will be used for the calculations of the building re-sponse.

The results of analysis will be compared in terms of spectral acceleration, base shear, storey shear, storey displacements and inter-storey drift.

1. Introduction

1

Performance based seismic design of reinforced concrete (RC) building structures

Jaime Landingin1, Hugo Rodrigues2, Humberto Varum3, António Arêde4, Aníbal Costa5

1,2,3,5 Department of Civil Engineering, University of Aveiro, Portugal4 Department of Civil Engineering, University of Porto, Portugal

ABSTRACT:

Inelastic static analysis is a tool for the study of structural seismic response of rein-forced concrete structures. The inelastic static pushover analysis is a simple option for estimating the strength capacity in the post-elastic range. The technique may also be used to highlight potential weak areas in the structures. This procedure involves apply-ing a predefined lateral load pattern which is distributed along the height of the build-ing. The lateral forces are then monotonically increased in constant proportion with a displacement control at the top of the building until a certain level of deformation is reached. The target top displacement may be the deformation expected in the design earthquake in case of designing a new structure, or the drift corresponding to the struc-tural collapse for the assessment purposes. The method allows tracing the sequence of yielding and failure on the member and the structural levels as well as the progress of the overall capacity curve of the structure.

The static pushover analysis procedure has been presented and developed over the past twenty years by Saiidi and Sozen [1], Fajfar and Gaspersic [2] and Bracci et al. [3], among others. The method is also described and recommended as a tool for design and assessment purposes by the National Earthquake Hazard Reduction Program ´NEHRP` (FEMA 273) [4] guidelines for the seismic rehabilitation of existing buildings. This ana-lysis procedure is selected for its applicability to performance-based seismic design ap-proaches and can be used at different levels to verify the performance targets. Finally it is clear from recent discussions in code-drafting committees in Europe that this ap-proach is likely to be implemented and recommended.

Research on the seismic performance of reinforced concrete structures designed by present codes includes several studies focused on US and European buildings. Kueht and Hueste [5] conducted a numerical investigation on the seismic performance of a four-story RC frame designed based on the 2003 International Building Code (IBC). In Europe, Fardis [6] analysed and assessed 3-storey irregular building or the SPEAR pro-ject. The SPEAR structure is a simplification of an actual three-storey building repres-entative of old constructions in European Countries, without specific provisions for earthquake resistance. Additionally, Landingin et al. [7] have conducted designed and analysis of 4-storey regular and irregular buildings according to National Structural Code of the Philippines (NSCP 2010) [10], 2009 International Building Code (2009 IBC)[9] and Eurocode 8 (EC8)[8]. Furthermore the results done by Landingin et.al proved that buildings designed using EC8 provided a safer design.

The objective of this study is to investigate the seismic performance of RC frame de-signed according to NSCP 2010 and EC8 using inelastic pushover analysis. The results are presented and compared in terms of key performance parameters, including inter-story drift, and capacity curve. The structural response is assessed to determine the overall safety of the structure under seismic demands.

2.0 Inelastic pushover methodology

3

The generalized nonlinear static analytical procedure is a key element in the methodo-logy introduced by ATC-40 for the seismic evaluation and retrofit design of existing buildings which represents a fundamental change for the structural engineering profes-sion. The methodology is performance based where the design criteria are expressed as performance objectives, which defined desired levels of seismic performance when the building is subjected to specified levels of seismic ground motion. The generalized non-linear static analytical procedure has three primary elements as shown in Figure 1. First, capacity curve of the structure using static pushover analysis, second a method to de-termine displacement demand by use of reduced demand spectra and finally the result-ing identification of the performance point and the subsequent check for acceptable per-formance.

Basically, a pushover analysis is a series of incremental static analysis carried out to de-velop a capacity curve for the building. Based on the capacity curve, a target displace-ment which is an estimate of the displacement that the design earthquake will produce on the building is determined. The extent of damage experienced by the building when subjected to design level ground shaking. Many methods were presented to apply the nonlinear static analysis procedures i.e., the capacity spectrum method [12], the dis-placement coefficient method [13] and modal pushover analysis. The approach has been developed by many researchers with variation in computation procedures.

The behaviour of reinforced concrete structures may be highly inelastic under seismic loads, the global inelastic performance of RC structures will be dominated by plastic yielding effects and consequently the accuracy of the pushover analysis will be influ-ence by the ability of the analytical models to capture these effects. Analytical model for the pushover analysis maybe divided into two main types: the distributed plasticity (plastic zones) and the concentrated plasticity (plastic hinge). Although the plastic hinge is simpler than the plastic zone, this method is limited to its incapacity to capture the more complex member behaviour that involve severe yielding under the combined actions of compression and bi-axial bending and buckling effects.

3

2.1 Key elements of the pushover analysis

Nonlinear behaviour is assumed to occur within frame elements at concentrated plastic hinges. In SAP2000 [14], the default types include an uncoupled moment hinges, an uncoupled axial hinges, and uncoupled shear hinges and a coupled axial force and biaxial bending moment hinges. Control node is the node used to monitor displacements of the structure. Its displacements versus the base shear forms the ca-pacity (pushover) curve of the structure. Developing the pushover curve includes the evaluation of the force distributions. To have a displacement similar or close to the actual displacement due to earthquake, it is important to consider a force displace-ment equivalent to the expected distribution of the inertial forces. Different forces distribution can be used to represent the earthquake load intensity. Estimation of the displacement demand is a crucial step when using the pushover analysis. The control is pushed to reach the demand displacement which represents the maximum expected displacement resulting from the earthquake intensity under consideration. Perform-ance evaluation is the main objective of the performance based design. A component or action is considered satisfactory it meets a prescribed performance. The main out-put of the pushover analysis is in terms of response demand versus capacity. If the de-mand curve intersects the capacity envelope near the elastic range, as shown in Figure 2, then the structure has a good resistance. If the demand curve intersects the capacity curve with little reserve strength and deformation capacity, as shown in Figure 2, then the structure will behave poorly during the imposed seismic excitation and the need to be retrofitted to avoid future major damage or collapse.

Figure 2.Typical seismic demand versus capacity (a) safe design; (b) unsafe design

2.2 Modelling inelastic behaviour of structural members

Building loaded beyond elastic range can be analysed with pushover analysis. The mod-elling is one of the important steps to be considered while conducting pushover ana-lysis. Appropriate model requires the determination of the nonlinear properties of each component in the structure that are quantified by strength and deformation capacities. Nonlinear static analysis procedures help in identifying the possible failure modes that the building is going to be experienced. Modelling the inelastic behaviour of the struc-tural elements for different levels of performance is an important step towards perform-ance evaluation of building. In performance based design the acceptance criteria and ca-pacity demand comparisons are expressed in terms of displacements.3.0 Description of the building

5

A 4-storey residential building is considered for the study. The plan and elevation of the building are shown in Figure 2. The 4-storey RC frame structure has a standard occu-pancy with the following site characteristics: stiff soil with a shear wave velocity of 300m/sec, the nearest seismic source is within 5 km, and the fault is capable of produ-cing a large magnitude event with high rate of seismic activity [10]. The site character-istics and seismic parameters are based on NSCP 2010. The seismic coefficients Ca = 0.53, Cv = 1.02 and 5% elastic damping were used in the SAP2000 model. The building is designed using NSCP 2010 and EC8 with their respective load combinations as shown in Table 1.

Floor Plan Elevation

Figure 3.Plan and Elevation of the 4-storey building.

Table 1.Load combinations

Case NSCP 2010 EC8

DL* 1.4DL -

DL&LL* 1.2DL + 1.6LL 1.35DL + 1.50LL

DL&EQ* 0.9DL 1.0EQX -

0.9DL 1.0EQY -

DL,LL&EQ* 1.2DL + 1.0LL 1.0EQX 1.0DL + 0.3LL 1.0EQX

1.2DL + 1.0LL 1.0EQY 1.0DL + 0.3LL 1.0EQY

- 1.0DL + 0.3LL 1.0EQX 1/3EQY

- 1.0DL + 0.3LL 1.0EQY 1/3EQX

Note* DL (Dead-Load), LL (Live-Load) and EQ (EarthQuake load in X and Y directions respectively)

5

The 4-storey RC building has a typical storey height of 3.0 m. Dead-load and live-load are and , respectively. The material properties used are:

for concrete and for reinforcement. The member sizes were: 400 mm x 400 mm (column), 250 mm x 500 mm (typical beam section), and 150 mm (slab thickness) This paper used 3D finite model of the building. The software package SAP2000, developed by Computer & Structures Inc. [11], was utilized for this purpose. Beams and columns are modelled as frame element while slab was modelled with shell element. The design of the structural concrete members follows the NSCP 2010 and EC8 load combinations.

4. Modelling the structure

The general finite element package SAP 2000 has been used for the analyses. A 3D model of each structure has been created to undertake the nonlinear static analysis. Beams and columns are modelled as nonlinear frame elements with lumped plasticity at the start and the end of each element. SAP 2000 provides default-hinge properties and recommends PMM hinges for columns and M3 hinges for beams. After designing and detailing the reinforced concrete frame structures, a nonlinear pushover analysis is car-ried out for evaluating the structural seismic response. The pushover analysis consists of the application of gravity loads and a representative lateral load pattern. The lateral loads were applied monotonically in a step-by-step nonlinear static analysis. The ap-plied lateral loads were applied in x and y directions representing the forces that would be experienced by the structures when subjected to ground shaking. Under increment-ally increasing loads some elements may yield sequentially. Consequently, at each event, the structures experiences a stiffness change as shown in Figure 4, where IO,LS and CP stand for immediate occupancy, life safety and collapse prevention respectively.

Figure 4. Load –Deformation curve

5. Results and Discussions

7

5.1 Capacity Curve5.2

References

[1] Saiidi Sozen MA. Simple nonlinear seismic analysis of R/C structures. Journal of the Structural Division, ASCE 1981;107(ST5):937-51.[2] Fajfar P, Gaspersic P. The N2 method for the seismic damage analysis of RC build-ings. Earthquake Engineering and Structural Dynamics 1996;25:31-46.[3] Bracci JM, Kunnath SK, Reinhorn AM. Seismic Performance and retrofit evaluation of reinforced concrete structures. Journal of Structural Engineering, ASCE 1997;123(1):3-10. [4] FEMA. NEHRP guidelines for the seismic rehabilitation of buildings. FEMA 273, Federal Emergency Management Agency, 1996.[5] Kueht E, Hueste MD. Impact of code requirements in the central United States: seismic per-formance assessment of a reinforced concrete buildings . ASCE Journal of Structural Engineer-ing 2009; 135(4):404-13.[6] Fardis, M.J. Design of Irregular building for the SPEAR project. Description of the 3-storey building. University of Patras, 2002.[7] Landingin, JM., Hugo, R., Varum, H., Arêde, A., Costa, A., COMPARATIVE ANALYSIS OF RC IRREGULAR BUILDINGS DESIGNED ACCORDING TO DIFFERENT SEISMIC DESIGN CODES, Paper Reference 2955, Proceedings of the 15 th International Conference on Experimental Mechanics (ICEM 15), Portugal, 2012.[8] European Standard. Eurocode 8: Design of concrete structures for earthquake resist-ance - Part 1-1: General rules and rules for buildings, Commission of the European Communities. Brussels: European Committee for Standardization; 200, pp. 229.[9] International Code Council, Inc., 2009 International Building Code. Falls Church, VA, USA: ICC Inc.; 2009, p. 303-345.[10] ASEP Inc., National Structural Code of the Philippines 2010 (C101-10) Buildings, Towers and Other Vertical Structures. Philippines: ASEP Inc.; 2010 pp. 758.[11] Computer & Structures Inc. Structural Analysis Programs, SAP2000, Computer Software Package. California: CSI Inc.; 2005.[12] Applied Technology Council, ATC-40. Seismic evaluation and retrofit of concrete buildings, Vols. 1 and 2, California, 1996.[13] Federal Emergency Management Agency, FEMA-356. Pre-standard and Commentary for Seismic Rehabilitation of Buildings, Washington DC, 2000.[14] SAP2000, Integrated finite element analysis and design of structures basic analysis refer -ence manual. Berkeley (CA, USA): Computer and Structures Inc., 2006.

7