Several two-dimensional analytical beam column joint models with varying complexities have been proposed in quantifying joint flexibility during seismic vulnerability assessment of non-ductile reinforced concrete (RC) frames. Notable models are the single component rotational spring element and the super element joint model that can effectively capture the governing inelastic mechanisms under severe ground motions. Even though both models have been extensively calibrated and verified using quasi-static test of joint sub-assemblages, a comparative study of the inelastic seismic responses under nonlinear time history analysis (NTHA) of RC frames has not been thoroughly evaluated. This study employs three hypothetical case study RC frames subjected to increasing ground motion intensities to study their inherent variations. Secondly, the issue of super-element joint models, causing numerical divergence in non-linear time history analysis of reinforced concrete frames, is investigated. The rigid joint assumption and a single rotational spring model are implemented for comparison. Reinforced concrete joint sub-assemblages and a one-third scaled frame have been employed for model validation. Results indicate that the super element joint model overestimates the transient drift ratio at the first storey and becomes highly un-conservative by under-predicting the drift ratios at the roof level when compared to the single-component model and the conventional rigid joint assumption. In addition, between these storey levels, a decline in the drift ratios is observed as the storey level increased. However, from this limited study, there is no consistent evidence to suggest that care should be taken in selecting either a single or multi component joint model for seismic risk assessment of buildings when a global demand measure, such as maximum inter-storey drift, is employed in the seismic assessment framework. Probabilistic seismic demand analysis also indicates that super-element joint model may be less vulnerable relative to the single-component joint model. Furthermore, the shift in fragility function may lie in between the rigid joint and single-component joint modelling schemes, implying non-divergence.

1.1 Background
In the present wake of performance-based earthquake engineering (PBEE), the assessment of the vulnerability of a structural system to withstand seismic forces has been addressed by employing probabilistic models to quantify the level of uncertainties associated with the estimation of the seismic demand imposed on a structure given an intensity of ground shaking (Liel et al., 2009). Reliable quantification of the seismic performance of existing reinforced concrete buildings has been one of the major challenges within the earthquake engineering research community. The performance-based earthquake engineering (PBEE) methodology, since its inception, has provided engineers with a systemic way to incorporate and propagate uncertainties relating to, for instance, the estimation of seismic responses of structures subjected to severe ground shaking. The process culminates in a probabilistic framework for seismic assessment. This developed probabilistic framework decouples the risk assessment problem into four key areas; hazard, structural, damage and loss analysis. The final output may be the conditional mean annual frequency of repair cost exceeding a specified percentage of the total replacement cost of a specific structural system given the intensity of the ground motion (Liel et al., 2009). Usually, a global scalar parameter, with a prescribed probability distribution, is used to interface the various stages of the assessment framework. In order to systematically quantify the degree of uncertainties, such as modelling of structural elements and record to record variability in selected ground motions, past researches have assumed the conditional distributions of the parameters in the PBEE methodology to be markovian dependent (Baker and Cornell, 2003). This assumption allows, for instance, to estimate the probability of execeedance of the structural response quantity (structural analysis), given a parameter describing the intensity of ground shaking (hazard analysis), without necessarily requiring knowledge of pertinent information such as the distribution of magnitudes and source-to-site distances during the probabilistic seismic hazard analysis (PSHA) as well as the ground motion attenuation model used. Hence, one can analytically estimate the fragility of the structural system without necessarily requiring certain site specific information.

In order to reduce the dispersion in the modelling uncertainties associated with structural components, past researches have emphasized the importance of modelling the behaviour of beam-column connections in a bid to predict the seismic demand efficiently (Park, 2010). This is due to the fact that recent earthquakes have shown that older type non ductile reinforced concrete buildings are very vulnerable and do sustain significant damage under seismic action (see Fig. 1.1). Existing earthquake reconnaissance surveys (Moehle and Mahin, 1991; Sezen et al., 2002) have stressed that non-ductile detailing of structural components should not be tolerated in highly seismic zones.

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