Collapse performance evaluation of structures has been a concern for researchers due to its complexity and uncertainty in modeling and simulation. Concentrate plastic hinges are best candidates for modeling Collapse behavior of structures. Collapse fragility curves are affected by various sources of uncertainty. Existing uncertainties in modified Ibarra and Krawinkler moment-rotation model for concrete moment frame buildings were investigated in this paper. LHS simulation method was used to generate random variables considering the correlation among modeling uncertainties in one component and two structural components. Collapse responses including mean Collapse capacity and standard deviation were obtained for each simulation by generating random samples for uncertainties using incremental dynamic analysis (IDA). As much effort is needed for implementation of IDA, MLP artificial neural networks, GMDH artificial neural network and response surface method were used to estimate and anticipate the Collapse behavior of the structure. Results show that using above methods will lead to high accuracy anticipations with an error of less than 10% for GMDH neural network and an error of less than 7% for MLP and response surface methods.

In this research, a method of probabilistic analysis of progressive Collapse has been introduced based on the concept of fragility curves. In order to develop the fragility curves, the stiffness of two columns is considered as the random variable and the displacement at the top of the removed columns is considered as the Damage Index (DI). Based on these measures, the fragility curves of a 4-story steel structure with Intermediate Moment Frame (IMF) system were developed. Six scenarios of progressive Collapse were investigated, including the removal of the corner, perimeter, and middle double-columns. The simulations were performed using OpenSees software. The structural analyses were performed using nonlinear time history approach in a three-dimensional framework. The results showed that the IDA capacity curve of the lower stories is weaker than the upper stories. According to the results, at each considered DI and assumed performance level, damage to the removed double-columns occurs at more stiffness in the upper stories compared to the lower ones. The results showed that considering the floor slab can reduce the probability of fragility of structures. The effect of the floor on the lower stories of the structure is more than on the upper stories. The increasing effect of the floor on the structural fragility corresponding to the first to fourth stories are 13, 9, 6, and 2%, respectively. The probability of exceedance of the performance levels of IO, LS and CP is almost zero until the reduction of the double-column stiffness is 50, 70 and 75%, respectively.

A new structural system of diagonally gridded elements, the so called ``diagrid'', has been introduced in recent years in which the frames that are made up of intersected members surround the main structure. This type of system provides excellent shear rigidity and stiffness, in contrast to the similar tubular structures. The triangular configuration offers structural stability for gravity and lateral loads, and the removal of external columns gives the building a unique architectural beauty. Swiss Re (London), Hearst Tower (New York), Cyclone Tower (Asan, South Korea), Capital Gate Tower (Abu Dhabi) and Jinling Tower (Nanjing, China) are prominent cases with diagrid system worldwide. The response modification factor (R-factor) for diagrid systems is not yet explicitly introduced in the existing building codes and few studies have been conducted on the assessment of this parameter. On the other hand, previous researches show that the angle of diagonals play an important role in the structural behavior. In this paper, the effect of the angle change of diagonal elements on R-factor, Collapse capacity and Collapse fragility curves of steel diagrid structures are investigated. To this end, 6, 8, 10, and 12 story diagrid buildings with different angles for diagonals varying from 580 to 780 were selected and modelled using OpenSees software. The post-buckling behaviour of diagonal members was taken into account in modelling process. The models were then analyzed using nonlinear static analysis and the R-factor of the system was calculated according to the proposed method by ATC-19 guielines. Nonlinear incremental dynamic analysis (IDA) were performed and Collapse fragility curves were extracted using 44 far-field records in order to evaluate their seismic performance and to validate the calculated R-factor. Next, the reliability of the applied seismic performance coefficients were controlled through the methodology proposed by FEMA P-695 taking into consideration the uncertainties in modeling, designing, earthquakes and experimental data. Results show that the effect of diagonal angles on the response modification factors depend on the building height. However, it can be stated that, in general, changing the angles of diagonals in steel diagrid systems do not have a significant effect on their R-factor. It is also observed that an increase in the angle of diagonal members will reduce the uncertainty in Collapse data.

This study aims to develop seismic fragility curves for a typical pilesupported wharf. fragility curve is one of the popular tools in seismic performance evaluation of a structure. The software FLAC2D was used to simulate the seismic performance of the wharf structure. Using eight time history records, occurred in past, as seismic loading, incremental dynamic analysis (IDA) was applied for seismic demand estimation. Based on the resulted seismic response matrix the analytical fragility curves were developed. As a prevailing tool, adopted fragility curves are useful for seismic risk assessment. They can also be used to optimize wharf-retrofit methods.

In this paper, a procedure has been presented to develop fragility curves of structures equipped with optimal variable damping or stiffness semi-active tuned mass dampers (SATMDs). To determine proper variable damping or stiffness of semi-active devices in each time step, instantaneous optimal control algorithm with clipped control concept has been used. Optimal SATMDs have been designed based on minimization of maximum interstory drift of nonlinear structure which genetic algorithm(GA) has been used to solve the optimization problem. For numerical analysis, a nonlinear eight-story shear building with bilinear hysteresis material behavior has been used. fragility curves for the structure equipped with optimal variable damping and stiffness SATMDs have been developed for different performance levels and compared with that of uncontrolled structure as well as structure controlled using passive TMD. Numerical analysis has shown that for most range of intensity measure optimal SATMDs have been effective in enhancement of the seismic fragility of the nonlinear structures which the improvement has been more than passive TMDs. Also, it has been found that, although variable stiffness SATMD shows to be more reliable in lower mass ratios, however in higher mass ratios variable stiffness and damping SATMDs performs similarly to improve reliability of the structure.

Earthquakes are undoubtedly a most important natural disaster and, therefore, in recent decades, the seismic vulnerability assessment of existing buildings has become an important issue. One of the latest achievements in seismic vulnerability assessment is the seismic fragility curve. fragility curves describe how the reliability of a structure changes over a range of loading conditions to which a structure may be exposed. Approaches to developing fragility curves can be classified into four main categories: judgmental, empirical, analytical, and hybrid. Fairly extensive studies have been done for concrete and steel structures and also for different types of bridges, while, for masonry buildings, only limited studies are available. Iran is in a high seismicity area in the world where a large number of masonry buildings have been constructed. In this study, an analytical approach was used to develop fragility curves for 1 story, 2 story and 3 story masonry school buildings on different soils. In order to achieve more realistic fragility curves, 24 analyses were performed for each building. The following conditions were considered in these analyses: applying lateral force in 2 main axes (x and y) and 2 main directions (positive and negative), eccentricity, applying lateral force in 2 cases (first mode and mass). The computer program, Tremuri, and the design spectrum of Standard No. 2800 have been used in this study. Finally, by assuming a log-normal distribution probability function, fragility curves were obtained. It is worth noting that the peak ground acceleration (PGA) is selected as a parameter that represents the intensity of seismic ground motion.

There are a few methods for seismic vulnerability assessment of bridge structural systems. The development of vulnerability information in the form of fragility curves is an approach when the information is to be developed accounting for a multitude of uncertain sources involved, such as, structural characteristics, estimation of seismic hazard and site condition. Inherent randomness is involved to these uncertain factors. The major effort of this study is placed on the development of empirical fragility functions by utilizing the damage data from past earthquakes considering composite inherent randomness of the uncertain factors. The introduced procedure is suitable for the development of fragility curves under the assumption that they can be presented by two-parameter lognormal distributions. The empirical fragility curves are developed using 768 bridge damage data obtained from the 1994 Northridge and the 1995 Kobe earthquakes, which could be used as reference curves for seismic risk assessment studies of the similar bridges in Iran.

Placing column lap-splice in the locations of possible nonlinear deformation may adversely affect the structures response to strong ground motions. Localization of damage in splice zone may change the structural response and prevent the load redistribution and development of a uniform pattern of nonlinear excursions among the various members. Validated by existing laboratory experiments, this study presents a model that could be used to evaluate the behavior of lap-spliced columns. The proposed model is able to include the effect of the longitudinal bars arrangement; bars yield stress, and the amount and spacing of transverse bars. Comparison with existing experimental tests, show a good correlation between the model and experimental results. Finally, to obtain an estimation of the importance of the bar slip in lap splice on the structures response, fragility curves for life safety and Collapse limit states are developed for an ordinary moment resisting frame of a one bay-ne story structure. Incremental dynamic analysis is used to derive the fragility curves. These fragility curves show that the bar slip have significant impact on the probability of exceeding Collapse limit state, while its impact on the life safety limit state is not so significant.

In this study, nonlinear dynamic response of 4, 7, and 10-story moment frame steel structures is investigated under seismic ground motions. An incrementally increasing intensity is accounted for to evaluate the Collapse fragility curves of the same buildings under different values of torsional eccentricity. The site soil of the buildings is assumed to be composed once of a firm and then of a soft soil. As a distinction of this study, the realistic maximum possible value of eccentricity ratio for moment frames, including both stiffness and mass eccentricities, is shown to be 10-15% that is much less than peak values of the past studies. Because of the three-dimensional aspect of the study, the eccentricity is selected to be bi-directional and the horizontal components of the earthquake motion are applied concurrently. It is exhibited that while torsional eccentricity lowers the median Collapse probability of the studied buildings, it does not have a sensible effect up to the eccentricity ratios not larger than 10%. Besides, the taller structures on the firm soil are affected more strongly from torsional eccentricity, as the median Collapse acceleration decreases up to 46% for the 10-story building suffering from 15% eccentricity ratio on the firm soil.