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.

Seismic risk assessment of structures is an important and practical tool for seismic safety assessment, earthquake consequence analysis, seismic strengthening planning and post-earthquake crisis management. This assessment consists of various parts including seismic hazard analysis, exposure evaluation, vulnerability analysis, and risk estimation. One of the most important parts of this process is the development of structural Fragility Functions or curves for undesired performance. Various methods have been used to determine Fragility Functions. In most of these methods, a general limit state such as maximum relative displacement of the floors is considered as failure mode, while in older buildings, more failure modes such as shear failure mode of structural members are usually prevailing.In this paper, a framework for determining the Fragility Functions of structural Collapse based on different failure modes of structural members using fault tree analysis is presented. This method includes developing the fault tree of the undesired performance of the structure (through possible failure modes in members), preparing a suitable computer model of the structure according to failure modes, selecting earthquake acceleration records for IDA analysis, determining the capacity and limit mode of failure modes based on laboratory results or standards, performing IDA analysis for the structure and forming a Fragility table, calculating the Fragility parameters using a suitable statistical distribution and plotting the seismic Fragility curve for each of the base events in fault tree and quantifying the fault tree, and finally deriving the Fragility curve of the structure.This method was applied on a reinforced concrete building frame made in Europe according to the design criteria of the 50s and 60s, and then the results were compared with the conventional method of developing Fragility Functions, which is based on the general limit state of maximum relative displacement of floors. Because the main reason for the weakness of the frame under study is the weakness in shear of the columns due to the lack of seismic transverse reinforcement details at the time of their design and construction, in next stage, the Fragility Function of the studied frame is determined by observing the criteria of seismic transverse reinforcement and is compared with the Fragility Function of the existing frame without observing these criteria. The results show a much lower median estimate of the capacity of the Fragility Function due to the shear weakness of the old frames in the proposed method compared to the conventional method. The Fragility curves derived from conventional methods match very well with the failure mode causing weak-storey on the first floor. This observation is in good agreement with the results presented in the references in which the main Collapse mode for this frame is the failure of the weak floor in the first floor. Another observable result in the proposed method is the reduction of the dispersion of the results using this method compared to the conventional method because the Fragility curve obtained from this method covers a narrower range than the conventional method.Considering the criteria of transverse reinforcement, it was observed that in many columns, the philosophy of designing new regulations, which is flexural failure before shear failure, has occurred, which shows the high importance of transverse reinforcement in column sections. By observing the criteria of transverse reinforcement of sections, the most vulnerable part of this frame are the columns of row 2 in shear failure mode, due to the significant difference in the cross-sectional height of the columns of this row compared to other rows. This difference in the height of the sections leads to high absorption of shear force in the section, which causes the force to pass through the capacity much faster and as a result, its high vulnerability. Finally, comparing the Fragility curves of frame Collapse in two cases with considering the seismic shear reinforcement criteria and without considering it shows the significant effect of cross-section reinforcement criteria on the seismic Fragility Function of structures.

Today, extensively eccentrically braced structures are used to absorb seismic energy using link beam elements on beams. The Function of this system is defined as yielding this beam elements during an earthquake and remaining safety and elastic of other structure elements. The length of the link beam is expressed as an effective parameter determining the type of behavior of it as shear or flexure, which determines the seismic performance and the amount of seismic energy absorbed by this element in this type of braced frames. In this research, using incremental dynamic analysis on steel frames under far field records and by performing modeling steps in Python version 3. 8 and using of OpenSeesPy documentation, the variables of failure and frame reliability have been investigated. In this research, two samples of 6 and 12-story frames with changes the link beam length from 0. 4, 0. 6 and 0. 8 m have been studied. The results show that the behavior of link beams is affected by the characteristics of the earthquake record and the capacity of the link beams with the same length is various for each record. The results of incremental dynamic analysis on the mentioned frames with different link lengths have shown that the length of short shear link beam in medium height frames has resulted in better seismic behavior and the optimal length of the link beam should be selected after seismic evaluation under different records. The maximum acceleration of the median Collapse in this research has been obtained for 6-story frames and the link with 0. 6 m length is 5. 10, and for 12-story frame with the link of 0. 6 m length, 4. 20 times the acceleration of the earth's gravity.

Although Buckling-Restrained Braces (BRBs) can dissipate a large amount of the seismic input energy. However, they need to be repaired or replaced due to large permanent deformation after a severe earthquake. To overcome this issue, the use of Shape Memory Alloys (SMAs) in the braces has recently received attention. These alloys are able to return to their original state after loading. The present study aims to analyze the Fragility curves and to investigate the sideway Collapse of the BRB frames equipped with SMA during near-field earthquakes in comparison with those given for the case without SMA. For the purposes, two 5 and 15-story BRB and BRB-SMA frames subjected to 7-pair of near-fault earthquake records are studied. Nonlinear Incremental Dynamic Analyses (IDAs) are carried out using OpenSees software. On average, the simulation results showed that the Collapse capacity and Collapse duration of the BRB-SMA frames are about 30% and 35% more than those given for the BRB frames, respectively. For instance, a Collapse probability of 38% for the 5-story BRB-SMA frame and a Collapse probability of 60% for the BRB frame is given for 3g spectral acceleration. Furthermore, at the performance level of 50% for the 15-story frame, the Collapse duration of the BRB-SMA frame is obtained 25.6 seconds, while it is given about 10 seconds for the BRB frame. In addition, the use of a memory alloy for spectral accelerations of 1 to 4 g resulted in a reduction of 50% to reach the Collapse performance level of the frames.

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.

Fragility Function of structures is the major requirement of seismic loss estimation which is widely used in the seismic risk management. In this paper, firstly, a comprehensive and simplifies stochastic methods are presented for development of analytical Fragility Functions. Secondly, the effect of damage threshold uncertainty on Fragility Functions is estimated. It is shown that the results of the method are almost comparable with the result of previous studies and the effect of uncertainty of damage state on the deviation of Fragility Function in the lower intensity of ground motion is high which gradually decreases.

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.

The steel braced frame system is one of the lateral load resisting systems which is used extensively for low-to mid-rise buildings. In this structural system, the braces can be arranged in different forms along the building height due to different reasons such as architectural and structural limitations or design considerations. The bracing arrangement affects the seismic performance of the structural system and each of the elements. In this study, the impact of bracing arrangement along the building height on ultimate failure capacity and Collapse Fragility curves of steel CBFs is investigated. For this purpose, 4 and 8-story steel CBF buildings with 6 different arrangements of braces were selected and modeled in PERFORM-3D software. The models were then analyzed using the incremental dynamic analysis (IDA) method. Afterwards, the Collapse capacity of the models and the uncertainty index were calculated, and the Collapse Fragility curves were generated. The results show that, by modifying the arrangement of braces without significant changes in lateral stiffness and fundamental period of structure, it is possible to increase the Collapse spectral acceleration and decrease the probability of Collapse at the maximum considered earthquake intensity.