تجزیه و تحلیل حساسیت از ساختمان های فولادی در معرض افت ستون

In this study, the sensitivity of design parameters of steel buildings subjected to progressive collapse is studied. To this end, design parameters such as yield strengths of beams, columns, and braces, live load, elastic modulus, and damping ratio were considered as random variables. The Monte Carlo simulation, the Tornado Diagram analysis, and the First-Order Second Moment method were applied to deal with the uncertainties involved in the design parameters. The analysis results showed that among the design variables beam yield strength was ultimately the most important design parameter in the moment-resisting frame buildings while the column yield strength was the most important design parameter in the dual system building. Sensitivity of the vertical displacement to uncertain member strength showed that progressive collapse mechanisms of the moment-resisting frame buildings and the dual system building completely differed due to different patterns of the vertical load redistribution.

When a structure is subjected to unexpected loads such as explosion, impact, fire, etc. that are not considered in the normal design process, the structure may become vulnerable. The phenomenon whereby the failure of one or more load-resisting structural members due to an unexpected load leads to the collapse of the entire structure, especially in a domino-like way, is commonly called progressive collapse [1]. The collapse of the Alfred P. Murrah Building in 1995 and the World Trade Center (WTC) Tower in 2001 are examples of progressive collapse due to a car-bombing and an aircraft impact, respectively. Before the collapse of the WTC, research on progressive collapse had only been conducted by a limited number of researchers because the probability that such an abnormal loading event would occur and that it would trigger progressive collapse was very low. However, the collapse of the WTC, where more than 2000 civilians lost their lives, reminded structural engineers that the mechanism of progressive collapse needs to be thoroughly understood to prevent such a disaster recurring in the future. To prevent the progressive collapse caused by abnormal loads, the National Building Code of Canada [2] specified requirements for the design of major elements, the establishment of connection elements, and ways of providing load transfer paths. Eurocode 1 [3] presented a design standard for selecting plan types for preventing progressive collapse and recommended that buildings should be integrated. In the United States, specific provisions related to progressive collapse have not yet been provided in design codes such as the International Building Code [4]. However, the American Concrete Institute [5] requires structural integrity (for example, continuity insurance of reinforcing bars) so that partial damage by abnormal loads does not result in the collapse of the entire structure. The ASCE 7-05 [6] also recommends a design method, a load combination, and structural integrity, as does ACI 318. The General Service Administration (GSA) presented a practical guideline for design to reduce the collapse potential of federal buildings [7]. The Department of Defense (DoD) also presented a guideline for new and existing DoD buildings [8]. These guidelines address design procedures and analysis methodology for progressive collapse. Research on progressive collapse can be categorized according to two different approaches: (1) developing structural systems that prevent progressive collapse, and (2) developing an analysis methodology. Crawford [9] proposed the use of connection details such as Side Plate™, developed for earthquakes, the use of cables imbedded in reinforced concrete beams to activate catenary action, and the use of mega-trusses in high-rise buildings to resist progressive collapse. Suzuki et al. [10] showed that the use of hat-bracing at the top of structures may increase the resistance to progressive collapse. Hayes Jr. et al. [11] investigated the relationship between seismic design and the blast or progressive collapse-resisting capacity. They mentioned that the seismic design details developed for special moment frames in high seismic zones would provide better resistance to external explosion or impact load than the less-rigorous design details of ordinary moment frames. Khandelwal et al. [12] also investigated the mechanism of the progressive collapse of seismically designed braced steel frames. Both linear and nonlinear analysis methods can be used to simulate progressive collapse. The linear analysis method can be readily adopted to the alternative path method [7] where the demand-capacity ratio of the structure is evaluated repeatedly. However, Powell [13] proposed that the nonlinear analysis method should be used for progressive collapse because the result of the linear analysis can be too conservative and is sensitive to input parameters. For realistic simulation of structural performance, the analysis process needs to include uncertain characteristics of material properties. Nevertheless, most recent research on progressive collapse of structures has been conducted based on deterministic approaches where the nominal or average values of the design parameters were used [14]. An application of the theory of probability to the structural analysis is one of the ways to deal with uncertain material properties which are considered as random variables [15]. The effect of variability of uncertain design parameters on structural behaviors can be estimated by a sensitivity analysis. Sensitivity analysis has been used for earthquake engineering to estimate sensitive design parameters to the seismic response of buildings [15]. Recently Park and Kim [16] carried out fragility analysis of steel structures subjected to progressive collapse considering the probability distribution of material properties. The progressive collapse mechanism and the capacity of structures can be affected by the probabilistic properties of the design parameters and load combinations. The sensitivity analysis is necessary to understand which design parameters are more important to progressive collapse than others. The objective of this study is to determine the important design parameters and structural members for the progressive collapse mechanism of buildings. To this end, three different probabilistic approaches were used on steel moment frame buildings and dual system buildings of various stories. Uncertainties associated with material properties and member capacities were considered in order to determine the influential material properties and members for the progressive collapse of the analysis model buildings.

Sensitivity of the progressive collapse mechanism to uncertain design parameters of steel buildings was investigated using MCS, TDA, and the FOSM method. Yield strengths of structural members, live load, elastic modulus, and damping ratio were considered as random variables. One of the first-story columns was removed to initiate progressive collapse. Two-dimensional nonlinear static and dynamic analyses were conducted within the procedure of the FOSM method to deal with uncertainties of design parameters and to evaluate the variability of structural responses in terms of the vertical displacement. This methodology was applied to a three-story, ten-story, and twenty-story moment-resisting frame buildings, and a ten-story dual system building. For sensitivity analysis of the three-story case study buildings, three different methods, the TDA method, the MCS method, and the FOSM method were applied to validate the efficiency of the FOSM method to the present examples. Sensitivity analyses of ten-story and twenty-story case study buildings were then conducted by the FOSM method. The beam yield strength and damping ratio were observed as the most influential design parameter to the vertical displacement in the three-story moment frame while elastic modulus and column yield strength were not influential parameters. From static pushdown analysis of the ten-story buildings, the beam yield strength and the column yield strength were observed as the most influential design parameters for the moment-resisting frame and the dual system buildings, respectively. The damping ratio was the most important parameter in dynamic analyses. The study on the vertical displacement sensitivity showed that, for the moment-resisting frame buildings, the lower story beams located in the bays containing the removed column were most influential to the progressive collapse mechanism. On the other hand, the progressive collapse mechanism of the dual system building involved many columns including those located far from the removed column. The sensitivity study on the twenty-story case study building showed that the lower story beams played more important roles in resisting progressive collapse than upper story beams. However, it should be pointed out that the accuracy of the research results may depend on the mathematical models for structural materials/members and the statistical data adopted in the sensitivity analysis. Therefore the validity of the analysis results will be enhanced if the analysis is based on more precise material/structural models and more statistical data for design parameters. The probabilistic approaches of identifying influential parameters to the progressive collapse of steel frame buildings, presented in this paper, can be useful to understand the progressive collapse mechanism and, eventually, to design safer structures against progressive collapse. To do so, it is recommended to understand the force redistribution mechanism and to reduce uncertainty of influential design parameters so that the expected performance of the structure can be achieved with confidence.