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The purpose of this paper is to study the method of hysteresis energy distribution and maximum relative lateral displacement in buildings’ stories, under the influence of scaled records for near-fault and far-fault earthquakes. The bracings in the considered buildings’ plan are distributed in two different ways: in the first case, the braces are added in external frames of the building, and in the second case, in the internal ones.

This research first selects some steel buildings with concentric braces and studies the seismic vulnerability of buildings under different earthquakes in accordance with the concepts of input and Hysteresis energy. In order to study the impact of braces’ distribution in the building’s plan, the buildings were modeled in this study in two ways. In the first way the braces were added to the building’s external frames and in the second way in its internal ones.

Results show that the need for far-fault scaled records’ displacement is more than the near ones and that the resultant relative lateral displacements in buildings with external braces are more than those with internal ones.

After these studies on the way of hysteresis energy distribution, it was shown that in case of buildings with internal braces, as the building’s height increases, the share of higher stories of the hysteresis energy rises. Also, it was illustrated that hysteresis energy distribution in buildings with internal braces is more uniform than those with external ones.

The purpose of this paper is to present a probabilistic assessment and verify the effectiveness of seismic improvement schemes against earthquake, blast and progressive collapse. The probabilistic analysis is performed by taking into account the uncertainties in loading such as planar configuration and amplitude of the blast loading. A standard Monte Carlo (MC) simulation method is employed to generate various concepts of the uncertain parameters within the problem. For a given concept, various local dynamic analyses are performed within a certain range of distance, in order to quantify and locate the damage induced by impact wave on structural elements. In the next step, a limit state analysis is performed in order to investigate whether a progressive collapse mechanism forms under the acting loads or not.

( | ) and ( | ) are blast fragility and seismic fragility, respectively; ( ) and ( ) are annual occurrence rate of earthquake and blast, respectively. The purpose of the current study is to calculate for the primary structure as well as the retrofitted structure. Annual occurrence rate of earthquake can be calculated by using probability seismic hazard analysis for the site of interest, where the structure is located. In this paper, blast fragility and seismic fragility are defined rather differently; in other words, seismic fragility is defined as the probability of structural collapse given a specified level of seismic intensity whereas blast fragility is defined as the probability of collapse given that a significant blast event takes place. Both blast and earthquake loading conditions involve the activation of energy dissipation mechanism and, as a consequence, both can be resisted employing ductility enhancing techniques, such as column wrapping or jacketing and steel bracing.

The current paper aims to present a probabilistic assessment of progressive collapse under blast and earthquake loads. Non-dependent and incompatible events are considered to obtain a general rate of collapse. Finally, probabilistic collapse rate was obtained for a moment frame before and after modifying with convergent steel brace (CBF). The purpose of doing so is to investigate whether seismic improvement schemes can reduce collapse risk of different critical events or not.

Objective of the present work is to present a methodology for calculating the annual risk of collapse for a civil structure subjected to both seismic and blast loads, using a bi-hazard approach. Given that a blast event takes place, the probability of progressive collapse is calculated using a MC simulation procedure. The simulation procedure implements an efficient non-linear limit state analysis, formulated and solved as a linear programming problem. The probability of collapse caused by an earthquake event can be calculated by integrating the seismic fragility of the structure and the seismic hazard for the site.