Probabilistic safety-checking with un-scaled records for the equivalent SDOF system

Abstract

The intensity-based Demand and Capacity Factor Design (DCFD) is a probabilistic closed-form analytical safety-checking format, derived based on a set of simplifying assumptions, that lends itself quite well to visual interpretation. Various sources of uncertainty can be considered within the frame of DCFD ﾖalbeit in a simplified manner. Adopting the critical demand to capacity ratio as a global damage measure directly within DCFD safety-checking, and thus skipping the engineering demand parameter, facilitates the identification of the onset of the prescribed limit states. The original N2 method for reasonably regular buildings oscillating predominantly in a single mode employs the equivalent single-degree-of-freedom (SDOF) system of a multi-degree-of-freedom (MDOF) structure to find the performance points associated to prescribed limit states. This procedure today forms the backbone of several building codesﾒ provisions for non-linear static analysis.

A nonlinear dynamic analysis procedure known as the Cloud Analysis can effectively be used for the equivalent SDOF system due to its simplicity and relatively small number of un-scaled records employed. It is to note that the Cloud Analysis is perfectly compatible with the underlying assumptions of DCFD safety-checking format. A modified version of the Cloud Analysis, referred to as Modified Cloud Analysis, has the capability of explicitly addressing the cases of global instability or numerical non-convergence. The modified Cloud Analysis procedure employed for the equivalent SDOF system is herein dubbed as N2-Cloud procedure. Safety-checking for the N2-Cloud procedure can be performed at the level of the equivalent SDOF system.

The 3D structural model of an existingfive-story RC building located in LﾒAquila (central Italy) is employed as a case-study. The structure in question has collapsed due to a soft-story mechanism in the LﾒAquila 2009 earthquake. It can be observed that DCFD safety-checking for the equivalent SDOF system leads to an extremely efficient yet vigorous and accurate safety-checking for this case-study building.