Detection of nonlinear seismic response of steel moment frames using Frequency Response Functions (FRFs) and Hilbert transforms of FRFs

Occurrence of the nonlinear behavior can be a sign of changes in structural parameters and the presence of damage in systems. This paper presents a method for detecting and quantifying of nonlinearity, as an indication of damage, using the indicators that are extracted from the frequency response functions (FRFs) and Hilbert transform of FRFs, for steel moment frame structural systems. Using time history analysis under selected harmonic ground motions, the results of FRFs for the studied 4-story system are illustrated and discussed.Nonlinear behavior is a result of formation plastic hinges under earthquake loading. FRFs and Hilbert transform of FRFs are extracted from both the linear and nonlinear behavior of 4, 8, and 12-stories steel moment frames under fifteen different earthquake records with different characteristics in their time histories. Some near and far field well-known earthquakes records have been selected for the present study as the ground motions input in time history analysis. Different levels of nonlinearity are determined based on the maximum rotation of hinges in column members of structures equal to 2θy, 4θy and 6θy, in which θy is yield limit rotation. The indicators of the studied systems are calculated and evaluated for linear and different levels of nonlinearity based on the mathematical power of changes for FRFs and Hilbert transform of FRFs. The presented indicators are extracted based on the frequency response functions (FRFs) and Hilbert transform of FRFs for the responses of absolute acceleration and relative displacement of stories. The indicators are calculated at the location of acceleration sensors (accelerometer) in four levels of the structural systems, while the formation of plastic hinges in the columns of the structures will occur only at the level of the distance between the adjacent sensors.It is shown that the proposed method and calculated indicators have enough accuracy and sensitivity in detecting the “existence”, “location” and “extent” of damage.