Local and modal damage indicators for RC frames subject to earthquakes

Local, modal, and overall damage indicators for reinforced concrete shear frames subject to seismic excitation are defined and studied. Each story of the shear frame is represented by a Clough and Johnston hysteretic oscillator with a degrading elastic fraction of the restoring force. The local maximum softening damage indicators are defined in a closed form based on the variation of the eigenfrequency of the local oscillators due to the local stiffness and strength deterioration. The modal maximum softening damage indicators are calculated from the variation of the eigenfrequencies of the structure during excitation. The linear and nonlinear parameters of the local oscillators are assumed to be known. Next, a statistical analysis is performed where a sample five-story shear frame is subject to sinusoidal and simulated earthquake excitations. The shear frame is subject to 30 independent simulations of the earthquake excitation, which is modeled as a stationary Gaussian stochastic process with the Kanai-Tajimi spectrum, multiplied by an envelope function. Equations of motion of the storys are solved by a Runge-Kutta fourth-order scheme, where the local softening value is recorded. The modal maximum softening indicators are calculated from the known instantaneous stiffness matrix, which is a function of the structural properties and local damage. Alternatively, a Fourier analysis is performed for consecutive time windows to measure the same evolution using the top story displacement. Finally, the relationship between local and modal damage indices are investigated statistically.