LOCAL AND MODAL DAMAGE INDICATORS FOR RC FRAMES SUBJECT TO EARTHQUAKES

Local, modal, and overall damage indicators for reinforced concrete sh ear frames subject to seismic excitation are defined and studied. Each story of the shear frame is represented by a Clough and Johnston hyst eretic oscillator with a degrading elastic fraction of the restoring f orce. The local maximum softening damage indicators are defined in a c losed form based on the variation of the eigenfrequency of the local o scillators due to the local stiffness and strength deterioration. The modal maximum softening damage indicators are calculated from the vari ation of the eigenfrequencies of the structure during excitation. The linear and nonlinear parameters of the local oscillators are assumed t o be known. Next, a statistical analysis is performed where a sample f ive-story shear frame is subject to sinusoidal and simulated earthquak e excitations. The shear frame is subject to 30 independent simulation s of the earthquake excitation, which is modeled as a stationary Gauss ian stochastic process with the Kanai-Tajimi spectrum, multiplied by a n envelope function. Equations of motion of the storys are solved by a Runge-Kutta fourth-order scheme, where the local softening value is r ecorded. The modal maximum softening indicators are calculated from th e known instantaneous stiffness matrix, which is a function of the str uctural properties and local damage. Alternatively, a Fourier analysis is performed for consecutive time windows to measure the same evoluti on using the top story displacement. Finally, the relationship between local and modal damage indices are investigated statistically.