Investigation on the modal strain energy for dynamic analysis of steel-concrete vertically mixed structures

Abstract

For a vertically mixed structure composed of two parts, a lower part made of concrete and an upper part made of steel, the damping matrix of the structure is non-proportional. This paper investigates the consequences of using the modal strain energy method to estimate equivalent viscous damping ratios for such an irregular structure. First, a steel-concrete vertically mixed structure is simulated by an equivalent SDOF-SDOF oscillator using the first modal characteristics of each subsystem. The equivalent modal damping ratios are plotted as functions of the mass ratios and frequency ratios of the two subsystems. The equivalent modal damping ratios predicted by the MSE method are confirmed by exact time history analysis under various seismic ground motions. The analysis indicates that the MSE method can properly represent the displacement responses of the subsystems and that the displacement error is mainly concentrated around a frequency ratio of R ω = 0.5-1.5. Finally, a formula is derived to obtain the relative steady-state error of the structural response under harmonic excitation. It is concluded that higher modes may generate greater response errors in modal superposition when the seismic spectrum provides intense amplification at high frequencies.