The single degree of freedom model was widely applied in anti-seismic analysis and design for regular girder bridges with medium-length or short-length piers. While for girder bridges with tall piers, due to the obvious influence of higher-order modes, simplified model and method with multiple degrees of freedom or even with distributed parameters, are still required to be developed. In this paper, based on the theory of Euler beam with distributed parameters, analytical derivation is presented for the Single Column and Mass system. The dynamical characteristics and modal mass distributions, as well as their control factors and properties, are studied. It is proved analytically and more strictly that, the girder-pier mass ratio plays the dominant role to determine the horizontal modal mass participation, and thus interpretation for the previous conclusion based on statistical and numerical analysis is presented. Purely analytical formulas, which show higher accuracy and better applicability than the previous numerical fitting formulas, are also given. The influence of higher-order vibration mode is analyzed and discussed. Finally, the manual calculation formula, for efficiency assessment of the single degree of freedom model, is also proposed.
Key words
Tall pier /
Single column and mass system /
Modal mass participation /
Analytical derivation
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References
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