Abstract
Abstract: A number of studies conducted after the Northridge and the Kobe earthquakes suggested the existence of important axial dynamic effects in the piers due to the vertical accelerations and indicated that these effects could not be properly reproduced with the usual models of Structural Dynamics, requiring instead wave propagation analyses. Although it is true that lumped mass models with a limited number of masses, or even consistent mass formulations with a small number of members, will not be able to reproduce correctly wave propagation effects, particularly for high frequencies (short wavelengths), these effects can be accurately reproduced when using a large number of masses or members, or more conveniently using a frequency domain formulation and the dynamic stiffness matrices for members with distributed mass. This article presents the detailed derivation of the dynamic stiffness matrix of a prismatic member with distributed masses (continuous mass distribution), and its application to the linear dynamic analysis of structures in the frequency domain. The formulation is then verified with a series of simple examples.
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