Equivalent Damping Ratios for Irregular in Height 3D Concrete/Steel Structures Under Seismic Excitations

Abstract eng:
The present work deals with the dynamic response of structures that are irregular in height consisting of two parts, a lower one made of concrete, founded on the ground, and an upper one made of steel. The concrete part is usually denoted as primary structure and supports the steel part which is denoted as secondary structure. Such structures are commonly encountered in stadiums, where the spectators’ seats are configured as concrete frames, and the cover of the seats is configured as a steel truss. Another frequently encountered application is the addition of light steel storeys resting upon concrete levels of buildings, in order to reduce inertial loading and achieve speed of construction. The concrete and the steel part, have different damping ratios, commonly adopted as 5% and 2% respectively. This may result in analysis difficulties since in most pertinent seismic design codes the loading of the structure due to seismic effects depends on its damping ratio. Therefore, when determining the seismic forces by means of a spectral analysis, a decision has to be made regarding the overall damping ratio of the structure. This decision is usually conservative, adopting a damping ratio equal to 2%, thus leading to a non economical design. Much research has been performed in order to estimate equivalent damping ratios for structures that are irregularly damped. Accordingly, for the specific case of concrete/steel structures, the authors of the present work have proposed in the past equivalent modal as well as uniform damping ratios in order to approximate the exact response of 2D frames with satisfactory results. These proposals depend on the first translational mode characteristics of each part. An expansion is now performed to include 3D irregular concrete/steel structures that may or may not be susceptible to torsional effects, ending in torsional modes that may be significant in the overall behaviour of the structure. Two 3D irregular structures are considered, one with regular plan distribution of mass and stiffness and one with plan irregularities resulting in intense torsional behaviour with the translational modes having small participation ratios. The structures are divided in two homogeneous parts and in accordance with the previous work of the authors, the 1st translational mode characteristics of each part lead to the equivalent damping ratios, ignoring the torsional modes. The estimated ratios are different for each horizontal direction examined, depending on the modal characteristics for the specific direction. Thus, the previously proposed equivalent damping ratios are now tested in two horizontal directions for 3D structures, and the loss of accuracy due to neglectd of the torsional modes is assessed. The complete structure is subjected to seismic excitation with its exact damping configuration and with the proposed equivalent ones and the approximation achieved by the equivalent damping ratios is investigated with satisfactory results for both buildings.

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