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A simple model for assessing periods of vibration and modal response quantities in symmetrical buildings
Author(s) -
Georgoussis George K.
Publication year - 2006
Publication title -
the structural design of tall and special buildings
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.895
H-Index - 43
eISSN - 1541-7808
pISSN - 1541-7794
DOI - 10.1002/tal.286
Subject(s) - structural engineering , bent molecular geometry , cantilever , flexural rigidity , modal , vibration , shear wall , normal mode , modal analysis , rigidity (electromagnetism) , engineering , flexural strength , simple (philosophy) , finite element method , physics , materials science , acoustics , philosophy , epistemology , polymer chemistry
A simple mathematical model is proposed for assessing periods of vibration and mode shapes of common cantilever bents used in concrete structures, such as shear walls, coupled walls, rigid frames and wall‐frame assemblies. The bent is treated as a continuum and the proposed model is based on the technique of decomposing a cantilever bent into two complementary subsystems (a flexural and a wall‐frame bent) and on the finding that the use of Dunkerley's formula for calculating natural frequencies yields reasonable results for the first three modes of vibration. The objective in proposing this model is to consider the effect of column axial shortenings in the analysis of structural bents. With this model any cantilever bent may be approximated by a simple incompressible shear–flexure system of equal flexural rigidity, but of equivalent modal shear rigidity. This approach has the advantage that the response of different structural bents may be combined in buildings composed of these bents in any arrangement. All bents are approximated by equivalent shear–flexure models and therefore the complete structure may be analysed by a simple methodology, which has been extensively used in the past. Particularly in symmetrical buildings, frequencies may be determined by a simple formula and modal response quantities by available design charts. A quick estimate of these quantities is of particular importance at the early stages of structural design, prior to a full dynamic analysis. In order to illustrate the application of the proposed model a symmetrical building of varying height, composed of different structural bents, is analysed and comparisons are made with more accurate results obtained by 3D computer dynamic analyses. Copyright © 2006 John Wiley & Sons, Ltd.