Sürekli Sistem Olarak Modellenen Yarı-Rijit Mesnetli Tek Katlı Çerçevelerin Tepki Spektrumları

Year 2006, Volume: 7 Issue: 2, 127 - 133, 05.08.2016

Oktay Demirdağ

Abstract

Çerçevelerin dinamik analizinde, ankastre bağlı oldukları ve kolonlarının kütle ve deformasyonunun ihmal edildiği kabulleri sıkça yapılır. Ancak gerçekte, çerçeve kolonlarının temele bağlı noktaları sismik etkiler sebebiyle ötelenme ve dönme gösterebilmektedir. Bu durumda, mesnet davranışı elastik yaylarıyla modellenebilir. Ayrıca, gerçekte kolonlar yayılı kütleye ve rijitliğe sahiptir. Bu çalışmada, Timoshenko kolonu olarak modellenen çerçevenin mesnedi ötelenmeye ve dönmeye karşı elastik yaylar ile modellenmiştir. Genelleştirilmiş hareket denklemi sistemin enerji ifadeleri kullanılarak Lagrange denklemi ile elde edilmiş, Newmark-β metodu kullanılarak sistemin dinamik tepkisi hesaplanmış ve 1999 İzmit depremi yer ivmeleri kullanılarak tepki spektrumları elde edilmiştir

Keywords

tepki spektrumu, timoshenko modeli, tek katlı çerçeve, yarı-rijit mesnet

RESPONSE SPECTRA OF SEMI-RIGID SUPPORTED SINGLE STOREY FRAMES MODELED AS CONTINUOUS SYSTEM

Abstract

The assumptions of frame supports being fully rigid and distributed masses and deformations of the columns being neglected are frequently taken into consideration in dynamic analysis of plane frames. In practice, however, column bases of frames may usually rotate and translate a little due to seismic effects. In this case, support behavior can be modeled using elastic springs at the column bases of frames. Besides, columns, in fact, are not massless, and have distributed mass and stiffness. In this study, the support of the frame modeled as Timoshenko column is modeled by elastic springs against rotation and translation. The generalized equation of motion is obtained by Lagrange equation using energy relations of the system, the dynaimc response is computed for different elastic spring coefficients using incremental Newmark-β method, and response spectra are obtained using ground accelerations of 1999 Izmit earthquake

Keywords

response spectrum, single-storey frame, semi-rigid support, timoshenko model

References

• 1. BHATTACHAYA, K., DUTTA, S.C. Assessing lateral period of building frames incorporating soil-flexibility. Journal of Sound and Vibration, 269, 795-821, 2004.
• 2. BIGGS, J.M. Introduction to Structural Dynamics. USA: McGraw-Hill, Inc, 1964.
• 3. CHOPRA, A.K. Dynamics of Structures-Theory and Applications to Earthquake Engineering. New Jersey: Prentice Hall, 1995.
• 4. GLABISZ, W. Vibration and stability of a beam with elastic supports and concentrated masses under conservative and nonconservative forces. Computers & Structures, 70, 305-313, 1999.
• 5. GÜLER, K. Effects of soil flexibility on free vibrations of tower-like structures. Proceedings of the I. Symposium on Mathematical & Computational Applications, Turkey, 1996.
• 6. HJELMSTAD, K.D. Dynamic stability of structural systems subjected to base excitation. Engineering Structures, 20, 425-432, 1998.
• 7. KARAMI, G., MALEKZADEH, P., SHAHPARİ, S.A. A DQEM for Vibration of Shear Deformable Nonuniform Beams With General Boundary Conditions. Engineering Structures, 25, 1169-1178, 2003.
• 8. MICHALTSOS, G.Th., ERMOPOULOS, J.Ch. Dynamic response of column bases. Engineering Structures, 23, 58-71, 2001.
• 9. RODRIGUEZ, M.E., MONTES, R. Seismic response and damage analysis of buildings supported on flexible soils. Earthquake Engineering and Structural Dynamics, 29, 647-665, 2000.