FREE VIBRATION OF SINGLE STOREY FRAMES MODELED AS TIMOSHENKO COLUMN INCLUDING SOIL FLEXIBILITY

Abstract

One of the assumptions mostly used in dynamic analysis of frames is writing the equation of motion according to concentrated mass at the storey height and modeling the columns as stiffness element. The other one is that the model of the frame is fixed supported. However, columns, in fact, have distributed mass and stiffness; and in practice, column bases of frames may usually rotate and translate a little due to elastic behavior of soil during dynamic loading. In this case, elastic support behavior can be modeled using elastic springs against translation and rotation at the column bases of frames. In this study, free vibration of single storey frames modeled as elastically supported Timoshenko column is studied including rotatory inertia of the columns and natural frequencies are obtained for different spring coefficients.

Keywords

• Elastic Support,Free Vibration,Single Storey Frame,Timoshenko Column

TIMOSHENKO KOLONU OLARAKMODELLENEN TEK KATLI ÇERÇEVELERİN ZEMİN FLEKSİBİLİTESİ DİKKATE ALINARAK SERBEST TİTREŞİMİ

Abstract

Çerçevelerin dinamik analizinde sıkça kullanılan kabullerden birisi hareket denklemini kat hizasında topaklanmış kütleye göre yazmak ve kolonları rijitlik elemanı olarak modellemektir. Ancak gerçekte, kolonlar yayılı kütleye ve rijitliğe sahiptir ve çerçevelerin zeminle bağlantı noktaları, pratikte, dinamik yük sırasında zeminin elastik davranışına bağlı olarak bir miktar dönebilmekte ve ötelenebilmektedir. Bu durumda, çerçevelerin mesnetlerinde dönmeye ve ötelenmeye karşı elastik yaylar kullanılarak, elastik mesnet davranışı modellenebilir. Bu çalışmada, elastik mesnetli Timoshenko kolonu olarak modellenen tek katlı çerçevelerin serbest titreşimi kolonların dönme ataleti de dikkate alınarak incelenmiş ve farklı yay sabitleri için doğal frekanslar elde edilmiştir.

Keywords

• Elastik mesnet,Serbest titreşim,Tek katlı çerçeve,Timoshenko kolonu

References

1. [1] Michaltsos, G.Th. and Ermopoulos, J.Ch., “Dynamic response of column bases”, Engineering Structures, 23: 58-71 (2001).
2. [2] 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).
3. [3] Güler, K., “Effects of soil flexibility on free vibrations of tower-like structures”, Proceedings of the I. Symposium on Mathematical & Computational Applications, Manisa, 67-72 (1996).
4. [4] Demirdağ, O., Obtaining Nonlinear response Spectrum of Semi-Rigid Supported Frames, Ph. D. Thesis, Dokuz Eylul University Graduate School of Natural and Applied Sciences, (2005).
5. [5] Rodriguez, M.E., and Montes, R., “Seismic response and damage analysis of buildings supported on flexible soils”, Earthquake Engineering and Structural Dynamics, 29: 647-665 (2000).
6. [6] Bhattachaya, K., and Dutta, S.C., “Assessing lateral period of building frames incorporating soil-flexibility”, Journal of Sound and Vibration, 269: 795-821 (2004).
7. [7] Hjelmstad, K.D. “Dynamic stability of structural systems subjected to base excitation”,Engineering Structures, 20: 425-432 (1998).
8. [8] Rogers, G.L., “Dynamics of Framed Structures”, John Wiley & Sons, New York, 202-208 (1959).

9. [9] Low, K.H., “A comprehensive approach for the eigenproblem of beams with arbitraryboundary Conditions”, Computers & Structures, 39: 671-678 (1991).