KAYMA EV GENIŞ MESNET ETKISINDEKI ÇUBUKLARIN GELIŞTIRILMIŞ RIJITLIK MATRISLERI IÇIN ANALITIK VE DENEYSEL BIR YAKLAŞIM

Year 2019, Volume: 6 Issue: 10, 32 - 46, 14.06.2019

Yaşar Ayaz , Ahmet Budak

Abstract

Bu
çalışmada, aynı anda hem kayma ve hem geniş mesnet etkisindeki çerçeveler
analitik, nümerik ve deneysel olarak incelenmiştir. Analitik çözüm için matris
deplasman yöntemi, sayısal çözüm için sonlu elemanlar yöntemi kullanılmıştır.
Hem kayma etkisi hem de geniş mesnet etkisini içeren rijitlik matrisi için açık
denklemler ortaya konmuştur. Bunun için bir model çerçeve deneysel olarak test
edildi ve maksimum çökme değeri elde edildi. Aynı çerçeve sonlu elemanlar
yöntemi ile modellenerek ve ayrıca önerilen yöntem ile de çözüldü. Üç yöntemin
sonuçları karşılaştırıldı. Önerilen yöntem başarıyla doğrulandı. Hem kayma hem
de geniş destek etkilerini içeren önerilen yöntem sonuçlarının, deneysel
sonuçlara ve sonlu elemanlar yöntemi sonuçlarına daha yakın olduğu görülmüştür.

Keywords

kayma etkisi, geniş destek etkisi, rijit uç bölge, rijitlik matrisi

AN ANALYTICAL AND EXPERIMENTAL APPROACH FOR IMPROVED STIFFNESS MATRIX OF BARS WITH SHEAR AND WIDE SUPPORT EFFECTS

Abstract

In
this study, frames including both the shear and the wide support effect was
examined analytically, numerically and experimentally. Stiffness method was
used for analytical solution and finite element method was used for numerical
solution. Explicit expressions for the stiffness matrix that includes both the
shear effect and the wide support effect are presented. A model frame was
tested experimentally, and a maximum deflection result was obtained. The same
frame was modeled and solved with the finite element method and with the
proposed method. The results of three methods were compared. The proposed
method was verified successfully. The proposed method, which includes both the
shear and wide support effects, produced results that were shown to be closer
to the experimental results and the results than were the results of the other
models that were investigated. 

Keywords

shear effect, wide support effect, rigid end zone, stiffness matrix

References

• [1]. Dym, C.L., Structural Modeling and Analysis. Cambridge University Press (1997)
• [2]. Megson, T.H.G., Structural and Stress Analysis. Butterworth-Heineman (2000)
• [2]. Liew, J.Y. R., Shanmugam, N.E. Theory and Analysis of Structures. In: Chen W . F ., Liew J . Y . R., editors. The Civil Engineering Handbook, Second Edition, CRC Press (2003)
• [4]. Hibeler, R. C., Structural Analysis. Prentice Hall (2005)
• [5]. Kassimali, A., Structural Analysis. Thomson (2005)
• [6]. Bhatt, P. and Marshall, W.T., Structures, A Revision of Structures by P. Bhatt and H.M. Nelson. Longman (1999)
• [7]. Tezcan, S., Çubuk Sistemlerin Elektronik Hesap Makineleri ile Çözümü. ITU Library (1970)
• [8]. Manolis Papadrakakis, Evangelos J. Sapountzakis, "Modified Stiffness Matrix Method Matrix Methods for Advanced Structural Analysis", 2018, Pages 281-298
• [9]. E. Marotta, P. Salvini, "Analytical Stiffness Matrix for Curved Metal Wires", Procedia Structural Integrity, Volume 8, 2018, Pages 43-55
• [10]. J.R. Banerjee, A. Ananthapuvirajah "An exact dynamic stiffness matrix for a beam incorporating Rayleigh–Love and Timoshenko theories", International Journal of Mechanical Sciences, Volume 150, January 2019, Pages 337-34
• [11]. H. Wimmer, K. Nachbagauer "Exact transfer- and stiffness matrix for the composite beam-column with Refined Zigzag kinematics" Composite Structures, Volume 189, 1 April 2018, Pages 700-706
• [12]. Chugh, A. K., 1977, Stiffness matrix for a beam element including transverse shear and axial force effects. Int. J. Numer. Meth. Eng. 11(11): 1681-1697 (1977)
• [13]. Beer, F.P., Johnston, E. R. , Mechanics of Materials. McGraw Hill (1992)
• [14]. ANSYS Release 12.0 Documentation.