SLOPE DEFLECTION TRANSFER MATRIX METHOD FOR CONTINOUS BEAMS

Year 2022, Volume: 8 Issue: 2, 243 - 252, 31.12.2022

Duygu Öztürk , Kanat Burak Bozdoğan

https://doi.org/10.34186/klujes.1184109

Abstract

The Slope Deflection Method is one of the displacement-based methods developed for structural analysis. In this study, an approach is proposed for the static analysis of continuous beams. The basis of this approach includes the Ricatti Transform, which was used in the literature to get the Transfer Matrix Method by using the Finite Element Method. In this study, Ricatti Transform was applied to the Slope Deflection Method for continuous beams. In the study, firstly, the application of Ricatti Transform to the Slope Deflection Method was shown theoretically, and then two numerical examples were solved to show the application and suitability of the presented approach. With the presented method, the number of system unknowns that are the basis for the solution is reduced, thus saving the analysis time.

Keywords

Slope deflection transfer deflection method, continuous beam, static analysis

References

• 1] Aslam Kassimali, Structural Analysis, Cengage Learning, 2011
• [2] Pestel, E.C., Leckie, F. A. Matrix Methods in Elastomechanics. New York: McGraw-Hill,1963
• [3] INAN, M. The Method of Initial Values and the Carry-over Matrix in Elastomechanics, Middle East Technical University, 1968
• [4] RUI, X., WANG, G., LU, Y. Transfer Matrix Method for Linear Multibody System. Multibody Syst. Dyn., 19, No.3,179-207, 2008
• [5] Feyzollahzadeh M, Bamdad M, A modified transfer matrix method to reduce the calculation time: A case study on beam vibration. Applied Mathematics and Computation 378, 2021
• [6] Feyzollahzadeh M, Bamdad M., An efficient technique in transfer matrix method for beam-like structures vibration analysis. Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, 236(14), 7641-7656, 2022
• [7] Adnan Çakıroğlu ve Enver Çetmeli, Yapı Statiği 2, Beta Basım Yayım, 2000
• [8] İbrahim Ekiz, Yapı Statiği 2, SeçYayın Dağıtım, 2005
• [9] Kutlu Darılmaz, Konuralp Girgin, M. Günhan Aksoylu, Yapı Statiği - Hiperstatik sistemler Konu Anlatımı ve Çözümlü Problemler, Birsen Yayinevi, 2011
• [10] Faruk Karadoğan, Sumru Pala, Ercan Yüksel ve Yavuz Durgun, Yapı Mühendisliğine Giriş Yapısal Çözümleme Cilt 3, 2016
• [11] Hoerner, G.C. The Riccati Transfer Matrix Method. Ph.D. Thesis, University of virginia, Charlottesvile, VA., 1975
• [12] CHOI, M.S. Free Vibration Analysis of Plate Structures Using Finite Element Transfer Stiffness Coefficient Method. J. Mech. Sci. Tech., 17, No. 6, 805-815, 2003
• [13] Rong, B., Rui, X.T., Wang, G.P. Modified Finite Element Transfer Matrix Method for Eigenvalue Problem of Flexible Structures. J. Appl. Mech., ASCE, 78, No.2, 021016, 2011
• [14] Ozturk, D., Bozdogan, K., Nuhoglu, A. Modified Finite Element-Transfer Matrix Method for The Static Analysis of Structures. Struct. Eng. Mech., 43, No.6, 761-769, 2012
• [15] Bozdogan, K.B.,Maleki,K.F. An Aplication of the Modified Finite element Transfer Matri Method for a Heat Transfer Problem, Kırklareli University Journal of Engineering and Science,5,No. 1,15-28, 2019