Mustafa Halûk SARAÇOĞLU, Gökhan GÜÇLÜ, Fethullah USLU

Çeşitli Parametrelere Göre Ortotrop Euler-Bernoulli ve Timoshenko Kirişlerinin Statik Analizi

Bu çalışmada kiriş uzunluğu boyunca ortotrop kirişlerin çökmeleri Euler-Bernoulli ve Timoshenko kiriş teorilerine göre statik analiz yapılarak hesaplanmıştır. Malzemelerin mekanik özellikleri, liflerin oryantasyon açısına bağlı olarak değiştiği için, yönetici denklemlerin türetilmesi, eşdeğer elastisite modülü ve eşdeğer kayma modülü kullanılarak gerçekleştirilmiştir. Ortotrop kirişler eşdeğer modüller kullanılarak izotrop kirişler olarak modellenmiştir. Farklı ortotrop malzemelerden oluşan iki sayısal örnek farklı sınır koşulları ve yükleme durumları için verilmiştir. Liflerin oryantasyon açılarının değişiminin çökme değerlerine etkisi de ele alınmıştır. Ortotrop kirişlerin statik analizinde oryantasyon açısı, malzeme özellikleri, uzunluk-derinlik oranı parametreler olarak alınmıştır. Sonuçlar ayrıca izotrop olan çelik malzemesi ile karşılaştırılmış ve faydalı olabilecek tablo ve grafikler şeklinde sunulmuştur.

Static Analysis of Orthotropic Euler-Bernoulli and Timoshenko Beams With Respect to Various Parameters

In this study, deflections of orthotropic beams along the beam length are calculated by using static analysisaccording to Euler-Bernoulli and Timoshenko beam theories. Since the mechanical properties of the materialschange as the orientation angle of fibers changes, the formulation is carried out using the equivalent Young’smodulus and the equivalent shear modulus. Orthotropic beams are modeled as isotropic beams by using equivalentmoduli. Governing equations are derived. Two numerical examples with different orthotropic materials are givenfor different boundary and loading conditions. The effect of changing the orientation angle of the fibers on thedeflection values is also considered. Orientation angle, material properties, length to depth ratio has beenconsidered as parameters in the static analysis of orthotropic beams. Results are also compared with steel which isan isotropic material and presented in the form of tables and graphs which may be useful.

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[1] Labuschange A., van Rensburg N.F.J., van der Merwe A.J. 2009. Comparison of linear beam theories. Mathematical and Computer Modelling, 49: 20-30.
[2] Reddy J.N. 2010. Nonlocal nonlinear formulations for bending of classical and shear deformation theories of beams and plates. International Journal of Engineering Science, 48: 1507–1518.
[3] Sayyad A.S. 2011. Comparison of various refined beam theories for the bending and free vibration analysis of thick beams. Applied and Computational Mechanics, 5: 217–230.
[4] Aykanat B.A. 2007. Investigation of a Cantilevered Bar Subjected to Uniformly Distributed Force in Nonlocal Elasticity. Master Thesis, Istanbul Technical University, Graduate School of Science Engineering and Technology, 29pp, Istanbul.
[5] Carrera E., Giunta G. 2010. Refined beam theories based on a unified formulation. International Journal of Applied Mechanics, 2: 117–143.
[6] Elshafei M.A. 2013. FE modeling and analysis of isotropic and orthotropic beams using first order shear deformation theory. Materials Sciences and Applications, 4: 77–102.
[7] Whitney J.M. 1985. Elasticity analysis of orthotropic beams under concentrated loads. Composites Science and Technology, 22: 167–184.
[8] Li X.F. 2008. A unified approach for analyzing static and dynamic behaviors of functionally graded Timoshenko and Euler–Bernoulli beams. Journal of Sound and Vibration, 318: 1210– 1229.
[9] De Rosa M.A., Franciosi C. 2013. A simple approach to detect the nonlocal effects in the static analysis of euler-bernoulli and timoshenko beams. Mechanics Research Communications, 48: 66-69.
[10] Palmeri A., Cicirello, A. 2011 Physically-based dirac's delta functions in the static analysis of multi-cracked euler-bernoulli and timoshenko beams. International Journal of Solids and Structures, 48 (14-15), 2184-2195
[11] Saraçoğlu M.H., Güçlü G. Uslu F. 2017 Static analysis of orthotropic beams by different beam theories. in Proc. 20th National Mechanical Congress pp 351-361 05-09 September 2017 Bursa.
[12] Carrera E., Giunta G., Petrolo M. 2011. Beam Structures: Classical and Advanced Theories 1st ed., John Wiley & Sons, New Delhi, India.
[13] Haque A. 2016 http://www.clearlyimpossible.com/ahaque/timoshenko.pdf (Date of access: 30.01.2018)
[14] Reddy J.N. 2004. Mechanics of Laminated Composite Plates and Shells: theory and analysis 2nd ed., CRC Press, Florida, USA.
[15] Jones R.M. 1999. Mechanics of Composite Materials 2nd ed., Taylor & Francis, Philadelphia, USA.