Araştırma Makalesi
BibTex RIS Kaynak Göster

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

Yıl 2019, Cilt: 8 Sayı: 2, 628 - 641, 28.06.2019
https://doi.org/10.17798/bitlisfen.495517

Öz


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




Kaynakça

  • 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. doi: 10.1016/j.mcm.2008.06.006
  • 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. doi: 10.1016/j.ijengsci.2010.09.020
  • 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.
  • Aykanat B.A. 2007. Investigation of a Cantilevered Bar Subjected to Uniformly Distributed Force in Nonlocal Elasticity. Istanbul Technical University, Graduate School of Science Engineering and Technology, Master Thesis, 29pp, Istanbul Turkey.
  • Carrera E., Giunta G. 2010. Refined beam theories based on a unified formulation, International Journal of Applied Mechanics 2, 117–143. doi: 10.1142/S1758825110000500
  • 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. doi: 10.4236/msa.2013.41010
  • Whitney J.M. 1985. Elasticity analysis of orthotropic beams under concentrated loads, Composites Science and Technology 22, 167–184. doi: 10.1016/0266-3538(85)90031 4
  • 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. doi: 10.1016/j.jsv.2008.04.056
  • Carrera E., Giunta G. and Petrolo M. 2011. Beam Structures: Classical and Advanced Theories 1st ed., John Wiley & Sons, New Delhi, India.
  • Haque, A. 2016 http://www.clearlyimpossible.com/ahaque/timoshenko.pdf (Date of access: 30.01.2018)
  • Reddy J.N. 2004. Mechanics of Laminated Composite Plates and Shells: theory and analysis 2nd ed., CRC Press, Florida, USA.
  • Jones R.M. 1999. Mechanics of Composite Materials 2nd ed., Taylor & Francis, Philadelphia, USA.
  • Saraçoğlu M.H., Güçlü G. and Uslu F. 2017 Static analysis of orthotropic beams by different beam theories, in Proc. 20th National Mechanical Congress (351-361pp) Bursa: Uludağ University

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

Yıl 2019, Cilt: 8 Sayı: 2, 628 - 641, 28.06.2019
https://doi.org/10.17798/bitlisfen.495517

Öz


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.




Kaynakça

  • 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. doi: 10.1016/j.mcm.2008.06.006
  • 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. doi: 10.1016/j.ijengsci.2010.09.020
  • 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.
  • Aykanat B.A. 2007. Investigation of a Cantilevered Bar Subjected to Uniformly Distributed Force in Nonlocal Elasticity. Istanbul Technical University, Graduate School of Science Engineering and Technology, Master Thesis, 29pp, Istanbul Turkey.
  • Carrera E., Giunta G. 2010. Refined beam theories based on a unified formulation, International Journal of Applied Mechanics 2, 117–143. doi: 10.1142/S1758825110000500
  • 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. doi: 10.4236/msa.2013.41010
  • Whitney J.M. 1985. Elasticity analysis of orthotropic beams under concentrated loads, Composites Science and Technology 22, 167–184. doi: 10.1016/0266-3538(85)90031 4
  • 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. doi: 10.1016/j.jsv.2008.04.056
  • Carrera E., Giunta G. and Petrolo M. 2011. Beam Structures: Classical and Advanced Theories 1st ed., John Wiley & Sons, New Delhi, India.
  • Haque, A. 2016 http://www.clearlyimpossible.com/ahaque/timoshenko.pdf (Date of access: 30.01.2018)
  • Reddy J.N. 2004. Mechanics of Laminated Composite Plates and Shells: theory and analysis 2nd ed., CRC Press, Florida, USA.
  • Jones R.M. 1999. Mechanics of Composite Materials 2nd ed., Taylor & Francis, Philadelphia, USA.
  • Saraçoğlu M.H., Güçlü G. and Uslu F. 2017 Static analysis of orthotropic beams by different beam theories, in Proc. 20th National Mechanical Congress (351-361pp) Bursa: Uludağ University
Toplam 13 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Bölüm Araştırma Makalesi
Yazarlar

Mustafa Saraçoğlu 0000-0003-3842-5699

Gökhan Güçlü Bu kişi benim 0000-0003-2931-9501

Fethullah Uslu 0000-0001-8057-5119

Yayımlanma Tarihi 28 Haziran 2019
Gönderilme Tarihi 11 Aralık 2018
Kabul Tarihi 29 Nisan 2019
Yayımlandığı Sayı Yıl 2019 Cilt: 8 Sayı: 2

Kaynak Göster

IEEE M. Saraçoğlu, G. Güçlü, ve F. Uslu, “Static Analysis of Orthotropic Euler-Bernoulli and Timoshenko Beams With Respect to Various Parameters”, Bitlis Eren Üniversitesi Fen Bilimleri Dergisi, c. 8, sy. 2, ss. 628–641, 2019, doi: 10.17798/bitlisfen.495517.



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