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

Year 2019, , 628 - 641, 28.06.2019

Mustafa Saraçoğlu , Gökhan Güçlü Fethullah Uslu

https://doi.org/10.17798/bitlisfen.495517

Cited By: 2

Abstract

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.

Keywords

Euler-Bernoulli Beam Theory, Timoshenko Beam Theory, Fiber Reinforced Composites, Equivalent Young’s and Shear Moduli, Orthotropic Beams

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

Abstract

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.

Keywords

Euler-Bernoulli Kiriş Teorisi, Timoshenko Kiriş Teorisi, Lifli Kompozitler, Eşdeğer Elastisite ve Kayma Modülleri, Ortotrop Kirişler

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