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

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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