Derivation of Equations for Flexure and Shear Deflections of Simply Supported Beams

Abstract

Shear deflection of wood beams generally is exluded in plannning calculations. Ignoring shear deflection could cause significant errors, expecially for short and thick beams. In this study, two deflection functions due to flexure and shear of simply supported composite beam subjected to single force are obtained analytically. Wood being high shear modulus according to other material is selected for sample problem. The deflections the mid point of the beam are calculated to see the effect of shear by using the obtained functions for 0, 15, 30, 45, 60 and 90 orientation angles. Also, bending stresses at the mid point of the short beam are given for 0, 15, 30, 45, 60 and 90 orientation angles. It is shown that the magnitude of shear deflection depends on force, length and height of the beam. The shear effect is the smallest for 45 orientation angle and the biggest for 0 orientation angle.

Keywords

• Shear effect, Shear deflection, Simply supported composite beam, Wood.

Basit Mesnetli Kirişlerde Eğilme ve Kaymadan Dolayı Oluşan Sehim Denklemlerinin Bulunması

Öz

Kiriş uygulamalarının genelinde kaymadan dolayı oluşan sehimler ihmal edilir. Fakat; yüksek kayma modülüne sahip, kısa ve kalın kirişlerde kaymadan dolayı oluşan sehimin ihmal edilmesi çok büyük hatalara neden olmaktadır. Bu çalışmada her iki tarafında mesnetlenmiş orta noktasından tekil yüke maruz kompozit kirişlerdeki eğilme ve kaymadan dolayı ortaya çıkan sehim denklemleri analitik olarak elde edilmiştir. Örnek malzeme olarak kayma modülü diğer malzemelere göre yüksek olan ahşap seçilmiştir. Kaymanın etkisini incelemek için, elde edilen fonksiyonlar kullanılarak, kirişin orta noktasındaki maksimum sehimler 0, 30, 45, 60 and 90 oryantasyon açıları için elde edilmiştir. Aynı zamanda kayma etkisinin en fazla olduğu kısa kirişin orta noktasındaki eğilme gerilmeleri 0, 30, 45, 60 ve 90 oryantasyon açıları için verilmiştir. Kaymadan dolayı oluşan sehimin; kirişe uygulanan yüke, kirişin uzunluğuna ve yüksekliğine göre değiştiği tespit edilmiştir. Kayma etkisi; 45 oryantasyon açısında en küçük, 0 oryantasyon açısında ise en büyük olmaktadır.

Anahtar Kelimeler

• Kayma etkisi, Kaymadan dolayı oluşan sehim, Basit desteklenmiş kompozit kiriş, Ahşap.

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