STATIC STABILITY ANALYSIS OF A CANTILEVER TIMOSHENKO BEAM WITH VARYING CROSS-SECTION

Abstract

In this study, effects of variation of various cross-sections on the static stability of cantilever beams subjected to axial loading have been investigated. The beam is the Timoshenko type where the effect of shear force upon the elastic curve is included to the elastic curve. Ten different types of continuous and stepped beams have been used in the analyses. In order to determine the critical buckling loads and buckling factors, the Finite Element and Finite Element-Transfer Matrix Methods have been employed. In both methods, the beam has been modeled as four degrees of freedom finite elements. Therefore, it has been possible to compare the advantages and disadvantages of both methods. Results obtained from both methods are similar to each other. Buckling parameters are determined from the solution of the eigenvalue problem obtained by the application of the variational principle to the potential energy terms of the integral form system. MATLAB 5.1 computer software has been used in numerical calculations. Results obtained for various kinds of beams have been presented in tables and graphics.

Keywords

• Static stability, Cantilever Timoshenko Beam, Finite Element Method

DEĞİŞKEN KESİTLİ ANKASTRE TIMOSHENKO KİRİŞİN STATİK STABİLİTE ANALİZİ

Abstract

Bu çalışmada, eksenel yüklemeye maruz ankastre kirişlerin statik stabilitesine, çeşitli kesit değişimlerinin etkileri incelenmiştir. Kiriş, elastik eğriye kesme kuvveti etkisinin de katıldığı Timoshenko kirişidir. Analizlerde kademesiz ve kademeli olmak üzere on çeşit kiriş kullanılmıştır. Kritik burkulma yükü ve burkulma faktörlerini tespit etmek için Sonlu Eleman ve Sonlu Eleman-Transfer Matris Metotları kullanılmıştır. Her iki yöntemde de kiriş dört serbestlik derecesine sahip sonlu eleman ile modellenmiştir. Bu şekilde, iki metodun birbirlerine olan üstünlüklerini görmek mümkün olmuştur. Her iki metottan elde edilen sonuçlar birbirine çok yakındır. Burkulma parametreleri, integral formdaki sistemin potansiyel enerji ifadelerine varyasyonel prensibi uygulanmasıyla elde edilen özdeğer probleminin çözümüyle saptanmıştır. Nümerik hesaplamalarda MATLAB 5.1 bilgisayar programlama dili kullanılmıştır. Çeşitli tipteki kirişler için elde edilen sonuçlar çizelge ve grafikler halinde sunulmuştur

Keywords

• Statik stabilite, Ankastre Timoshenko Kirişi, Sonlu Elemanlar Metodu

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