Ayfer TEKİN ATACAN, Receb Faruk YÜKSELER

Sinüzoidal Yük Etkisindeki Küçük İlkel Kusurlu Kirişlerin Doğrusal Olmayan Davranışı

Bu çalışmada; sinüzoidal yüke maruz, uçları sabit mesnetli, başlangıçta küçük sinüzoidal kusura sahip kirişlerin burkulma ve burkulma sonrası davranışları Euler-Bernoulli kiriş teorisi kullanılarak incelenmiştir. Denge denklemleri, kinematik denklemler ve bünye denklemlerini içeren, geometrik olarak doğrusal olmayan problemin yönetici diferansiyel denklemleri, sonlu farklar yöntemi ile cebirsel denklemlere dönüştürülmüş ve NewtonRaphson yöntemi kullanılarak sayısal olarak çözülmüştür. Burkulma yükleri ve burkulma çökmelerinin değerleri, yük-çökme eğrileri çizilerek belirlenmiştir. İlkel kusurun burkulma değerleri üzerindeki etkisi incelenmiştir. Küçük ilkel kusurun değeri arttıkça, boyutsuz burkulma yükünün arttığı ve boyutsuz burkulma yer değiştirmesinin azaldığı görülmüştür. Konuyla ilgili daha önceki çalışmalardan farklı olarak; başlangıçta sinüzoidal ilkel kusurlu kirişlerin, şekil değiştirmenin çeşitli aşamalarındaki elastik eğri diyagramlarının yanı sıra; burkulma öncesindeki, burkulma sırasındaki ve burkulma sonrasındaki durumlarına karşı gelen kesit tesirlerinin diyagramları ilkel kusurun çeşitli değerleri için sunulmuştur.

Nonlinear Behavior of Beams Having Initially Small Imperfection Subjected to Sinusoidal Load

In the present study, the buckling and postbuckling behaviors of beams having initially small sinusoidalimperfection with pinned ends subjected to sinusoidal loading are examined by using Euler-Bernoulli beam theory.The governing differential equations of the geometrically nonlinear problem consisting of the equilibriumequations, kinematical equations and the constitutive equations are converted into algebraic equations via the finitedifferences and solved numerically by using the Newton-Raphson method. The values of buckling loads andbuckling deflections are determined by drawing load-deflection curves. The effect of the initial imperfection onthe buckling values is investigated. It is seen that as the value of the small initial imperfection is increased, thebuckling force is increased and buckling deflection is decreased. Unlike previous studies on the subject, thediagrams of the deformed shapes of the beam having initially small imperfection as well as the diagrams of theinternal forces at various stages of the deformation including the prebuckling, buckling and postbuckling statesare presented for various values of the initial imperfection.

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