Gövde boşluklu betonarme kirişlerde taşıma gücünün sonlu elemanlar yönetimiyle incelenmesi

Abstract

Günümüzde modern binalarda, havalandırma, elektrik su, atık su ve mekanik tesisatlar için kullanılan kanallar ve borular asma tavanlar üzerindeki boşluklarda bulunmaktadır. Kiriş gövdesinde açılacak boşluklar arasından bu tesisat kanallarını geçirmek suretiyle önemli miktarda bir alan kazanılarak daha ekonomik bir çözüm elde edilebilmektedir. Ancak gövdesinde boşluk bulunan bir kiriş, servis yükleri altında büyük çatlaklar, deformasyonlar ve kiriş rij itliğinin azalması gibi bir takım sorunları da beraberinde getirmektedir. Bilindiği gibi boşluklu betonarme kirişlerin taşıma gücünün klasik hesap yöntemleriyle incelenmesi oldukça zor ve karmaşık bir problemdir. Bu tür problemlerde analizin güçlüğü, betonun yapısal özelliği ve yük altındaki davranışının henüz kesin olarak ifade edilememiş olmasından kaynaklanmaktadır. Bu nedenle gerek bilimsel çalışmalarda gerekse uygulama projelerinin çözümünde analizin sonlu elemanlar yöntemiyle yapılması büyük üstünlükler sağlamakta ve gerçeğe daha yakın sonuçlar elde edilebilmektedir. Bu çalışmada gövdesinde boşluk açılarak zayıflatılmış tek açıklıklı ve iki tekil simetrik yükle yüklenmiş basit mesnetli betonarme kirişlerin artan yükler altındaki davranışı lineer olmayan sonlu elemanlar yöntemiyle incelenmiş ve bu kirişlerin taşıma güçleri elde edilmiştir. Çalışmanın 1. Bölümünde literatürdeki benzer araştırmalar hakkında kısaca bilgi verildikten sonra 2. Bölümde betonarmenin davranışı ve lineer olmayan analizi için esas alman çözüm yöntemi açıklanmıştır. 3. Bölümde lineer olmayan sonlu elemanlar yönteminin betonarme yapı elemanlarına uygulanması ve kullanılan bilgisayar programı hakkında bilgi verilmiştir. 4. Bölümde çeşitli boşluk konumları ve sayıları için gövde donatışız ve gövde donatılı olmak üzere gözönüne alınan iki grup kiriş sonlu elemanlar yöntemiyle analiz edilmiş, gövde boşluğu ve gövde donatısının kirişlerin taşıma gücü üzerindeki etkileri kirişlerde oluşan çatlak durumlarıda dikkate alınarak araştırılmıştır. Çalışmada gövde boşluklu kirişlerin tasarımında oldukça önemli yer tutan boşluk yeri ve boyutlarıyla ilgili öneriler getirilirken bu önerilerin 1. Bölümdeki literatürdeki deney verileriyle uyumlu olduğu sonucuna varılmaktadır.

In modern building construction, ducts and pipes for air conditioning, water supply, sewage and other electrical and mechanical services are accommodated in the space above the false ceiling. Passing these ducts through openings in the floor beams eliminates a significant amount of dead space and results in more compact and economical design. Unless proper provisions are made in the design office for these openings, there is a risk that each of the subtrades will knock out holes to suit their installations and possibly weaken the structural frame of the building to a critical degree. Therefore, provision of these passings after a rigorous engineering analysis will not only satisfy a general popular demand but also solve a significant problem. In this study, behaviour of reinforced concrete beams containing rectangular openings, subjected to two point loads and simply supported at its ends are studied under increasing loads by nonlinear finite element method and effects of the loss of section due to openings on the load- carrying capacity of the beams and the necessary conditions in design are investigated. In the first chapter, some information is given about previous similar researches. Unfortunately, only a limited amount of research work on this subject has been performed. Among these researches carried out by the experimental and theoretical ones, there is no detailed study concerning the application of finite element method to reinforced concrete beams with web openings. The behaviour of concrete considered in the analysis, selected mathematical model and the types of analysis all play an important role in obtaining more realistic results by using nonlinear finite element method. Therefore, investigations concerning the behaviour of materials and nonlinear finite element analysis are also given at the stage of searching literature. In the second chapter, a method of analysis for the behaviour of reinforced concrete elements and nonlinear analysis is fully explained. Starting from the behaviour of concrete under biaxial loading, stress-strain relations based on the results obtained by Kupfer et al [4], [9], and viii formulated by Link is considered. Relations given in dimensionless parameters of Kupfer for orthotropic and nonlinear behaviour of concrete and failure criteria are used. The deformation responses of reinforcing steel bars are represented by ideal elasto-plastic relationship. This relationship is linear elastic up to yielding, as from this point for the final branch that has been given a slight inclination in order to avoid the numerical instabilities associated with zero stiffness. In the third chapter, information about the application of nonlinear finite element method to plane reinforced concrete structures and the computer program are provided. Two element types are selected to represent reinforced concrete structures, rectangular elements to simulate concrete and bar elements for steel. The numerical representation of cracking is based on the smeared crack approach. The smeared crack approach spreads the effect of cracking over a large region where bond slip actually occurs. As a result the assumption of perfect bond is considered to describe adequately the interaction between steel and concrete. The failure mode in finite elements representing concrete is controlled according to failure envelope curve of Kupfer and the failure is described in three types modes. Separation mode cracking, separation-crushing mode cracking and crushing mode cracking. The failure mode in bar elements representing steel is controlled according to whether the stresses have reached to yielding point or not. Under incremental load, the following descriptions concerning the behaviour of the structural system are given. *In case separation mode cracking occurs in one or more elements, microcracks have a tendency to propogate. *In a certain region, in many neighboring elements, when the separation mode cracking occurs, the cracks in these elements form into greater and continuous cracks. *In consequence of cracks growing up gradually, structural system collapses in separation mode cracking. *When the crushing mode cracking occurs in an element, the structural system collapses in crushing mode cracking. IX *Also in case of separation-crushing mode cracking in an element, structural system collapses in separation- crushing mode cracking. *As a result of yielding of the bar elements, structural system collapses in yielding mode as well. The collapse load of the structural system is determined by following up the failure modes, load- deformation and stress-strain curves in critical points of the system. In addition, since the nonlinear finite element procedure used has already been fully described, this method will be discussed only briefly here. The application to structural analysis requires the use of constitutive laws describing the strength and deformation properties of concrete and steel as well as the consideration of interaction between steel and concrete. According to this, *A load increment at adequately frequent intervals is selected so as to estimate the approximate collapse load of the structural system. *In the beginning, concrete is assumed as a linear elastic material, initial elasticity modulus and poisson ratio are adopted and linear elastic analysis of the problem is performed by finite element method.