Gövde boşluklu betonarme kirişlerde taşıma gücünün sonlu elemanlar yöntemiyle incelenmesi
Analysis of the ultimate strength of reinforced concrete beams with web openings by nonlinear finite element method
- Tez No: 39297
- Danışmanlar: PROF.DR. ÖZKAN İŞLER
- Tez Türü: Doktora
- Konular: İnşaat Mühendisliği, Civil Engineering
- Anahtar Kelimeler: Betonarme kiriş, Sonlu elemanlar yöntemi, Taşıma gücü, Reinforced concrete beam, Finite element method, Bearing capacity
- Yıl: 1994
- Dil: Türkçe
- Üniversite: İstanbul Teknik Üniversitesi
- Enstitü: Fen Bilimleri Enstitüsü
- Ana Bilim Dalı: Belirtilmemiş.
- Bilim Dalı: Belirtilmemiş.
- Sayfa Sayısı: Belirtilmemiş.
Özet
ÖZET 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. vıı
Özet (Çeviri)
SUMMARY ANALYSIS OF THE ULTIMATE STRENGTH OF REINFORCED CONCRETE BEAMS WITH WEB OPENINGS BY NONLINEAR FINITE ELEMENT METHOD 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 viiiformulated 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. *In this linear elastic analysis, <JX and a2 principal stresses and a=ff1/(r2 principal stress ratio are calculated from ffx,öy and Txy. *By means of the charts prepared according to 0\/0i principal stress ratio and a2 compression stress, tangent modulus and poisson ratio of concrete exhibiting orthotropic behaviour are obtained. *By means of nodal displacements, the nodal forces of the bar elements are calculated and then the stresses are obtained. ?According to updated characteristics of the materials, the problem is solved again. *Until the realistic characteristics of the material behaviour calculated for finite elements are attained, the iteration could be made. *In all finite elements, stresses obtained in every step are added to total stresses which are calculated in the preceding steps. x*By means of the accepted failure criteria, cracking in concrete elements and yielding in steel elements are controlled. *If separation mode cracking occurs in concrete element, the element is assumed to be cracked and lost strength in one direction. *If crushing mode cracking occurs in a concrete element and/ or yielding in a steel element, it is assumed that the structural system collapses. *If there is no collapse, load level is increased and analysis is continued up to collapse. In the fourth chapter, for various of opening locality and numbers, beams with web reinforcement and without web reinforcement are analyzed by nonlinear finite element method and the effects on load-carrying capacity of beams of web openings and web reinforcements are investigated by also considering the crack conditions. In the numerical procedures, two major group beams are considered. Every one of the groups is extended over three series beams provided loading condition and type of supporting are the same. In these beams carried out both of the group, the location of the openings on the beam is changed on vertical and horizontal direction. Otherwise in every series beam, number of openings on the beam is changed provided that the opening area is kept constant. In other words, provided the total area of the web openings on the beam is fixed. Six openings in first series of beams, four in the second series and two in the third ones are considered and the variation of load-carrying capacity due to web openings is investigated. The results of this investigation are compared with those of experimental research works. The results of the experiments of Mansur et al [29] are used. The results obtained from this study match well with the results of tests. In the fifth chapter, the results of the analysis that is obtained by nonlinear finite element method and the effects on load-carrying capacity of web openings and web reinforcements are evaluated. In this evaluation, important aspects and parameters are considered such as location of web openings, eccentricity of web openings below or above the beam axis, number of web openings, size of web openings, effects of web reinforcement, collapse load, mode of failure, load- deflection behaviour and general cracking behaviour. XIThe following conclusions may be drawn from the investigation, ?Openings affect load-carrying capacity of the beams by corrupting stress transfer on beam. *The load carrying capacity of the beams containing a few small openings that have the same area is greater than those of beams containing a large opening. *The load carrying capacity of the beams decreases significantly as openings are close to the loading point. That is, openings located in a relatively high-moment region give larger deflections and smaller collapse load. *Web opening located in high-moment region has influence on loading capacity of the beam and this opening determines collapse load. *The ultimate strength of the beams increases in case of reinforcement near the sides of the openings. *The load-carrying capacity of the beams increase significantly as the openings are close to the tension zone. While recommendations concerned in location and size of openings which are important in detailing beams with web openings are given, good agreement between the theoretical and experimental results is concluded. XXI
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