Betonarme çerçevelerin tekrarlı yükler altında taşıma gücü
Limit design of reinforced concrete structures under repeated loading
- Tez No: 39701
- Danışmanlar: PROF.DR. NAHİT KUMBASAR
- Tez Türü: Yüksek Lisans
- Konular: İnşaat Mühendisliği, Civil Engineering
- Anahtar Kelimeler: Belirtilmemiş.
- Yıl: 1994
- Dil: Türkçe
- Üniversite: İstanbul Teknik Üniversitesi
- Enstitü: Fen Bilimleri Enstitüsü
- Ana Bilim Dalı: Belirtilmemiş.
- Bilim Dalı: Belirtilmemiş.
- Sayfa Sayısı: 64
Özet
ÖZET Betonarme çerçevelerin lineer olmayan davranışını başlıca iki etki belirler. Bu etkilerden birincisi, malzemelerin çatlama sonucu ortaya çıkan lineer olmayan davranışları ve malzemelerin plastik davranışıdır. Betonarme çerçevelerin lineer olmayan davranışını belirleyen ikinci tür etki ise, oluşan büyük yer değiştirmeler sonucu sistemin geometrisinin lineer olmama durumudur. Bu iki etkinin aynı anda söz konusu olma durumu ise, malzeme ve geometri açısından lineer olmama durumudur. Bu çalışmada malzeme açısından lineer olmayan sistemlerin, tekrarlı yükler altındaki davranışı incelenmiştir. Tekrarlı yükleme söz konusu olduğu için, sadece sisteme o anda etkiyen yükler değil, sistemin tüm yükleme geçmişi göz - önüne alınmaktadır. Geliştirilen yöntem ile tekrarlı yükler altında, betonarme çerçevelerde oluşabilecek plastik mafsalların hangi yükleme sonucu ve nerede oluşacağı. ve betonarme çerçevelerin göçme yükü belirlenebilmektedir. Çalışmanın ilk bölümünde, konunun tanıtılmasına ve bu konuda yapılan çalışmalara yer verilmiştir. ikinci bölümde, sabit şiddette bir normal kuvvet ve mono - ton artan eğilme momenti etkisindeki betonarme bir kesitte oluşacak sekil değiştirmeleri, bir ardışık yaklaşım yönteminden yararlanarak, hesaplayan bir bilgisayar programı hazırlanmıştır. üçüncü bölümde, tekrarlı yükleme durumunda, kesit şekil değiştirmelerini, gene bir ardışık yaklaşım yöntemi yardımı ile belirleyen bir bilgisayar programı hazırlanmıştır. Dördüncü bölümde, tekrarlı yükler altında, kesit şekil - değiştirmelerini belirleyen bilgisayar programı ve düzlem çerçeveler için statik hesap yapan bir bilgisayar programı birlikte çalıştırılarak, düzlem çerçevelerin, tekrarlı yükler altındaki lineer olmayan davranışları belirlenmiş ve bir örnek düzlem çerçeve için hesap yapılmıştır. Son bölümde, geliştirilen bilgisayar programları ile elde edilen sonuçlar değerlendirilip, bu sonuçlara değinilmiştir. iv
Özet (Çeviri)
SUMMARY LIMIT DESIGN OF REINFORCED CONCRETE STRUCTURES UNDER REPEATED LOADING The most important task of the structural engineer is the design of structures. By design is meant the determina - tion of the general shape and all specific dimensions of a particular structure so that it will perform the function for which it is created and will safely withstand the influences that will act on it during its useful life. These influences are primarily the loads and other forces to which it will be subjected, as well as other agents, like temperature fluctuations, foundation settlements, and corrosive influences. Structural mechanics is the most important tool in this process of design. It is scientific knowledge that lets one to predict wih a good degree of certainty how a structure of given shape and dimensions will behave when acted upon by known forces or other mechanical influences. The chief items of behavior that are of practical interest are ; 1- The strength of the structure: The magnitude of loads of a given distribution that wi 11 cause the struc - ture to fail. 2- The deformations: Like deflections and extent of cracking, that the structure will undergo when loaded under service conditions. The basic propositions on which the mechanics of reinfor - ced concrete is based are as follows: 1- The internal forces, such as bending moments, shear forces, and normal and shear stresses, at any sec - tion of a member are in equilibrium with the effects of the external loads at that section. This proposition is not an assumption but a fact, because any body or any portion thereof can be at rest only if all forces acting on it are in equilibrium. 2- The strain in an embedded reinforcing bar is the same as that of the surrounding concrete. If it is expressed in a different way, it is assumed that perfect bonding exists between concrete and steel at the interface, so that no slip can occur between the two materials.Therefore, as one deforms, must the other. With modern deformed bars a high degree of mechanical interlocking is provided besides the natural surface adhesion, so this assumption is very close to correct. 3- Cross sections which were plane prior to loading continue to be plane in the member under load. Accurate measurements have shown that when a reinforced concrete member is loaded close to failure, this assumption is not absolutely accurate. However, the deviations are usually minor, and the results of theory based on this assumption check well with extensive test information. 4- As the fact that the tensile strength of concrete is a small fraction of its compressive strength, the con - crete in that part of a member which is in tension is usually cracked. While these cracks, in well designed members, are generally so narrow as to be hardly visible, they evidently render the cracked concrete incapable of resisting any tension stress whatever. This assumption is evidently a simplification of the actual situation because in fact, concrete prior to cracking, as well as the con - crete located between cracks, does resist tension stresses of small magnitude. 5- The theory is based on the actual stress-strain relationships and strength properties of the two materials concrete and steel or some reasonable simplifications thereof. The fact that nonelastic behavior is reflected in modern theory, that concrete is assumed to be ineffec - tive in tension. These assumptions permit one to predict by calculation the performance of reinforced concrete members only for some simple situations. Actually the joint action of two ma - terials as dissimilar and complicated as concrete and steel is so complex that it has not yet lent itself to purely analytical treatment. For this reason, methods of design and analysis, while utilizing these assumptions. are very largely based on the results of extensive and continuing experimental research. The nonlinear behavior of reinforced concrete frames with sideways is governed by two effects; 1- The nonlinearity of materials due to cracking and the plastic behavior of materials. 2- The nonlinearity of geometry caused by the large displacements. VIIn general applications of structural engineering, the structural analysis generally depends on linear theory, that it is assumed that the materials behave linear elastic and the displacements of the structure are small» while the design of reinforced concrete members, generally is based on the design concept, which is known as strength design. The nonlinear, inelastic range of the behavior of the ma - terials concrete and steel is taken into account during strength design. That is, concrete in a structural member reaches its maximum strength and subsequent fracture at stresses and strains far beyond the initial elastic range in which stresses and strains are fairly proportional. Similarly, steel close to and at failure of the member is usually stressed beyond its elastic domain into and even beyond the yield region. Consequently, the nominal strength of a member must be calculated on the basis of this inelastic behavior of materials. As an alternative to the strength design method, members are sometimes proportioned so that stresses in the steel and concrete resulting from normal service loads are within specified limits. These limits, known as allowable stresses, are only fractions of the failure stresses of the materials. So, members are designed on an elastic basis as long as the stresses under service loads remain below these limits. In the older service load design method, all types of loads are treated the same no matter how different their individual variability and uncertainty. Also, stresses are calculated on an elastic basis, while in reality the strength of a member depends on the inelastic stress - strain behavior near and at failure. So. the service load design method does not permit an explicit evaluation of the margin of safety. In contrast, in the newer strength design method, individual load factors may be adjusted to represent different degrees of uncertainty for the various types of loads, and strength reduction factors likewise may be adjusted to the precision with which various types of strength are calculable, and the strength itself in each case is calculated with explicit regard for inelastic action. Because of these differences in realism and reliability, over the past 25 years the strength design method has rapidly displaced the older service load design method. In recent years, as more common use of computers increases viithe use of nonlinear theory for analysis of structures also increases rapidly. This study is also concerned with the nonlinear theory for the analysis of structures. The nonlinear behavior of reinforced concrete frames under monotonous increasing and repeated loading is examined. Reinforced concrete frames are frequently used to resist earthquake or wind forces. These forces will accentuate the complexity of the frame behavior because of the con - tinuous change of the shape of the bending moment diagram. The change of moment diagram will in turn affect the mag - nitude of cumulative plastic rotations. The main part of this study is to develop two computer programs, one of which determines the plastic rotations of a cross section of a reinforced concrete member under monotonous increasing loads, and the other, the plastic rotations of a" cross section of a reinforced concrete member under repeated loading. The history of loading is taken into account by the com - puter program, that determines the plastic rotations, un - der repeated loading, since the history of loading plays an important role in the behavior of the reinforced con - crete member, when the member is subjected to repeated loading. Both the two computer programs, used for determining plastic rotations, under monotonous increasing and repe - ated loading are based on the nonlinear behavior of the materials, concrete and steel. During developing these computer programs, the stress - strain relationships of these two materials are princi - pally used. These relationships have vital importance to determine the deformations of cross sections in reinforced concrete members. So, firstly two basic computer programs about the behavior of concrete and steel are developed. One of these computer programs determines the stress of a con - crete fiber in a reinforced concrete cross section, corresponding to an arbitrary strain of this fiber. This computer program, taking into account the repeated loading, can also determine stresses, considering the strain history. So, by using this computer program, for any fiber of concrete, whose present strain and strain history are known, the stresses can be determined. viiiThis computer program that determines the stresses of a certain concrete fiber, when the strains are input, is named as BETGER. The second of these basic programs about the behavior of materials, determines the stresses of steel, when the strains of steel are known. This computer program, which is named as ÇELÎK, also taking into account the repeated loading case, determines the steel stresses, considering the history of steel strains. The detailed explanation about the computer programs BETGER and ÇELİK is presented in the related chapter. After these two main computer programs about the stress - strain relationships of concrete and steel are developed, a more complex computer program that determines the deformations of cross sections of reinforced concrete members is developed. At first, this computer program is developed for determining the rotations and axial deformations under monotonous increasing loading. This computer program, which is named as KMFOR, determines the rotations and all axial deformations where needed in a cross section of a reinforced concrete member. So, by using this computer program, the moment - curvature relationship of any reinforced concrete cross section can be obtained, under monotonous increasing loading. Example moment - curvature diagrams, obtained by using the com - puter program KMFOR is represented in the related chapter. Also more detailed explanation and the flowchart of this computer program are presented in that chapter. The input data for KMFOR includes : 1- Acceptable maximum relative error. 2- Strengths of materials, concrete and steel. 3- Critical strains for the materials, concrete and steel. 4- Dimensions of the cross section. 5- Amount of reinforcement. 6- Internal forces acting on the cross section of the reinforced concrete member. As output, the strain of cross section in the mid plane, the curvature of the cross section, strains of reinforce - ment and strains of outer fibers of the concrete are obtained. IXFor repeated loading, another computer program which is more complex than KMFOR is needed to determine the curvature and axial deformations of a cross section of a reinforced concrete member. A computer program which is named as BETKE is developed for this complicated task. The main difference between the computer programs BETKE and KMFOR is, the assumptions used for the behaviors of the materials, concrete and steel. For the computer program BETKE» the stress - strain relationships of concrete and steel for repeated loading is accepted, while for KMFOR, the usual stress - strain relationships of these materials under monotonous increasing loads, have been accepted. As a second difference between KMFOR and BETKE; in com - puter program KMFOR, since it is used for only monotonous increasing loading and no unloading is present, and as the strains along the cross section changes linearly, the distribution of concrete stresses present in the cross section can be determined according to the strength method in the traditional way. So, as the distribution of the concrete stresses is known, the normal force and bending moment that all concrete cross section will have, can be determined. If we add the normal forces and bending moments of concrete section and reinforcement, the total normal force and bending moment in the cross section which are needed for determining the deformations, are deter - mined. For repeated loading case, in the computer program BETKE, since when unloading is present, the change of stresses along the cross section is not known, the distribution of stresses along the cross section can not be determined. So, the normal force and the bending moment that the concrete cross section bears are determined by dividing the cross section into several divisons. The normal force and the bending moment, that these divisons have, are determined for each divison seperately by using the computer program BETGER as a subroutine in BETKE. Total forces that the whole concrete cross section have, are determined by adding the normal forces, and the bending moments of each divisons. These two computer programs. KMFOR and BETKE are the chief work of this study. After these two computer programs are developed, between these two, only BETKE is used, since the subject of this study concerns repeated loading. The input data for BETKE includes all input data of KMFOR. and additionally the number of the divisons, that the cross section is divided is used as an input data.For nonlinear structural analysis of reinforced concrete frames under repeated loading, the computer program BETKE and a statical analysis computer program that determines internal forces according to the linear theory when external forces are given, are used together. The nonlinear structural analysis is carried out for a single span, symmetrical reinforced concrete frame of beam length 10.00 m., and column height 6.00 m.. The system is analysed under uniform distributed vertical load of 30.00 kN/m, and a horizontal load of 10.00 kN according to the linear theory. The internal forces at every critical cross section of the members of the reinforced concrete frame determined by the statical analysis program, are used as input data, for the computer program BETKE, to determine the curvatures and axial deformations of these critical cross sections. Making use of the calculated curvatures, the changes in the EI values of each cross section are also determined by the computer program BETKE. For the next loading, the new EI values of the members of the reinforced concrete frame calculated by BETKE are used as input data for the linear structural analysis computer program. Following the same procedure, the loads are in creased until yielding occurs and plastic hinges are formed in certain cross sections. Before the necessary number of plastic hinges to cause failure of the structure are formed, the acting horizontal load is decreased. During the gradual decrease of horizontal force, the same procedure for nonlinear analysis is used as the case of increasing horizontal load. Using this procedure, the places of the forming plastic hinges are determined, as well as determining the corres - ponding horizontal load, that causes plastic hinges to form. If the acting horizantal load is increased, until enough number of plastic hinges are formed to cause the failure of the structure, the load that causes the structure to collapse can also be determined according to the nonlinear theory. The study is composed of five chapters. In the first chapter, general outline and an introduction of the subject are presented. In the second chapter, the details about the computer program that determines the deformations of cross sections of reinforced concrete members under monotonous increasing loading are presented. xiIn the third chapter, the details about the computer program, that determines the deformations of the cross sections of reinforced concrete members under repeated loading are presented. In the fourth chapter, information on the nonlinear structural analysis of reinforced concrete frames under repeated loading is presented. An example reinforced concrete frame is also analysed nonlinearly under repeated loading. This nonlinear analysis is presented in this chapter with details. In the last chapter, the obtained results of nonlinearly analysed reinforced concrete frame under repeated loading and the results obtained by using the computer programs KMFOR and BETKE are presented. Xll
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