Aderansta mekanik etkileşim olayı

Abstract

IV ÖZET Bu çalışmanın konusu betonarme bir yapı ı _ - ^ ^ beton ile donatı arasında oluşan mekanik `etki ' c dır. Çalışmada bu olayın genel olarak gerek bir it,.^ yapı elemaıımdaki gerek aderans konusundaki y=-ri ve on^m incelenecek ve olayın özellikle iki ana öğesi ele alına - çaktır. Yarılma çatlakları (splitting cracks) ve agrega kenetlenmesi (aggregate interlock). Mekanik etkileşim sü resince hemen daima yarılma çatlakları oluştuğu bilinmekte dir, Agrega. kenetlenmesi olayının ise genel olarak gerek, kârgir veya. beton gerek betonarme, yapı elemaniarındaki çat laklar boyunca kayma day.anımmdaki çok önemli, katkısı bi - 1 inmek t e ve mekanik etkileşim olayını ele almada temel bir model ve. kavram olduğu kabul edilmektedir. Çalışmada yarılma çatlaklarının mekanik etkileşim saf hasındaki rolü, özellikle, Politecııico di Milano'da 1981-82 ders yılında gerçekleştirilen deneysel program ve bu progra mın sonuçları ışığında ele alınacaktır. Aynı safhayla ilgili diğer bir ana öğe olan agrega kenetlenmesi olayı ise, sonuç ları 1982 de Daschner tarafından kısmen açıklanan ve bu ko - nuda şimdiye kadar yapılanların teknik yönden en gelişmişi görünen deneylere dayanılarak yapılan bir araştırmanın çer çevesinde geliştirilen ger i İme- deplasman bağıntıları formüle edilerek ve mekanik etkileşim olayından bağımsız olarak ince lenecektir. Politecnico di Milano'da gerçekleştirilen deneysel programda simüle edilmiş olarak önceden hazırlanmış olan değişik genişlikte yarılma çatlaklarını içeren tek donatılıve nervürlü betonarme numuneler kullanılmış ve donatı üze rinde çekip çıkarma deneyi uygulanmıştır. Çalışma dört bölümden oluşmaktadır. Birinci bölümde çalışmanın konusu sunulacak, incelenecek- öğelerin betonar me ve aderans olgusundaki yeri ele alınırken konu ile il - gili çalışmalar tanıtılacaktır. ikinci bölümde, mekanik etkileşim safhası, `yürütülen deneysel program açıklanarak ve deney sonucu elde edilen- bulguların ışığında şu parametrelere bağlı olarak ele alı nacaktır :. 1) Çekme deneyi süresince elde edilen aderans gerilme leri, 2) Bu gerilmeler doğrultusundaki deplasmanlar, 3) Yarılma çatlağı genişlikleri, 4) Donatı doğrultusuna ve yarılma çatlaklarına dik o- larak uygulanan basınç gerilmeleri. Bu dört parametrenin mekanik etkileşim olgusu üzerindeki etkileri deplasmanT geri İme eğrileri, aracılığıyla gösteri -' lecek ve enine basınç gerilmelerinin nihai aderans kapasi tesine olan olumlu ve, çok önemli katkısı üzerinde özellik le durulacaktır. Deney süresince söz konusu dört paramet - reden sadece yarılma çatlağı genişlikleri sabit tutulmuş -- tur. İkinci bölüm şu alt bölümlerden oluşmaktadır: 1) Giriş:. Deneysel çalışmanın konusu, betonarme ve aderans olgusundaki, yeri, 2). Aderans mekanizmaları, 3) Deneysel programın amacı ve kapsamı, 4) Deneysel program, 5) Deneysel sonuçlar, 6) Sonuçların uygulama alanındaki etkinliği. Çalışmanın üçüncü bölümünde ise agrega kenetlenmesi.olgusu üzerinde durulacak, bu olgu ile ilgili olarak ge - rilme-deplasman bağıntıları en son deneysel sonuçlara gö re yeniden formüle edileceklerdir. Söz konusu bağmtıla - rm elde edilmesinde deneysel sonuçlara dayanan gerilme-VI deplasman diyagramlarından yararlanılmıştır, j kayma ge rilmesi ve o enine basınç gerilmesi ile bu serilmelerin nn. doğrultularmdakı deplasmanlar (ît, cn) arasındaki bağın - tıları gösteren- bu diyagramlara çok iyi bir uyum sağlayan teorik Tormulasvon. çıkarılacak ve bu f ormülasyonun agrega kenetlenmesi olgusunun gerektirdiği fiziksel özelliklerle tarn bir uyum sağladığı gösterilecektir. Sonuç bölümünde varılma çatlakları ve agrega kenet - leı1 -.. `? 1 m »-U alan bu çalışmanın mekanik etkileşim konasa`uiı K çalışmada açıklanan deneysel bul gulara ve elde euıieii »c.ori.k formu lasyonla ra dayanılarak özetlenecektir,'

VII Mechanical Interaction in Bond SUMMARY The scope of this thesis- is the analysis of the mec hanical interaction between a bar and th<_ surrounding concrete, which is accompanied by the formation of splitting craks. This mechanical interaction is one of the components of the complex and many-sided phenomenon of bond, and is in fact the primary bond mechanism in the case of deformed bars. Though st eel- to-concrete bond is the fpundamental phenomenon' of any reinforced concrete element, and affects many aspects of the behaviour. of r.c. elements, the large amount of work devoted both to the experimental and to the theoretical research within the field of bond cannot be considered sufficient, namely for large values of bar slip. After a first phase characterized by chemical adhesion (zero or negligible bar slip) and a second phase with trans verse cracking and limited longitudinal cracking at increa sing values of the average bond stress, the splitting cracks propagate and outbreak throughout the whole bar cover, in this situation bond strength is strongly dependent on. the amount of confinement action produced by the transverse reinforcement, and bond strength can reach values as high as f/3, provided that the confinement is adequate. The study of bond strength and stiffness after the outbreak of splitting cracks (when the confinement action is due only to the transverse reinforcement) may be carried out by means of pull-out tests performed on r.c. specimensVIII with a single preformed crack in a plane passing through the bar axis. These tests could be either at given confi nement (a = constant) or a given width of the (preformed) splitting crack (6 = constant): the tests carried out wit hin- the scope of this thesis are of are of the second type. In this thesis same very recent results on the interac tion between the shear stress (bond stress) and the confi nement stress at the bar-to-concrete interface aire shown. The pull-out tests have been performed on concrete models, only a f.ew lugs being actually engaged in the concrete. In the models, a real deformed bar ($= 18 mm) is embedded in the mean plane of- a concrete plate (thickness 50 mm), and the concrete- continuity round the bar is partly destroyed, so that the confinement action (which is kept constant throughout each test, but differs from test to test) is due only to the boundary restraints of the concrete plate, and can be measured at increasing loads applied to the bar. In each test the. splitting width was kept constant (5 - 0.00, 0.11, 0.22, 0.44 mm), the pull-out force was. applied through a hydraulic push-pull press and the confi nement action was controlled through a special device. The pull-out force was increased step-by step and each increment was applied only after the stabilization of the bar slip produced by the previous load step (constant rate of bar slip). Though limited to four values of the splitting width and to one value of the bar diameter, the test results lead to the following remarks: - (a) maximum bond strength is not markedly affected by the splitting width, ' (b) bond/slip curves are characterized by an extended fal ling branch after the maximum strength has been reached. (c) conf inement/slip curves are characterized by a bilateral. behaviour, with an extended quasi-horizontal branch, (d) the secant friction coefficient keeps constant throughout the plateaus 'of the bond/slip curves; the values k^ and k2 are in inverse proportion to the splitting width, (e) Maximum confinement values are in inverse proportion to the splitting width.IX A full set of bond/slip curves and of confinement/slip curves at, constant splitting width makes it possible to solve ?the following problem relevant to a reinforced concrete beam subjected to shear and bending: - for a given allowable width of the flexural cracks: (a) what amount of transverse reinforcement is needed in order to achieve a required bond stress level? (b) what bond-stress level can be assured by a given amount of transverse reinf orceraent? In recent years extensive,researchwork has been devo ted to the analysis of the behaviour of the, cracks in conc rete (either plain or reinforced), in order to get a better knowledge of Shear Transfer by Aggregate Interlock, which depends mostly on the crack relative displacements (opening and slip). Very recently a few researchers have worked out analytical models for modelling Shear Transfer by Aggregate Interlock-, these models being mainly based on the mechanical behaviour of the crack faces. `Aggregate Interlock` is the most typical mechanism for. shear transmission in a cracked, planar concrete ele ment..This phenomenon occurs between the.crack faces, which are rough because of the aggregate particles protruding from the cracked mortar. A comprehensive approach to the analysis of shear transfer via Aggregate Interlock should be based on the analysis of the random distribution. of interface, asperities, but a simpler approach based on simplified micromechanic models and on the test results can more effectively lead to the formulation of general ` equations among the static and kinematic parameters characterizing a' crack (shear and confinement stresses, relative displacements at the interface, namely slip and opening). In a regularly cracked, planar element, with evenly spaced and locally parallel cracks, the stress-displacement equations may be considered as constitut'`` 1 iws for the cracked material, once the displacements are replaced with equivalent strains obtained by smearing the displacements over a distance equal to the crack spacing. ' The stiffness coefficients of the above-mentioned incremental equations can be worked out on the basis of some speculative properties of the cracks (suggested bymicromechanic models) and on the basis of test results at constant crack opening and at constant crack slip (or al ternatively, at constant confinement stress). In the past the lack of test results of the second type bas not impaired the formulation of suitable stress-displacement relations which predict reasonably well the shear response of a crack subjected to imposed displacements, but are less reliable in the prediction of the required confinement (which is much more sensitive. than the shear' to crack -dilatancy and to crack opening). Starting from the response curves obtained so; far by different authors (at constant crack opening and at constant confinement), and within the already well known ROUGH CRACK MODEL, a. new formulation is worked out for the relation between the confinement stress and the crack displacements, and some improvements are introduced into the shear-displa cement relation,. A crass-examination of the theoretical results at constant crack opening (as obtained by Bazant and Gambarova in the so-called Rough Crack Model) and of some very' recent test results at constant confinement stress (Daschner. Munich, 1980-82) makes it possible to give a new formulation -to >the confinement equation along a crack. Although obtained through a cross-examination of very different theoretical' and experimental results, the new formulation of. the confi nement leads to a good fitting of the experimental curves at variable crack opening (as those obtained in Aggregate. Interlock Tests with the confinement directly applied or provided by external, unbonded stirrups or bars). With reference to the relations between the interface shear and the crack displacements, the improvements which are introduced into the previous formulation (Rough Crack Model), give a better description of the effects of aggre gate size, and for a better formulation of the tangent shear modulus G whenever cracking occurs. The reliability of the new formulation is checked against test results at a given crack opening(<$ '- constant, 5 being the value of the splitting crack) and at a given confinement stiffness (produced by the transverse reinforcement) characterized by imposed displacement history.XI According to the new formulation, at constant crack opening and for small values of the crack slip the required confinement stress tends to be zero while for large values of the crack slip increasing confinement action is required. The proposed formulation is a step toward a better 'analytical description of the confinement action, which has a critical role in shear transfer via Aggregate Interlock; as a conse quence, a better desription and updating of the stiffness characteristics of cracked concrete is possible, as highly desirable in F.E.M. programs dealing with cracking in concrete. One of the objects of this thesis is to provide the reader with more insight to see. whether the analytical mo dels developed for rough cracks may be valid also for the rough interface between a bar and the surrounding concrete. Such comparison, however, is beyond the scope of this thesis. In the first chanter, after the introduction of the subiect,a brief summary of the related nrevious studies is given.; - In. the. second chapter, mechanical interaction between a deformed bar and the surrounding concrete is analised ba sed on the parameters of confinement (0), its related disp lacement (£n) » bond stress (T) and the related displacement (-t). For this purpose experimental results of. püll-out tests are presented. A method of application is introduced in relation to design based on bond. In the third chapter, the mechanism of the aggregate interlock is analised and the related formulations of stresses occuring` on the crack faces are introduced. A summary of conclusions is given in the fourth chanter. '??'.. '