Tek eksenli gerilme altında betonun sünmesi ve hasarı /
Yazar: BÜLENT TANIRCAN
Danışman: PROF. DR. SAİM AKYÜZ
İstanbul Teknik Üniversitesi / Fen Bilimleri Enstitüsü / İnşaat Mühendisliği Ana Bilim Dalı
Derece: Yüksek Lisans, 1996
Konu: İnşaat Mühendisliği = Civil Engineering
Dizin: Beton = Concrete ; Deformasyon = Deformation ; Gerilme = Stress ; Sünme = Creep

Özet:
Sünme, sabit gerilme altında malzemelerde zamanla sürekli oluşan şekil değiştirme olarak tanımlanır. Yapılarda kullanılan birçok malzeme sünme olayını gösterir. Beton, oda sıcaklığında ve yüksek olmayan gerilmeler altında sünme yapabilen bir malzemedir. Yapı sistemlerinde gerilmenin yanında şekil değiştirmenin de sınırlı olması gerekir. Sünme sonunda meydana gelen deformasyonlar, gerilme yayılış değişmesine yol açar. Bu nedenle zamanın da bir değişken olarak hesaba katılması zorunludur. Sünme sonucu meydana gelen değişiklikler mekanik özellikleri zayıflatarak hasara neden olur. Bu hasarın derecesinin önceden tahmin edilebilmesi için hasar olayı mekanik terimler cinsinden ifade edilmelidir. Bu sayede analitik ve hesaplamalı tekniklerle çeşitli mühendislik problemleri formüle edilebilir. Bu çalışmada, yaygın olarak kullanılan katkılı portland çimentosuyla üretilmiş betonların, değişik gerilme düzeylerinde sünme nedeniyle uğradığı hasar incelenmiştir. Deneysel çalışmalarda su/çimento oram ve çimento dozajı sabit tutulmuştur. Numunelere 14 günlük silindir basınç mukavemetinin %67, %50, %40 ve %30'u oranında gerilme uygulanmıştır. Ayrıca, üzerinde yük bulunmayan şahit numuneler de incelenmiştir. g/R nin küçük değerlerinde de nonlineer sünme ortaya çıkmaktadır. Gerilmenin artmasıyla hasar ve hasar hızı artmaktadır. Hasarın hasar hızına etkisi, gerilmenin hasar hızına etkisinden önemlidir. o/R nin artmasıyla sünme numunelerinin kırılma zamanı azalmaktadır.

Abstract:
To be able to calculate the deformation and deflection of structural members, we have to know the relation between stress and strain. In common with most structural materials, concrete behaves nearly elastically when load is firs applied. However, under sustained loading, concrete exhibits creep, ie. the strain increases with time under a constant stress, even at very low stresses and under normal enviromental conditions of temperature and humidity. In concretes subjected to a stress below about 60 or 70 percent of the short- term strength there is no creep rupture. The importance of creep in structural concrete lies mainly in the fact that the creep deformation is of the same order of magnitude as the elastic deformation. There are also other effects of creep. Creep of concrete increases the deflection of ^ reinforced concrete beams, and in some cases may be a critical consideration in design. Creep is a slow continuous deformation of a material under constant stress. However, creep in general may be described in term of three different stages. The first stage in which creep occurs at a decreasing rate is called primary creep; the second, called the secondary stage, proceeds at a nearly constant rate; and the third or tertiary stage occurs at an increasing rate and terminates in fracture. When a specimen is unloaded, the instantaneous recovery is approximately the same as the instantaneous strain on first application of the load, but creep recovery, although it occurs more rapidly than creep, is by no means complete: a considerable portion of the total creep is irreversible. Creep is substantially increased when the concrete is simultaneously drying, i.e. creep and shrinkage are interdependent. This leads to the definitions of creep strains. Free shrinkage is defined as the shrinkage of the unloaded concrete in drying condition, and basic creep as the creep of similar specimen under load but no drying, ie. sealed so that there is no moisture movement to or from the surrounding environment. The total strain is that measured on the concrete whilst simultaneously shrinking and creeping. If the free shrinkage and the basic creep are added together, their sum is less than the total strain. The excess deformation is called drying creep. Total creep strain is the sum of basic creep and drying creep.When subjected to compression, concrete contracts longitudinally and expands laterally. The ratio of the lateral strain to the longitudinal strain is known as poisson's ratio, and within the normal working range of loading may be taken to have a value of 0,2. Apart from the increase in creep with simultaneous shrinkage, the following factors have a significant effect on creep:. The level of applied stress; for any given concrete and loading conditions, the creep is found to increase approximately linearly with the applied stress up to stress/strength ratios of about 0,4 to 0,6. It is therefore often useful to define the specific creep as the creep strain per unit stress in the region. At higher stress levels increased creep is observed.. An increase in strength usually leads to a reduction in creep.. Creep increases with increasing water/cement ratio.. The rate of creep decreases as the concrete ages.. Creep decreases as cement hydration proceeds, so that concrete kept continuosly wet creeps less than that cured in air.. Increasing temperature, increases the creep significantly.. A reduced moisture content before loading, reduces creep. In fact, completely dried concrete has very small, perhaps zero, creep.. Generally the type of cement is not of great importance, except that creep is related to the stress/strength ratio for the concrete, and strength development is related to cement type.. Admixtures that increase drying shrinkage also increase creep. Admixtures proposed for use should be tested to evaluate their influence on creep.. Aggregates act as a restraint to reduce the potential deformations of the paste. The aggregate content and modulus of elasticity are the most important parameters affecting creep of concrete. Aggregate size, grading, and surface texture have little influence.. Increasing size, decreases the creep. Creep process is occuring within the cement paste, and the moisture content and movement have a significant effect on its magnitude. The applied stress causes changes in the internal stresses and strain energy within the cement paste, resulting inan upset to the thermodynamic equilibrium; moisture than moves down the induced free energy gradient; implying a movement from smaller to larger pores, which can occur at several levels: 1. In capillary water as a rapid and reversible pressure drop; 2. In adsorbed water moving more gradually from zones of hindered adsorption - this movement should be reversible; 3. In interlayer water in diffusing very slowly out of the gel pores. Some extra bonding may men develop between the solid layers, and so this process may not be completely recoverable. Stress concentrations arise throughout the cement paste structure because of iys heterogeneous nature, and consolidation to a more stable state without loss of strength occurs at these points by either: 1. Viscous flow, with adjacent particles sliding past each other; or 2. Local bond breakage, closely followed by reçonnection nearby after some movement. Cement paste and concrete contain defects and cracks before loading, and propagation of these and the formation of new cracks will contribute to the creep strains, particularly at higher levels of stress. This is the most likely explanation of the non-linearity of creep strain with stress at high stress levels. Some mathematical models are capable of describing the main features of creep behaviour of viscoelastic materials with good accuracy both in the early stage and over a wide time span. For materials whose creep response may be described by a separable time-independent and time-dependent strain the following expression has often be found to yield a good description of creep, s = 80 + btn (1) 8 is the strain, t the time, n a constant independent of stress, So is the time-independent strain, and b is the coefficent of the time-dependent term. 8o and b are functions of stress. Rearraging (1) and taking logarithms yiels log(s-80) = logb + nlogt (2) If log(s-so) is plotted versus logt,it gives a straight line of slope n and intercept b. 'n' is independent of stress and state of sress.Creep functions ((p) for non-linear creep were obtained. If stress/strength ratio is 0,25 the behaviour of concrete is found non-linear. Time-deformation functions were found by: 8x(t) = OKPi(t) + CTi2Cp2(t) + Gl3(p3(t) + 0!V(t) s2(t) = a2(pi(t) + cr22(p2(t) + c23(p3(t) + a2V(t) s3(t) = c3(pi(t) + a32cp2(t) + cr33(p3(t) + a3V(t) s4(t) = a4(pi(t) + cj42(p2(t) + a43(p3(t) + a44cp4(t) Engineering materials are subjected to unfavorable mechanical and environmental conditions. It is essential to formulate the damage phenomenon in terms of mechanics when designing reliable structures. Then it is possible to analyse various engineering problems using analytical and computational techniques. In general a theoretical description of damage can be rather complicated. The experiments in this field are difficult. Experimental data, as a rule, are scarce. Determination of functions and constants, which play a role in the complex variants of the theory, from available experimental data is often practically impossible. A measurement of the speed or propagation time of plain waves in a specimen of damaged material leads to the determination of the elasticity modulus E of the damaged material and of the damage by /v D = 1 - E/E (3) Expressed in terms of the velocity of longitudinal waves VL and transverse waves Vr 3VL2-4VT2 E Vt2VL2-VT2 In the framework of the isotropic damage hypothesis (constant Poisson's coefficient) and neglecting the variation in p, we have: 1-v E 1-v (5)/v D=1-Vlz/Vl" (6) According to Kachanov's creep damage law: D = Ao(l-D) (7) Ao and r are the two characteristic creep damage coefficients for the material. Introducing an extra coefficient k : D = (a/A)r (1-D)k (8) In general and in this work k is found larger than r. The damage rate is influenced more strongly by the degree of damage than the global mechanical behaviour is. This study is presented in five chapters. In the first chapter general information about the theme, and related literature are given. In the second chapter, basic approach of damage mechanics and creep damage are given. In the third chapter experimental work and the materials that are used in the concrete mixture are given. The test results obtained from hardened concrete are given in the fourth chapter. The conclusions obtained from this work are the subject of the fifth chapter. Prismatic specimens of 10x10x50 cm. were used for creep tests. In the experiments, grading curve of aggregate mixture was kept constant and regulated to be near the B-16 curve. The maximum aggregate size was also kept constant and chosen to be 19,1 mm. The cement content of the mix was 300 kg/m3. The water/cement ratio was 0,65. Four different stress levels are applied to specimens. cr/R=0,67 ; 0,50 ; 0,40 ; 0,30. One specimen is not loaded. Two specimens are used for each stress level. Longitudinal and lateral creep strains are measured from the specimens. Strain-time functions were obtained. In addition, non-linear creep functions were obtained. Using ultrasonic dynamic method, damage of specimens were obtained. Damage rate was found according to (8) with regression analysis. The time to rupture (tc) was found for every stress levels.