Fracture process zone size and true fracture energy of concrete using acoustic emission

Acoustic emission (AE) energy, instead of amplitude, associated with each of the event is used to estimate the fracture process zone (FPZ) size. A steep increase in the cumulative AE energy of the events with respect to time is correlated with the formation of FPZ. Based on the AE energy released during these events and the locations of the events, FPZ size is obtained. The size-independent fracture energy is computed using the expressions given in the boundary effect model by least squares method since over-determined system of equations are obtained when data from several specimens are used. Instead of least squares method a different method is suggested in which the transition ligament length, measured from the plot of histograms of AE events plotted over the un-cracked ligament, is used directly to obtain size-independent fracture energy. The fracture energy thus calculated seems to be size-independent.

Prediction of fatigue strength in plain and reinforced concrete beams

A fatigue crack propagation model for concrete is proposed based on the concepts of fracture mechanics. This model takes into account the loading history, frequency of applied load, and size, effect parameters. Using this model, a method is described based on linear elastic fracture mechanics to assess the residual strength of cracked plain and reinforced concrete (RC) beams. This could be used to predict the residual strength (load carrying capacity) of cracked or damaged plain and reinforced concrete beams at a given level of damage. It has been seen that the fatigue crack propagation rate increases as. the size of plain concrete, beam increases indicating an increase in brittleness. In reinforced concrete (RC) beams, the fracture process becomes stable only when the beam is sufficiently reinforced.

Non-Gaussianities and Preheating from N-flation and Magnetogenesis via rotating cosmic string loops

In this thesis we examine multi-field inflationary models of the early Universe. Since non-Gaussianities may allow for the possibility to discriminate between models of inflation, we compute deviations from a Gaussian spectrum of primordial perturbations by extending the delta-N formalism. We use N-flation as a concrete model; our findings show that these models are generically indistinguishable as long as the slow roll approximation is still valid. Besides computing non-Guassinities, we also investigate Preheating after multi-field inflation. Within the framework of N-flation, we find that preheating via parametric resonance is suppressed, an indication that it is the old theory of preheating that is applicable. In addition to studying non-Gaussianities and preheatng in multi-field inflationary models, we study magnetogenesis in the early universe. To this aim, we propose a mechanism to generate primordial magnetic fields via rotating cosmic string loops. Magnetic fields in the micro-Gauss range have been observed in galaxies and clusters, but their origin has remained elusive. We consider a network of strings and find that rotating cosmic string loops, which are continuously produced in such networks, are viable candidates for magnetogenesis with relevant strength and length scales, provided we use a high string tension and an efficient dynamo.

Boundary value problems for third-order nonlinear ordinary differential equations

In this paper, we describe how to analyze boundary value problems for third-order nonlinear ordinary differential equations over an infinite interval. Several physical problems of interest are governed by such systems. The seminumerical schemes described here offer some advantages over solutions obtained by using traditional methods such as finite differences, shooting method, etc. These techniques also reveal the analytic structure of the solution function. For illustrative purposes, several physical problems, mainly drawn from fluid mechanics, are considered; they clearly demonstrate the efficiency of the techniques presented here.

Boundary value problems for third-order nonlinear ordinary differential equations

In this paper, we describe how to analyze boundary value problems for third-order nonlinear ordinary differential equations over an infinite interval. Several physical problems of interest are governed by such systems. The seminumerical schemes described here offer some advantages over solutions obtained by using traditional methods such as finite differences, shooting method, etc. These techniques also reveal the analytic structure of the solution function. For illustrative purposes, several physical problems, mainly drawn from fluid mechanics, are considered; they clearly demonstrate the efficiency of the techniques presented here.

A model to similate the strength and deformation of concrete in compression

A simple model is developed to represent the strength and deformational characteristics of concrete when subjected to a rate of strain or rate of stress or creep or relaxation testing under uniaxial compression.

Design of rectangular reinforced concrete slabs supported on all the sides with a short discontinuous edge

Bending moment coefficients for the design of rectangular reinforced concrete panels supported on four sides with a short discontinuous edge are derived using the strip theory. The moment fields resulting from the use of proposed coefficients are examined in terms of the moment volume for possible savings in reinforcement and compared with other codified procedures. The strip coefficients averaged over the corresponding sides of the panel, besides resulting in considerable savings in reinforcement, are found to be identical with the coefficients predicted by simple yield line theory using an orthotropic layout of reinforcement.

Microcracking in concrete under repeated compressive loads

The nature of microcracks formed in concrete under repeated uniaxial compressive loads are investigated by experiments on prismatic specimens. The distribution and orientation of cracks formed are studied by optical microscopic techniques. The basic failure mechanism of concrete at the phenomenological and internal structural level are examined by the formation and propagation of cracks. The tests have indicated that local tensile failures constitute the dominant mode of fracture, with the bond cracks forming the major percentage of the total magnitude of cracks. Significant differences were observed in the proportion of bond cracks formed under static and repeated load systems.

Numerical procedure for second order non-linear ordinary differential equations and application to heat transfer problem

In this paper, we have first given a numerical procedure for the solution of second order non-linear ordinary differential equations of the type y″ = f (x;y, y′) with given initial conditions. The method is based on geometrical interpretation of the equation, which suggests a simple geometrical construction of the integral curve. We then translate this geometrical method to the numerical procedure adaptable to desk calculators and digital computers. We have studied the efficacy of this method with the help of an illustrative example with known exact solution. We have also compared it with Runge-Kutta method. We have then applied this method to a physical problem, namely, the study of the temperature distribution in a semi-infinite solid homogeneous medium for temperature-dependent conductivity coefficient.

Markov Chain Model for Cracking Behavior of Reinforced Concrete Beams

In this paper, nonhomogeneous Markov chains are proposed for modeling the cracking behavior of reinforced concrete beams subjected to monotonically increasing loads. The model facilitates prediction of the maximum crackwidth at a given load given the crackwidth at a lower load level, and thus leads to a better understanding of the cracking phenomenon. To illustrate the methodology developed, the results of three reinforced concrete beams tested in the laboratory are analyzed and presented.

Size effect in self consolidating concrete beams with and without notches

The aim of this study is to obtain the fracture characteristics of low and medium compressive strength self consolidating concrete (SCC) for notched and un-notched plain concrete beams by using work of fracture G(F) and size effect model G(f) methods and comparing them with those of normal concrete and high performance concrete. The results show that; (i) with an increase in compressive strength, G(F) increases and G(f) decreases; (ii) with an increase in depth of beam, the decrease in nominal stress of notched beam is more when compared with that of a notchless beam.

Probabilistic Analysis of Cracking Moment of Reinforced Concrete Beams

Probabilistic analysis of cracking moment from 22 simply supported reinforced concrete beams is performed. When the basic variables follow the distribution considered in this study, the cracking moment of a beam is found to follow a normal distribution. An expression is derived, for characteristic cracking moment, which will be useful in examining reinforced concrete beams for a limit state of cracking.

Elasto-plastic Cracking Analysis of Reinforced Concrete

A new elasto-plastic cracking constitutive model for reinforced concrete is presented. The nonlinear effects considered cover almost all the nonlinearities exhibited by reinforced concrete under short term monotonic loading. They include concrete cracking in tension, plasticity in compression, aggregate interlock, tension softening, elasto-plastic behavior of steel, bond-slip between concrete, and steel reinforcement and tension stiffening. A new procedure for incorporating bondslip in smeared steel elements is described. A modified Huber-Hencky-Mises failure criterion for plastic deformation of concrete, which fits the experimental results under biaxial stresses better, is proposed. Multiple cracking at Gauss points and their opening and closing are considered. Matrix expressions are developed and are incorporated in a nonlinear finite element program. After the objectivity of the model is demonstrated, the model is used to analyze two different types of problems: one, a set of four shear panels, and the other, a reinforced concrete beam without shear reinforcement. The results of the analysis agree favorably with the experimental results.