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.

Deformational Behavior of Fiber-Reinforced Concrete Beams in Bending

An experimental study aimed at understanding the deformational behavior of conventionally reinforced steel fiber concrete beams in pure bending is reported in this paper. One group of beams has steel fibers dispersed in the entire volume of the beam and the second has fibers dispersed over half the depth of the beam on the tension side. A comparative study of the deformational characteristics of these beams has been made. Half-depth fiber inclusion, requiring only half the quantity of fibers of full-depth inclusion, is found to be equally effective in improving the deformational behavior of beams. Thus, by such modes of inclusion of fibers, an economical and efficient use of expensive steel fibers can be realized.

An experimental study on acoustic emission energy as a quantitative measure of size independent specific fracture energy of concrete beams

Notched three point bend specimens (TPB) were tested under crack mouth opening displacement (CMOD) control at a rate of 0.0004 mm/s and during the fracture process acoustic emissions (AE) were simultaneously monitored. It was observed that AE energy could be related to fracture energy. An experimental study was done to understand the behavior of AE energy with parameters of concrete like its strength and size. In this study, AE energy was used as a quantitative measure of size independent specific fracture energy of concrete beams and the concepts of boundary effect and local fracture energy were used to obtain size independent AE energy from which size independent fracture energy was obtained. (C) 2010 Elsevier Ltd. All rights reserved.

A finite element assessment of flexural strength of prestressed concrete beams with fiber reinforcement

This paper presents an assessment of the flexural behavior of 15 fully/partially prestressed high strength concrete beams containing steel fibers investigated using three-dimensional nonlinear finite elemental analysis. The experimental results consisted of eight fully and seven partially prestressed beams, which were designed to be flexure dominant in the absence of fibers. The main parameters varied in the tests were: the levels of prestressing force (i.e, in partially prestressed beams 50% of the prestress was reduced with the introduction of two high strength deformed bars instead), fiber volume fractions (0%, 0.5%, 1.0% and 1.5%), fiber location (full depth and partial depth over full length and half the depth over the shear span only). A three-dimensional nonlinear finite element analysis was conducted using ANSYS 5.5 [Theory Reference Manual. In: Kohnke P, editor. Elements Reference Manual. 8th ed. September 1998] general purpose finite element software to study the flexural behavior of both fully and partially prestressed fiber reinforced concrete beams. Influence of fibers on the concrete failure surface and stress-strain response of high strength concrete and the nonlinear stress-strain curves of prestressing wire and deformed bar were considered in the present analysis. In the finite element model. tension stiffening and bond slip between concrete and reinforcement (fibers., prestressing wire, and conventional reinforcing steel bar) have also been considered explicitly. The fraction of the entire volume of the fiber present along the longitudinal axis of the prestressed beams alone has been modeled explicitly as it is expected that these fibers would contribute to the mobilization of forces required to sustain the applied loads across the crack interfaces through their bridging action. A comparison of results from both tests and analysis on all 15 specimens confirm that, inclusion of fibers over a partial depth in the tensile side of the prestressed flexural structural members was economical and led to considerable cost saving without sacrificing on the desired performance. However. beams having fibers over half the depth in only the shear span, did not show any increase in the ultimate load or deformational characteristics when compared to plain concrete beams. (C) 2002 Published by Elsevier Science Ltd.

Effect of shear deformation on interfacial stresses in plated beams subjected to arbitrary loading

Bonding a fibre reinforced polymer (FRP) composite or metallic plate to the soffit of a reinforced concrete (RC), timber or metallic beam can significantly increase its strength and other aspects of structural performance. These hybrid beams are often found to fail due to premature debonding of the plate from the original beam in a brittle manner. This has led to the development of many analytical solutions over the last two decades to quantify the interfacial shear and normal stresses between the adherends. The adherends are subjected to axial, bending and shear deformations. However, most analytical solutions have neglected the influence of shear deformation of the adherends. For the few solutions which consider this effect in an approximate manner, their applicability is limited to one or two specific load cases. This paper presents a general analytical solution for the interfacial stresses in plated beams under an arbitrary loading with the shear deformation of the adherends duly considered. The shear stress distribution is assumed to be parabolic through the depth of the adherends in predicting the interfacial shear stress and Timoshenko's beam theory is adopted in predicting interfacial normal stress to account for the shear deformation. The solution is applicable to a beam of arbitrary prismatic cross-section bonded symmetrically or asymmetrically with a thin or thick plate, both having linear elastic material properties. The effect of shear deformation is illustrated through an example beam. The influence of material and geometric parameters of the adherends and adhesive on the interfacial stress concentrations at the plate end is discussed. (C) 2011 Elsevier Ltd. All rights reserved.

Fracture Analysis of High strength and Ultra high strength Concrete beams by using Finite Element Method

This paper presents the details of nonlinear finite element analysis (FEA) of three point bending specimens made up of high strength concrete (HSC, HSC1) and ultra high strength concrete (UHSC). Brief details about characterization and experimentation of HSC, HSC1 and UHSC have been provided. Cracking strength criterion has been used for simulation of crack propagation by conducting nonlinear FEA. The description about FEA using crack strength criterion has been outlined. Bi-linear tension softening relation has been used for modeling the cohesive stresses ahead of the crack tip. Numerical studies have been carried out on fracture analysis of three point bending specimens. It is observed from the studies that the computed values from FEA are in very good agreement with the corresponding experimental values. The computed values of stress vs crack width will be useful for evaluation of fracture energy, crack tip opening displacement and fracture toughness. Further, these values can also be used for crack growth study, remaining life assessment and residual strength evaluation of concrete structural components.

Evaluation of Fracture Parameters by Double-G, Double-K Models and Crack Extension Resistance for High Strength and Ultra High Strength Concrete Beams

This paper presents the advanced analytical methodologies such as Double- G and Double - K models for fracture analysis of concrete specimens made up of high strength concrete (HSC, HSC1) and ultra high strength concrete. Brief details about characterization and experimentation of HSC, HSC1 and UHSC have been provided. Double-G model is based on energy concept and couples the Griffith's brittle fracture theory with the bridging softening property of concrete. The double-K fracture model is based on stress intensity factor approach. Various fracture parameters such as cohesive fracture toughness (4), unstable fracture toughness (K-Ic(c)), unstable fracture toughness (K-Ic(un)) and initiation fracture toughness (K-Ic(ini)) have been evaluated based on linear elastic fracture mechanics and nonlinear fracture mechanics principles. Double-G and double-K method uses the secant compliance at the peak point of measured P-CMOD curves for determining the effective crack length. Bi-linear tension softening model has been employed to account for cohesive stresses ahead of the crack tip. From the studies, it is observed that the fracture parameters obtained by using double - G and double - K models are in good agreement with each other. Crack extension resistance has been estimated by using the fracture parameters obtained through double - K model. It is observed that the values of the crack extension resistance at the critical unstable point are almost equal to the values of the unstable fracture toughness K-Ic(un) of the materials. The computed fracture parameters will be useful for crack growth study, remaining life and residual strength evaluation of concrete structural components.

Size independent fracture energy from fracture energy release rate in plain concrete beams

Size independent fracture energy and size effect on fracture energy are the key concerns for characterization of concrete fracture. Although there have been inconsistencies in results, a consensual fact is that the fracture energy from a large specimen is size independent. The fracture energy is proportional to the size of the fracture process zone (FPZ). FPZ size increases with size of the specimen, but the rate of increase of FPZ size decreases with increase in specimen size 1] implying that rate of increase of fracture energy decreases with increase in specimen size, more appropriately with increase in un-cracked ligament length. The ratio of fracture energy to the un-cracked ligament length almost becomes a constant at larger un-cracked ligament lengths. In the present study an attempt is made to obtain size independent fracture energy from fracture energy release rate. (C) 2012 Elsevier Ltd. All rights reserved.

Fatigue Crack Growth Study and Remaining Life Assessment of High Strength and Ultra High Strength Concrete Beams

This paper presents the details of crack growth study and remaining life assessment of concrete specimens made up of high strength concrete (HSC, HSC1) and ultra high strength concrete (UHSC). Flexural fatigue tests have been conducted on HSC, HSC1 and UHSC beams under constant amplitude loading with a stress ratio of 0.2. It is observed from the studies that (i) the failure patterns of HSC1 and UHSC beams indicate their ductility as the member was intact till the crack propagated up to 90% of the beam depth and (ii) the remaining life decreases with increase of notch depth (iii) the failure of the specimen is influenced by the frequency of loading. A ``Net K'' model has been proposed by using non-linear fracture mechanics principles for crack growth analysis and remaining life prediction. SIF (K) has been computed by using the principle of superposition. SIP due to the cohesive forces applied on the effective crack face inside the process zone has been obtained through Green's function approach by applying bi-linear tension softening relationship to consider the cohesive the stresses acting ahead of the crack tip. Remaining life values have been have been predicted and compared with the corresponding experimental values and observed that they are in good agreement with each other.

Estimation of fracture properties for high strength and ultra high strength concrete beams and size effect

This article presents the details of estimation of fracture parameters for high strength concrete (HSC, HSC1) and ultra high strength concrete (UHSC). Brief details about characterization of ingredients of HSC, HSC1 and UHSC have been provided. Experiments have been carried out on beams made up of HSC, HSC1 and UHSC considering various sizes and notch depths. Fracture characteristics such as size independent fracture energy (G(f)), size of fracture process zone (C-f), fracture toughness (K-IC) and crack tip opening displacement (CTODc) have been estimated based on the experimental observations. From the studies, it is observed that (i) UHSC has high fracture energy and ductility inspite of having a very low value of C-f; (ii) relatively much more homogeneous than other concretes, because of absence of coarse aggregates and well-graded smaller size particles; (iii) the critical SIF (K-IC) values are increasing with increase of beam depth and decreasing with increase of notch depth. Generally, it can be noted that there is significant increase in fracture toughness and CTODc. They are about 7 times in HSC1 and about 10 times in UHSC compared to those in HSC; (iv) for notch-to-depth ratio 0.1, Bazant's size effect model slightly overestimates the maximum failure loads compared to experimental observations and Karihaloo's model slightly underestimates the maximum failure loads. For the notch-to-depth ratio ranging from 0.2 to 0.4 for the case of UHSC, it can be observed that, both the size effect models predict more or less similar maximum failure loads compared to corresponding experimental values.

Analysis of fatigue crack growth in reinforced concrete beams

Mechanical behavior of reinforced concrete members is influenced by the action of unknown crack bridging reactions of rebars. Under cyclic loading, due to progressive growth of cracks, this bridging action contributes to the overall strength, stiffness and hysteretic behavior of the member. In this work, fatigue behavior of reinforced concrete beams are studied using a crack propagation law, developed using dimensional analysis for plain concrete with the effect of reinforcement being simulated through constraint exerted on the crack opening. The parameters considered in the model are fracture toughness, crack length, loading ratio and structural size. A numerical procedure is followed to compute fatigue life of RC beams and the dissipated energy in the steel reinforcement due to the shake down phenomenon under cyclic loading. Through a sensitivity study, it is concluded that the structural size is the most sensitive parameter in the fatigue crack propagation phenomenon. Furthermore, the residual moment carrying capacity of an RC member is determined as a function of crack extension by including the bond-slip mechanism.