• Computers and Concrete
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• v.30 no.4
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• pp.289-299
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• 2022

Based on the random cracking theory, the cylinder RVE model of reinforced concrete is established and the damage process is divided into three stages as the evolution of the cracks. The stress distribution along longitude direction of the concrete and the steel bar in the cylinder model are derived. The equivalent elastic modulus of the RVE are derived and the user-defined field variable subroutine (USDFLD) for the equivalent elastic modulus is well integrated into the ABAQUS. Regarding the tensile rebars and the concrete surrounding the rebars as the equivalent homogeneous transversely isotropic material, and the FEM analysis for the reinforced concrete beams is conducted with the USDFLD subroutine. Considering the concrete cracking and interfacial debonding, the macroscopic damage process of the reinforced concrete beam under four-point bending loading in the simulation. The volume fraction of rebar and the cracking degree are mainly discussed to reveal their influence on the macro-performance and they are calibrated with experimental results. Comparing with the bending experiment performed with 8 reinforced concrete beams, the bending stiffness of the second stage and the ultimate load simulated are in good agreement with the experimental values, which verifies the effectiveness and the accuracy of the improved finite element method for reinforced concrete beam.

• Computers and Concrete
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• v.22 no.1
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• pp.39-51
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• 2018

This study introduces a new algorithm to determine size independent values of fracture energy, fracture toughness, and fracture process zone length in three-point bending specimens with shallow to deep notches. By using the exact beam theory, a concept of equivalent notch length is introduced for specimens with no notches in order to predict the peak loads with acceptable precisions. Moreover, the method considers the variations of fracture process zone length and effects of higher order terms of stress field in each specimen size. In this paper, it was demonstrated that the use of some recently developed size effect laws raises some concerns due to the use of nonlinear regression analysis. By using a comprehensive fracture test data, provided by Hoover and Bazant, the algorithm has been assessed. It could be concluded that the proposed algorithm can facilitate a powerful tool for size effect study of three-point bending specimens with different notch lengths.

• Structural Engineering and Mechanics
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• v.66 no.4
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• pp.453-463
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• 2018

Three points bending flexural test was modelled numerically to study the crack propagation in the pre-cracked beams. The pre-existing double internal cracks inside the beam models were considered to investigate the crack propagation and coalescence paths within the modelled samples. Notch configuration effects on the failure stress were considered too. This numerical analysis shown that the propagation of wing cracks emanating from the tips of the pre-existing internal cracks caused the final breaking of beams specimens. It was also shown that when two notches were overlapped, they both mobilized in the failure process and the failure stress was decreased when the notches were located in centre line. However, the failure stress was increased by increasing the bridge area angle. Finally, it was shown that in all cases, there were good agreements between the discrete element method results and, the other numerical and experimental results. In this research, it is tried to improve the understanding of the crack propagation and crack coalescence phenomena in brittle materials which is of paramount importance in the stability analyses of rock and concrete structures, such as the underground openings, rock slopes and tunnel construction.

• Structural Engineering and Mechanics
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• v.65 no.4
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• pp.381-388
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• 2018

Dynamic behaviour of beam carrying masses has attracted attention of many researchers and engineers. Many studies on the analytical solution of beam with concentric tip mass have been published. However, there are limited works on vibration analysis of beam with an eccentric three dimensional object. In this case, bending and torsional deformations of beam are coupled due to the boundary conditions. Analytical solution of equations of motion of the system is complicated and lengthy. Therefore, in this study, Differential Transform Method (DTM) is applied to solve the relevant equations. First, the Timoshenko beam with 3D tip attachment whose centre of gravity is not coincident with beam end point is considered. The beam is assumed to undergo bending in two orthogonal planes and torsional deformation about beam axis. Using Hamilton's principle the equations of motion of the system along with the possible boundary conditions are derived. Later DTM is applied to obtain natural frequencies and mode shapes of the system. According to the relevant literature DTM has not been applied to such a system so far. Moreover, the problem is modelled by Ansys, the well-known finite element method, and impact test is applied to extract experimental modal data. Comparing DTM results with finite element and experimental results it is concluded that the proposed approach produces accurate results.

• Magazine of the Korean Society of Agricultural Engineers
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• v.42 no.2
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• pp.108-114
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• 2000

This paper explores the non-linear behavior of tapered beam subjected to a floating concentration load. For applying the Bernoulli-Euler beam theory to this beam, the bending moment at any point of elastical is obtained from the final equilibrium stage. By using the bending moment equation and the Bernoulli-Euler beam theory, the differential equations governing the elastica of simple beam are derived , and solved numberically . Three kinds of tapered beam types are considered . The numerical results of the non-linear behavior obtained in this study are agreed quite well to the results obtained from the laboratory-scale experiments.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2000.10a
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• pp.201-208
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• 2000

This paper explores the non-linear behavior of tapered beam subjected to a floating concentrated load. For applying the Bernoulli-Euler beam theory to this beam, the bending moment at any point of elastica is obtained from the final equilibrium state. By using the bending moment equation and the Bernoulli-Euler beam theory, the differential equations governing the elastica of clamped-roller beam are derived, and solved numerically. Three kinds of tapered beam types are considered. The numerical results of the non-linear behavior obtained in this study are agreed quite well to the results obtained from the laboratory-scale experiments.

• Applied Chemistry for Engineering
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• v.9 no.5
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• pp.715-718
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• 1998

In this work, bisphenol type vinyl ester was impregnated into the three-dimensional glass fabrics fabricated from different thickness changes. Their mechanical properties of the specimens have been investigated by three-point bending and flatwise compression tests. Also, interlaminar shear strength (ILSS) has been determined through short-beam test for the evaluation of interfacial adhesion at interfaces between fibers and matrix of the composites. The effect of thickness changes in three-dimensional glass fabric-reinforced composites have been described in this work.

• Steel and Composite Structures
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• v.32 no.1
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• pp.127-139
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• 2019

Bridges, offshore oil platforms and other infrastructures usually require at some point in their service life rehabilitation for reasons such as aging and corrosion. This study explores the application of adhesively bonded CFRP patches in repair of corroded circular hollow sectional (CHS) steel beams. An experimental program involving three-point bending tests was conducted on intact, corroded, and repaired CHS beams. Meso-scale finite element (FE) models of the tested beams were developed and validated by the experimental results. A parametric study using the validated FE models was performed to examine the effects of different CFRP patch parameters, including patch dimensions, number of plies and stacking sequence, on efficiency of the repair system. Results indicates that the corrosion reduced elastic stiffness and flexural strength of the undamaged beam by 8.9 and 15.1%, respectively, and composite repair recovered 10.7 and 18.9% of those, respectively, compared to undamaged beam. These findings demonstrated the ability of CFRP patch repair to restore full bending capacity of the corroded CHS steel beam. The parametric study revealed that strength and stiffness of the repaired CHS beam can be enhanced by changing the fiber orientations of wet composite patch without increasing the quantity of repair materials.

• Computers and Concrete
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• v.14 no.5
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• pp.527-546
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• 2014

Portland cement concrete, which has higher strength and stiffness than asphalt concrete, has been widely applied on pavements. However, the brittle fracture characteristic of cement concrete restricts its application in highway pavement construction. Since the polypropylene fiber can improve the fracture toughness of cement concrete, Polypropylene Fiber-Reinforced Concrete (PFRC) is attracting more and more attention in civil engineering. In order to study the effect of polypropylene fiber on the generation and evolution process of the local deformation band in concrete, a series of three-point bending tests were performed using the new technology of the digital speckle correlation method for FRC notched beams with different volumetric contents of polypropylene fiber. The modified Double-K model was utilized for the first time to calculate the stress intensity factors of instability and crack initiation of fiber-reinforced concrete beams. The results indicate that the polypropylene fiber can enhance the fracture toughness. Based on the modified Double-K fracture theory, the maximum fracture energy of concrete with 3.2% fiber (in volume) is 47 times higher than the plain concrete. No effort of fiber content on the strength of the concrete was found. Meanwhile to balance the strength and resistant fracture toughness, concrete with 1.6% fiber is recommended to be applied in pavement construction.

• Smart Structures and Systems
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• v.10 no.6
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• pp.547-555
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• 2012

Measuring crack length in concrete fracture test is not a trivial problem due to high speed crack propagation. In this study, mechanoluminascent (ML) material, which emits visible light under stress condition, was employed to visualize crack propagation during concrete fracture test. Three-point bending test was conducted with a notched concrete beam specimen. The cracking images due to ML phenomenon were recorded by using a high speed camera as a function of time and external loadings. The experimental results successfully demonstrated the capability of ML material as a promising visualization tool for concrete crack propagation. In addition, an interesting cracking behavior of concrete bending fracture was observed in which the crack propagated fast while the load decreased slowly at early fracture stage.