• Computers and Concrete
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• v.19 no.6
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• pp.631-639
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• 2017

This study experimentally investigated the flexural capacity of a concrete beam reinforced with a newly developed GFRP bar that overcomes the lower modulus of elasticity and bond strength compared to a steel bar. The GFRP bar was fabricated by thermosetting a braided pultrusion process to form the outer fiber ribs. The mechanical properties of the modulus of elasticity and bond strength were enhanced compared with those of commercial GFRP bars. In the four-point bending test results, all specimens failed according to the intended failure mode due to flexural design in compliance with ACI 440.1R-15. The effects of the reinforcement ratio and concrete compressive strength were investigated. Equations from the code were used to predict the deflection, and they overestimated the deflection compared with the experimental results. A modified model using two coefficients was developed to provide much better predictive ability, even when the effective moment of inertia was less than the theoretical $I_{cr}$. The deformability of the test beams satisfied the specified value of 4.0 in compliance with CSA S6-10. A modified effective moment of inertia with two correction factors was proposed and it could provide much better predictability in prediction even at the effective moment of inertia less than that of theoretical cracked moment of inertia.

• Structural Engineering and Mechanics
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• v.10 no.5
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• pp.463-478
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• 2000

An iterative procedure for the analysis of reinforced concrete frames with beams in cracked state is presented. ACI and CEB model equations are used for the effective moment of inertia of the cracked members. In the analysis, shear deformations are taken into account and reduced shear stiffness is considered by using effective shear modulus models available in the literature. Based on the aforementioned procedure, a computer program has been developed. The results of the computer program have been compared with the experimental results available in the literature and found to be in good agreement. Finally, a parametric study is carried out on a two story reinforced concrete frame.

• Structural Engineering and Mechanics
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• v.38 no.4
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• pp.459-477
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• 2011

Due to the low elastic modulus of FRP, concrete members reinforced with FRP rebars show greater deflections than members reinforced with steel rebars. Deflection is one of the important factors to consider the serviceability of horizontal members. In this study flexural test of AFRP reinforced concrete beams was performed considering reinforcement ratio and compressive strength as parameters. The test results indicated that flexural capacity and stiffness increase in proportion to the reinforcement ratio. The test results were compared with existing proposed equations for the effective moment of inertia including ACI 440. The most of the proposed equations were found to over-estimate the effective moment of inertia while the equation proposed by Bischoff and Scanlon (2007) most accurately predicted the values obtained through actual testing.

• Proceedings of the Korea Concrete Institute Conference
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• 2002.10a
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• pp.397-400
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• 2002

The mechanical properties of concrete such as modulus of elasticity, bond strength and shear strength are proportional to square root of compressive strength. And compressive strength of concrete is developed rapidly at early ages. Thus the relationship between compressive strength and its mechanical properties should be verified because the mechanical properties of early age concrete and hardened concrete are different. In this study, to predict the concrete slab deflection at early ages, modulus of elasticity and effective moment of inertia(Ie) are observed and compared with experimental results.

• Computers and Concrete
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• v.9 no.2
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• pp.133-151
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• 2012

This paper presents an analytical procedure for the analysis of high strength steel fiber reinforced concrete members considering the cracking effect in the serviceability loading range. Modifications to a previously proposed formula for the effective moment of inertia are presented. Shear deformation effect is also taken into account in the analysis, and the variation of shear stiffness in the cracked regions of members has been considered by reduced shear stiffness model. The effect of steel fibers on the behavior of reinforced concrete members have been investigated by the developed computer program based on the aforementioned procedure. The inclusion of steel fibers into high strength concrete beams and columns enhances the effective moment of inertia and consequently reduces the deflection reinforced concrete members. The contribution of the shear deformation to the total vertical deflection of the beams is found to be lower for beams with fibers than that of beams with no fibers. Verification of the proposed procedure has been confirmed from series of reinforced concrete beam and column tests available in the literature. The analytical procedure can provide an accurate and efficient prediction of deflections of high strength steel fiber reinforced concrete members due to cracking under service loads. This procedure also forms the basis for the three dimensional analysis of frames with steel fiber reinforced concrete members.

• Journal of the Korea Academia-Industrial cooperation Society
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• v.12 no.2
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• pp.936-943
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• 2011

The effective moment of inertia revising the expression proposed by Branson has been used in ACI 440.1R-06 design guide for calculating deflections of FRP-reinforced concrete members. However, its adequacy has been questioned by several researchers. The propose of this study is to provide fundamental data for the rational design of deflection by the comparison of the experimental results obtained from twelve specimens with rectangular section and nine specimens with T-shaped section to the theoretical results. As a result, it found that calculated results for specimens with rectangular section were underestimated comparing to test results, while calculated results for specimens with T-shaped section were overestimated comparing to test results.

• Proceedings of the Korea Concrete Institute Conference
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• 2006.05a
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• pp.114-117
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• 2006

Concrete beams reinforced with fiber reinforced polymer (FRP) bars exhibit large deflection and crack width as compared to concrete beams reinforced steel due to modulus of elasticity of FRP bars. Current design code for prediction and crack width developed in concrete structures reinforced with steel bars may not be used for concrete beams reinforced with FRP bars. Thus a number of researcher have attempted to propose modifications to the ACI 318 empirical equation for estimating the effective moment of inertia of reinforced concrete beams. Others used numerical method to calculate the deflection. The purpose of this paper is to evaluation of methods of ACI 440.1 R-01, ISIS Canada design manual, and others for predicting deflection for glass fiber reinforced polymer reinforced concrete beams.

• Smart Structures and Systems
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• v.26 no.3
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• pp.361-371
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• 2020

Exact solution for nonlinear behavior of clamped-clamped functionally graded (FG) buckled beams is presented. The effective material properties are considered to vary along the thickness direction according to exponential-law form. The in-plane inertia and damping are neglected, and hence the governing equations are reduced to a single nonlinear fourth-order partial-integral-differential equation. The von Kármán geometric nonlinearity has been considered in the formulation. Galerkin procedure is used to obtain a second order nonlinear ordinary equation with quadratic and cubic nonlinear terms. Based on the mode of the corresponding linear problem, which readily satisfy the boundary conditions, the frequencies for the nonlinear problem are obtained using the Jacobi elliptic functions. The effects of various parameters such as the Young's modulus ratio, the beam slenderness ratio, the vibration amplitude and the magnitude of axial load on the nonlinear behavior are examined.

• Journal of the Korea Concrete Institute
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• v.20 no.2
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• pp.185-191
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• 2008

To fundamentally solve the problem of deterioration of concrete structures, it has been researched that the high durable concrete structure reinforced with the FRP rebar can be one of major solution to the newly-developed concrete structure. FRP rebar has lots of advantages such as non-corrosive, high performance and light weight against the conventional steel rebar. Among these kinds of FRP rebars, GFRP rebar has usually been considered as the best reinforcement because of its economic point of view. Even though the material capacity of the GFRP rebar was already investigated, there are some problems such as low modulus of elastic that will be cause for degrade of the serviceability of flexural concrete member reinforced with the GFRP rebar. Thus, the deflection characteristics of the GFRP rebar reinforced concrete structure should be considered then investigated. In this study, ACI 440 guideline (2003), ISIS Canada Design Manual (2001) and Toutanji et al. (2000) was considered for predicting the moment of inertia of the concrete beam reinforced with the GFRP rebar. And it was also evaluated that load-deflection relationship had a good accordance with the test and analysis result. In the result of this study, it could be estimated that the load-deflection relationship using the suggested equation of moment of inertia in this study indicated better accordance with the test result than that of the others until failure.

• Journal of the Earthquake Engineering Society of Korea
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• v.14 no.1
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• pp.43-50
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• 2010

To address the problems caused by the corrosion of steel rebar, active research has recently been carried out on members where fiber-reinforced polymer (FRP) is used in place of rebar. As FRP bar is highly brittle and has a low modulus of elasticity, further research is needed on the evaluation of serviceability, in other words on the deflection of flexural concrete members reinforced with FRP rebars. Taking the reinforcement ratio as a variable, this paper analyzes the flexural capacity of concrete beams reinforced with CFRP rebar. The test results of specimens reinforced with CFRP rebar show an increase in stiffness and resisting force along with an increase in the reinforcement ratio. A reinforcement ratio of about 1.3 is needed for the member reinforced with CFRP rebar to show same section property of a steel member. Through a comparison for the value of an effective moment of inertia, the equation suggested by Bischoff & Scanlon predicted values closest to the actual results.