• Journal of the Korea Concrete Institute
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• v.20 no.3
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• pp.393-404
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• 2008

The approaches in many design codes for the estimation of the deflection of flexural reinforced concrete (RC) members utilize the concept of the effective moment of inertia which considers the reduction of flexural rigidity of RC beams after cracking. However, the effective moment of inertia in design codes are primarily based on the ratio of maximum moment and cracking moment of beam subjected to loading without proper consideration on many other possible influencing factors such as span length, member end condition, sectional size, loading geometry, materials, sectional properties, amount of cracks and its distribution, and etc. In this study, therefore, an experimental investigation was conducted to provide fundamental test data on the effective moment of inertia of RC beams for the evaluation of flexural deflection, and to develop a modified method on the estimation of the effective moment of inertia based on test results. 14 specimens were fabricated with the primary test parameters of concrete strength, cover thickness, reinforcement ratio, and bar diameters, and the effective moments of inertia obtained from the test results were compared with those by design codes, existing equations, and the modified equation proposed in this study. The proposed method considered the effect of the length of cracking region, reinforcement ratio, and the effective concrete area per bar on the effective moment of inertia, which estimated the effective moment of inertia more close to the test results compared to other approaches.

• Proceedings of the Korea Concrete Institute Conference
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• 2008.04a
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• pp.329-332
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• 2008

The member deflection is one of the most important considerations for the serviceability evaluation of reinforced concrete structures, and the concept of the effective moment of inertia has been generally used for the estimation of beam deflections. The KCI design code adopted Branson's equation for the calculation of the effective moment of inertia, which was formulated based on the results of beam tests subjected to uniformly distributed loads. Therefore, it is worthwhile to check the applicability of the code approach on the estimation of the effective moment of inertia for the cases of beams under different loading conditions. In this study, an experimental investigation has been conducted on six beams, where primary variables were concrete compressive strengths and loading distances from supports. The test results were compared with various approaches proposed by Branson and others as well. The test results indicated that the effective moment of inertia was somewhat influenced by the moment distribution shape. Despite the different moment distribution shapes for specimens, however, the effective moment of inertia of all test beams were closely predicted by the existing methods considered in this study.

• Journal of the Korea Concrete Institute
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• v.12 no.2
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• pp.71-78
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• 2000

This paper presents a study on the flexural rigidity of reinforced high strength concrete beams. Thirty six beams with different compressive strength of concrete, tensile reinforcement ratio, compressive reinforcement ratio, and pattern of loadings(1 point loading and 2 points loading) were tested to evaluate the effective moment of inertia. According to the experimental results, the eqation(1) proposed by ACI code for the effective moment of inertia overestimated that of simply supported reinforced high strength concrete beams. Thus, in this paper, an empirical equation(3) is proposed as a lower bound of 90% confidence limit to estimate the effective moment of inertia of simply supported reinforced high strength concrete beams.

• Structural Engineering and Mechanics
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• v.7 no.1
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• pp.95-110
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• 1999

An effective moment of inertia is developed for a rectangular, prismatic elastoplastic beam with elastic, linear-hardening material behavior. The particular solution for a beam with elastic, perfectly plastic material behavior is also presented with applications for beam bending in closed-form. Equations are presented for the direct application of the virtual work method for elastoplastic beams with concentrated and distributed loads. Comparisons are made between the virtual work method deflections and the deflections obtained by using an average effective moment of inertia over two lengths of the beam in the elastoplastic region.

• 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.12 no.1
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• pp.1-16
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• 2001

A reliable and accurate method has been developed to predict the flexural deformation response of structural concrete members subject to service load. The method that has been developed relates the extent of concrete cracking, measured as a function of the magnitude of applied moment in a member, to the reduction in the effective moment of inertia of cracked reinforced concrete members under service load conditions. The ratio of the area of the moment diagram where the moment exceeds the cracking moment, to the total area of the moment diagram for any loading, provides the basis for the calculation of the effective moment of inertia. This ratio also represents mathematically a probability of crack occurrence. Verification of this method for the determination of the effective moment of inertia has been achieved from an experimental test program, and has included beam tests with different loading configurations, and shear wall tests subjected to a range of vertical and lateral load levels. Further verification of this method has been made with reference to the experimental investigation of other recently published work.

• Structural Engineering and Mechanics
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• v.67 no.2
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• pp.155-163
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• 2018

The Early-age construction loading and changing properties of concrete, especially in the multi-story structures can affect the slab deflection, significantly. Based on previously conducted experiment on eight simply-supported one-way slabs this paper investigates the effect of concrete type, fiber type and content, loading value, cracking moment, ultimate moment and applied moment on the instantaneous deflection of Self-Compacting Concrete (SCC) slabs. Two distinct loading levels equal to 30% and 40% of the ultimate capacity of the slab section were applied on the slabs at the age of 14 days. A wide range of the existing models of the effective moment of inertia which are mainly developed for conventional concrete elements, were investigated. Comparison of the experimental deflection values with predictions of the existing models shows considerable differences between the recorded and estimated instantaneous deflection of SCC slabs. Calculated elastic deflection of slabs at the ages of 14 and 28 days were also compared with the experimental deflection of slabs. Based on sensitivity analysis of the effective parameters, a new model is proposed and verified to predict the effective moment of inertia in SCC slabs with and without fiber reinforcing under two different loading levels at the age of 14 days.

• Proceedings of the Korea Concrete Institute Conference
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• 2008.11a
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• pp.209-212
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• 2008

Corrugated steel-concrete composite deck with I-beam welded is lighter and has higher load carrying capacity than RC slabs due to an I-beam embedded in the corrugated deck. The methods suggested from ACI and design standard of roadway bridge are used to evaluate effective moment inertia of RC structures. This paper presents evaluation and application of effective moment inertia for corrugated steel-concrete composite deck with I-beam welded by using the methods suggested from design standard of roadway bridge, ACI and CEB-FIP MC-90. In order to evaluate effective moment inertia, a series of flexural experiments were carried out. Five beams were built and the parameters considered in the experiments were studs, shape of the sections and connections of the beams. By using the aforementioned methods, effective moments of inertia was calculated and they were compared with the experimental results. As a result, The method suggested from CEB-FIP MC-90 yielded more satisfactory agreement than that from ACI. It was found that the beam has studs showed high load-carrying capacity and high effective moment of inertia.

• Journal of the Korea Concrete Institute
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• v.21 no.1
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• pp.93-103
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• 2009

The concept of the effective moment of inertia has been generally used for the deflection estimation of reinforced concrete flexural members. The KCI design code adopted Branson's equation for simple calculation of deflection, in which a representative value of the effective moment of inertia is used for the whole length of a member. However, the code equation for the effective moment of inertia was formulated based on the results of beam tests subjected to uniformly distributed loads, which may not effectively account for those of members under different loading conditions. Therefore, this study aimed to verify the influences of moment shapes resulting from different loading patterns by experiments. Six beams were fabricated and tested in this study, where primary variables were concrete compressive strengths and loading distances from supports, and test results were compared to the code equation and other existing approaches. A method utilizing variational analysis for the deflection estimation has been also proposed, which accounts for the influences of moment shapes to the effective moment of inertia. The test results indicated that the effective moment of inertia was somewhat influenced by the moment shape, and that this influence of moment shape to the effective moment of inertia was not captured by the code equation. Compared to the code equation, the proposed method had smaller variation in the ratios of the test results to the estimated values of beam deflections. Therefore, the proposed method is considered to be a good approach to take into account the influence of moment shape for the estimation of beam deflection, however, the differences between test results and estimated deflections show that more researches are still required to improve its accuracy by modifying the shape function of deflection.

• Structural Engineering and Mechanics
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• v.24 no.5
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• pp.601-620
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• 2006

The paper presents an effective stiffness model for deformational analysis of reinforced concrete cracked members in bending throughout the short-term loading up to the near failure. The method generally involves the analytical derivation of an effective moment of inertia based on the smeared crack technique. The method, in a simplified way, enables us to take into account the non linear properties of concrete, the effects of cracking and tension stiffening. A statistical analysis has shown that proposed technique is of adequate accuracy of calculated and experimental deflections data provided for beams with small, average and normal reinforcement ratios.