• 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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• 2008.11a
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• pp.285-288
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• 2008

A model for the effective moment of inertia $I_{\epsilon}$ as expressed in Branson's equation, in which reduction of the flexural rigidity of RC beams due to cracking are aptly taken into accoun,t is presented. However, KCI Code isn`t considered tension stiffening as it is in debonding of reinforcing bar. Therefore, this equation need to set up suitable to our design Code. The experimental work consisted of casting and testing a total of 6 simply supported reinforced concrete beams and a total of 4 continuos reinforced concrete beams under two point concentrated loads. Main parameters are concrete strength, coverage, bond between concrete and reinforcing bars, are known as have an effect on deflection and tension stiffening. Every test beams had the same $250{\times}350$mm rectangular section, with a simply supported clear span of 4,400 mm and a continuos clear span of 6,500 mm. Comparison of the test results with values obtained using the KCI Code equation of the effective moment of inertia showed a noticeable difference.

• Journal of the Korea institute for structural maintenance and inspection
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• v.14 no.2
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• pp.184-192
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• 2010

The member deflection is one of the most important considerations for the serviceability evaluation of reinforced concrete (RC) structures, and the concept of the effective moment of inertia has been generally used for its estimation. However, the actual service load applied on an existing RC beam may not be easily obtained, for which the estimation of beam deflection by existing methods can be difficult to obtain. Therefore, based on the correlation between cracks and deflection in a RC beam, this study proposed a method to estimate the deflection of RC beams directly from the condition of cracks not using the actual loads acting on the member as its input data. The proposed method extensively utilized the relationships among sums of crack widths, average strains, and curvatures, and modification factors obtained from regression analysis were also introduced to improve its accuracy. The deflections of members were successfully estimated by the proposed method independent from applied loads, which was also easy to apply compared to the existing methods based on the effective moment of inertia.

• Journal of the Korea institute for structural maintenance and inspection
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• v.19 no.6
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• pp.95-102
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• 2015

Recently, the maintenance activity for aging of bridge structures was difficult because of traffic jam, environment pollution and increasing cost. And to solve these problems, modular bridge research has been studied. After static and cyclic loading test was conducted for serviceability and bending performance with one way slab, effective moment of inertia of modular specimen was analyzed to estimate the deflection by KCI(2012). To conduct the test, one integral slab and three modular slabs were made for static loading and one integral and modular slab were made for cyclic. As a result of the test, the modular slab had the similar bending performance of the integral. But the ultimate deflection showed the insufficient which was smaller than 20%. In the cyclic loading test, the modular slab has different behavior of deflection with the integral, so it was evaluated difficult for serviceability. In addition, effective moment of inertia by KCI(2012) was not estimated for modular slab with connection. The new value of m which was ratio between moments is 4.53 based on result of test for predicting deflection of modular.

• 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.

• Journal of the Korean Recycled Construction Resources Institute
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• v.11 no.4
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• pp.484-492
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• 2023

The structural behaviour of concrete beam was examined by the three points bending test after the completion of the electrochemical chloride extraction (ECE), rather than bond strength mostly measured in previous studies. It was found that the flexural rigidity of concrete was lowered by the ECE, but the strength was enhanced in terms of the maximum load.The flexural rigidity, in the linear elastic range, was reduced by the loss of effective cross-section area. In fact, the inertia moment was substantially subjected to 70 % loss of the cross-section by the tensile strain at the condition of the failure. However, a lower rate of the inertia moment reduction was achieved by the ECE, implying the higher resistance to the cracking, but the higher risk of deformation.

• Magazine of the Korea Concrete Institute
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• v.10 no.6
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• pp.253-260
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• 1998

An approximate method for the calculation of creep deflections of reinforced concrete beams under sustained service loads is proposed. The position of neutral axis and strain and stress distribution of fully cracked section after creep is determined from the requirements of strain compatibility and equilibruim of a section and then the long-term flexural rigidity of fully cracked section is determined based on the new neutral axis. The long-term flexural rigidity of uncracked section at the level of the reinforcenment. The approach of calculating long-term effective flexural rigidity and defections is similar to the current American Concrete Institue procedure for calculating effecitve moment of inertia and short-term deflections. The accuracy of the analysis is verified by comparison with several experimental mesurements of beam deflectons. The result is good between the theotetical values and mesured valus.

• Journal of the Korea Concrete Institute
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• v.21 no.6
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• pp.797-804
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• 2009

The structural designs of RC flat plates that have insufficient flexural stiffness due to lack of support from boundary beams may be governed by serviceability as well as a strength criteira. Specially, since over-loading and tensile cracking in early-aged slabs significantly increase the deflection of a flat plate system under construction, a construction sequence and its impact on the slab deflections may be decisive factors in designs of flat plate systems. In this study, the procedure of calculating slab deflections considering construction sequences and concrete cracking effects is proposed. The construction steps and the construction loads are defined by the simplified method, and then the slab moments, elastic deflections, and the effective moment of inertia are calculated in each construction step. The elastic deflections in column and middle strips are magnified to inelastic deflections by the effective moment of inertia, and the center deflection of slab are calculated by the crossing beam method. The proposed method is verified by comparisons with the existing test result and the nonlinear analysis result. Also, by applications of the proposed method, the effects of the slab construction cycle and the number of shored floors on the deflections of flat plates under construction are analyzed.

• Proceedings of the Korea Concrete Institute Conference
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• 2008.11a
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• pp.293-296
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• 2008

The member deflection is one of the most important considerations for the serviceability evaluation of reinforced concrete (RC) structures, and the concept of the effective moment of inertia has been generally used for its estimation. However, the actual service load applied on an existing RC beam may not be easily obtained, for which the estimation of beam deflection by existing methods can be difficult work. Therefore, based on the close relationships between cracks and deflection in a RC beam, this study proposed a method to estimate the deflection of RC beams directly from the condition of cracks not using the actual loads acting on the member as its input data. The proposed method extensively utilized the relationships among sums of crack widths, average strains, and curvatures, and modification factors obtained from regression analysis were also introduced to improve its accuracy. The deflections of members were successfully estimated by the proposed method independent from applied loads, which was also easy to apply compared to the existing methods based on the effective moment of inertia. This new method, however, has limitations in its applicability in that it is less accurate than the existing methods because the magnitude of acting load is not involved in the estimation process of member deflection, and that it requires the measurement of crack widths along the whole length of a member.

• Proceedings of the Korea Concrete Institute Conference
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• 2010.05a
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• pp.157-158
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• 2010

Based on the relation between cracks and deflection in a RC beam, this study proposed a method to estimate the deflection of RC beams directly from the condition of cracks not using the actual loads acting on the member. The deflections of members were successfully estimated by the proposed method, which was also easy to apply compared to the existing methods.