• 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.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.39 no.2
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• pp.241-266
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• 2011

The Self Compacting Concrete, SCC is the new generation type of concrete which is not needed to be compacted by vibrator and it will be compacted by its own weight. Since SCC is a new innovation and also the high strength self compacting concrete, HSSCC behavior is like a brittle material, therefore, understanding the strength effect on the serviceability performance of reinforced self compacting concretes is critical. For this aim, first the normal and high strength self compacting concrete, NSSCC and HSSCC was designed. Then, the serviceability performance of reinforced connections consisting of NSSCC and HSSCC were investigated. Twelve reinforced concrete connections (L = 3 m, b = 0.15 m, h = 0.3 m) were simulated, by this concretes, the maximum and minimum reinforcement ratios ${\rho}$ and ${\rho}^{\prime}$ (percentage of tensile and compressive steel reinforcement) are in accordance with the provision of the ACI-05 for conventional RC structures. This study was limited to the case of bending without axial load, utilizing simple connections loaded at mid span through a stub (b = 0.15 m, h = 0.3 m, L = 0.3 m) to simulate a beam-column connection. During the test, concrete and steel strains, deflections and crack widths were measured at different locations along each member. Based on the experimental readings and observations, the cracked moment of inertia ($I_{cr}$) of members was determined and the results were compared with some selective theoretical methods. Also, the flexural crack widths of the members were measured and the applicability for conventional vibrated concrete, as for ACI, BS and CSA code, was verified for SCCs members tested. A comparison between two Codes (ACI and CSA) for the theoretical values cracking moment is indicate that, irrespective of the concrete strength, for the specimens reported, the prediction values of two codes are almost equale. The experimental cracked moment of inertia $(I_{cr})_{\exp}$ is lower than its theoretical $(I_{cr})_{th}$ values, and therefore theoretically it is overestimated. Also, a general conclusion is that, by increasing the percentage of ${\rho}$, the value of $I_{cr}$ is increased.

• 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.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.

• 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.

• Structural Engineering and Mechanics
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• v.8 no.6
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• pp.531-546
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• 1999

The paper presents an experimental and theoretical study on the influence of steel fibers and longitudinal tension and compression reinforcements on immediate and long-term deflections of high-strength concrete beams of 85 MPa (12,300 psi) compressive, strength. Test results of eighteen beams subjected to sustained load for 180 days show that the deflection behavior depends on the longitudinal tension and compression reinforcement ratios and fiber content; excessive amount of compression reinforcement and fibers may have an unfavorable effect on the long-term deflections. The beams having the ACI Code's minimum longitudinal tension reinforcement showed much higher time-dependent deflection to immediate deflection ratio, when compared with that of the beams having about 50 percent of the balanced tension reinforcement. The results of theoretical analysis of tested beams and those of a parametric study show that the influence of steel fibers in increasing the moment of inertia of cracked transformed sections is most pronounced in beams having small amount of longitudinal tension reinforcement.

• 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.31 no.2
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• pp.163-180
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• 2009

In the design of tall reinforced concrete (R/C) buildings, the serviceability stiffness criteria in terms of maximum lateral displacement and inter-story drift must be satisfied to prevent large second-order P-delta effects. To accurately assess the lateral deflection and stiffness of tall R/C structures, cracked members in these structures need to be identified and their effective member flexural stiffness determined. In addition, the implementation of the geometric nonlinearity in the analysis can be significant for an accurate prediction of lateral deflection of the structure, particularly in the case of tall R/C building under lateral loading. It can therefore be important to consider the cracking effect together with the geometric nonlinearity in the analysis in order to obtain more accurate results. In the present study, a computer program based on the iterative procedure has been developed for the three dimensional analysis of reinforced concrete frames with cracked beam and column elements. Probability-based effective stiffness model is used for the effective flexural stiffness of a cracked member. In the analysis, the geometric nonlinearity due to the interaction of axial force and bending moment and the displacements of joints are also taken into account. The analytical procedure has been demonstrated through the application of R/C frame examples in which its accuracy and efficiency in comparison with experimental and other analytical results are verified. The effectiveness of the analytical procedure is also illustrated through a practical four story R/C frame example. The iterative procedure provides equally good and consistent prediction of lateral deflection and effective flexural member stiffness. The proposed analytical procedure is efficient from the viewpoints of computational effort and convergence rate.

• Structural Engineering and Mechanics
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• v.63 no.5
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• pp.669-681
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• 2017

The design of reinforced concrete buildings must satisfy the serviceability stiffness criteria in terms of maximum lateral deflections and inter story drift in order to prevent both structural and non-structural damages. Consideration of plastic hinge formation is also important to obtain accurate failure mechanism and ultimate strength of reinforced concrete frames. In the present study, an iterative procedure has been developed for the analysis of reinforced concrete frames with cracked elements and consideration of plastic hinge formation. The ACI and probability-based effective stiffness models are used for the effective moment of inertia of cracked members. Shear deformation effect is also considered, and the variation of shear stiffness due to cracking is evaluated by reduced shear stiffness models available in the literature. The analytical procedure has been demonstrated through the application to three reinforced concrete frame examples available in the literature. It has been shown that the iterative analytical procedure can provide accurate and efficient predictions of deflections and ultimate strength of the frames studied under lateral and vertical loads. The proposed procedure is also efficient from the viewpoint of computational time and convergence rate. The developed technique was able to accurately predict the locations and sequential development of plastic hinges in frames. The results also show that shear deformation can contribute significantly to frame deflections.