• Computers and Concrete
• /
• v.9 no.4
• /
• pp.275-291
• /
• 2012

The service loads are often decisive in the design of concrete structures. The evaluation of the cracking moment, $M_{cr}$, is an important issue to predict the performance of the structure, such as, the deflections of the reinforced concrete beams and slabs. To neglect the steel bars of the section is a simplification that is normally used in the computation of the cracking moment. Such simplification leads to small errors in the value of this moment (typically less than 20%). However, these small errors can conduce to significant errors when the values of deflections need to be computed from $M_{cr}$. The article shows that an error of 10% on the evaluation of $M_{cr}$ can lead to errors over 100% in the deformation values. When the deformation of the structure is the decisive design parameter, the exact computing of the cracking moment is obviously very important. Such rigorous computing might lead to important savings in the cost of the structure. With this article the authors wish to draw the attention of the technical community to this fact. A simple equation to evaluate the cracking moment, $M_{cr}$, is proposed for a rectangular cross-section. This equation leads to cracking moments higher than those obtained by neglecting the reinforcement bars and is a simple rule that can be included in Eurocode 2. To verify the accuracy of the developed model, the results of the proposed equation was compared with a rigorous computational procedure. The proposed equation corresponds to a good agreement when compared with the previous approach and, therefore, this model can be used as a practical aid for calculating an accurate value of the cracking moment.

• Structural Engineering and Mechanics
• /
• v.17 no.1
• /
• pp.15-27
• /
• 2004

A rational and simple analytical model to predict the time varying cracking moment of reinforced concrete sections under sustained loading is developed. The modeling procedure is based on equilibrium and compatibility requirements and takes into account the interdependent effects of creep and shrinkage as well as the presence of axial loading. A parametric study is conducted in which particular consideration is given to the effects of reinforcement ratio, level of loading, and creep and shrinkage characteristics of concrete. It is concluded that the reduction in cracking moment is mainly attributed to shrinkage. The effect of shrinkage is more pronounced at low levels of sustained loading and at high reinforcement ratios. This effect is lessened by the compression steel and creep particularly when the applied moment is near the cracking moment.

• Proceedings of the Korea Concrete Institute Conference
• /
• 2006.11a
• /
• pp.173-176
• /
• 2006

The one of the commonly reported failure mode of the RC beam strengthened with FRP was caused by the separation of the concrete cover, so called delamination. Therefore, ACI440 recommended that concrete cover delamination can be prevented in strengthened beams if bond length of FRP composite be exteneded over a point of cracking moment. In this study, the failure mode and the flexural performance of RC beam with different bond length of FRP are estimated. Each bonded length is calculated based on the point of cracking moment with addition or subtraction of specific length(=150mm). The results of this study show that mid-span debonding occurs in the specimen strengthened with CFRP strips which are bonded over the point of cracking moment, while concrete cover deliamination occurs at the termination point of CFRP in the specimen with less bonded length than the point of cracking moment region.

• Structural Engineering and Mechanics
• /
• v.12 no.1
• /
• pp.1-16
• /
• 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
• /
• v.39 no.2
• /
• pp.267-285
• /
• 2011

There can be a significant amount of moment redistribution in composite frames consisting of steel columns and composite beams, due to cracking, creep and shrinkage of concrete. Considerable amount of computational effort is required for taking into account these effects for large composite frames. A methodology has been presented in this paper for taking into account these effects. In the methodology that has been demonstrated for moderately high frames, neural network models are developed for rapid prediction of the inelastic moments (typically for 20 years, considering instantaneous cracking, and time effects, i.e., creep and shrinkage, in concrete) at a joint in a frame from the elastic moments (neglecting instantaneous cracking and time effects). The proposed models predict the inelastic moment ratios (ratio of elastic moment to inelastic moment) using eleven input parameters for interior joints and seven input parameters for exterior joints. The training and testing data sets are generated using a hybrid procedure developed by the authors. The neural network models have been validated for frames of different number of spans and storeys. The models drastically reduce the computational effort and predict the inelastic moments, with reasonable accuracy for practical purposes, from the elastic moments, that can be obtained from any of the readily available software.

• Steel and Composite Structures
• /
• v.42 no.6
• /
• pp.765-777
• /
• 2022

Ultra high performance concrete (UHPC) can be used in the UHPC-steel composite structures especially for bridge structures to achieve high stiffness and high fatigue resistance with low self-weight. The structural performances of UHPC-steel composite slabs subjected to hogging moment have a significant influence on the global stiffness and durability of UHPC-steel composite structures. In order to study the structural behaviors of non-steam-cured UHPC-steel composite slabs subjected to negative moment, five composite slabs combined the thin UHPC layers to steel plates via shear stud connecters with the diameter of 16mm were fabricated and tested under negative moment. The test program aimed to investigate the effect of stud spacing and longitudinal reinforcement ratios on the failure mode, load-deflection behaviors, cracking patterns, bond-slips, and carrying capacities of composite slabs subjected to negative moment. In addition, direct tensile tests for the dog-bone UHPC specimens with longitudinal reinforcement bars were carried out to study the effect of reinforcement bars on the tensile strength of UHPC in the thin structure members. Based on the experimental results, analytical models were also developed to predict the cracking load and ultimate load of UHPC-steel composite slabs subjected to negative moment.

• KCI Concrete Journal
• /
• v.12 no.2
• /
• pp.11-21
• /
• 2000

It is not easy to correctly predict deflections of reinforced concrete beams and one-way slabs due to the variability of parameters involved in the calculation of deflections. Monte Carlo simulation is used to assess the variability of deflections with known statistical data and probability distributions of variables. A deterministic deflection value is obtained using the layered beam model based on the finite element approach in which a finite element is divided into a number of layers over the depth. The model takes into account nonlinear effects such as cracking, creep and shrinkage. Statistical parameters were obtained from the literature. For the assessment of variability of deflections, 12 cases of one-way slabs and T-beams are designed on the basis of ultimate moment capacity. Several results of a probabilistic study are presented to indicate general trends indicated by results and demonstrate the effect of certain design parameters on the variability of deflections. From simulation results, the variability of deflections relies primarily on the ratio of applied moment to cracking moment and the corre-sponding reinforcement ratio.

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

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

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