Importance of a rigorous evaluation of the cracking moment in RC beams and slabs

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.