Numerical Procedure for Evaluating Stresses Serviceability in Orthogonal Reinforcement of Reinforced Concrete Shells
reinforced concrete; shells; membranes; serviceability behavior; reinforcement stresses at the crack.
Shell elements are present in important engineering works such as reservoirs and bridge deck slabs. In service, the performance of these structures may be compromised due to cracking of the concrete, putting at risk, for example, watertightness and the fatigue limit state. These problems have a dependence on the stress in the reinforcement. Thus, it is at the crack that the greatest stress fluctuations are observed, therefore greater deformations of the reinforcement, which translates into crack opening. Therefore, it is evident that there is a need to understand these stresses to guarantee the functionality and durability of structures. In light of this, this work presents a computational routine implemented in Python called Cracked Shell Model (CSM), capable of calculating the stresses in orthogonal reinforcement in reinforced concrete shell elements. To this end, the thickness of the shell is discretized into layers subject to a plane state of stress. The reinforcements are evaluated using the Cracked Membrane Model (CMM), which considers the effect of tension stiffening via the Tension Chord Model (TCM). Furthermore, an implementation of the CMM was also developed using optimization techniques to solve the system of equations. Validation of the CMM and CSM was carried out using experimental and numerical results from panels available in the literature, where good accuracy and low computational cost were observed. Additionally, a study was conducted on the effect of compressive membranes on bridge deck slabs, which increases the resistance of these slabs. The study demonstrated that models based on Kirchhoff's theory, such as the CSM, cannot capture the efforts arising from this effect, leading to an ultimate load lower than that observed in tests.