Crack Resistance and Rigidity of Bending Reinforced Concrete Structures Based on a Non-linear Deformation Model

The deformation method for the structural analysis is recognized as more accurate and reliable, as it is based on experimental deformation diagrams of materials (concrete and reinforcement). However, in practice, there are still no detailed examples of calculating the crack resistance and rigidity of bending reinforced concrete elements using a deformation model, despite its convenience and the ability to quickly obtain results through iterative procedures.

Purpose: The aim is to calculate deformation of crack resistance and rigidity of bending reinforced concrete elements (service limit state), using design parameters obtained from calculating the deformation strength of the structure (ultimate limit state).

Methodology: The study is based on initial data and design parameters obtained in the strength calculation. The methodology includes the following steps: determination of the crack formation moment by summing internal forces, arising from normal stresses in each small section; calculation of the distance between adjacent cracks, taking into account the tensile zone in the limit state; calculation of the crack opening width depending on stresses in tensile reinforcement. Determination of the element deflection taking into account the maximum curvature calculated using the deformation modulus.

The paper also presents the adopted assumptions and prerequisites, theoretical formulas with respect to calculated ultimate strains and stresses (including the strain modulus).

Research findings: A practical calculation example was performed, and a comparative analysis was conducted, calculating the percentage difference in between the deformation and standard (limit state) methods.

Value: The novelty of the paper lies in the algorithm development for practical calculation of the crack resistance and rigidity of bending element based on the deformation model for the structural analysis.

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