Abstract
Concrete cracking causes a gradual change in strain distributions along the cross section height of reinforced concrete beams, which will finally affect their instantaneous stiffness. A method for assessing the stiffness is proposed based on the gradual change, which is considered through modeling different strain distributions for key sections in cracked regions. Internal force equilibria are adopted to find a solution to top strains and neutral axes in the models, and then the inertias of the key sections are calculated to assess the beam stiffness. The proposed method has been validated using experimental results obtained from tests on five reinforced concrete beams. The predicted stiffness and displacements are shown to provide a good agreement with experimental data. The instantaneous stiffness is proven to greatly depend on the crack number and depth. This dependence can be exactly reflected by the proposed method through simulating the gradual change in concrete strain distributions.
Highlights
To ensure the serviceability of reinforced concrete beams, stiffness control is an important design objective
In this method, selected points in the cracks are mapped to the x-axis; a clustering technique is used to identify the points on the x-axis that are related to the same crack, and the average distance of the adjacent point cluster is taken as the crack spacing
Cracks do not show exactly the same pattern when observed from either side of the beams, so the crack spacing should be estimated from both the south and north sides. e inertias along the beam span should be assessed from the two sides
Summary
To ensure the serviceability of reinforced concrete beams, stiffness control is an important design objective. E effective inertia of cross section is widely adopted by engineers in design for the deflection control of cracked reinforced concrete beams. Branson [1] developed a model based on a weighted average of two types of inertias, respectively, representing the uncracked and fully cracked inertias of reinforced concrete cross sections. To consider the effect of crack location on the beam stiffness, François et al [6] proposed a macro-finite-element method characterized by the homogenized average inertias of cross sections, which were calculated based on the concept of a transfer length necessary for the transmission of tensile loads from steel to concrete, thanks to a steel-concrete bond. To exactly analyze the instantaneous stiffness of cracked reinforced concrete beams, the change in the strain distributions is taken into account in this paper. The section inertias can be exactly calculated to assess the instantaneous stiffness
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