Bi-Linear Bond-Slip Modelling for 1-D Tension Stiffening Behavior of a RC Element

Cracking is an inherent characteristic of a reinforced-concrete (RC) element subjected to tension or bending. The crack width growth with loading depends on the rebar-concrete bond behavior. RC bridges are designed under strict requirements to ensure their proper long lifetime performance. Limiting the crack widths improves the performance and safety of bridges that are exposed to harsh climatic and environmental effects and enhances bridge service life-cycle expectancy. This paper presents an extended one-dimensional formulation for analyzing RC elements subjected to tensile loads and solves the one-dimensional tension stiffening problem. The extended bond-slip model analyses the entire range of loading, following cracks growth up to their maximum allowed width, employing a bi-linear bond-slip relationship. The analytical solution refers to the early loading stage where the first bond-slip segment governs the entire element and a closed form solution is obtained, followed by the higher loading stage where two different bond-slip relationships govern two complementary segments of the element. Analytical expressions for the stresses, strains, and displacements in concrete, steel, and interface are developed. Cracking is followed until rebar yielding. Validation of the model with available test results shows good agreement that is superior to the commonly used linear bond-slip model.

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