Bond-slip Model to Capture Strain Penetration Effects

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    Capturing the response and damage of concrete structures requires accurate modeling of localized inelastic deformations occurring at the member end regions as identified by shaded areas. The member end deformations consist of two components: 1) the flexural deformation that causes inelastic strains in the longitudinal bars and concrete, and 2) the member end rotation caused be the slip of longitudinal reinforcement. Such slip, different from the slip due to poor anchorage condition, results from strain penetration of the bars into the adjoining concrete members.  Strain penetration describes the gradual transferring of bar forces to the surrounding concrete. The accumulative strain difference between the bar and concrete causes a slip at the loaded end of the anchored bar. Consequently, a crack forms and an end rotation occurs to the flexural member at the connection interface.

    Experimental studies have generally reported that this end rotation contributes up to 35 percent to the lateral deformation of flexural members.(Kowalsky et al., 1999, Calderone et al., 2000, and Saatcioglu et al. 1992) The strain penetration and the associated end rotation  greatly influence the localized strains and curvature in the critical regions, and stiffness of the flexural member. Ignoring the strain penetration also affects the energy dissipation capacity of the members, but to a lesser extent.

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    Significant research efforts have made to model the bond slip of bars anchored into building joints:

• General 3-D finite element models incorporating gap/interface elements. (Gilard and Bastien 2002, Salem and Maekawa 2004, and Lowes, 1999)
• Special fiber-based, beam-column elements considering the slippage of the reinforcing bars in the state determination at the section level. (Monti and Spacone, 2000, Spacone et al., 1996)
• Nonlinear rotational springs at the end of beam-column elements for 2-D analysis. (Otani, 1974, Priestley et al., 1996)
• Super-elements consists of uniaxial springs at member ends for 2-D analysis. (Saatcioglu and Ozcebe, 1989, Lowes and Altoontash, 2003)

    These models are not suitable for conveniently capturing the strain penetration effects in a flexural member that has an arbitrary cross-section or that is subjected to multi-directional loads. In addition, the existing techniques and models for the bar stress vs. slip relationships are typically verified against the results of tests that simulated typical bond conditions in building joints. However, the bond-slip behavior of bars anchored in building joints is different from that in footings and bridge joints:

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• Anchorage length limited by column width
• Entire bar likely experiences slip
• Tension at one end and compression at the other end
• End bearing not available
• Confinement steel parallel to the bars

• Adequate anchorage length
• A portion of the bar experiences slip
• Tension/compression only at one end
• End bearing helps to transfer compression
• Confinement steel perpendicular to the bars

    This study focuses on the member end rotation due to strain penetration along reinforcing bars anchored in footings and bridge joints. A zero-length section element is used to consider the member end rotation in fiber-based analysis of concrete structures.  A hysteretic model for the reinforcing bar stress vs. slip response is proposed to describe the bond-slip behavior of fully anchored steel reinforcements.