Modeling of Strain Penetration Effects in Fiber-Based Analysis of Reinforced Concrete Structures

ACI Structural Journal, Mar/Apr 2007 by Zhao, Jian, Sritharan, Sri

In flexural concrete members, strain penetration occurs along longitudinal reinforcing bars that are fully anchored into connecting concrete members, causing bar slips along a partial anchoring length and thus end rotations to the flexural members at the connection intersections. Ignoring the strain penetration in linear and nonlinear analyses of concrete structures will underestimate the deflections and member elongation, and overestimate the stiffness, hysteretic energy dissipation capacities, strains, and section curvature. Focusing on the member end rotation due to strain penetration along reinforcing bars fully anchored in footings and bridge joints, this paper introduces a hysteretic model for the reinforcing bar stress versus slip response that can be integrated into fiber-based analysis of concrete structures using a zero-length section element. The ability of the proposed hysteretic model to capture the strain penetration effects is demonstrated by simulating the measured global and local responses of two concrete columns and a bridge T-joint system. Unless the strain penetration effects are satisfactorily modeled, it is shown that the analysis of concrete structures will appreciably underestimate the local response parameters that are used to quantify structural damage.

Keywords: bond; column; reinforced concrete; strain; wall.

(ProQuest-CSA LLC: ... denotes formulae omitted.)

INTRODUCTION

There is a growing demand for developing reliable numerical simulation tools that can assist with improving safety of concrete structures under extreme lateral loads, as well as advancing seismic design of structures by addressing multiple performance limits. For reinforced concrete structures subjected to moderate to large earthquakes, capturing the structural response and associated damage require accurate modeling of localized inelastic deformations occurring at the member end regions as identified by shaded areas 1 and 2 in Fig. 1. These 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, as indicated by arrows in Fig. 1, due to reinforcement slip. This slip, which is characteristically different from the slip that occurs to the entire bar embedment length due to poor anchorage condition,1 results from strain penetration along a portion of the fully anchored bars into the adjoining concrete members (for example, footings and joints) during the elastic and inelastic response of a structure. As demonstrated by Sritharan et al.,1 ignoring the strain penetration component may appear to produce satisfactory force-displacement response of the structural system by overestimating the flexural action for a given lateral load. This approach will appreciably overestimate the reinforcing bar and concrete strains as well as section curvatures in the critical inelastic regions of the member, however, thereby overestimating the structural damage. These strain increases do not necessarily lead to a significant increase in the moment resistance at the section level because the increase in the resultant force magnitudes will be compensated by reduction in the moment arms, thereby producing satisfactory force-displacement response for the member. Because the objective of the finite element analyses is to produce satisfactory global and local responses, an accurate representation of the strain penetration effects is critical when developing finite element models of concrete structures.

In beam-column joints of building frames, plastic hinges are designed to form at the beam ends (see shaded area 2 in Fig. 1), causing the beam longitudinal bars to experience slip due to strain penetration that occurs along the bars into the joint. Furthermore, the beam bars embedded in the interior joints of a frame structure responding to earthquake loads will be subjected simultaneously to tension at one end and compression at the other end. This condition, combined with the effects of load reversals, will progressively damage bond along the full length of the beam bar within the joint, essentially causing slippage of the entire bar within the joint. Hence, the bond-slip of beam bars within the joint is expected to be relatively more sensitive to the concrete strength, anchorage length, and joint force transfer mechanism compared to the column/wall longitudinal bars anchored in footings and bridge joints.

Unlike the beam bars anchored into the interior building joints, the column and wall longitudinal bars extended into footings and bridge joints are typically designed with generous anchorage length (shaded area 1 in Fig. 1). Furthermore, the bars anchored into footings are often detailed with 90-degree hooks at the ends to improve constructibility. In these cases, the embedded longitudinal bars that are loaded only at one end experience slip along a portion of the anchorage length and use end bearing to transfer forces when they are subjected to compression.2 Hence, the monotonic and cyclic behavior of anchored bars (for example, bar stress versus slip responses) at the intersection between a flexural member and a footing/bridge joint is expected to be different from that occurring at the building joint interfaces. For these reasons, the hysteretic bar stress versus slip response of these bars anchored in footings and bridge joints will be relatively more stable and dependable. This hypothesis was evident in the cyclic load tests documented by Lin3 on a few reinforcing bars that were fully anchored in concrete with straight and hooked ends.