Behavior and Design of Concrete Frame Corners: Strut-and-Tie Method Approach

Reinforced concrete frame corners (that is, knee joints) subjected to closing moments plays an important role of transmitting stress between the two adjoining members. Being categorized as geometric discontinuity regions (D-regions), knee joints cannot be correctly analyzed and designed using traditional sectional analysis procedures. Instead, the strut-and-tie method is particularly suitable for such joints. Although strut-and-tie models provide the means to represent the distribution of stresses within a closing knee joint, questions arise when a curved-bar node is used to model the bar bend of the longitudinal reinforcement at the outer corner. The code-specified design expressions for curved-bar nodes have not been experimentally verified; therefore, the accuracy and conservativeness of the expressions remain unknown. This research project is aimed to provide insights to the proper application of the strut-and-tie method, through the concept of curved-bar nodes, to knee joints under closing moments.

An experimental program consisting of 24 specimens was conducted to investigate the effect of curved-bar nodes on knee joints under closing moments. An evaluation of the code-specified design expressions was included. The results demonstrate that the minimum code-specified bend radius is appropriate. The current requirements related to bond along the bar bend and clear side cover are shown to be conservative. Based on the test results, a procedure for constructing proper strut-and-tie models for closing knee joints is proposed and verified using an evaluation database consisting of 116 knee joint tests from the literature. Compared to other strength predictive methods and the code-specified strut-and-tie method, the proposed strut-and-tie method mitigates unconservativeness and delivers improved accuracy.
In addition to the experimental program and the proposed procedure, non-linear finite element analysis (FEA) using the software ATENA-3D was employed to conduct a parametric analysis as a supplement to the experimental data. Seventy-two numerical models were analyzed to further evaluate the code-specified expressions and the proposed strut-and-tie method. The FEA results are in a good agreement with the experimental observations and corroborate the conclusions from the experimental program regarding current code requirements. Moreover, the parametric analysis further supports the application of the proposed strut-and-tie methodology to knee joints under closing moments.