Three-dimensional grid strut-And-Tie model approach in structural concrete design

The strut-And-Tie model approach has now been incorporated in current U.S. design codes and guidelines for the design of disturbed regions in structural concrete elements. However, more work is needed to extend the approach to design of three-dimensional (3-D) structural concrete. It is also important to consider its verification with experimental evidence. The application to 3-D design situations of this approach brings more uncertainties with its proper application and limitations. To reduce uncertainty and assist designers in the application of the strut-And-Tie model to 3-D situations, the authors present in this paper a 3-D grid strut-And-Tie model approach consisting of three key steps: 1) grid elements to construct a 3-D strut-And-Tie model; 2) triaxial failure model of concrete to determine effective strengths of concrete struts and nodal zones; and 3) iterative technique to evaluate the axial stiffness of struts and ties. In this paper, the authors also incorporate in the strut-And-Tie model a new concept of maximum cross-sectional areas of struts and ties to examine the strut-And-Tie model's geometrical compatibility. The approach is illustrated with the redesign of a deep pile cap with tension piles available in the literature. In a subsequent paper, the authors will evaluate the approach with test results of 157 specimens tested to failure. The tests include 78 reinforced concrete pile caps, 19 slab-column joints, and 60 beams subjected to torsion.