A three-dimensional strut-and-tie model for a four-pile reinforced concrete cap

Reinforced concrete pile caps have been traditionally designed with sectional methods in codes and specifications. Since the 1990s, the two-dimensional strut-and-tie model (2D STM) methods, introduced in codes and specifications (Ref. ACI 318-14 and the 8^th Edition of the AASHTO LRFD Specifications), have become the design method of choice for pile cap designs. However, sectional methods and 2D STM provisions in current design codes have serious limitations when applied to the design of members with behavior more appropriately captured using three-dimensional (3D) approaches. In this paper, a refined 3D STM method for analysis and design of pile caps is illustrated. In the proposed method, a statically indeterminate 3D STM with diagonal ties is employed to account for the load-carrying capacity in tension of some regions in four-pile caps. The effective strengths of 3D concrete struts and nodal zones are determined by reflecting the effects of the 3D stress states and the degree of concrete confinement provided by reinforcement. The load-carrying capacities of struts and ties are determined using an iterative technique with the axial stresses of concrete struts equal to effective strengths. An extensive comparison between current and proposed methods is conducted using experimental data from 115 reinforced concrete pile caps tested to failure. Besides, several pile caps are designed using the current and proposed methods, and a comparison of the results from the design is conducted.