Nonlinear Truss Analogy Approach to Realize the Full Response of Pile Caps

This study introduces a nonlinear analytical framework developed to simulate the full structural behavior of reinforced concrete (RC) pile caps without stirrups using a matrix-based truss modeling approach. The proposed method captures the complete load–deflection response by identifying key performance stages, including cracking, yielding, and ultimate points. A strut-and-tie (STM) idealization is employed to represent internal force transfer mechanisms, where nodal displacements are first obtained under a unit load and subsequently scaled to determine the actual load levels associated with critical structural states. The evolution of strain, stress, and elongation within each truss member is evaluated iteratively throughout the loading process. Unlike conventional approaches, this method does not rely on assumed nonlinear strain distributions along the depth or span of the pile cap. In addition, secant stiffness formulations are incorporated and their predictions are assessed against experimental data. The results demonstrate strong agreement with observed behavior and confirm the capability of the proposed approach to accurately predict failure modes while promoting efficient and sustainable structural design.