Bond-Slip Analytical Formulation toward Optimal Embedment of Concrete-Filled Circular FRP Tubes into Concrete Footings

This paper presents a robust analytical model for a moment connection of concrete-filled fiber reinforced-polymer (FRP) tubes (CFFTs) to concrete footings. The CFFT connection is based on a simple approach of direct embedment into the footing, thereby eliminating the need for connection rebar or mechanical devices. The CFFT is externally subjected to lateral and axial loads, resembling practical applications such as piles affixed to pile caps, bridge columns, or utility poles. The model adopts the concepts of equilibrium, deformations compatibility, and nonlinear concrete stress-strain behavior. It also employs a “bond stress-slip” relation that can be obtained from simple push-through tests on some of the commercially used tubes. The model can predict the critical embedment length $X_{\text{cr}}$ , which is the minimum length required to achieve material failure of the CFFT outside the footing, and bond failure inside the footing, simultaneously. If the actual embedment length is less than $X_{\text{cr}}$ , bond failure occurs prematurely at a lower strength that can also be predicted by the model. The model was verified using experimental data and showed that $X_{\text{cr}}$ was only 0.7 of the diameter for that case. A sensitivity parametric analysis was carried out that led to some approximations. Based on which, a simple closed-form expression was established for $X_{\text{cr}}$ in the case of lateral loading only.