Enhanced deflection method for large-curvature problems: Formulation, verification and application to fiber-reinforced polymer-enabled arches

Abstract

Motivated by a curiosity to explore the behavior of innovative arch structures enabled by the use of fiber-reinforced polymer (FRP) composites, this paper proposes a theoretical model built upon an enhanced formulation of the deflection method, broadening its scope to large-curvature problems. Traditionally, the deflection method approximates curvature as the second-order derivative of deflection, a simplification valid only for small curvatures. This limitation poses a challenge when applying the deflection method to problems involving large curvatures, a characteristic inherent in FRP-enabled arches where significant curvatures arise either initially or due to deformation. The enhanced formulation at the core of the proposed model addresses this challenge by incorporating a circular deflection function. This function posits that each deformed segment of the structural member can be represented by a circular arc, with its curvature and length related to the internal axial force and bending moment at the midpoint section of the segment. This feature facilitates the exact representation of curvature, offering the proposed model a unified approach capable of addressing both small- and large-curvature problems. The paper details the formulation and verification of the theoretical model, with an emphasis on its application to representative cases of FRP-enabled arches.