Elastic solutions for stresses in compliance-tailored adhesive anchors

Abstract

Joining of structures via adhesive anchors is of theoretical and practical engineering importance, including anchors that support concrete ceilings in urban infrastructure. Such anchors typically fail due to stress concentrations at the loaded and/or embedded ends, captured by the well-known ‘shear-lag’ model. Herein, such anchors are revisited by considering elastic properties variation of the adhesive along the embedment length in discrete steps, to reduce critical stress concentrations, and thereby minimize the propensity of failure. Initially, a closed-form solution is developed for a system with single-step variation in adhesive compliance along the embedment length (henceforth referred to as double-adhesive bondline), which agrees well with Finite Element simulations. The simplest double-adhesive tailoring is found to reduce the maximum shear stress by 43% while maintaining the super-critical bondlength characteristics of such designs. The theoretical framework thus developed is extended to systems comprising an arbitrary number of discrete adhesives along the embedment length considering, fixed and free boundary conditions of the embedded-end, to allow for parametric evaluation of the adhesive compliance tailoring for optimal stress reduction (maximum shear stress reduces by 46% for triple-adhesive bondline) while maintaining critical-length characteristics. The adhesive tailoring could be effectively applied to anchors with critical-length characteristics by employing a facile double-adhesive bondline with the compliant adhesive near the loaded-end and stiffer adhesive near the embedded-end. The particular case of the well-known Boston tunnel anchor problem is analyzed as an exemplary demonstration of the approach.