A first level‐of‐approximation to analytically derive temperature profiles of adhesive anchors and post‐installed rebars exposed to <scp>ISO</scp> ‐834 fire

Abstract There is a lack in the current state‐of‐the‐art for the evaluation of the temperature profile of adhesive anchors and post‐installed rebars (PIR) exposed to fire. Although the problem is generally governed by Fourier's partial differential equation of heat transfer, at the current state, the only way to determine the temperature along the anchorage length is through finite‐element analysis (FEM), which is very time‐consuming and often impractical for many design scenarios. To address this, a first Level‐of‐Approximation (LoA‐I) is introduced, following the Levels‐of‐Approximation approach widely used by the fib community. Essentially, LoA‐I employs a closed‐form solution of Fourier's equation for uni‐axial heat flow in concrete elements, adapted for both a single anchor embedded in concrete and PIR. As a key element of the method, an equivalent constant thermal diffusivity is introduced on the basis of sound engineering assumptions. Validation of LoA‐I is achieved by comparing the analytically derived temperatures to both numerically derived (LoA‐II) and experimental temperatures for five benchmark cases. Additionally, pull‐out axial load‐bearing capacities are analytically derived using the Resistance Integration Method. Although LoA‐I results are generally more conservative than those from LoA‐II, the reduction in computational costs is considerable. Therefore, LoA‐I is recommended for quick design assessment as well as for all design cases in which pullout failure is expected to be not decisive.