Analytical Model for Non-linear M-θ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\user2{M - }\\,\\,{\\varvec{\ heta}}$$\\end{document} Relationships of Dowel-Type Timber Connections Exposed to Fire

Abstract

Recent experimental evidence has shown that wood–steel–wood dowel-type connections exhibit a semi-rigid behaviour even after 90 min of fire exposure. Because a semi-rigid behaviour influences the bending moment distribution among structural members, considering the moment–rotation relationships within frame analyses in which structural members are modelled as beam elements can enable a realistic fire response analysis that is significantly simpler than the three-dimensional finite element method. This study proposes an analytical methodology that accounts for the thermo-mechanical behaviour of timber and dowels, enabling the simulation of the non-linear moment–rotation relationships under fire conditions. The proposed analytical model divides dowels into a series of elements on an elastoplastic foundation and performs a direct stiffness method in a time-incremental procedure using an element stiffness matrix derived from beam-on-elastic-foundation theory. This study also presents the results of load-carrying tests on timber frames with dowel-type connections performed under ambient and fire conditions. The analytical results were consistent with the fire test results. Additionally, the analyses were also performed under three conditions in which the dowels were rigid, linear elastic, and elastoplastic bodies. These three results converged to the same value after 65 min of heating, which suggests that the ultimate states of beams with dowel-type connections exposed to fire can be modelled by assuming that dowels are rigid bodies.