Derivation of the bearing strength perpendicular to the grain of locally loaded timber blocks

Abstract

Based on the equilibrium method of plasticity, the theoretical explanation of the bearing strengths of locally loaded timber blocks is given in the Appendices. The result of the numerical construction of the slip-lines can precisely be represented by an analytical function of a logarithmic spiral that can be shown to be the exact solution. This function in one variable can be given in the power law form leading to a theoretical and experimental value of that power of 0.5. This power representation of the stress spreading model of the strength increase, by confined dilatation, provides simple rules for the code and a simple design method that precisely matches to the data in all circumstances and loading cases and explains the apparent contradictory test results of Suenson, the Eurocode, the French rules, Graf, Korin and Augustin et al. and, as shown before, explains other comparable loading cases as e.g. by pin dowel connections (see literature).