Probability distribution of gaps between tenon and mortise of traditional timber structures

Abstract

The existence of gaps between tenon and mortise in traditional timber structures is very common. Accurate estimation of its probability distribution is essential for the stress and reliability analysis. This paper presents the probability distributions for the horizontal and vertical gaps based on measurement. The gap data were collected from four traditional timber buildings in a heritage building complex by manual on-site measurement. Statistical analysis of data for each building was performed. Results show that the statistical features of all four buildings are similar. All the measured gap data were then categorized into two groups in horizontal and vertical directions. The optimal distribution to represent these gap data was obtained using the probability plot correlation coefficient method and Anderson–Darling test. Results demonstrate that the Weibull distribution is the most appropriate model for fitting both the horizontal and vertical gaps. Parameters of the distributions were obtained from the maximum likelihood estimate. A finite-element (FE) numerical investigation for a joint was conducted. Gaps were randomly created using the obtained probability model in the joints. Static analysis results show that the gaps will weaken the mechanical behavior of the tenon–mortise joint, especially the initial stiffness. Compared with the horizontal gaps, the vertical gaps affect the mechanical properties of the joint more directly.