Investigations on the critical load of mid-span Kiewitt-type single-layer timber reticulated shells considering the effect of joint stiffness

The method for predicting the critical load of the mid-span Kiewitt-type single-layer timber reticulated shells (STRSs) have not yet been proposed, and there are few experimental tests related to the stability behavior of the Kiewitt-type STRSs. In this study, two Kiewitt-6 (K6) STRSs with bolted joints were designed and tested to investigate the elasto-plastic stability behavior of the K6 STRSs. The results showed that the failure mode of the K6 STRSs was global instability, which was characterized by the descending of the top and the first ring joints. The finite element analysis (FEA) of the K6 STRSs was conducted to verify the feasibility of the simplified FEA model of the K6 STRSs. The load-displacement curves and failure modes obtained from FEA were consistent with those obtained from tests, implying that the simplified FEA model was valid for K6 STRSs. Based on the mechanical characteristic of the bolted joints for STRSs, the equivalent rotational stiffness for rigid joint was derived and verified through FEA of the two-member timber structures. Joint stiffness coefficient kappa and critical load coefficient phi were defined, and introduced to establish the boundary of the kappa for the stability design of the K6 STRSs. Considering the effect of the geometric parameters and material property of timber, more than 450 mid- span K6 STRS models were analyzed. The results showed that the boundary value kappa of the -ln kappa-phi kappa-phi curves for K6 STRSs with different span, height-to-span ratio, initial geometric imperfection and material properties of timber was similar, while the boundary value kappa of the-ln kappa-phi kappa-phi curves decreased in the cases that the load distribution of the K6 STRSs was non-uniform and the slenderness of the K6 STRSs was smaller. Finally, an equation for estimating phi was proposed, which provides an easy way to estimate the critical load of the mid-span K6 STRSs with semi-rigid joints.