| Summary |
A fundamental equation for reliability analysis of a membrane structure attached to a steel space structure is proposed using a concept of perturbation of a nonlinear equilibrium equation considering interaction between a membrane and its supporting steel space structure. First, the nonlinear equilibrium equation is formulated based on FEM considering the material and geometrical nonlinearities of a membrane structure including the effect of initial tension introduced into the membrane structure. Second, the membrane stresses in the warp and fill directions are formulated by a concept of perturbation method, in which main probabilistic structural parameters are initial tensions introduced into membrane and loading effects of snow and wind. Third, the reliability function is formulated as the difference between the membrane strength, warp or fill stress, and a stress effect due to external load, snow or wind. The reliability function is nonlinear in general to be solved by AFOSM already established and validated past by researchers. Several discussions on probabilistic parameters are also provided. The reason why magnitudes of membrane stresses, being assumed bi-axially equal under initial stress introduction, are non-uniform even in an initial equilibrium without an external load. Experiments, on-site measurements and FEM analysis on membrane stresses, performed by Japanese researchers, are introduced and explained with not only measured data but also FEM simulations, all showing the effects due to crimp interchange, visco-elasticity of the fabric material, membrane cutting patterning, and on-site development of membrane fabrics to structural steel members. |