Mechanism of coupled instability of single-layer reticulated domes

•We study interaction between member buckling and overall buckling of the structure.•We define the progressive instability and synchronous instability of the structure.•Progressive instability is member buckling occurs before overall buckling of structure.•Synchronous instability is buckling of members and whole structure happens simultaneously.•Instable members form a region of member buckling when overall buckling of the structure.

Single-layer reticulated domes are typical structures with high degree of static indeterminacy. The stability of the reticulated dome structures is complicated and closely related to both the member buckling and the overall buckling of the structure. However, little theoretical research work deals with this very complex phenomenon. Meanwhile, for the statically indeterminate structures, it is a common belief that the local failure would occur first and result in the change of internal force paths, while the structure could support load continually before the overall collapse of the structure. In this paper, the interaction between the member buckling and the overall buckling of the structure was investigated, and this common belief was explored. The geometrically and materially nonlinear analyses (GMNA) were carried out for the reticulated domes with eight types of different grid forms, and the examination of member buckling for each dome was conducted based on the examination method of the P–δend curve or the P–δmid curve of the member. The relationship between the member buckling and the global instability of the structure was obtained by evaluation results of member buckling. Consequently, for the common reticulated domes, two instability patterns were identified, i.e. progressive instability and synchronous instability. In the case of progressive instability, the member buckling occurs in advance of the overall buckling of the structure. Then the number of the instable member increases, and finally the overall buckling of the structure occurs. In the case of synchronous instability, the member buckling and the overall buckling of the structure happen simultaneously. The interaction mechanism between the member buckling and the global instability of the structure was analyzed for both instability patterns.