Tension members strengthening stability of two-way grid single-layer cylindrical shell in greenhouse

Single-layer two-way grid cylindrical shell with tension members is superior in providing high transparency, aesthetic appeal and material efficiency, and it is suitable for greenhouse structure. For testing its suitability for greenhouse use, tension member installation, tension member initial axial forces and out-of-plane tension member placement were considered in a two-way grid cylindrical surface because of the in-plane rigidity of a two-way grid shell was lower than that of a three-way grid shell. So, the single layer two-way grid cylindrical shell roof with tension members in out-of-plane and diagonal members was developed for the purpose of examining the tension member arrangement on the strength behavior of single layer cylindrical shell. A tension member''s function was to increase the in-plane and out-of-plane rigidity of a single layer two-way grid and to improve its stability behavior. In order to understand the effect of tension members, we determined the stability of cylindrical shells based on elastic and elasto-plastic complete-process analysis by using the finite element software ANSYS and self-compiled pre-post-processing programs. Some characteristic responses such as critical loads, buckling modes and distribution maps of plastic level were collected. The effects of various geometrical and structural parameters such as initial imperfection, different supporting conditions, unsymmetrical distribution of loads, rise span ratio and tension member prestress were investigated by elasto-plastic stability analysis. In the numerical calculations, out-of-plane tension member placement caused an increase in critical load and rigidity of load-deflection relationship under symmetrical and asymmetrical loadings. The critical load of two-way grid shell increased also by the introduction of the initial axial force to tension member. The results showed that the cylindrical shells were concluded to be sensitive to initial geometric imperfection, when the rise span ratio reached 1/6, the critical loads of cylindrical shells supported along four edges would be reduced by 24%. Unlike the other cylindrical shells, the critical load of two-way grid shell with tension member trended towards enlarger under the influence of unsymmetrical distributed load with the rise span ratio was 1/4, the critical loads would increase by 25% of the maximum degree. The plasticity distribution of grid member assumed the transversal grid members in the both sides of the central regions going into plastic easily caused by the large axial forces, the central regions were still characterized by sensitive areas. The out-of-plane tension members in the central section reached plastic status easily, so it was very important to design out-of-plane tension members in the practical engineering. Through a statistical analysis of elastic and elasto-plastic stability critical loads, “3σ” principle was suggested to determine the effect of initial geometric imperfection on the stability of cylindrical shells. A plasticity reduction coefficient for the single layer two-way grid shells with tension member was proposed to reveal the influence of material nonlinearity on critical loads. As a result, the plastic reduced coefficients of cylindrical shells were summarized to be 0.46~0.84. Through the analytical results, the elasto-plastic stability behaviors of single layer two-way grid shells with tension members were concluded, and the results provided a theoretical basis and technical support for the practical engineering in modern greenhouse construction.