Research On The Influence Of The P-δ Affection To Ultimate Bearing Capacity Of Single Layer Latticed Shell Structures

People need large architecture space to satisfy society needs with the development of society. Thesingle-layer latticed shell structure has come into general application in practice with attractive appearance,reasonable stress, easy making and construction. The latticed shell structure resists external loadsdepending on membrane stresses that are transferred in the form of axial forces. The buckling has occurredwhen the strain energy has a certain accumulation. Once the structure destroyed, it will cause seriouslosses.In the ordinary the size of members is determined by designed load. The limited load is far greaterthan designed load. The member may be in instability state before the structure instability. In other worlds,the instability of member is the key factor which influences the ultimate bearing capacity. So we shouldconsider the influence of single-member instability in calculating the ultimate bearing capacity. At presentthe ultimate bearing capacity of the single-layer latticed shell structure, calculated without considering thesingle-member instability, was greater than the actual value of ultimate bearing capacity in practice, whichis not safe. In order to consider the influence of single-member instability，Shen Zuyan put forward a newmechanical model, which can consider the influence of single-member instability accurately. But thismethod applies with difficulties which require many theories. This paper put forward a multi-elementsimulation technique that the member is simulated by BEAM188, which can accurately calculate thelimited load and easily apply in practices. The research methods in paper include three processes: the creation the model of the single-layerlatticed shell structure；the selection method for numerical analysis; the analysis influences of instability ofsingle-member for limited load.(1) The creation the model of the single-layer latticed shell structureThe model of the single-layer latticed shell structure is created by MST2008. Then the file of datainterface is exported. Last it was import in ANSYS.(2) The selection method for numerical analysisThe equilibrium path is tracked by Arc-length Method. Arc-length Method takes the load coefficientand unknown displacement as variables. For example the load step is controlled by curve arc length.The first limited load is further more than subsequent limited loads. The load is more than the firstlimited load. The structure lost ultimate bearing capacity and the deformation is more than designeddeformation.(3) The analysis influences of instability of single-member for limited load.The analysis of stability and limited load of single-layer latticed shell structure are completed byANSYS. The member is simulated by BEAM188.In order to simulated instability of single-member, everymember is divided into multi-element. It can be tracked for different spans, rise-span ratios ofsingle-layer latticed shell structures. The ultimate bearing capacity can be analyzed.First according to analysis of a Keiwitt single-layer latticed shell structure with span40m, radius42.5m,rise5m., number of lengthwise grid8, number of radial direction grid8, the single-member is obviousinstability from Instability modal picture. The ultimate bearing capacity with considering the single-memberinstability is lower15.6%than that without considering the single-member instability. In order tocomprehend the degree of influence of instability of single member in ultimate capacity, we carry out an analysis for single-layer reticulated spherical shells and single-layer cylindrical spherical shells withdifferent spans, different rise to span ratios, different types. It mainly resists the load by the bent stress for thesingle-layer reticulated spherical shell with smaller span, higher rise to span ratio, the failure mechanism ofwhich is strength failure. So it is more remarkable in ultimate bearing capacity for these structures withconsidering the single-member instability. But it mainly resists the load by the membrane stress for thesingle-layer reticulated spherical shell with larger span, lower rise to span ratio, the failure mechanism ofwhich is the whole instability. So it is less remarkable in ultimate bearing capacity for these structures withconsidering the instability of single member.As for cylinder single layer latticed shells supported by opposite side, they have a smaller restraint thanspherical single layer latticed shell. It always happens the whole instability destroy with small verticalrigidity. So it has a smaller influence than spherical single layer latticed shell in instability when theinstability of single member is considered.