Stability & Strength Of The Single-Layer Ribbed Domes

The single-layer ribbed dome is an attractive & known reticulated structure, in this paper the structure is analysed. It is emphasized that how to analyse this structure and how to form it.In this paper,the formex algebra is used to describe the configuration of the ribbed dome.The finite element method and the beam-column method are introduced;the optimization of the single-layer reticulated shell is also discussed,a simple algorithm is presented,and an example showes the effectness of the algorithm. Based on the theory of the beam-column,it is studied that how to analyse the structure with the random imperfect members. The comparison of the limit loads of a structure with random imperfect members and of it with ideal members reveals that the limit load of the latter is much more than that of the former. The ribbed domes loaded the symmetrical uniform loads are analysed comprehensively with full pinned supports,some formulas are fitted according the limit loads calculated by the finite element method. In the process of introduction of the nonlinear finite element method, the updated-Lagrange method is employed, it is derived that a geometrical stiffenss considered the nonlinear strain of the member axile direction,comparison of the stiffnesses with the interpolating function of the Hermite curve and the sine curve is given. In the process of introduction of the beam-column method,the member oritentation matrix is emphasized.From both the finite element method and the beam-column method, two FORTRAN codes are programmed. The same structure's displacements calculated by both programs are compared.In this paper ,the conclusions as following can be derived.i The members must not be subdivided when the structure is analysed with consideration of the random imperfection of the members. It can be revealed that the internal forces can be large when the value k(the meaning of k can be found in Chapter 5 in this paper.) approaches to the value n .Theoretically the values k of all of the structures composed of beam-column members can not approach to the value n ,it is needed to be testified by the experiments.ii With the same geometrical & material parameters,the limit loads of ribbed domes are much less than that of the 3-direction reticulated shell.In the process of fitting the foumulas in the paper, the following parameters are considered:the equivalent effective thinness,the equivalent effective moment of inertia,the radius of the spherical dome and the ration of the height and the span. With so many parameters considered , but the errors can not be ignored yet. The problem is much complicated than that it is imagined.iii The formex algebra is an effective method to describe the geometrical configuration of the complex structures.iv Theoretically the errors can be inevitably discovered when the medium-sized rotations are dealt with by the nonlinear finite method and nonlinear beam-columnmethod.It it the effective method to reduce the errors that the members of the structures are subdivided .v It is common that the stresses of the steel members are much less than the yield stress when the single-layer reticulated shells are destroyed ,so it can be concluded that the uaual destruction of a single reticulated shell is short of the stability. As the stresses of the member are much less than the yield stress ,the material nonlinearity is not consideredIn this paper,most of the problems are considered elementarily and theoretically,and it is necesarry to study the problems further,it is essential for some of them to be testified by the experiments.