Inner Force Analysis of Two Typical Frames with Vertical Displacement
Finite element method is often used to obtain exact solution in the course of internal force calculation of some complex frames which contain nodal vertical displacement such as frames with transferring layer and mega-frames with sub-structure. In the phase of scheme comparison and schematic design, methods which can quickly produce calculation results of the above said frameworks are necessary. Based on the basic principle of displacement method, this paper proposes a simple analytical method for frameworks that contain nodal vertical displacement. According to the proposal, the basic structure for calculation is the framework in which is added vertical chain-pole at relevant node; the basic unknown quantities are the nodal vertical displacement of the basic structure; the basic equation is fixed according to the equilibrium of node forces; unit vertical displacement as well as bending moment and shear diagram of the basic structure under external load are respectively obtained by using moment redistribution method; nodal vertical displacement is determined through substitution of shear force of relevant rod into the equilibrium equation of the chain-pole node; the actual internal force is determined through superposition of actual vertical displacement and internal force diagram algebra of the basic structure under vertical external load. An engineering example is introduced, which is intended to provide reference for the simple calculation for the above said complex frameworks.
Jingsi Huo, Yan Xiao, Zongjin Li and Shuaib Ahmad
W. Zhou "Inner Force Analysis of Two Typical Frames with Vertical Displacement", Key Engineering Materials, Vols. 400-402, pp. 341-346, 2009