QR-Method For The Static Elastic-Plastic Analysis Of Plane Steel Frame With Semi-Rigid Connection

The performance of beam-column connections in steel frame affects directly the sideways and internal forces of the frame. In the traditional steel structure design, beams and columns generally were assumed to be fully rigid connected or hinged ideally. Extensive tests and studies show that all connections of the steel structures in practice are between fully rigid and ideal pinned link and belong to semi-rigid connections. If the semi-rigid connections are simplified fully rigid connections, the sideways of the frame will be underestimated, the ultimate load-carrying capacity will be magnified, and the structure will lean to unsafe. If the semi-rigid connections are simplified ideal pinned connections, the design will be conservative, and the consumption of steel will increase. In order to make the design of steel frame more reasonable, the effect of semi-rigid connections must be taken account of.This paper studies the plane semi-rigid connections steel frame, according to the big displacement theory under small deformation, uses the theory of beam-to-column and stability function to derive the element stiffness matrix which considers geometric nonlinearity, the material nonlinearity and the beam-column semi-rigid connection, and using Kishi-Chen power function to describe the nonlinear behavior of semi-rigid connections.This paper use the QR method to study the static analysis of plane steel frame which considers triple non-linearity, has established the QR method computational scheme, has edited the corresponding computational programs by C programming language, has analyzed the influence to the structure of each kind of nonlinear factor by the program computation result of typical examples. Analysis shows that the geometry nonlinearity, the material nonlinearity and the semi-rigid connection mutual influence, and increase the sideways of the frame, influence the structure internal force and ductility, while reducing the ultimate bearing capacity. Compared with the traditional finite element method, this QR method has its advantages, such as high precision, fewer unknown quantity, and simple computational scheme.