QR-Method For Geometrical Nonlinear Stability Analysis Of Tall Frames Structures

Beams and columns are main load-bearing structure of tall frames in high buildings. It is flexible to arrange in plane and it is easy to satisfy the demand of large space. Especially steel structure frames with advantages of light deadweight, high strength, large extension, good anti-seismic capability, rapid construction speed, small structural member section, high headroom and long span, easy to reconstruct and well comprehensive economic target. So steel structure frames are very popular used in high buildings in developed countries. It is usually use first-order method such as effective lengths method in engineering practical stability compute. Because of much hypothesis adopted, so it can only make approximate analysis. In order to ensure the safety of design and calculate the stability problem of frames accurately, second-order effect must be concerned, that the influence of nonlinear to frames structure.This paper concern the influence of axis force to stiffness matrixes, introduce the geometrical stiffness matrixes. Builds structure stability equations by QR-method, ignore the quadratic item, hold one time item, simplify the geometrical nonlinear problem. Change the stability problem to solve the eigenvalue, then extract the critical load factor, and research its effect factor. Wrote corresponding computational programs with C language and calculate some examples. Results show that QR-method have fewer unknown quantities, avoids the shortcomings of traditional method such as finite elements and finite strip method and the results are consistent. It is convenient to build stiffness matrixes and load vectors, high precision of calculation. It is an economical, effective and practical method. This paper is valuable not only in theory but also with reference value in engineering practice.