Research On The Second Order Analysis Method Of Frame Structures

Instruction about first order analysis method of frames is given by most of the current textbooks on mechanics of structure, and this method is generally used by civil engineers in calculating the internal forces of the frames, however, as the first order analysis does not consider of the additional internal forces caused by the global lateral displacement of the frame, the solution given by this way is obviously not very accurate and safe. With the development of computer technology, to analyze the complex structures with second-order nonlinear method is practicable, and it is obviously that the nonlinear analysis method will be used as a prevalent method. So the studies of second-order effect of the frames are very important and meaningful, because it can provide theoretic foundation for the second-order design and practical analysis method for practical projects.The present findings of nonlinear research in frame structures, and the methods for design of second-order effect in the codes from China and other countries, were briefly introduced in this paper. The contents and methods of design and calculating about second-order effect in GB50017-2003 were discussed as well. A rotational displacement equation for geometric nonlinear structures was derived, and then a nonlinear finite element program for rigid frames was compiled by FORTRAN. With this program, several examples were analyzed. The reasons why second-order effect should be taken into account and the factors which influenced the second-order effect were discussed.The geometric nonlinear effect should be taken into account in the calculating of steel frames, for its big proportion of height to breadth and small section. On the one hand, the program provided by this paper can be used to get the accurate solution, on the other hand, some approximate answer can be gotten by simplify some regular structures. The latter is also very important to the designers, it is because that the simplified method can be used as a preliminary design, and as a method to check the answer derived by computer. In this paper,the main simplified methods of the second-order analysis was summarized according to the rigid frames. For the needing of practical projects, a simple method to take P-A effect into account was derived. The counting result manifest that the new method is more simple and practical, and it can get accurate answer. Finally, based on the work of this paper, some problems about this research worth to be studied afterward are put forward.