The analysis of the plane frames having columns which has principal axes not in the plane of frame

Abstract

The structural analysis of space frames in most cases is not practical because of some complications in data preparation and interpretation of results. Therefore the analysis of reinforced concrete and steel structures realized sometimes by idealization of them as plane frames although they are space frames. This approach seems to be sufficient for the design of structures and can be applied to the idealized plane frames provided that at least one of the principal axes of the elements (beams and columns) is laying in the plane of frame. Although the beams of the frames generally do satisfy this condition the columns may or may not satisfy. For these types of columns the frame plane and bending plane are not coinciding and the columns are actually being under the effect of asymmetric bending. For the structural analysis of such frames the frame must be taken as a space frame (Kuo and Yang 1993, Aristazabal-Ochoa 2003), or a special plane frame analysis technique (Kim and Lee 2000, Nunes and Soriano 2003) which takes into consideration the asymmetric bending of columns must be used. In this work a displacement type of finite element method is proposed for a plane frame having columns which has principal axes not in the plane of frame. The global axes of the plane frame (X, Y, Z ) and the local axes of column 1 are shown in Fig. 1. In the analysis of a frame using the method of Finite Elements it is sufficient to define the stiffness matrix of the column in the X, Y system. The local displacements and the forces can be determined by transformation.