Lateral Stiffness of Frames and Effective Length of Framed Columns

Abstract

After obtaining shear force, which creates unit lateral displacement in columns of a framed system, from an assumed deformation shape, the lateral-stiffness value of a related story is obtained. By employing these lateral-stiffness values, a system lateral-stiffness matrix, which is in banded matrix form, can be established easily. By using this banded matrix, established through the aforementioned method, natural angular frequency and characteristic model shape can be easily obtained. Also presented is a method to calculate the effective length of framed columns by using c factors, which depend on the stiffnesses of columns and girders of the framed system. First-mode values calculated by the presented method are compatible with classic shear-beam solutions and exact solutions. Furthermore, results obtained from the application of c factors, giving effective length factors for various end-connection conditions at the far ends of columns, are on the conservative side compared with exact values.