A Study on Effective Length of Slender Column with Elastic Restraints

The bottom slender columns are widely used in modern high rise buildings because of the existence of floor with opening, and the effective length will deeply affect bearing capacity of the column. This paper presents a new methodology for calculate the effective length of the bottom slender columns based on the equivalent model. The elastic restraints of beams are considered as lateral support spring, and the effective length of the column is determined through buckling analysis of the column fixed at bottom and elastic supported at top. A case study of high rise building with 20 m bottom slender column was conducted as follows: A horizontal force was applied on the floor supporting of the slender column top, and the lateral displacement of the column could be calculated through whole structure analysis in design procedure, therefore, the spring stiffness can be figured out through the applied horizontal force divided by the displacement. Then, eigenvalue buckling analysis was conducted on the column by using software ANSYS. The buckling mode shape were checked and the lowest buckling mode was solved, the buckling critical load could be obtained by multiplying the critical load coefficient by compression stress of the member. Finally, the effective length factor could be determined by comparing the bearing capacity of the bottom slender column with bearing capacity of that column with hinge joint at both ends. The results indicate that the effective length factor of the bottom slender column based on the proposed method is 21% larger than that in the design code. The weakness in bearing capacity of the bottom slender column should be considered during design.