Effective Length of Columns with Semi-Rigid Connections

The effective length of a column depends on the boundary conditions at the ends of its unbraced length. In a framed structure, the boundary conditions depend on the stiffness of the beams framed to the column. Design guides available for determining the effective length are provided for cases where beams are rigidly framed to the column and have their far ends rigidly framed to another column, fixed, or hinged. This paper will present a solution for the case where beams are framed to columns using semi-rigid connections. Frequently, in the design of frames for tall buildings, it is found that beams must be selected based on their stiffness to resist frame drift, rather than on the strength needed to resist wind forces. In this case the actual bending moments required to be resisted at the ends of beams may be substantially smaller than the moment capacity of the beams. It is economically attractive to consider the use of semi-rigid connections adequate for the actual bending moment. However, the semi-rigid connection may have a lower stiffness than an equivalent portion of the beam, since its strength is weaker than the beam. This paper will present a set-up for a general solution for the stiffness of beams with semi-rigid connections. A solution will be made for a simplified case and available information for one type of semi-rigid connection will be used to illustrate the effect on the effective length of a column.