The Accuracy of Column Stability Calculations in Unbraced Frames and the Influence of Columns with Effective Length Factors Less Than One

Abstract

Until 1993, AISC design specifications did not permit the use of effective length (K) factors less than one in unbraced frames. However, it is well known that, in certain practical situations, a column which is in an unbraced moment resisting frame may exhibit a K factor less than one. While there are a number of equations that have been suggested for the calculation of effective length, to the authors knowledge the accuracy of these different equations has not been thoroughly studied and compared for unbraced frames in which the K factor of one or more of the columns is less than one. This paper investigates and attempts to elucidate the stability behavior associated with columns in unbraced frameworks which possess this effective length characteristic. Based on an isolated column subassembly and a set of small frames that are felt to be representative of a wide range of situations encountered in practice, the accuracy of various methods for calculating effective length factors is identified. Although a variety of methods may be used to calculate the effective length factors in such frames, some of the formulas appear to be consistently more accurate than others. In addition, and perhaps more importantly, it is demonstrated that, for any of the effective length approaches considered in this paper, the accuracy of the effective length computations is identical for every column in a given story, regardless of whether these values are less than or greater than one. Thus, the conclusions from this paper are in many respects relevant to all unbraced frames, regardless of whether some of the frames members have an effective length factor less than one.