Lateral Bracing Forces in Columns with Two Unequal Spans

Elastic columns with two spans of arbitrary length ratio are investigated. The base is pinned and may include a rotational spring. An elastic support acts between the spans, and the top is pinned or supported elastically. An axial load is applied. For perfect columns, the effects of the internal support location and the spring stiffnesses on the critical load and buckling mode are determined. Under special conditions, an ideal spring stiffness exists, such that the elastic supports do not deflect when the column buckles. Imperfect columns with an initial deflection of the same shape as the buckling mode of the corresponding perfect column are also considered. Deflections and bracing forces at the elastic supports are obtained as functions of the axial load, and approximations in terms of the amplification factor are discussed. These results are utilized in a sequel to this paper, which examines design rules for the required stiffness and strength of bracing.