Behavior of Three-Span Braced Columns with Equal or Unequal Spans

Abstract

The behavior of uniform, elastic, braced columns with three spans is investigated. The spans may have equal or unequal lengths. The base of the column is pinned and the top is either pinned or flexibly supported. The braces are represented by elastic translational springs, and a compressive axial load is applied to the column. For perfect columns, critical loads and buckling modes are determined. Full bracing is possible if the spans are equal. For imperfect columns with an initial deflection, additional deflections and bracing forces are obtained, and the effects of the stiffnesses and locations of the braces are examined. Examples of design curves for required bracing stiffness and strength are presented. Extensions involving nonuniform loading and cross section, unequal bracing stiffnesses, and rotational resistance at the braces are also discussed. General conditions are derived for full bracing of columns with an arbitrary number of equal or unequal spans and braces, and with uniform or piecewise-constant loading and cross section. The corresponding critical loads are found, and equations and simple bounds for ideal bracing stiffnesses are given.