# Bridge and Yeung 1993

The authors presented a design formula to determine the limiting slenderness (L/r) of a 'short' composite column. Columns defined as 'short' are columns which can be designed for their full cross-section strength without considering the strength-reducing effects of stability. In their formulation, the authors considered the effects of cross-section type (CFTs and SRCs of different sizes), slenderness ratio, initial imperfections, loading eccentricities, and the ratio of applied end moments. An inelastic non-linear column analysis was used to verify the proposed equation.

## Theoretical Discussion

The proposed equation is as follows:

where Lsr is the limiting slenderness ratio for a composite column to be considered 'short'. P is the applied load, Po is the cross-section strength, and β is the ratio of end moments. This equation obviates the need for a column curve (which relates the slenderness ratio to the axial load ratio). First, a short column slenderness λ s was defined as:

For practical steel ratios (As/Ac) and concrete strengths between 3 and 7 ksi, the parameter γ only varies from 0.0087 to 0.0113, and was taken as an average, 0.01. The authors further assumed a conservative approximation to the column curve as

Then, by substituting these values into an equation proposed by Rotter (1982):

the above equation was obtained.

The parametric study verified the validity of this expression. For columns bent in double curvature, the formula proved accurate. For single curvature, it was conservative. Columns bent in symmetric single curvature by equal end moments (β = -1) are very sensitive to initial imperfections and the column can never be considered short because the moment at midheight is always magnified. The effect of initial-out-of-straightness diminishes, though, as the end moment ratio increases and the column approaches double curvature. Changing the parameter β may have a significant effect on the slenderness ratio. A change in the load P will also induce a large change in the slenderness ratio. The effect of concrete strength in both CFTs and SRCs was negligible.