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The concept of effective length is the only common method for designing columns without nonlinear structural analysis. In the past, due to the complexity of the analytical equations that govern the column stability, effective length factor for columns with variable cross-section was determined approximately through diagrams. In the recent years, with the introduction of powerful mathematical software, the analytical mathematical equations (slope-deflection) and the effective length factor can be accurately calculated. Many studied have been conducted on the design of columns with variable cross-section in single-span gable frames. However, no study has addressed the two-span frames which are often used in industrial buildings. In this paper, a mathematical analytical method is presented for determining the effective length factor of non-prismatic columns in two-span gable frames. The accuracy of the analytical results was examined though stability analysis using ABAQUS. Finally, a number of practical diagrams were presented for determining the effective length factor of the columns in such frames.

Determination of the Effective Length Factor for Non-Prismatic Columns in two-Span Gable Frames