“Investigation of Effective Length Method For Slender Reinforced Concrete Column Having Linearly Varying Cross-Section”

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Addis Ababa University


Effective length is the length of the equivalent pin ended column, which has the same elastic buckling load as the actual column. The effective length method has been used for many decades as the basis for the design of columns made of reinforced concrete, structural steel or steel-concrete components. The underlying assumption with this method is the sweeping generalization that; because the actual column and the equivalent column have the same elastic buckling load, they also posses the same design resistances in the ultimate limit state. This assumption has been the subject of many investigations and it was found out that, although the method gives reliable results that lie on the safe side in many cases, it could sometimes lie on the unsafe side. The present investigation deals with slender reinforced concrete columns with linearly varying cross-sections. The effective length method for such columns poses an additional complication. That is; unlike prismatic columns, the choice of cross-section for the equivalent column is not straight forward since the cross-section of actual column is not constant. The results of the present investigation which is limited to pin ended columns with equal and opposite end moments, have shown that the effective length method gives reliable results if the cross-section of the equivalent column is chosen as per certain rules and computations indicated in this document. Extensive tables are compiled for the determination of equivalent section and effective length for any pin-ended tapered column which has the same and opposite end moments. Computer programs, which are done using FORTRAN (FTN95) programming language and MICROSOFT EXCEL spread sheets are used as a supporting tools for analysis processes committed in this investigation. The result of this research can be taken as an approach, which replaces the cumbersome and lengthy way of traditional iterative analysis for tapered columns. KEY PHRASES AND WORDS: Effective length, Elastic buckling load, Equivalent section, Failure node, Moment-curvature, second order analysis, Slender columns, Stabilized length, Tapered column.



Effective length; Elastic buckling load; Equivalent section; Failure node; Moment-curvature; second order analysis; Slender columns; Stabilized length;Tapered colu