A numerical method is presented for the instability analysis of reinforced concrete columns from direct calculations without having to go through an iterative process as in other methods. The solution starts with assuming a deflection distribution of the column at the state of critical equilibrium. The value of the deflection at the column center is determined from the maximum moment capacity of the column cross-section, which corresponds to the point of section instability. With the aid of the deflection distribution discrete values of curvature are calculated at stations located along the column span (the curvature value at the column center will then correspond to the point of section instability). The obtained discrete values of curvature will be exact values if their respective stations are located in their exact positions along the column span. The curvature is assumed to have a linear distribution between every two successive stations. From the discrete values of the curvature at the stations the moment and hence the deflection values are determined at these stations. Then, the lengths of the segments between the stations are calculated with the aid of classic methods of deflection computation to give the exact positions of the stations. Finally, the critical column length can be determined and the deflection profile as well. Upon arriving to a solution for the column problem, the solution of many beam-columns of the same section and material properties as the column, can be extracted from the column solution using the equivalent column concept.

Although the new technique for the instability analysis of columns presented in this paper is numerical, the technique does not require any iterations and it directly leads to the (exact) solution with one step of calculations. The term exact is meant here to refer to the exact results within the limits of the method assumptions. The method is therefore computationally more efficient than the other available methods and should result in more reliable solutions. Though the results from the proposed method have been compared with experimental tests and the comparison was very satisfactory.

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