Alternative Design Procedure for RC-Braced Long Columns Based on New Moment Magnifiers Matrix

Based on modified methods for the results of first_order analysis of RC columns, different codes approximate the second-order effects by using equations focusing on the maximum additional moment through the column height. These equations did not refer to the additional moments between the column and the connected beam, only the effect of the connected beams is taken into consideration by dealing with the effective length of the column, not the total length. Moreover, these equations did not take into account the second-order effect, which is caused by axial force and the inverse moments due to beam restriction for the column ends. This paper presents a new moment magnifiers matrix for the additional moments at the connection between braced columns and the connected beams as a simplified computation that can be used in the design procedure. That is through an equation based on transforming the original long column in second-order analysis to an equivalent isolated column. The equivalent column was represented as an element restricted with rotational spring support at its ends, and it is subjected to lateral distributed loads that have the same influence of the second-order effect on the induced additional moments in the long column. The suggested equivalent column can be used to form the additional bending moment diagram, also to compute the additional deformations as well. Numerous factors were analyzed linearly by using the presented new moment magnifiers matrix and finite element method, and the results proved the efficiency of the proposed model. Although the presented suggested model is based on the isolated analysis of the long column, the effect of the additional moments in the adjacent long column can be considered by presented two suggestions to improve the model. Also, development was proceeded on the model by modifying the flexural rigidity (EI) which is recommended in ACI to appropriate the time of failure. The additional moment values of the developed model were close to the values calculated by the ACI equation.

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