Set standards, specifications, and codes regulate the design and construction of beam-columns. For instance, the design of nonsway beam-columns subjected to end moments require that the maximum second-order moment be greater than or equal to the maximum first-order moment without the axial compression effects. An amplification factor, obtained through second-order elastic analysis, has been applied in the literature to determine the magnitude of these moments. However, the determination of the adjustment factor for nonsway beam-columns subjected to end moments is very complicated as it depends on locating where the maximum second moments occur, which is difficult and time-consuming. Recently, an equivalent uniform moment concept was introduced for ease determination of the location. Still, despite being different from the adjustment factor, the conflicts between the two factors lead to inaccurate prediction of the maximum moments and often affects the design and specification of nonsway beam-columns.
Herein, Dr. Zhanke Liu from the College of Civil Engineering and Mechanics at Lanzhou University developed a direct determination method for predicting the maximum moments of nonsway beam-columns subjected to end moments or eccentric loads. Of importance, the amplification factor obtained by second-order elastic analysis is rewritten in a new format to reconcile the conflicts emanating from its theoretical derivations. In this format, the application factor was expressed in terms of the end moment ratio and the term sec(kl/2) commonly used for beam-columns subjected to opposite and equal end moments. The work is currently published in the Journal of Structural Engineering.
The reported experiment also proposed the use of a condition governed by the maximum second-order moment at the span of the nonsway beam-columns instead of that governed by the location of the maximum second-order moment used in the previous studies. This new condition, together with the rewritten amplification factor, was used to develop and simply an exact amplification factor for design purposes. The feasibility of the newly proposed amplification factor was validated by comparing it to the actual values of amplification factors provided in the literature. Results showed good consistency and agreement between the values indicating that the exact determination approach could accurately and adequately predict the first-order maximum moment. Additionally, the condition allowed the exact prediction of the amplification factor without the need to determine the location of the maximum-second order moment.
In summary, Dr. Liu developed a direct determination method for the correct prediction of amplification factor in nonsway beam-columns. The conflicts existing in the theoretical derivation of the equivalent moment were resolved by rewriting a new format for amplification factor derivation and introducing a new condition for determining the occurrence of the maximum second-order moment at the span of the nonsway beam-columns. In a statement to Advances in Engineering, Professor Zhanke Liu noted that his findings would be useful in the design and specification of nonsway beam-columns for various applications.
Liu, Z. (2020). Direct Determination Method for In-Plane Strength of Nonsway Beam-Columns Subjected to End Moments or Eccentric Loads. Journal of Structural Engineering, 146(3), 04020011.