Direct Determination Method for In-Plane Strength of Nonsway Beam-Columns Subjected to End Moments or Eccentric Loads

The equivalent moment concept for the in-plane strength problem of nonsway beam-columns is widely accepted, and the equivalent uniform moment factor is widely adopted by current design specifications, standards, or codes around the world. However, the equivalent moment concept and equivalent uniform moment factor fail to predict the maximum moment properly due to several conflicts in theoretical derivation, i.e., the term $\sec (kl/2)$ included in the amplification factor was treated by two different methods and the condition of the amplification factor was ignored. The direct determination method (DDM) for predicting the maximum moment of nonsway bean-columns subjected to end moments or eccentric loads is developed in this paper. The amplification factor provided by the elastic second-order analysis is rewritten as a new format with explicit physical significance. A simple condition for the maximum second-order moment occurs at the span of nonsway beam-columns is proposed. By employing the rewritten amplification factor and the new condition, the exact $C_m$ factor is proposed and then simplified for providing a design approach. The proposed $C_m$ factor is assessed by comparing with actual values of $C_m$. The results showed that the conflicts that existed in the equivalent moment concept are well resolved by the DDM, and the proposed $C_m$ factor is more accurate than those in the literature or adopted in the current design specifications, standards, or codes.