An AI-based Lagrange optimization for a design for concrete columns encasing H-shaped steel sections under a biaxial bending

shaped steel sections subjected to biaxial loads. The Lagrange multiplier method is used to optimize cost index (CIc), and CO2 emission of the columns. ANNs can be implemented to generalize functions for objective parameters CIc, and CO2 emission. Generalized functions can replace complex analytical functions that are difficult to derive when optimizing objective functions. In the AI-based Lagrange multiplier method, dimensions of columns and steel sections are calculated as output parameters corresponding to minimized CIc, and CO2 emission. Note that 3D interaction diagrams of SRC columns subjected to biaxial bending and concentric axial loads are also formulated based on optimal results. An accuracy of the ANN-based optimal designs is demonstrated using structural mechanics based on a strain compatibility. A hybrid network based on both ANNs and Lagrange multiplier method identified design parameters which reduced CIc, and CO2 emission of a column by 30.7% and 40.4% respectively, when compared with those of a conventionally designed column.