The study explores a practical engineering paradigm that aims to augment the cost and carbon analysis of steel building structures. Cost and carbon functions were developed specifically for this purpose including raw material, fabrication, design, fire protection, and erection components. A customised computational model for the analysis of structural alternatives is investigated. The proposed model is tested in an actual building case where several benchmark designs are computed. The outputs from the model are compared with a small number of actual design alternatives which were developed by engineering practitioners. The proposed method can significantly increase the understanding of the design space's boundaries whilst the computed solutions have exhibited enhanced cost and carbon performance compared to actual designs.