This paper investigates the reduction of bending moment in critical members by adding some extra members in the optimum location. Instead of enlarging the size of members to resist the moment, eight additional members are added in the optimum location to reduce the bending moment in the critical members. The total weight of the proposed structure with extra members is less than that of the original structure that resists the induced bending moment. Moreover, the location of the additional bars significantly reduces the nodal displacements. This paper investigates the effect of placing extra members on vertically and/or horizontally loaded egg-shaped single-layer frames. An egg-shaped structure is designed based on the maximum induced moment; in such frames, the bending moment is the dominant internal force. Then some extra members are suggested to be added to the structure to reduce the maximum bending moment to the lowest possible value; thus, the designed cross-sectional area is minimized. Furthermore, the optimized structure's total weight and shape deformation is less than the ordinary structure's. The study results show that the extra bars' location depends on the loadings' direction. Moreover, the weight of the horizontally loaded egg-shaped structure can be optimized by up to 28%. The results were verified by MATLAB and SAP2000 software.