The aesthetic and architectural shapes of the beam-column elements may enhance the elements strength depending on the maximum and minimum bending moments effect. Therefore, the stability value of the non-linear taper member in concave configuration may be more efficient than linear taper or prismatic members. The modified stability functions will be obtained from the solution of the basic differential equation, where this basic differential equation depends on the non-linearity factor of the beam-column shape and the shape factor of the cross-sectional area. These two factors, multiplied by others, produce the modified shape factor, which affects the results of the basic differential equation solutions.