$$A_\alpha = \sum \limits_{i=1}^{nc} b_i \; t_i + \alpha_e \sum \limits_{i=1}^{ns} A_{s,i}$$

$$S_{\alpha,x} = \sum \limits_{i=1}^{nc} b_i \; t_i \left[ \left( \sum \limits_{j=1}^{i-1} t_j \right) + \frac{t_i}{2} - h_x \right] + \alpha_e \sum \limits_{i=1}^{ns} A_{s,i} \left( d_i - h_x \right) $$

$$h_G = \frac{S_{\alpha,x}}{A_\alpha} $$

$$I_{\alpha,x} = \sum \limits_{i=1}^{nc} \left\{ \frac{1}{12} b_i \; t_i^3 + b_i \; t_i \left[ \left( \sum \limits_{j=1}^{i-1} t_j \right) + \frac{t_i}{2} - h_x \right]^2 \right\} + \alpha_e \sum \limits_{i=1}^{ns} A_{s,i} \left( d_i - h_x \right)^2 $$