The total cost of a doubly reinforced beam per unit length is given by

The total cost of a doubly reinforced beam per unit length is given by

It can be shown that the relationship between the tension reinforcement ratio  and the compression reinforcement ratio ’ is

’ =  - 0.2314 f_cu/f_y (16)

assuming that the stress in the compression reinforcement has reached yield stress and the ratio d'/d  0.215, where d' is the depth from the top of the compression face to the centroid of the compression reinforcement (see Fig. 3).