Cost optimization of singly and doubly reinforced concrete beams with EC2-2001

A model for the optimal design of rectangular reinforced concrete sections is presented considering the stress–strain diagrams described in EC2-2001 and MC90. The following expressions are developed: economic bending moment; optimal area of steel and optimal steel ratio between upper and lower steel. All the expressions are in nondimensional form. The present model is applied to four different classes of concrete described in MC90. It is concluded that in nondimensional form the equations are nearly coincident for both singly and doubly reinforcement. It is also concluded that the ultimate strain for concrete in the compression zone, ε cm , lies between the strain for peak stress ε c1 and the ultimate strain ε cu . This result is relevant once that the maximum moment is obtained for this value, and not the value ε cu , as defined in EC2-2001. Cost optimization is implemented in the code and compared with other optimum models based on the ultimate design of ACI.