Minimum cost design of RC beams with segmentation using continuum-type optimality criteria

Economic designs of reinforced concrete beams with segmentation involving costs of concrete, reinforcing steel and formwork are considered. For practical reasons, the design variables are prescribed by means of an unknown constant and given shape function, whereas the constraints in addition to lower and upper bounds on design variables include maximum deflection in the span, flexural and shear strengths. Conditions of minimality are rigorously derived using calculus of variation on an augmented Lagrangian. An iterative procedure describing the computational aspects of the design is presented using a segmented propped cantilever beam as an example. Numerical examples are presented when the design variables involved are the depth alone or both the depth and steel ratio. A practical application of a simply supported beam is also considered and results compared with those obtained using nonlinear programming techniques (Karihaloo 1993; Kanagasundaram and Karihaloo 1990). An examination of the rate of convergence shows that the present technique is very promising.