Minimum cost design of reinforced concrete beams using continuum-type optimality criteria

Abstract

This paper outlines a general procedure for obtaining, on the basis of continut~m-type optimality criteria (COC), economic designs for reinforced concrete beams under various design constraints. The costs to be minimized include those of concrete, reinforcing steel and formwork. The constraints consist of limits on the maximum deflection, and on the bending and shear strengths. However, the formulation can easily cater for other types of constraints such as those on axial strength. Conditions of cost minimality are derived using calculus of variation on an augmented Lagrangian. An iterative procedure based on optimality criteria is applied to a test example involving a reinforced concrete propped cantilever beam whose cross-section varies continuously. Numerical examples are presented in which the design variables are both the width and the depth or the depth alone, and the optimal costs are compared. The solution of the test example with depth alone as the design variable is confirmed by an alternative approach using discretized continuum-type optimality criteria (DCOC).

Minimum cost design of RC beams using DCOC Part I: Beams with freely-varying cross-sections

“…Ve (Le~2At J ,,}TTe Pe ( (28) and (29) are identical with the respective constraints in the COC formulation (Adamu et al, 1994) except for some rearrangement of terms to suit the DCOC derivation.…”

“…The optimum design of structural members and assemblies have been obtained using mathematical programming methods (direct methods) (Haug and Arora 1979;Kanagasundaram and Karihaloo 1990;Karihaloo 1993;Kanagasundaram 1986, 1988;Kirsch 1981), and methods based on optimality criteria (indirect methods) (Adamu et al 1994;Chou 1977;Fleury 1979;Gellatly et al 1978;Haug and Arora 1979;Khot 1981;Khot el al. 1978;Kitsch 1981;Moharrami and Grierson 1993;l~ozvany 1989;Rozvany el al.…”

“…In a recent paper (Adamu et al 1994), methods based on COC were used to find the minimum cost designs of simple RC members for which the analysis of both real and adjoint systems could be easily accomplished. In order to extend the range of applicability of these methods to RC members and assemblies with arbitrary boundary conditions, DCOC methods developed by Rozvany (1992/1993) are useful.…”

“…As in the paper by Adamu et al (1994), the strength constraints have been chosen according to the CEB/FIB code, whereas the deflection constraint is imposed arbitrarily or according to the Australian Standard.…”

Minimum cost design of RC frames using the DCOC method Part I: Columns under uniaxial bending actions

“…The fundamental features of the methods based on COC (Rozvany 1989;Rozvany et al 1990;Rozvany and Zhou 1993a, b) to obtain the minimum-cost design of RC beams subject to strength and deflection constraints, in addition to side constraints, were explained by Adamu et al (1994), and Adamu and Karihaloo (1995) using several test examples of single-span beams. These methods were generalized in their discretized version Rozvany 1992, 1993) to multispan beams with freely varying design variables or uniform cross-section per span by Adamu and Karihaloo (1994a, b).…”