Sensitivity analysis and optimum design curves for the minimum cost design of singly and doubly reinforced concrete beams

Abstract

This paper reports on the application of the Lagrangian Multiplier Method (LMM) to the minimum cost design of both singly and doubly reinforced concrete rectangular beams under limit state design conditions. Cost objective functions and stress constraints are derived and implemented within the optimisation method. Cost sensitivity analysis, detailed testing and comparisons with conventional design office methods are performed and the results reported, showing that the Lagrangian Multiplier Method can be successfully applied to the minimum cost design of reinforced concrete beams. The proposed approach is effective and reliable without the need for iterative trials. Optimum design curves have been developed that can be used without prior knowledge of optimisation. Despite the simplification of the cost model and the assumptions made, satisfactory and reliable results have been obtained and confirmed by using standard design office procedures

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

“…5 it is observed that the optimum reinforcement in the present model is greater than in the constant stress diagram. The limit for the singly reinforcement is also greater in the present model than in Ceranic et al (2000).…”

“…The model is implemented with the costs of the materials, the cost optimization is performed and the results are compared to Ceranic et al (2000).…”

“…For the cost optimization process the global cost including concrete steel and form work is the objective function and the equilibrium equations are restrictions. The optimum reinforcement related to the cost ratio and strength ratio of the materials is obtained and compared with the results of Ceranic et al (2000).…”

“…In the figure the optimum reinforcement percentile, ρ cd , derived in Ceranic et al (2000), resulting from the application of the constant stress diagram in ACI (1995), is also…”

Cost optimum design of doubly reinforced high strength concrete T-beams

“…Thus, the doubly reinforced high-strength concrete T-beams are recommended for structures requiring low height such as parking spaces and bridge decks beams with lower template. The present optimization model is developed for HSC T-beams in exure [6][7][8][9].…”