Reinforced-concrete sections are usually designed at the ultimate limit state, while the checks at the serviceability limit states are made afterwards. Unfortunately, since the serviceability requirements are often not met, then R/C sections have to be re-designed with a trial-and-error procedure which encumbers the design. Since in many cases the design of R/C beams requires that their section depth is as small as possible, in this paper minimizing the depth of a R/C section is the main objective. For given material properties, we identify the minimum effective depth for different values of both the neutral axis-effective depth ratio and the compressive-tensile steel ratio. In fact, these two ratios highly affect the effective depth of the section; therefore, these ratios are the design variables in order to reduce the depth, when the other design conditions have been assigned. It is shown that the traditional design by trial-and-errors can be rationalized by modelling it as a constrained nonlinear programming problem, where the beam effective depth is minimized, and the constraints come from the serviceability requirements.
A nonlinear programming approach in the ultimate design of R/C beam sections including the serviceability requirements
FENU, LUIGI
2004-01-01
Abstract
Reinforced-concrete sections are usually designed at the ultimate limit state, while the checks at the serviceability limit states are made afterwards. Unfortunately, since the serviceability requirements are often not met, then R/C sections have to be re-designed with a trial-and-error procedure which encumbers the design. Since in many cases the design of R/C beams requires that their section depth is as small as possible, in this paper minimizing the depth of a R/C section is the main objective. For given material properties, we identify the minimum effective depth for different values of both the neutral axis-effective depth ratio and the compressive-tensile steel ratio. In fact, these two ratios highly affect the effective depth of the section; therefore, these ratios are the design variables in order to reduce the depth, when the other design conditions have been assigned. It is shown that the traditional design by trial-and-errors can be rationalized by modelling it as a constrained nonlinear programming problem, where the beam effective depth is minimized, and the constraints come from the serviceability requirements.
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