Verification of simplified optimum designs for reinforced concrete beams (original) (raw)
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Reinforced Concrete Design with Topology Optimization
Structures Congress 2010, 2010
Topology optimization techniques are employed to automate the design of reinforced concrete members. Truss models are derived with maximum stiffness (minimum total strain energy) from an initial ground structure defined over a general concrete member. The optimization routine, implemented with a freely available computer program, produces strut and tie geometries consistent with elastic tensile and compressive stress trajectories, resulting in steel reinforcement layouts with the potential to minimize crack widths and improve member performance over traditional strut and tie models. Ongoing work in continuum topology optimization of reinforced concrete members is summarized, including consideration of constructability in the optimized solution and the development of solutions with curved compressive struts which are more consistent with elastic stress trajectories than traditional strut-and-tie models derived by hand.
Analysis and Design of Reinforced Concrete Structures as a Topology Optimization Problem
Proceedings of the VII European Congress on Computational Methods in Applied Sciences and Engineering (ECCOMAS Congress 2016), 2016
Technical codes for buildings deal with cracked reinforced concrete structures assuming concrete as a compression-only material, whereas rebar provides the structural component with the required tensile strength [1]. Numerical methods can handle reinforced concrete structures calling for demanding non-linear analysis. Indeed, well-known convergence issues arise when copying with concrete as a compression-only material. Recently, an alternative energy-based approach has been proposed to solve the equilibrium of a linear elastic notension medium exploiting its hyper-elasticity [2]. A topology optimization problem distributes an equivalent orthotropic material to minimize the strain energy of the no-tension body, thus avoiding more demanding non-linear analysis. This contribution provides an extension to the analysis and optimal design of reinforced concrete structures. Following [3], truss members are modeled within a two-dimensional no-tension continuum in order to model structural elements made of reinforced concrete. The solution of the equilibrium is straightforward within the approach proposed in [2], thus allowing performing analysis at the serviceability limit state with cracked sections. Also, introducing the areas of the reinforcement bars as an additional set of unknowns, a problem of size optimization is outlined to cope with the optimal rebar of r.c. structures. Preliminary numerical simulations are shown to assess the proposed procedure.
Topology Optimization of Reinforced Concrete Plane Frames
Revista Sul-americana de Engenharia Estrutural, 2016
The definition of the number of columns, as well as their positions in the structure, is one of the tasks of the designer, and has a significant impact on both cost and structural behavior. This work presents a study developed in order to obtain the spacing of reinforced concrete columns of building structures corresponding to the smallest global cost (concrete, steel, and formworks). To achieve this objective, the plane frame was modeled as beam elements supported by springs with rotational rigidity. The optimization design variables are the height of beams and the length of columns. At the beginning of the process, columns were closely positioned, with small spacing among them, being the cost of the whole structure minimized. The less stressed column were removed from the structure, generating a redistribution of efforts. The optimization process was repeated, with the columns being successively removed from the structure. The optimal spacing corresponds to the configuration of mi...
TOPOLOGY OPTIMIZATION OF PRETENSIONED CONCRETE BEAMS CONSIDERING MATERIAL NONLINEARITY
INTERNATIONAL JOURNAL OF OPTIMIZATION IN CIVIL ENGINEERING, 2019
In this paper, the bi-directional evolutionary structural optimization (BESO) method is used to find optimal layouts of 3D prestressed concrete beams. Considering the element sensitivity number as the design variable, the mathematical formulation of topology optimization is developed based on the ABAQUS finite element software package. The surface-to-surface contact with a small sliding between concrete and prestressing steels is assumed to accurately model the prestressing effects. The concrete constitutive model used is the concrete damaged plasticity (CDP) model in ABAQUS. The integration of the optimization algorithm and finite element analysis (FEA) tools is done by using the ABAQUS scripting interface. A pretensioned prestressed simply supported beam is modeled to show capabilities of the proposed method in finding optimal topologies of prestressed concrete beams. Many issues relating to topology optimization of prestressed concrete beams such as the effects of prestressing stress, geometrical discontinuities and height constraints on optimal designs and strut-and-tie models (STMs) are studied in the example. The results show that the proposed method can efficiently be used for layout optimization of prestressed concrete beams.
Optimizing Reinforcement Layout in Concrete Design Considering Constructability
Structural topology optimization is increasingly being used to remove the guesswork in identifying natural force flow paths for reinforced concrete and prestressed concrete, particularly for complex 3D design domains. Tension and compressive forces that follow the principle stress trajectories, i.e., ties and struts, are automatically identified with topology optimization using a formulation that minimizes strain energy, or equivalently that minimize crack widths. While a useful alternative to trial-and-error process of generating strut-and-tie models (STM), the approach falls short of design objectives as it neglects constructability and rebar detailing, which is often the governing cost. This paper uses a new advancement in topology optimization for addressing constructability issues by considering both material and construction costs. By assigning different construction costs for each tension tie (rebar or prestressing), the placement of steel can be controlled to a large extent ...
Structural optimization of reinforced concrete structures
International Journal of Engineering Research and, 2016
The structural optimization plays a vital role in today's highly competitive industry, where there is continuous increase in customer demand for superior quality, better safety and affordable cost. The conventional ways of design development largely depends on excessive material usage, very high design marginshence, in turn ending up consuming more material into the structures, buildings. Since last couple of decades, computational power is becoming more efficient and affordable to everyone. This availability of high capacity computational power gave of designer the opportunity for evaluating multiple options during the development phase itself, using finite element analysis methods. Also, the efforts of the researchers helped our field with many innovative and matured algorithms for optimizing the multiple design variables considering given constraints, scenarios at the same time. The combination of high power computation with these algorithms is giving the designers limitless opportunities for managing the development more effectively and efficiently. This paper discusses various optimization techniques and apply them to real world cases like reinforced concrete structures in virtual environment. The study includes survey of structural optimization principles, procedures, software tools available for structural design & analysis. Further, it discusses about the optimization of multi-storey reinforced concrete structures (RCC) building structure using structural analysis software like STAAD-PRO along with modern optimization tools like MINITAB and Evolutionary Algorithm.
Design optimization of reinforced concrete structures
2006
A novel formulation aiming to achieve optimal design of reinforced concrete (RC) structures is presented here. Optimal sizing and reinforcing for beam and column members in multi-bay and multistory RC structures incorporates optimal stiffness correlation among all structural members and results in cost savings over typical-practice design solutions. A Nonlinear Programming algorithm searches for a minimum cost solution that satisfies ACI 2005 code requirements for axial and flexural loads. Material and labor costs for forming and placing concrete and steel are incorporated as a function of member size using RS Means 2005 cost data. Successful implementation demonstrates the abilities and performance of MATLAB's (The Mathworks, Inc.) Sequential Quadratic Programming algorithm for the design optimization of RC structures. A number of examples are presented that demonstrate the ability of this formulation to achieve optimal designs.
Procedia Engineering, 2015
Strut-and-Tie models are well-known worldwide as valuable tool in designing D-Regions of Reinforced Concrete members. It has been adopted in many Concrete Structural Codes in many countries. Recently strut-and-tie-models have been included in Indonesia Concrete Structural Code (SNI-03-2847-2012). In this paper, it will be shown how a Strut-and-Tie Model can be developed for various structural concrete deep beams using Evolutionary Structural Optimization. As a tool for this study the author used Bi-Directional Evolutionary Structural Optimization (BESO2D) computer programs, developed by X. Huang and Y.M. Xie [1]. Three tested concrete beams with small, medium, and large opening [2] will be taken as the case study. It will be shown the optimal topology of a plane stress of continuum structures produced from BESO2D can be taken as the basic strutand-tie-model. For design process the best strut-and-tie-model can be delivered from the optimal topology structure only with the deep knowledge of the basic load transfer from loading to support point
rdoapp.psu.ac.th
The definition of the number of columns, as well as their positions in the structure, is one of the tasks of the designer, and has a significant impact on both cost and structural behavior. This work presents a study developed in order to obtain the spacing of reinforced concrete columns of building structures corresponding to the smallest global cost (concrete, steel, and formworks). To achieve this objective, the plane frame was modeled as beam elements supported by springs with rotational rigidity. The optimization design variables are the height of beams and the length of columns. At the beginning of the process, columns were closely positioned, with small spacing among them, being the cost of the whole structure minimized. The less stressed column were removed from the structure, generating a redistribution of efforts. The optimization process was repeated, with the columns being successively removed from the structure. The optimal spacing corresponds to the configuration of minimum cost. The present work presents some examples of structures analyzed by the proposed procedure. It was observed that the optimum column spacing is similar to those suggested by practice.