Optimizing Reinforcement Layout in Concrete Design Considering Constructability (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.
Strut and tie models (STM) are widely used by designers of reinforced concrete and prestressed concrete structures. Selection of an efficient model, however, becomes a challenging task for complex design domains, such as 3d domains with cutouts. Topology optimization has therefore been promoted as means of automating the development of highly efficient (minimum strain energy) STM. Current drawbacks of such methods are that solutions may complex and fail to properly account for secondary tensile stresses; that is, the case where the major principal stresses are compressive and minor principal stresses are tensile. A hybrid truss-continuum topology optimization scheme was recently developed to overcome these challenges in 2D concrete design. That work is modified and extended herein to three-dimensional domains and mechanics models. The stiffness of the elements are formulated such that truss elements carry only tensile forces and thus represent straight steel rebar, while the continu...
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.
Journal of Engineering Mechanics, 2015
Strut-and-tie models (STMs) are widely used by RC designers. However, selection of a viable model is a challenging task, especially in complex three-dimensional (3D) design domains with irregular cutouts, which are common in building cores and shear walls. Therefore, topology optimization has been promoted as a means of automating the development of minimum strain energy STMs, which can lead to improved structural behavior. Current drawbacks of such methods are that solutions may be difficult to construct and may fail to properly account for tensile stresses resulting from force spreading. A two-dimensional hybrid truss-continuum topology optimization scheme was recently developed to overcome these challenges with the goal of reconfiguring traditional reinforcement layouts to automatically follow principal tensile stresses, reducing cracking at service loads and increasing strength and ductility at an ultimate limit state. That work is generalized and extended herein to 3D domains and mechanics models. Stiffness is formulated such that truss elements carry only tensile forces and thus represent straight steel rebar, while the continuum elements carry only compressive forces and thus represent concrete compression load paths. The latter is achieved using a stress-dependent orthotropic material model. The algorithm is demonstrated on several benchmark design examples.
Journal of Structural Engineering, 2013
A new force visualization and design tool employing hybrid topology optimization is introduced for RC and prestressed concrete structural members. The optimization scheme couples a minimum compliance (maximum stiffness) objective function with a hybrid trusscontinuum ground structure that can generate a strut-and-tie model for any general concrete member, loading, and set of boundary conditions. The truss ground structure represents discrete steel reinforcing bars (tensile load paths) that can be sized based on axial forces output directly by the optimization routine, whereas the continuum elements simulate concrete compression struts. This separation of compressive and tensile load-carrying elements is achieved through bilinear elastic models with an orthotropic constitutive relationship for the continuum. Examples are provided demonstrating the potential value of the optimization tool to RC design. Reinforcing layouts that can minimize cracking and reduce steel quantities when compared with traditional designs are provided for a prismatic beam, a hammerhead pier, a stepped beam with a cutout, and the local anchorage zone of a prestressed concrete block. A minimum length scale constraint is employed to control complexity of the strutand-tie topology, accommodating design solutions that balance material savings, structural performance, and constructability.
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.
Structural Topology Optimisation in Steel Structural Applications
This study introduces applications of structural topology optimisation to buildings and civil engineering structures. Topology optimisation problems utilize the firmest mathematical basis, to account for improved weight-to-stiffness ratio and perceived aesthetic appeal of specific structural forms, enabling the solid isotropic material with penalization (SIMP) technique. Structural topology optimisation is a technique for finding the optimum number, location and shape of "openings" within a given continua subject to a series of loads and boundary conditions. Aerospace and automotive engineers routinely employ topology optimisation and have reported significant structural performance gains as a result. This paper examines two examples of where topology optimisation may be a useful design tool in civil/structural engineering in order to overcome the frontiers between civil engineers and engineers from other disciplines. The first example presents the optimised structural design of a geometrically complex high-rise structure, while the second one focuses on the optimisation and design of a perforated steel I-section beam, since such structural members are widely used nowadays in the vast majority of steel buildings.
Jordan Journal of Civil Engineering, 2015
This study introduces applications of structural topology optimisation to buildings and civil engineering structures. Topology optimisation problems utilize the firmest mathematical basis, to account for improved weight-to-stiffness ratio and perceived aesthetic appeal of specific structural forms, enabling the solid isotropic material with penalization (SIMP) technique. Structural topology optimisation is a technique for finding the boundary conditions. Aerospace and automotive engineers routinely employ topology optimisation and have reported significant structural performance gains as a result. Recently designers of buildings and structures have also started investigating the use of topology optimisation, for the design of efficient and aesthetically pleasing developments. This paper examines two examples of where topology optimisation may be a useful design tool in civil/structural engineering in order to overcome the frontiers between civil engineers and engineers from other disciplines. The first example presents the optimised structural design of a geometrically complex high-rise structure and the optimal design of its architectural building shape. The second one focuses on the optimisation and design of a perforated steel I-section beam, since such structural members are widely used nowadays in the vast majority of steel buildings and structures while they provide numerous of advances. Conclusions are drawn regarding the potential benefits to the more widespread implementation of topology optimisation within the civil/structural engineering industry.
Strut-and-Tie Design Methodology for Three-Dimensional Reinforced Concrete Structures
Journal of structural …, 2006
A strut-and-tie design methodology is presented for three-dimensional reinforced concrete structures. The unknown strut-andtie model is realized through the machinery of a refined evolutionary structural optimization method. Stiffness of struts and ties is computed from an evolved topology of a finite element model to solve statically indeterminate strut-and-tie problems. In addition, compressive strength for struts and nodal zones is evaluated using Ottosen's four-parameter strength criterion. Numerical examples are studied to demonstrate that the proposed design methodology is suitable for developing and analyzing three-dimensional strut-and-tie models for reinforced concrete structures.