Strut-and-Tie Design Methodology for Three-Dimensional Reinforced Concrete Structures

Journal of Structural Engineering (Impact Factor: 1.5). 06/2006; 132(6). DOI: 10.1061/(ASCE)0733-9445(2006)132:6(929)


A strut-and-tie design methodology is presented for three-dimensional reinforced concrete structures. The unknown strut-and-tie 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.

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Available from: Chang-Wei Huang, Jan 03, 2014
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    • "Liang (2006) employed the PBO technique for the design and detailing of optimal STM in RC beam-column connections like: opening knee joints and exterior and interior beam-column connections. Leu et al. (2006) presented a strut-and-tie design methodology for three-dimensional reinforced concrete structures, using the Refined Evolutionary Structural Optimization method (RESO). Nagarajan and Madhavan Pillai (2008) discussed the development of strutand-tie models for simply supported deep beams subject to different types of loadings using topology optimization. "
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    ABSTRACT: The Strut-and-Tie Method is considered a basic tool for analysis and design of reinforced concrete structures and has been incorporated in different codes of practice such as: EC-2, BS 8110, ACI 318-08, EHE-08, etc. The stress trajectories or load path methods have been used to generate strut-and-tie models. However, the models produced by these methods are not unique, with the result depending on the intuition or expertise of the designer, specifically with regards to region D of the structure, where the load path distribution is non-linear. Topology optimization can offer new opportunities to eliminate the limitations of traditional methods. The aim of this work was to study the effect of using different mechanical properties for the steel reinforcement and for the concrete on the emerging topology of strut-and-tie models. The Isolines Topology Design (ITD) method was used for this research. Three examples are presented to show the effect of different mechanical properties used for the tensile (steel) and compressive (concrete) regions of the structure, the: (1) Single short corbel; (2) Deep beam with opening; and (3) Double-sided beam-to-column joint. KeywordsTopology design–Strut-and-tie model–Dual material–Tension and compression–Isolines topology design
    Full-text · Article · Aug 2011 · Structural and Multidisciplinary Optimization
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    • "Liang et al. (2000) implemented a heuristic plane stress topology optimization approach, commonly referred to as Evolutionary Structural Optimization (ESO), to derive concrete truss model shapes for common cases including a deep beam and a corbel. Kwak and Noh (2006) and Leu et al. (2006) employ similar ESO-based algorithms. Recently a more general continuum topology optimization approach was implemented to improve strut-and-tie solution efficiency and optimality (Bruggi 2009). "
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    ABSTRACT: 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.
    Full-text · Article · May 2010
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