Generation of strut-and-tie models by topology design using different material properties in tension and compression

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.

[1]  Hong Guan,et al.  Evolutionary Structural Optimisation Incorporating Tension and Compression Materials , 1999 .

[2]  Muhammad N. S Hadi Neural networks applications in concrete structures , 2003 .

[3]  Donald E. Grierson,et al.  Design optimization of 3D reinforced concrete structures , 1996 .

[4]  J Schlaich,et al.  TOWARD A CONSISTENT DESIGN OF STRUCTURAL CONCRETE , 1987 .

[5]  Osvaldo M. Querin,et al.  Growth method for size, topology, and geometry optimization of truss structures , 2006 .

[6]  Peter Marti,et al.  BASIC TOOLS OF REINFORCED CONCRETE BEAM DESIGN , 1985 .

[7]  Abdulsallam A Alshegeir Analysis and design of disturbed regions with strut-tie models , 1992 .

[8]  R. P. Johnson,et al.  Composite Structures of Steel and Concrete: Beams, Slabs, Columns, and Frames for Buildings , 1994 .

[9]  David M. Rogowsky,et al.  Tests of Reinforced Concrete Deep Beams , 1986 .

[10]  Michael E. Kreger,et al.  Detailing for structural concrete , 1993 .

[11]  Yi Min Xie,et al.  Generating optimal strut-and-tie models in prestressed concrete beams by performance-based optimization , 2001 .

[12]  Franco Bontempi,et al.  Stress path adapting Strut-and-Tie models in cracked and uncracked R.C. elements , 2001 .

[13]  M. A. Ali,et al.  Formulation of Optimal Strut-and-Tie Models in Design of Reinforced Concrete Structures , 2000 .

[14]  Peter Müller Plastische Berechnung von Stahlbetonscheiben und -balken , 1978 .

[15]  H Kim,et al.  Topology optimization for reinforced concrete design , 2002 .

[16]  J. Z. Zhu,et al.  The finite element method , 1977 .

[17]  Aurelio Muttoni,et al.  On Development of Suitable Stress Fields for Structural Concrete , 2007 .

[18]  Wolfgang Achtziger Truss topology optimization including bar properties different for tension and compression , 1996 .

[19]  Peter Dewhurst,et al.  Comparisons of optimality criteria for minimum-weight dual material structures , 2003 .

[20]  Hong Guan,et al.  Bridge topology optimisation with stress, displacement and frequency constraints , 2003 .

[21]  Richard N. White,et al.  Automatic Generation of Truss Model for Optimal Design of Reinforced Concrete Structures , 1998 .

[22]  M. Goedkoop,et al.  The Eco-indicator 99, A damage oriented method for Life Cycle Impact Assessment , 1999 .

[23]  Pierre Duysinx,et al.  Topology Optimization with Different Stress Limit in Tension and Compression , 1999 .

[24]  Fabio Biondini,et al.  Morphologic Evolutionary Structural Optimization , 2007 .

[25]  Daniel A. Kuchma,et al.  Integrated analysis and design tool for the strut-and-tie method , 2007 .

[26]  Young Mook Yun Computer Graphics for Nonlinear Strut-Tie Model Approach , 2000 .

[27]  J. Minx,et al.  A definition of “carbon footprint” , 2010 .

[29]  G. Rozvany Some shortcomings in Michell's truss theory , 1996 .

[30]  Daniel A. Kuchma,et al.  COMPUTER-BASED TOOLS FOR DESIGN BY STRUT-AND-TIE METHOD: ADVANCES AND CHALLENGES , 2002 .

[31]  Franco Bontempi,et al.  Optimal strut-and-tie models in reinforced concrete structures , 1999 .

[32]  Won Choi,et al.  Development of the Stress Path Search Model using Triangulated Irregular Network and Refined Evolutionary Structural Optimization , 2007 .

[33]  Yi Min Xie,et al.  Topology Optimization of Strut-and-Tie Models in Reinforced Concrete Structures Using an Evolutionary Procedure , 2000 .

[34]  Yi Min Xie,et al.  Optimal Topology Design of Bracing Systems for Multistory Steel Frames , 2000 .

[35]  Osvaldo M. Querin,et al.  Topology design of two-dimensional continuum structures using isolines , 2009 .

[36]  Bhushan Lal Karihaloo,et al.  Minimum cost design of reinforced concrete structures , 1990 .

[37]  Qing Quan Liang Performance-Based Optimization of Structures: Theory and Applications , 2004 .

[38]  H Alicia Kim,et al.  Topology optimisation of reinforced concrete structures , 2000 .

[39]  Victor Yepes,et al.  Design of reinforced concrete bridge frames by heuristic optimization , 2008, Adv. Eng. Softw..

[40]  Antonio Hospitaler,et al.  CO2-optimization of reinforced concrete frames by simulated annealing , 2009 .

[41]  Osvaldo M. Querin,et al.  Topology optimization of truss-like continua with different material properties in tension and compression , 2010 .

[42]  S. Timoshenko History of strength of materials , 1953 .

[43]  Sergey Selyugin,et al.  Some general results for optimal structures , 2004 .

[44]  G. I. N. Rozvany,et al.  Minimum cost design of reinforced concrete beams using continuum-type optimality criteria , 1994 .

[45]  Hong Guan Effect of Sizes and Positions of Web Openings on Strut-and-Tie Models of Deep Beams , 2005 .

[46]  O. C. Zienkiewicz,et al.  The Finite Element Method: Its Basis and Fundamentals , 2005 .

[47]  Matteo Bruggi,et al.  Generating strut-and-tie patterns for reinforced concrete structures using topology optimization , 2009 .

[48]  Brian Uy,et al.  Performance-Based Optimization for Strut-Tie Modeling of Structural Concrete , 2002 .

[49]  Hyo-Gyoung Kwak,et al.  Determination of Strut-and-Tie Models using Evolutionary Structural Optimization , 2002 .

[50]  Davis Langdon,et al.  Spon's Civil Engineering and Highway Works Price Book 2011 , 2010 .

[51]  Kun Cai,et al.  A Heuristic Approach to Solve Stiffness Design of Continuum Structures with Tension/Compression-Only Materials , 2008, 2008 Fourth International Conference on Natural Computation.

[52]  Liang-Jenq Leu,et al.  Strut-and-Tie Design Methodology for Three-Dimensional Reinforced Concrete Structures , 2006 .

[53]  Ashraf F. Ashour,et al.  Cost optimisation of reinforced concrete flat slab buildings , 2005 .

[54]  James G. MacGregor,et al.  Reinforced Concrete: Mechanics and Design , 1996 .

[55]  Michael P. Collins,et al.  SHEAR AND TORSION DESIGN OF PRESTRESSED AND NON PRESTRESSED CONCRETE BEAMS , 1980 .

[56]  Matteo Bruggi,et al.  On the Automatic Generation of Strut and Tie Patterns under Multiple Load Cases with Application to the Aseismic Design of Concrete Structures , 2010 .

[57]  Bruno Thürlimann,et al.  Ultimate Strength and Design of Reinforced Concrete Beams in Torsion and Bending , 1972 .

[58]  Daniel A. Kuchma,et al.  Automated Finite-Element-Based Validation of Structures Designed by the Strut-and-Tie Method , 2010 .

[59]  F. Leondardt,et al.  Reducing the shear reinforcement in reinforced concrete beams and slabs , 1965 .

[60]  Prabhat Kumar Optimal force transmission in reinforced concrete deep beams , 1978 .

[61]  Olivier Bruls,et al.  Topology and generalized shape optimization: Why stress constraints are so important? , 2008 .

[62]  Osvaldo M. Querin,et al.  Topology design for multiple loading conditions of continuum structures using isolines and isosurfaces , 2010 .

[63]  R. P. Johnson Beams, slabs, columns, and frames for buildings , 1994 .

[64]  Ernest Payson Goodrich,et al.  Concrete-steel Construction: , 2010 .

[65]  Qing Quan Liang Performance-based optimization of strut-and-tie models in reinforced concrete beam-column connections , 2006 .

[66]  R. P. Johnson Composite Structures of Steel and Concrete , 1975 .

[67]  Michał Nowak,et al.  Structural optimization system based on trabecular bone surface adaptation , 2006 .

[68]  Julio A. Ramirez,et al.  COMPUTER GRAPHICS IN DETAILING STRUT-TIE MODELS , 1992 .

[69]  Jeung-Hwan Doh,et al.  Development of Strut-And-Tie Models in Deep Beams with Web Openings , 2007 .

[70]  F. Kong Reinforced Concrete Deep Beams , 1990 .

[71]  Peter Dewhurst,et al.  A general optimality criterion for strength and stiffness of dual-material-property structures , 2005 .

[72]  Julio A. Ramirez,et al.  COMPUTER GRAPHICS IN TRUSS-MODEL DESIGN APPROACH , 1989 .