TECHNICAL PAPERS
May 15, 2002

Performance-Based Optimization for Strut-Tie Modeling of Structural Concrete

Publication: Journal of Structural Engineering
Volume 128, Issue 6

Abstract

Conventional trial-and-error methods are not efficient in developing appropriate strut-and-tie models in complex structural concrete members. This paper describes a performance-based optimization (PBO) technique for automatically producing optimal strut-and-tie models for the design and detailing of structural concrete. The PBO algorithm utilizes the finite element method as a modeling and analytical tool. Developing strut-and-tie models in structural concrete is treated as an optimal topology design problem of continuum structures. The optimal strut-and-tie model that idealizes the load transfer mechanism in cracked structural concrete is generated by gradually removing regions that are ineffective in carrying loads from a structural concrete member based on overall stiffness performance criteria. A performance index is derived for evaluating the performance of strut-and-tie systems in an optimization process. Fundamental concepts underlying the development of strut-and-tie models are introduced. Design examples of a low-rise concrete shearwall with openings and a bridge pier are presented to demonstrate the validity and effectiveness of the PBO technique as a rational and reliable design tool for structural concrete.

Get full access to this article

View all available purchase options and get full access to this article.

References

Ali, M. A., and White, R. N.(2001). “Automatic generation of truss model for optimal design of reinforced concrete structures.” ACI Struct. J., 98(4), 431–442.
Alshegeir, A., and Ramirez, J.(1992). “Computer graphics in detailing strut-tie models.” J. Comput. Civ. Eng., 6(2), 220–232.
Anderheggen, E., and Schlaich, M. (1990). “Computer-aided design of reinforced concrete structures using the truss model approach.” Computer Aided Analysis and Design of Concrete Structures, N. Bicanic and H. Mang, eds., Proc., SCI-C 1990 2nd Int. Conf., Zell am See, Austria, Pineridge, Swansea, U.K., 539–550., Zell am See, Austria, Pineridge, Swansea, U.K., 539–550.
Atrek, E. (1989). “Shape: a program for shape optimization of continuum structures.” Computer Aided Optimization Design of Structures: Applications, C. A. Brebbia and S. Hernandez, eds., Computational Mechanics, Southampton, U.K., 135–144.
Baumgartner, A., Harzheim, L., and Mattheck, C.(1992). “SKO (soft kill option): the biological way to find an optimum topology.” Int. J. Fatigue, 14(6), 387–393.
Bendsøe, M. P., Diaz, A. R., Lipton, R., and Taylor, J. E.(1995). “Optimal design of material properties and material distribution for multiple loading conditions.” Int. J. Numer. Methods Eng., 35, 1449–1170.
Bendsøe, M. P., and Kikuchi, N.(1988). “Generating optimal topologies in structural design using a homogenization method.” Comput. Methods Appl. Mech. Eng., 71, 197–224.
Cagley, J. R.(2001). “Changing from ACI 318-99 to ACI 318-02—What's new?” Concr. Int.: Des. Constr., 23(6), 125–132.
Collins, M. P., and Mitchell, D.(1980). “Shear and torsion design of prestressed and non-prestressed concrete beams.” PCI J., 25(5), 32–100.
Diaz, A. R., and Bendsøe, M. P.(1992). “Shape optimization of structures for multiple loading condition using a homogenization method.” Struct. Optim., 4, 17–22.
Diaz, A. R., and Kikuchi, N.(1992). “Solution to shape and topology eigenvalue optimization problems using a homogenization method.” Int. J. Numer. Methods Eng., 35, 1487–1502.
Haftka, R. T., and Grandhi, R. V.(1986). “Structural shape optimization—A survey.” Comput. Methods Appl. Mech. Eng., 57(1), 91–106.
Kirsch, U.(1982). “Optimal design based on approximate scaling.” J. Struct. Eng., 108(ST4), 888–909.
Krog, L. A., and Olhoff, N.(1999). “Optimum topology and reinforcement design of disk and plate structures with multiple stiffness and eigenfrequency objectives.” Comput. Struct., 72, 535–563.
Kumar, P.(1978). “Optimal force transmission in reinforced concrete deep beams.” Comput. Struct., 8(2), 223–229.
Kupfer, H. (1964). “Generalization of Mörsch's truss analogy using principle of minimum strain energy.” CEB Bull. d'information, No. 40, Comite Ero-International du Beton, No. 40, 44–57.
Lampert, P., and Thurlimann, B. (1971). “Ultimate strength and design of reinforced concrete beams in torsion and bending.” Publication No. 31-I, IABSE, Zürich, 107–131.
Leonhardt, F.(1965). “Reducing the shear reinforcement in reinforced concrete beams and slabs.” Mag. Concrete Res., 17(53), 187.
Liang, Q. Q. (2001). “Performance-based optimization method for structural topology and shape design.” PhD thesis, School of the Built Environment, Victoria Univ. of Technology, Australia.
Liang, Q. Q., Xie, Y. M., and Steven, G. P.(1999). “Optimal selection of topologies for the minimum-weight design of continuum structures with stress constraints.” Proc. Inst. Mech. Engrs., Part C; J. Mech. Eng. Sci., 213(C8), 755–762.
Liang, Q. Q., Xie, Y. M., and Steven, G. P.(2000a). “Topology optimization of strut-and-tie models in reinforced concrete structures using an evolutionary procedure.” ACI Struct. J., 97(2), 322–330.
Liang, Q. Q., Xie, Y. M., and Steven, G. P.(2000b). “Optimal topology design of bracing systems for multistory steel frames.” J. Struct. Eng., 126(7), 823–829.
Liang, Q. Q., Xie, Y. M., and Steven, G. P.(2000c). “Optimal topology selection of continuum structures with displacement constraints.” Comput. Struct., 77(6), 635–644.
Liang, Q. Q., Xie, Y. M., and Steven, G. P.(2001). “Generating optimal strut-and-tie models in prestressed concrete beams by performance-based optimization.” ACI Struct. J., 98(2), 226–232.
Ma, Z. D., Kikuchi, N., and Cheng, H. C.(1995). “Topological design for vibrating structures.” Comput. Methods Appl. Mech. Eng., 121, 259–280.
Marti, P.(1985). “Basic tools of reinforced concrete beam design.” ACI Struct. J., 82(1), 46–56.
Marti, P.(1999). “A simple, consistent approach to structural concrete.” Struct. Eng., 77(9), 20–26.
Mish, K. D. (1994). “Strut-and-tie modeling of reinforced concrete: a case study in interactive visualization.” Proc., National Science Foundation Workshop on Visualization Applications in Earthquake Engineering, Chico, Calif.
Mlejnek, H. P., and Schirrmacher, R.(1993). “An engineer's approach to optimal material distribution and shape finding.” Comput. Methods Appl. Mech. Eng., 106, 1–26.
Mörsch, E. (1909). Concrete-steel construction, McGraw-Hill, New York (English translation by E. P. Goodrich).
Nielsen, M. P. (1984). Limit analysis and concrete plasticity, Prentice–Hall, Englewood Cliffs, NJ.
Ramirez, J. A.(1994). “Strut-and-tie design of pretensioned concrete members.” ACI Struct. J., 91(4), 572–578.
Ramirez, J. A., and Breen, J. E.(1991). “Evaluation of a modified truss-model approach for beams in shear.” ACI Struct. J., 88(5), 562–571.
ASCE-ACI Committee 445 on Shear Torsion.(1998) “Recent approaches to shear design of structural concrete.” J. Struct. Eng., 124(12), 1375–1417.
STRAND6 (1993). Reference Manual and User Guide, G+D Computing Pty Ltd., Sydney, Australia.
Ritter, W.(1899). “The hennebique design method (Die bauweise henebique).” Schweiz. Bauzeitung (Zürich), 33(7), 59–61.
Rodriguez, J., and Seireg, A.(1985). “Optimizating the shapes of structures via a rule-based computer program.” J. Comput. Mech. Eng., 40(1), 20–29.
Rozvany, G. I. N., Bendsøe, M. P., and Kirsch, U.(1995). “Layout optimization of structures.” Appl. Mech. Rev., 48(2), 41–119.
Rozvany, G. I. N., Zhou, M., and Birker, T.(1992). “Generalized shape optimization without homogenization.” Struct. Optim., 4, 250–252.
Sanders, D. H., and Breen, J. E.(1997). “Post-tensioned anchorage zone with single straight concentric anchorages. ” ACI Struct. J., 94(2), 146–158.
Schlaich, J., and Schäfer, K.(1991). “Design and detailing of structural concrete using strut-and-tie models.” Struct. Eng., 69(6), 113–125.
Schlaich, J., Schäfer, K., and Jennewein, M.(1987). “Toward a consistent design of structural concrete.” PCI J., 32(3), 74–150.
Suzuki, K., and Kikuchi, N.(1991). “A homogenization method for shape and topology optimization.” Comput. Methods Appl. Mech. Eng., 93, 291–318.
Tenek, L. H., and Hagiwara, I.(1993). “Static and vibrational shape and topology optimization using homogenization and mathematical programming.” Comput. Methods Appl. Mech. Eng., 109, 143–154.
Warner, R. F., Rangan, B. V., Hall, A. S., and Faulkes, K. A. (1998). Concrete structures, Addison–Wesley Longman, Austrailia Pty Limited, Melbourne, Australia.
Xie, Y. M., and Steven, G. P.(1993). “A simple evolutionary procedure for structural optimization.” Comput. Struct., 49(5), 885–896.
Yang, R. J., and Chuang, C. H.(1994). “Optimal topology design using linear programming.” Comput. Struct., 52(2), 265–275.
Yun, Y. M.(2000). “Computer graphics for nonlinear strut-tie model approach.” J. Comput. Civ. Eng., 14(2), 127–133.

Information & Authors

Information

Published In

Go to Journal of Structural Engineering
Journal of Structural Engineering
Volume 128Issue 6June 2002
Pages: 815 - 823

History

Received: Jul 17, 2001
Accepted: Oct 9, 2001
Published online: May 15, 2002
Published in print: Jun 2002

Permissions

Request permissions for this article.

Authors

Affiliations

Qing Quan Liang
Research Fellow, School of Civil and Environmental Engineering, Univ. of New South Wales, Sydney NSW 2052, Australia.
Brian Uy, M.ASCE
Senior Lecturer, School of Civil and Environmental Engineering, Univ. of New South Wales, Sydney NSW 2052, Australia.
Grant P. Steven
Professor, School of Engineering, Univ. of Durham, Durham DH1 3LE, U.K.

Metrics & Citations

Metrics

Citations

Download citation

If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.

Cited by

View Options

Get Access

Access content

Please select your options to get access

Log in/Register Log in via your institution (Shibboleth)
ASCE Members: Please log in to see member pricing

Purchase

Save for later Information on ASCE Library Cards
ASCE Library Cards let you download journal articles, proceedings papers, and available book chapters across the entire ASCE Library platform. ASCE Library Cards remain active for 24 months or until all downloads are used. Note: This content will be debited as one download at time of checkout.

Terms of Use: ASCE Library Cards are for individual, personal use only. Reselling, republishing, or forwarding the materials to libraries or reading rooms is prohibited.
ASCE Library Card (5 downloads)
$105.00
Add to cart
ASCE Library Card (20 downloads)
$280.00
Add to cart
Buy Single Article
$35.00
Add to cart

Get Access

Access content

Please select your options to get access

Log in/Register Log in via your institution (Shibboleth)
ASCE Members: Please log in to see member pricing

Purchase

Save for later Information on ASCE Library Cards
ASCE Library Cards let you download journal articles, proceedings papers, and available book chapters across the entire ASCE Library platform. ASCE Library Cards remain active for 24 months or until all downloads are used. Note: This content will be debited as one download at time of checkout.

Terms of Use: ASCE Library Cards are for individual, personal use only. Reselling, republishing, or forwarding the materials to libraries or reading rooms is prohibited.
ASCE Library Card (5 downloads)
$105.00
Add to cart
ASCE Library Card (20 downloads)
$280.00
Add to cart
Buy Single Article
$35.00
Add to cart

Media

Figures

Other

Tables

Share

Share

Copy the content Link

Share with email

Email a colleague

Share