Title:
Application of Evaluation System for Strut-and-Tie Models of Reinforced Concrete Structures
Author(s):
Man Zhou, Ji Tao Zhong, Lai Wang, and Hai Tao Chen
Publication:
Structural Journal
Volume:
118
Issue:
1
Appears on pages(s):
17-30
Keywords:
evaluation system; optimization; strut-and-tie model
DOI:
10.14359/51728088
Date:
1/1/2021
Abstract:
Plenty of strut-and-tie models (STMs) typically exist for the same discontinuity region (D-region). Although these STMs constructed by different researchers may have their own advantages, only a reasonable STM is needed by designers during the process of structure design. Therefore, identifying a more appropriate model from all the existing ones seems to be a meaningful and challenging
research task. It is in this situation that the evaluation system is proposed in this study. To demonstrate the effectiveness of the evaluation system, almost all the existing STMs of a special-shaped
beam are collected together and analyzed in detail. Furthermore, experimental analysis is conducted to validate the numerical results. The comparison indicates that the evaluation system is capable of ranking the performance of different STMs derived from the same member. The system provides a unified evaluation criterion for judging STMs and can be considered a comprehensive and practical technique for civil engineering.
Related References:
1. Ritter, W., “Die Bauweise Hennebique,” Schweizerische Bauzeitung, V. 33, No. 7, 1899, pp. 59-61.
2. Mörsch, E., Reinforced Concrete, Theory and Application, Verlag Konrad Wittwer, Stuttgart, Germany, 1912.
3. Leonhardt, F., “Reducing the Shear Reinforcement in Reinforced Concrete Beams and Slabs,” Magazine of Concrete Research, V. 17, No. 53, 1965, pp. 187-198. doi: 10.1680/macr.1965.17.53.187
4. Schlaich, J.; Schäfer, K.; and Jennewein, M., “Toward a Consistent Design of Structural Concrete,” PCI Journal, V. 32, No. 3, 1987, pp. 74-150. doi: 10.15554/pcij.05011987.74.150
5. Breen, J. E., “Anchorage Zone Reinforcement for Post-Tensioned Concrete Girders,” Transportation Research Board, Washington, DC, 1994.
6. Gao, G.; Li, Y.; Pan, H.; Chen, L. M.; and Liu, Z. Y., “An Effective Members-Adding Method for Truss Topology Optimization Based on Principal Stress Trajectories,” Engineering Computations, V. 34, No. 6, 2017, pp. 2088-2104. doi: 10.1108/EC-05-2016-0166
7. Palmisano, F., “Rapid Diagnosis of Crack Patterns of Masonry Buildings Subjected to Landslide-Induced Settlements by Using the Load Path Method,” International Journal of Architectural Heritage, V. 10, No. 4, 2016, pp. 438-456. doi: 10.1080/15583058.2014.996922
8. Palmisano, F.; Vitone, A.; and Vitone, C., “Load Path Method in the Interpretation of Masonry Vault Behaviour,” WIT Transactions on the Built Environment, V. 83, 2005, pp. 155-167.
9. Mezzina, M.; Palmisano, F.; and Raffaele, D., “Designing Simply Supported R.C. Bridge Decks Subjected to In-Plane Actions: Strut-and-Tie Model Approach,” Journal of Earthquake Engineering, V. 16, No. 4, 2012, pp. 496-514. doi: 10.1080/13632469.2011.653866
10. Xie, Y. M., and Steven, G. P., “A Simple Evolutionary Procedure for Structural Optimization,” Computers & Structures, V. 49, No. 5, 1993, pp. 885-896. doi: 10.1016/0045-7949(93)90035-C
11. Yang, X. Y.; Xie, Y. M.; Steven, G. P.; and Querin, O. M., “Bidirectional Evolutionary Method for Stiffness Optimization,” AIAA Journal, V. 37, No. 11, 1999, pp. 1483-1488. doi: 10.2514/2.626
12. Liang, Q. Q.; Xie, Y. M.; and Steven, G. P., “Generating Optimal Strut-and-Tie Models in Prestressed Concrete Beams by Performance-Based Optimization,” ACI Structural Journal, V. 98, No. 2, Mar.-Apr. 2001, pp. 226-232.
13. Ali, M. A., and White, R. N., “Formulation of Optimal Strut-and-Tie Models in Design of Reinforced Concrete Structures,” Repair, Rehabilitation, and Maintenance of Concrete Structures, and Innovations in Design and Construction, V. SP-193, American Concrete Institute, Farmington Hills, MI, 2000, pp. 979-998.
14. Nagarajan, P., and Pillai, T. M. M., “Development of Strut and Tie Models for Simply Supported Deep Beams Using Topology Optimization,” Songklanakarin Journal of Science and Technology, V. 30, No. 5, Sept.-Oct. 2008, pp. 641-647.
15. Bruggi, M., “Generating Strut-and-Tie Patterns for Reinforced Concrete Structures Using Topology Optimization,” Computers & Structures, V. 87, No. 23-24, 2009, pp. 1483-1495. doi: 10.1016/j.compstruc.2009.06.003
16. Leu, L. J.; Huang, C. W.; Chen, C. S.; and Liao, Y. P., “Strut-and-Tie Design Methodology for Three-Dimensional Reinforced Concrete Structures,” Journal of Structural Engineering, ASCE, V. 132, No. 6, 2006, pp. 929-938. doi: 10.1061/(ASCE)0733-9445(2006)132:6(929)
17. Victoria, M.; Querin, O. M.; and Martí, P., “Generation of Strut-and-Tie Models by Topology Design Using Different Material Properties in Tension and Compression,” Structural and Multidisciplinary Optimization, V. 44, No. 2, 2011, pp. 247-258. doi: 10.1007/s00158-011-0633-z
18. Herranz, J. P.; María, H. S.; Gutiérrez, S.; and Riddell, R., “Optimal Strut-and-Tie Models Using Full Homogenization Optimization Method,” ACI Structural Journal, V. 109, No. 5, Sept.-Oct. 2012, pp. 605-613.
19. Bogomolny, M., and Amir, O., “Conceptual Design of Reinforced Concrete Structures Using Topology Optimization with Elastoplastic Material Modeling,” International Journal for Numerical Methods in Engineering, V. 90, No. 13, 2012, pp. 1578-1597. doi: 10.1002/nme.4253
20. Almeida, V. S.; Simonetti, H. L.; and Neto, L. O., “Comparative Analysis of Strut-and-Tie Models Using Smooth Evolutionary Structural Optimization,” Engineering Structures, V. 56, No. 6, 2013, pp. 1665-1675. doi: 10.1016/j.engstruct.2013.07.007
21. Gaynor, A. T.; Guest, J. K.; and Moen, C. D., “Reinforced Concrete Force Visualization and Design Using Bilinear Truss-Continuum Topology Optimization,” Journal of Structural Engineering, ASCE, V. 139, No. 4, 2013, pp. 607-618. doi: 10.1061/(ASCE)ST.1943-541X.0000692
22. Luo, Y., and Kang, Z., “Layout Design of Reinforced Concrete Structures Using Two-Material Topology Optimization with Drucker–Prager Yield Constraints,” Structural and Multidisciplinary Optimization, V. 47, No. 1, 2013, pp. 95-110. doi: 10.1007/s00158-012-0809-1
23. Bruggi, M., “A Numerical Method to Generate Optimal Load Paths in Plain and Reinforced Concrete Structures,” Computers & Structures, V. 170, 2016, pp. 26-36. doi: 10.1016/j.compstruc.2016.03.012
24. Najafian, H. A. N., and Vollum, R. L., “Automated Nonlinear Design of Reinforced Concrete D Regions,” Structural Engineering and Mechanics, V. 46, No. 1, 2013, pp. 91-110. doi: 10.12989/sem.2013.46.1.091
25. Maxwell, B. S., “An Experimental Study of a Structural Concrete Deep Beam with a Large Opening Using the Strut-and-Tie Model,” The University of Texas at Austin, Austin, TX, 1996.
26. Siao, W. B., “Deep Beams Revisited,” ACI Structural Journal, V. 92, No. 1, Jan.-Feb. 1995, pp. 95-102.
27. Campione, G., and Minafò, G., “Behaviour of Concrete Deep Beams with Openings and Low Shear Span-to-Depth Ratio,” Engineering Structures, V. 41, Aug, 2012, pp. 294-306. doi: 10.1016/j.engstruct.2012.03.055
28. Fernández Ruiz, M., and Muttoni, A., “On Development of Suitable Stress Fields for Structural Concrete,” ACI Structural Journal, V. 104, No. 4, July-Aug. 2007, pp. 495-502.
29. Guan, H., and Doh, J. H., “Development of Strut-and-Tie Models in Deep Beams with Web Openings,” Advances in Structural Engineering, V. 10, No. 6, 2007, pp. 697-711. doi: 10.1260/136943307783571427
30. Yang, K. H.; Chung, H. S.; and Ashour, A. F., “Influence of Inclined Web Reinforcement on Reinforced Concrete Deep Beams with Openings,” ACI Structural Journal, V. 104, No. 5, Sept.-Oct. 2007, pp. 580-589.
31. Yoo, T. M.; Doh, J. H.; Guan, H.; and Fragomeni, S., “Experimental Behaviour of High-Strength Concrete Deep Beams with Web Openings,” Structural Design of Tall and Special Buildings, V. 22, No. 8, 2013, pp. 655-676. doi: 10.1002/tal.718
32. Doh, J. H.; Yoo, T. M.; Miller, D.; Guan, H.; and Fragomeni, S., “Investigation into the Behaviour of Deep Beam with Web Openings by Finite Element,” Computers and Concrete, V. 10, No. 6, 2012, pp. 609-630. doi: 10.12989/cac.2012.10.6.609
33. Zhang, H. Z.; Liu, X.; and Yi, W. J., “Reinforcement Layout Optimisation of RC D-Regions,” Advances in Structural Engineering, V. 17, No. 7, 2014, pp. 979-992. doi: 10.1260/1369-4332.17.7.979
34. Hardjasaputra, H., “Evolutionary Structural Optimization as Tool in Finding Strut-and-Tie Models for Designing Reinforced Concrete Deep Beam,” Procedia Engineering, V. 125, 2015, pp. 995-1000. doi: 10.1016/j.proeng.2015.11.153
35. Ali, M. A., “Automatic Generation of Truss Models for the Optimal Design of Reinforced Concrete Structures,” Cornell University, Ithaca, NY, 1998.
36. Liang, Q. Q.; Xie, Y. M.; and Steven, G. P., “Topology Optimization of Strut-and-Tie Models in Reinforced Concrete Structures Using an Evolutionary Procedure,” ACI Structural Journal, V. 97, No. 2, Mar.-Apr. 2000, pp. 322-332.
37. Maxwell, B. S., and Breen, J. E., “Experimental Evaluation of Strut-and-Tie Model Applied to Deep Beam with Opening,” ACI Structural Journal, V. 97, No. 1, Jan.-Feb. 2000, pp. 142-148.
38. Biondini, F.; Bontempi, F.; and Malerba, P. G., “Modelli Strut-and-Tie Emergenti Dall’ottimizzazione Topologica Evolutiva di Strutture Composite,” Proceedings, National Workshop Tecniche di Progettazione Strut and Tie di Elementi in Cemento Armato, Firenze, Italia, 2002.
39. Kwak, H. G., and Noh, S. H., “Determination of Strut-and-Tie Models Using Evolutionary Structural Optimization,” Engineering Structures, V. 28, No. 10, 2006, pp. 1440-1449. doi: 10.1016/j.engstruct.2006.01.013
40. Breña, S. F., and Morrison, M. C., “Factors Affecting Strength of Elements Designed Using Strut-and-Tie Models,” ACI Structural Journal, V. 104, No. 3, May-June 2007, pp. 267-277.
41. Pareek, T., “Use of Steel Fiber Reinforced Concrete in Structural Members with Highly Complex Stress Fields,” MS thesis, University of Texas at Arlington, Arlington, TX, 2012.
42. Sahoo, D. R.; Flores, C. A.; and Chao, S. H., “Behavior of Steel Fiber-Reinforced Concrete Deep Beams with Large Opening,” ACI Structural Journal, V. 109, No. 2, Mar.-Apr. 2012, pp. 193-204.
43. Amir, O., and Sigmund, O., “Reinforcement Layout Design for Concrete Structures Based on Continuum Damage and Truss Topology Optimization,” Structural and Multidisciplinary Optimization, V. 47, No. 2, 2013, pp. 157-174. doi: 10.1007/s00158-012-0817-1
44. Moradi, M., and Esfahani, M. R., “Application of the Strut-and-Tie Method for Steel Fiber Reinforced Concrete Deep Beams,” Construction and Building Materials, V. 131, 2017, pp. 423-437. doi: 10.1016/j.conbuildmat.2016.11.042
45. Zhong, J. T.; Wang, L.; Deng, P.; and Zhou, M., “A New Evaluation Procedure for the Strut-and-Tie Models of the Disturbed Regions of Reinforced Concrete Structures,” Engineering Structures, V. 148, 2017, pp. 660-672. doi: 10.1016/j.engstruct.2017.07.012
46. Putke, T., and Mark, P., “Strut-and-Tie Modelling with Topological Optimisation,” Beton- und Stahlbetonbau, V. 109, No. 9, 2014, pp. 618-627. doi: 10.1002/best.201400039
47. van Mier, J. G. M.; Van Vliet, M. R. A.; and Wang, T. K., “Fracture Mechanisms in Particle Composites: Statistical Aspects in Lattice Type Analysis,” Mechanics of Materials, V. 34, No. 11, 2002, pp. 705-724. doi: 10.1016/S0167-6636(02)00170-9
48. Griffiths, D. V., and Fenton, G. A., “Probabilistic Slope Stability Analysis by Finite Elements,” Journal of Geotechnical and Geoenvironmental Engineering, ASCE, V. 130, No. 5, 2004, pp. 507-518. doi: 10.1061/(ASCE)1090-0241(2004)130:5(507)
49. Tang, X. W., “Study on Damage and Fracture Behavior of Concrete Based on Macro and Meso Mechanics,” Tsinghua University, Beijing, China, 2008.
50. GB 50010-2010, “Code for Design of Concrete Structures,” Ministry of Housing and Urban-Rural Development, Beijing, China, 2015.
51. Kuchma, D. A., and Tjhin, T. N., “CAST (Computer Aided Strut-and-Tie) Design Tool,” Proceedings, Structures Congress 2001, Washington, DC, May 2001, pp. 1-7.
52. Yun, Y. M., and Kim, B. H., “Two-Dimensional Grid Strut-Tie Model Approach for Structural Concrete,” Journal of Structural Engineering, ASCE, V. 134, No. 7, 2008, pp. 1199-1214. doi: 10.1061/(ASCE)0733-9445(2008)134:7(1199)
53. Park, J. W.; Yindeesuk, S.; Tjhin, T.; and Kuchma, D., “Automated Finite-Element-Based Validation of Structures Designed by the Strut-and-Tie Method,” Journal of Structural Engineering, ASCE, V. 136, No. 2, 2010, pp. 203-210. doi: 10.1061/(ASCE)0733-9445(2010)136:2(203)
54. GB 50010-2010, “Code for Design of Reinforced Concrete Structures,” Ministry of Housing and Urban-Rural Construction of the People’s Republic of China, Architecture and Building Press, Beijing, China, 2010.