International Journal of Steel Structures

, Volume 19, Issue 1, pp 269–282 | Cite as

Optimal Formation Assessment of Multi-layered Ground Retrofit with Arch-Grid Units Considering Buckling Load Factor

  • Quoc Hoan Doan
  • Dongkyu LeeEmail author


This study presents an optimal shape generation method of local steel unit plates in arch-grid structures by using buckling load factor. ETABS software is utilized for a computational modeling of arch-grid to consider buckling analysis. According to the present optimal shape generation method, first, some shape types of a horizontal unit cell plate of arch-grid are assumed as initial designs. Second, they are analyzed through ETABS in terms of their buckling capacities. At the same time, appropriate vertical column bar sizes are achieved with respect to maximal stress of steel material and buckling load factor. Third, the generated arch-grid are combined to achieve optimal conditions of width and height of a given arch-grid structure, which shows the best structural feasibility to resist a given building. The arch-grid structure is extended by considering four different cases: a combined grid, an extended grid, a multi-story grid and a pyramid grid to verify the effectiveness of the present optimal shape generation method of steel arch-grid as numerical examples.


Arch-grid Buckling load factor ETABS Optimal shape Horizontal steel plate Vertical steel bar 



This research was supported by a Grant (2017R1A2B4001960) from the National Research Foundation of Korea (NRF) funded by the Korea government.


  1. Afzali, S. H., Darabi, A., & Niazkar, M. (2016). Steel frame optimal design using MHBMO algorithm. International Journal of Steel Structures, 16(2), 455–465. Scholar
  2. Bendsøe, M. P. (1989). Optimal shape design as a material distribution problem. Structural Optimization, 1(4), 193–202. Scholar
  3. Bierlaire, M. (2015). Simulation and optimization: A short review. Transportation Research Part C: Emerging Technologies, 55(Supplement C), 4–13. Scholar
  4. Chai, J., & Carter, J. P. (2011). Deformation analysis in soft ground improvement (1st ed.). Dordrecht: Springer. Scholar
  5. Chau, K. N., et al. (2018). A polytree-based adaptive polygonal finite element method for multi-material topology optimization. Computer Methods in Applied Mechanics and Engineering, 332, 712–739. Scholar
  6. Dimopoulos, C. A., & Gantes, C. J. (2012). Comparison of alternative algorithms for buckling analysis of slender steel structures. Structural Engineering and Mechanics, 44(2), 219–238. Scholar
  7. Ding, Y. (1986). Shape optimization of structures: a literature survey. Computers & Structures, 24(6), 985–1004. Scholar
  8. ETABS®. (2016). Computers & Structures, Inc.
  9. Feng, R., & Ge, J. (2013). Shape optimization method of free-form cable-braced grid shells based on the translational surfaces technique. International Journal of Steel Structures, 13(3), 435–444. Scholar
  10. Hejazi, S. M., et al. (2012). A simple review of soil reinforcement by using natural and synthetic fibers. Construction and Building Materials, 30(Supplement C), 100–116. Scholar
  11. Kamiński, M., & Świta, P. (2015). Structural stability and reliability of the underground steel tanks with the stochastic finite element method. Archives of Civil and Mechanical Engineering, 15(2), 593–602. Scholar
  12. Lee, J., Jeong, Y., & Kim, W. (2016). Buckling behavior of steel girder in integral abutment bridges under thermal loadings in summer season during deck replacement. International Journal of Steel Structures, 16(4), 1071–1082. Scholar
  13. Lee, D., Lee, J., & Doan, Q. H. (2017). Multi-layered UL700 arch-grid module with inelastic buckling for localized reinforcement of soft ground. Advances in Engineering Software. Scholar
  14. Lee, J., Nguyen, H. T., & Kim, S.-E. (2009). Buckling and post buckling of thin-walled composite columns with intermediate-stiffened open cross-section under axial compression. International Journal of Steel Structures, 9(3), 175–184. Scholar
  15. Lee, D., & Shin, S. (2015). High tensile UL700 frame module with adjustable control of length and angle. Journal of Constructional Steel Research, 106, 246–257. Scholar
  16. Lee, D., et al. (2014). Reinforcement structure and method for reinforcing soft ground using unit module of steel grid. Seoul: C&S Patent and Law Office.Google Scholar
  17. Li, K. (2014). A story buckling method for evaluating system buckling load of plane sway frames. International Journal of Steel Structures, 14(1), 173–183. Scholar
  18. Li, J., et al. (2014). Effect of discrete fibre reinforcement on soil tensile strength. Journal of Rock Mechanics and Geotechnical Engineering, 6(2), 133–137. Scholar
  19. Nguyen, P.-C., & Kim, S.-E. (2014). An advanced analysis method for three-dimensional steel frames with semi-rigid connections. Finite Elements in Analysis and Design, 80, 23–32. Scholar
  20. Nguyen, P.-C., & Kim, S.-E. (2016). Advanced analysis for planar steel frames with semi-rigid connections using plastic-zone method. Steel and Composite Structures, 21, 1121–1144.Google Scholar
  21. Nguyen-Thoi, T., et al. (2014). An edge-based smoothed three-node mindlin plate element (ES-MIN3) for static and free vibration analyses of plates. KSCE Journal of Civil Engineering, 18(4), 1072–1082. Scholar
  22. Palmeira, E. M., Tatsuoka, F., Bathurst, R. J., Stevenson, P. E., & Zornberg, J. G. (2008). Advances in geosynthetics materials and applications for soil reinforcement and environmental protection works. Electronic Journal of Geotechnical Engineering, 13, 1–38.Google Scholar
  23. Phung-Van, P., Abdel-Wahab, M., et al. (2015a). Isogeometric analysis of functionally graded carbon nanotube-reinforced composite plates using higher-order shear deformation theory. Composite Structures, 123, 137–149. Scholar
  24. Phung-Van, P., Lorenzis, L. De, et al. (2015b). Analysis of laminated composite plates integrated with piezoelectric sensors and actuators using higher-order shear deformation theory and isogeometric finite elements. Computational Materials Science, 96, Part B, 495–505. Scholar
  25. Phung-Van, P., et al. (2013). A cell-based smoothed discrete shear gap method (CS-DSG3) based on the C0-type higher-order shear deformation theory for static and free vibration analyses of functionally graded plates. Computational Materials Science, 79, 857–872. Scholar
  26. Phung-Van, P., et al. (2014). A cell-based smoothed discrete shear gap method (CS-FEM-DSG3) based on the C0-type higher-order shear deformation theory for dynamic responses of Mindlin plates on viscoelastic foundations subjected to a moving sprung vehicle. International Journal for Numerical Methods in Engineering, 98(13), 988–1014. Scholar
  27. Phung-Van, P., et al. (2017). Nonlinear transient isogeometric analysis of smart piezoelectric functionally graded material plates based on generalized shear deformation theory under thermo-electro-mechanical loads. Nonlinear Dynamics, 87(2), 879–894. Scholar
  28. POSCO Steel. (2015). POSCO steel product guide. Pohang: POSCO Steel.Google Scholar
  29. Shukla, S. K. (2017). Applications of fibre-reinforced soil. In B. M. Das & N. Sivakugan (Eds.), Fundamentals of fibre-reinforced soil engineering. Developments in geotechnical engineering (pp. 145–180). Singapore: Springer.
  30. Sigmund, O. (2007). Morphology-based black and white filters for topology optimization. Structural and Multidisciplinary Optimization, 33(4–5), 401–424. Scholar
  31. Wang, Z., & Richwien, W. (2002). A study of soil-reinforcement interface friction. Journal of Geotechnical and Geoenvironmental Engineering, 128(1), 92–94.Google Scholar
  32. Xanthakos, P. P., Abramson, L. W., & Bruce, D. A. (1994). Ground control and improvement. Hoboken: Wiley.Google Scholar

Copyright information

© Korean Society of Steel Construction 2018

Authors and Affiliations

  1. 1.Department of Architectural EngineeringSejong UniversitySeoulKorea

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