Stable Length in Inelastic Design Considering Ductility Requirement

  • Abhay KulkarniEmail author
  • L. M. Gupta
Research Paper


The region close to plastic hinge is vulnerable to lateral instability due to the formation of the mechanism. A stable length between lateral restraint at the plastic hinge and adjacent lateral restraint plays a significant role in preventing lateral instability and until after the required hinge rotation has taken place. This phenomenon is studied for beams under uniform moment loading by carrying out an extensive parametric study on a mixed set of I-shaped hybrid and homogeneous plate girders using nonlinear finite element analysis. Geometric dimensions and steel grade of plate girder elements are varied to account for their effect on member slenderness. Effect of overall slenderness is included by varying lateral bracing configuration. Attention is given to the interaction between local and lateral buckling and their influence on inelastic rotation. Regression analysis of the database is carried out to arrive at a prediction equation for stable length to achieve the required rotation capacity. The equation is validated by applying it to thirty-nine selected experiments conducted by others and comparing results with the results of available prediction equations. Statistical analysis of the validation study shows that the proposed equation provides more refined results as compared to available equations. It is observed that use of the new prediction equation when used along with rotation capacity prediction equation suggested by authors in the previous study proves to be a rational solution as available stable length equations that are based only on geometric proportions of sections. At the end of the paper, a flowchart and demonstration examples for use of these equations are presented.


Hybrid section Slenderness Stable length Nonlinear analysis Strain hardening Rotation capacity 


  1. AISC-LFRD (2010) Specifications for structural steel buildings. AISC, ChicagoGoogle Scholar
  2. ANSYS Inc (2010) Release 12.0, mechanical user guide, southpointe, vol 275. Technology Drive, CanonsburgGoogle Scholar
  3. Bayer A, Boissonnade N, Khelil A, Bureau A (2018) Influence of assumed geometric and material imperfections on the numerically determined ultimate resistance of hot-rolled U-shaped steel members. J Constr Steel Res. Google Scholar
  4. Earls CJ (2000a) Geometric factors influencing structural ductility of compact I-shaped beams. J Struct Eng. Google Scholar
  5. Earls CJ (2000b) Influence of material effect on structural ductility of compact I-shaped beams. J Strut Eng. Google Scholar
  6. Earls CJ (2001) Constant moment behavior of high performance steel I-shaped beams. J Constr Steel Res 57:711–728CrossRefGoogle Scholar
  7. EN 1993-1-1: Eurocode 3 – Design of steel structures – Part 1-1: General rules and rules for buildingsGoogle Scholar
  8. EN 1993-1-5: Eurocode 3—Design of steel structures—Part 1-5: Plated structural elementsGoogle Scholar
  9. Galambos TV (1967) Summary report on deformation and energy absorption capacity of steel structures in the inelastic range. American Iron and Steel Institute, Washington, DCGoogle Scholar
  10. Greco N, Earls CJ (2003) Structural ductility in hybrid high performance steel beams. J Struct Eng. Google Scholar
  11. Green PS, Sause R, Ricles JM (2002) Strength and ductility of HPS flexural members. J Constr Steel Res. Google Scholar
  12. Holtz NM, Kulak GL (1973) Web slenderness limit for compact beams. Structural Engineering Report No. 43. Department of Civil Engineering, University of Alberta, Edmonton AltaGoogle Scholar
  13. Holtz NM, Kulak GL (1975) Web slenderness limit for non-compact beams. Structural Engineering Report No. 51. Department of Civil Engineering, University of Alberta, Edmonton AltaGoogle Scholar
  14. IS 800-(2007) Indian standard-general construction in steel—code of practice, 3rd edn. Bureau of Indian Standards, New DelhiGoogle Scholar
  15. Kulkarni AS, Gupta LM (2017) Experimental investigation on flexural response of hybrid steel plate girder. KSCE J Civ Eng. Google Scholar
  16. Kulkarni A, Gupta LM (2018) Evaluation of rotation capacity of I-shaped welded steel plate girders. Arab J Sci Eng. Google Scholar
  17. Lay MG, Adams P F, Galambos TV (1965) Experiments on high strength steel members. Welding research council, bulletin No 110/287Google Scholar
  18. Lee CH, Han KH, Uang CM, Kim DK, Park CH, Kim JH (2013) Flexural strength and rotation capacity of I-shaped beams fabricated from 800-MPa steel. J Struct Eng. Google Scholar
  19. Memon BA, Xiao-Zu S (2004) Arc-length technique for nonlinear finite element analysis. J Zhejiang Univ. Google Scholar
  20. Montgomery DC, Runger GC (2014) Applied statistics and probability for engineers ISV, 6th edn. Wiley, New DelhizbMATHGoogle Scholar
  21. Nakashima M (1994) Variation of ductility capacity of steel beam-column. J Struct Eng. Google Scholar
  22. Ramanan L (2006) Simulation of nonlinear analysis in ANSYS. In: ANSYS India users conferenceGoogle Scholar
  23. Shokouhian M, Shi Y (2014a) Investigation of ductility in hybrid and high strength steel beams. Int J Steel Struct. Google Scholar
  24. Shokouhian M, Shi Y (2014b) Classification of I-section flexural members based on member ductility. J Constr Steel Res. Google Scholar
  25. Shokouhian M, Shi Y (2015) Flexural strength of hybrid I-beams based on slenderness. Eng Struct. Google Scholar
  26. SPSS (2015) SPSS—statistical package for social sciences. SPSS, IBM, ArmonkGoogle Scholar
  27. Trahair N, Bradford M, Nethercot D, Gardner L (2007) The behavior and design of steel structures to EN 1993-1-1, 4th edn. Taylor and Francis, New YorkGoogle Scholar
  28. Wang CS, Duan L, Chen YF, Wang SC (2016) Flexural behavior and ductility of hybrid high performance steel I-girders. J Constr Steel Res. Google Scholar

Copyright information

© Shiraz University 2019

Authors and Affiliations

  1. 1.Visvesvaraya National Institute of TechnologyNagpurIndia
  2. 2.Department of Applied MechanicsVisvesvaraya National Institute of TechnologyNagpurIndia

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