Cross-section design

  • Ioannis VayasEmail author
  • John Ermopoulos
  • George Ioannidis
Part of the Springer Tracts in Civil Engineering book series (SPRTRCIENG)


During loading of the structure, cross-sections of structural members are subjected to internal forces and moments. This chapter provides the design resistances of cross-sections to individual internal forces and moments and their combinations. It starts with axial tension, where design resistances are given for cross-sections with or without holes and goes to the compression resistance of sections, accounting for possible local buckling effects. It then presents the elastic and plastic bending resistance, depending on the cross-section class, and the resistance to shear forces. Torsion and its uniform and non-uniform mechanisms with the corresponding design resistances are described. The properties and main characteristics in respect to torsion are given for open and hollow sections. Elastic and plastic resistances to St Venant and warping torsion are determined. Subsequently, cross-section design to combined internal forces and moments is given. Elastic design is expressed in terms of limitation of the von Mises stresses. For plastic design, interaction relations between internal forces and moments are defined including biaxial bending and axial force as well as shear forces and torsion. Interaction relations for plastic design of I-, H-, rectangular or circular hollow sections and angle sections as proposed by Eurocode 3 or derived by the authors are presented.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [3.1] Cochrane VH (1922) Rules for rivet-hole deduction in tension members. Engineering News-Record 89(20):847–848.Google Scholar
  2. [3.2] Dowling PJ, Knowles P, Owens GW (1988) Structural Steel Design. The Steel Construction Institute & Butterworths, London.Google Scholar
  3. [3.3] Salmon CG, Johnson JE (1980) Steel Structures. 2nd Edition, Harper & Row.Google Scholar
  4. [3.4] Moze P, Beg D, Lopatic J (2007) Net cross-section design resistance and local ductility of elements made of high strength steel. Journal of Constructional Steel Research, 63(11):1431–1441.CrossRefGoogle Scholar
  5. [3.5] Rombouts IMJ, Francken WL, Dekker RWA, Snijder HH (2014) Investigation of the net cross-section failure mechanism, experimental research. Proc. Eurosteel Conference.Google Scholar
  6. [3.6] Wei F, Fang C, Yam M, Zhang Y (2014) Fracture behaviour and design of steel tensile connections with staggered bolt arrangements, International Journal of Steel Structures,
  7. [3.7] Petersen C (1988) Stahlbauten. Vieweg Verlag, Braunschweig.Google Scholar
  8. [3.8] EN 1993-1-1 (2005) Eurocode 3: Design of steel structures - Part 1-1: General rules and rules for buildings. CEN.Google Scholar
  9. [3.9] Timoshenko SP, Goodier JN (1970) Theory of elasticity Mc-Graw-Hill. New York.Google Scholar
  10. [3.10] Kollbrunner CF, Hajdin N (1969) Torsion in Structures. Springer, Berlin.Google Scholar
  11. [3.11] Sapountzakis EJ, Dikaros IC (2015) Advanced 3–D Beam Element of Arbitrary Composite Cross-section Including Generalized Warping Effects. International Journal for Numerical Methods in Engineering, 102:44–78.MathSciNetCrossRefGoogle Scholar
  12. [3.12] Vayas I (2016) Models for stability analysis and design of steel and composite plate girders. In The International Colloqium on Stability and Ductility of Steel Structures ‘16, Ernst&Sohn, Berlin, pp. 39–48.Google Scholar
  13. [3.13] Vayas I, Iliopoulos A (2014) Design of Steel-Concrete Composite Bridges to Eurocodes. CRC Press, Ney York.Google Scholar
  14. [3.14] EN 1993-1-3 (2005) Eurocode 3: Design of steel structures - Part 1-3: General rules. Supplementary rules for cold-formed thin gauge members and sheeting. CEN.Google Scholar
  15. [3.15] EN 1993-1-5 (2006) Eurocode 3: Design of steel structures - Part 1-5: Plated structural elements. CEN.Google Scholar
  16. [3.16] Kindmann R, Frickel J (1999) Ultimate load carrying capacity of I-cross-sections under the loading of arbitrary internal forces and moments. Stahlbau 68:290–301.CrossRefGoogle Scholar
  17. [3.17] Kindmann, R, Frickel J (1999) Ultimate load carrying capacity of often used beam cross-sections. Stahlbau 68:817–828.CrossRefGoogle Scholar
  18. [3.18] Rubin H (1978) Interaktionsbeziehungen für doppelsymmetrische I- und Kastenquerschnitte bei zweiachsiger Biegung und Normalkraft. Stahlbau 47(5):145–151 and 47(6):147–181.Google Scholar
  19. [3.19] Vayas I (2000) Interaktion of the plastic internal forces and moments of doubly symmetrical I-sections. Stahlbau 69(9):693–706.CrossRefGoogle Scholar
  20. [3.20] Dowling PJ, Owens GW, Knowles P (1988) Structural Steel Design. Butterworths.Google Scholar
  21. [3.21] Trahair NS, Bradford MA (1988) The Behaviour and Design of Steel Structures. Chapman and Hall.Google Scholar
  22. [3.22] McGinley TJ, Ang TC (1987) Structural Steelwork Design to Limit State Theory. Butterworths.Google Scholar
  23. [3.23] EN 1993-1-1 (2005) Eurocode 3: Design of steel structures - Part 1-1: General rules and rules for buildings. CEN.Google Scholar
  24. [3.24] American Institute of Steel Construction, Inc. (2000) Load and Resistance Factor Design Specification for Steel Hollow Structural Sections AISC.Google Scholar
  25. [3.25] Vayas I (2001) Interaktion of the plastic internal forces and moments of symmetrical box cross-sections, Stahlbau 70(11):869–884.CrossRefGoogle Scholar
  26. [3.26] Kindmann R, Jonczyk D, Knobloch M (2017) Plastic resistance of square and rectangular hollow sections. Stahlbau 86(6):497–514.CrossRefGoogle Scholar
  27. [3.27] Nowzartash F, Mohareb M (2009) Plastic Interaction Relations for Elliptical Hollow Sections. Thin-Walled Structures, Vol. 47(6-7):681–691.CrossRefGoogle Scholar
  28. [3.28] Gardner L, Chan TM, Abela JM (2011) Structural behaviour of elliptical hollow sections under combined compression and uniaxial bending. Advanced Steel Construction, Vol. 7(1):86–112.Google Scholar
  29. [3.29] AISC, Load and Resistance Factor Design Specification for Single-Angle Members, 2000.Google Scholar
  30. [3.30] Vayas I, Charalambakis A, Koumousis V (2009) Inelastic resistance of angle sections subjected to biaxial bending and normal forces. Steel Construction design and research, 2(2):138–146.CrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Ioannis Vayas
    • 1
    Email author
  • John Ermopoulos
    • 2
  • George Ioannidis
    • 2
  1. 1.Civil EngineeringNational Technical University of AthensAthensGreece
  2. 2.National Technical University of AthensAthensGreece

Personalised recommendations