Effect of layer geometry and stiffness on the fields of normal stresses in multilayer beams under asymmetric bending

  • J. Bareišis
  • V. Kleiza

A mathematical model is suggested for calculating the bending stiffness and fields of normal stresses (strength) at any point in the cross section of a multilayer beam. It is found that the structure of the scalar field of normal stresses allows one to solve some optimization problems with multivariant parameters. The method is illustrated with an example of two-layer beams. The results of an investigation into the strength and stiffness of two-layer beams, with a geometric and (or) stiffness asymmetry, in asymmetric bending are presented. The kinetics of bending stiffness and strength in relation to variations in the geometric parameters of cross sections and in the ratio of elastic moduli of layers is examined. It is established that the normal stresses in multilayer beams under asymmetric bending considerably depend on the location of the flexural center, neutral plane, and bending stiffnesses relative to the principal axes of cross sections of the beams.


multilayer beam asymmetric structural elements bending stiffness strength asymmetric bending 


  1. 1.
    F. Bulavs, I. Radinsh, and N. Tirans, “Improvement of capacity in bending by the use of FRP layers on RC beams,” J. Civil Eng. Manag., 11, No. 3, 169–174 (2005).Google Scholar
  2. 2.
    V. G. Piskunov, “An iterative analytical theory in the mechanics of layered composite systems,” Mech. Compos. Mater., 39, No. 1, 1–16 (2003).CrossRefGoogle Scholar
  3. 3.
    H. Altenbach, J. Altenbach, and E. Nast, “Modelling and analysis of multilayered shells based on a Timoshenko-type with six degrees of freedom,” Mech. Compos. Mater., 29, No. 4, 500–511 (1993).Google Scholar
  4. 4.
    K. Gurksnys, A. Kvedaras, and S. Kavaliauskas, “Behaviour evaluation of ‘sleeved’ connectors in composite timber-concrete floors,” J. Civil Eng. Manag., 11, No. 4, 277–282 (2005).Google Scholar
  5. 5.
    A. Jaras and R. Kačianauskas, “Deflection analysis of bisteel I-section beams with elastic-perfectly plastic behavior of the web,” Mechanika, 43, No. 5, 5–10 (2003).Google Scholar
  6. 6.
    A. Lapko, B. Sadovska-Buraczewska, and A. Tomaszewicz, “Experimental and numerical analysis of flexural composite beams with use of high strength,” J. Civil Eng. Manag., 11, No. 2, 115–120 (2005).Google Scholar
  7. 7.
    J. Bareišis, “Stiffness and strength of multilayer beams,” J. Compos. Mater., 40, No. 6, 515–531 (2006).CrossRefGoogle Scholar
  8. 8.
    J. Bareišis, V. Kleiza, and J. Kleiza, “Investigation of the flexural stiffness of asymmetric multilayer beams,” Strength Mater., 38, No. 6, 601–612 (2006).CrossRefGoogle Scholar
  9. 9.
    D. Garuckas and J. Bareisis, “Influence of different factors on the stiffness and strength of multilayered composite elements,” Mech. Compos. Mater., 39, No. 2, 153–164 (2003).CrossRefGoogle Scholar
  10. 10.
    J. Bareišis and V. Kleiza, “Stiffness center and neutral layer direction investigation method and its application to asymmetric multilayer structural elements,” Mechanika, 48, No. 4, 5–12 (2004).Google Scholar
  11. 11.
    De-Gan Gu, “Calculation in the unsymmetrical bending problem of thin plates by spline boundary layer method,” Comput. Struct., 34, Iss. 4, 663–668 (1990).MATHCrossRefGoogle Scholar
  12. 12.
    Jingming Ma and Meifeng Le, “A simple model of couple-stress theory for fiber-reinforced composites,” Comput. Struct., 53, Iss. 5, 1053–1057 (1994).MATHCrossRefGoogle Scholar
  13. 13.
    L. Bonet, M. L. Romero, P. F. Miguel, and M. A. Fernandez, “A fast stress integration algorithm for reinforced concrete sections with axial loads and biaxial bending,” Comput. Struct., 82, Iss. 2–3, 213–225 (2004).CrossRefGoogle Scholar
  14. 14.
    Mel M. Schwartz, Composite Materials. Vol. 2, Prentice-Hall, Inc., New Jersey (1997).Google Scholar

Copyright information

© Springer Science+Business Media, Inc. 2009

Authors and Affiliations

  • J. Bareišis
    • 1
  • V. Kleiza
    • 1
  1. 1.Kaunas Technological UniversityKaunasLithuania

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