Skip to main content
SpringerLink
Log in

The thermal bend of RTP with one edge clamped and two edges simply supported and one edge free

  • Reply
  • Published:
Archive of Applied Mechanics Aims and scope Submit manuscript

Abstract

Small-deflection plate theory and superposition principle, with consideration of temperature variation that is perpendicular to the surface, reveal that a rectangular thin plate (RTP) with one edge clamped, two edges simply supported, and one edge free under temperature disparity can be regarded as a superposition of an RTP with three simply supported edges and one free edge under temperature disparity and an RTP with three simply supported edges and one free edge under bending moment on one edge. First, by supposing the deflection function that has undetermined parameters at the free edge and by adopting the Levy method, the closed solution for an RTP with three simply supported edges and one free edge is obtained. Second, the closed solution for an RTP with three simply supported edges and one free edge is obtained under temperature disparity. Third, with the use of the solution for an RTP with four simply supported edges under bending moment on one edge, the solution for an RTP with three simply supported edges and one free edge under bending moment on one edge is obtained. Finally, the deflection and bending analytical solution for an RTP with one edge clamped, two edges simply supported, and one edge free under temperature disparity is obtained by adopting the superposition principle. The calculation coefficient table for a concrete RTP with one edge clamped, two edges simply supported, and one edge free under temperature disparity is established by using MATLAB. Thus, a theoretical calculation based on a concrete RTP with one edge clamped, two edges simply supported, and one edge free under temperature disparity in an engineering structure is provided for engineering design.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Misra J.C.: On the thermal bending of a thin elastic simply supported rectangular plate resting on an elastic foundation. Pure Appl. Geophys. 112(1), 83–89 (1974)

    Article  Google Scholar 

  2. Pachinger F., Lrschik H.: Fast convergent series solutions for thermal bending of thin rectangular plates. J. Therm. Stress. 21(7), 763–775 (1998)

    Article  Google Scholar 

  3. Zhong Y., Zhang Y.S.: Theoretic solution for rectangular thin plate with arbitrary boundary conditions by symplectic geometry method. Chin. J. Appl. Mech. 22(2), 293–297 (2005)

    Google Scholar 

  4. Deshmukh K.C., Khandait M.V., Warbhe S.D. et al.: Thermal stresses in a simply supported plate with thermal bending moments. Appl. Math. Mech. 6(18), 1–12 (2010)

    Google Scholar 

  5. Cheng X.S., Du Y.F.: The discussion of the analytical solution about rectangular thin slab under temperature disparity with four simply supported edges. Low Temp. Archit. Technol. 4, 76–78 (2006)

    Google Scholar 

  6. Cheng X.S., Du Y.F., Li H.: Analytic solution to rectangular thin plate with three clamped edges and one simply supported edge under temperature disparity. Adv. Struct. Eng. 8, 789–794 (2006)

    Google Scholar 

  7. Cheng X.S., Du Y.F., Li H.: Discuss of analytic solution about rectangular thin plate with four clamped edges under temperature disparity. Spec. Struct. 23(4), 42–45 (2006)

    Google Scholar 

  8. Cheng X.S., Du Y.F., Li H.: A discussion on the analytical solution of rectangular thin slab under temperature load with four simply supported edges. Mech. Eng. 28(6), 28–32 (2006)

    Google Scholar 

  9. Cheng X.S., Du Y.F., Li H. et al.: Analytic solution about rectangular thin slab with three simply supported edges and one clamped edge under temperature load. Low Temp. Archit. Technol. 4, 59–61 (2007)

    Google Scholar 

  10. Cheng X.S., Du Y.F., Li H. et al.: The analytical solution about rectangular thin slab with three clamped edges and one simply supported edges under temperature load. Struct. Environ. Eng. 34(4), 8–13 (2007)

    Google Scholar 

  11. Cheng X.S., Du Y.F., Li H. et al.: The analytical solution about thin rectangular slab with two opposite clamped edges and two opposite simply supported edges under temperature loads. J. Gansu Sci. 19(2), 39–43 (2007)

    Google Scholar 

  12. Cheng X.S., Du Y.F., Li H.: An analytic solution for rectangular thin slab with two adjacent clamped edges and two adjacent simply supported edges under temperature loads. J. Gansu Sci. 20(1), 116–118 (2008)

    Google Scholar 

  13. Cheng X.S., Du Y.F., Li H., Su J.X.: The analytical Solution about rectangular thin slab with two opposite edges clamped and two opposite edges simply supported under temperature load. Proc. Tenth Int. Symp. Struct. Eng. Young Expert 10, 213–217 (2008)

    Google Scholar 

  14. Cheng X.S., Su J.X., Shi X.Y.: The thermal bend of concrete rectangular thin plate with four sides supported. Spec. Struct. 26(4), 56–60 (2009)

    Google Scholar 

  15. Liu J.X., Guo X.h., Su J.C.: Water Supply and Drainage Engineering Structure, pp. 295–344. China Construction Industry Press, Beijing (2006)

    Google Scholar 

  16. Cheng X.S., Du X.L.: The thermal bend of concrete rectangular thin plate with three clamped sides and one free side. Eng. Mech. 30(4), 97–106 (2013)

    MathSciNet  Google Scholar 

  17. Cheng X.S., Du X.L., Zhang G.W. et al.: The thermal bend of concrete rectangular thin plate with three simply supported sides and one free side. Chin. J. Appl. Mech. 30(1), 37–42 (2013)

    Google Scholar 

  18. Fu B.L.: The Energy Principle and Its Application in Elastic Mechanics. Science Press, Beijing (2004)

    Google Scholar 

  19. Zhang F.F.: Elastic Thin Plate. Science Press, Beijing (1984)

    Google Scholar 

  20. Guo Z.H., Shi X.D.: Behaviour of Reinforced Concrete at Elevated Temperature and Its Calculation, pp. 106–108. Tsinghua University Press, Beijing (2003)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. School of Civil Engineering, Lanzhou University of Technology, Lanzhou, 730050, China

    Xuansheng Cheng, Jun Nie, Liang Zhao & Wei Shi

Authors
  1. Xuansheng Cheng
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Jun Nie
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Liang Zhao
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Wei Shi
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Xuansheng Cheng.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Cheng, X., Nie, J., Zhao, L. et al. The thermal bend of RTP with one edge clamped and two edges simply supported and one edge free. Arch Appl Mech 85, 287–302 (2015). https://doi.org/10.1007/s00419-014-0909-z

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00419-014-0909-z

Keywords

Search

Navigation