Skip to main content
SpringerLink
Log in

Evaluation of stresses in a circular ring by the relaxation method

  • Published:
Applied Scientific Research, Section A Aims and scope Submit manuscript

Summary

The relaxation method is used to find the sum of the principal stresses at any point in a circular ring. Used in combination with the stress pattern it yields the stresses at that point.

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

Abbreviations

σ1,σ2:

Principal stresses

σ x ,σ y :

Direct stresses in the horizontal and vertical

R 1 :

Inner radius of the circular ring

R 2 :

Outer radius of the circular ring

ϕ:

Harmonic function

K :

Constant of proportionality

a, b, c, … x, y, z, a, β:

Uneven joints of the relaxation network

f :

Fringe order

τ:

Shearing stress

C :

Photoelastic constant

d :

Thickness of specimen

μ:

Poisson’s ratio

References

  1. Timoshenko, S., Bull. Polytechn. Inst. Kiew, 1910.

  2. Filon, L. X. G., Selected Engineering Papers of the Institution of Civil Engineers, 1924.

  3. Frocht, M. M., Photoelasticity, Vol. I, John Wiley and Sons, New York, 1941.

    Google Scholar 

  4. Coker, E.G. and L. N. G. Filon, A Treatise on Photoelasticity, Cambridge, 1931.

  5. Southwell, R. V., Relaxation Methods in Theoretical Physics, Oxford, 1946.

  6. Frocht, M. M., Photoelasticity, Vol. II, John Wiley and Sons, New York, 1943.

    Google Scholar 

  7. Lee, G. H., Experimental Stress Analysis, John Wiley and Sons, New York, 1950.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Laboratorium voor Aero- en Hydrodynamica der Technische Hogeschool te Delft, Netherlands

    Y. V. G. Acharya

  2. Indian Institute of Science, Bangalore, India

    L. S. Srinath & C. N. Lakshminarayana

Authors
  1. Y. V. G. Acharya
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. L. S. Srinath
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. C. N. Lakshminarayana
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

The solution of the stresses around the point of singularity that is under the load is reserved for a future investigation.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Acharya, Y.V.G., Srinath, L.S. & Lakshminarayana, C.N. Evaluation of stresses in a circular ring by the relaxation method. Appl. sci. Res. 3, 415–428 (1953). https://doi.org/10.1007/BF03184722

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF03184722

Keywords

Search

Navigation