Summary
The stresses in a circular ring are found by an elementary theory and compared with the values obtained for a particular one by the authors in previous experiments. There is good agreement, and it is concluded that for rings of like proportion the elementary theory can be safely used.
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Abbreviations
- R 1 :
-
Internal radius of ring
- R 2 :
-
External radius of ring
- R :
-
Mean radius of ring
- y :
-
Distance of any point from the neutral axis of the ring cross-section, along a radius
- b :
-
Width of ring
- t :
-
Thickness of ring
- e :
-
Eccentricity of neutral axis
- P :
-
Normal load
- r,θ:
-
Polar coordinates of any point on the ring
- r n :
-
Radial ordinate for the neutral axis
- M 1 :
-
Moment acting at the vertical section of the ring
- M :
-
Moment acting at any sectionθ
- N :
-
Normal Force acting at any sectionθ
- V :
-
Shear Force acting at any sectionθ
- dU :
-
Energy stored due to strain in an element dS =R dθ of the ring
- A :
-
bt. Area of cross-section of ring
- σ θ :
-
normal stress at any section θ
- \(\sigma _{\theta _1 } \) :
-
Component bending stress at any section θ
- \(\sigma _{\theta _2 } \) :
-
Component direct stress at any section θ
References
Acharya, Y. V. G., L. S. Srinath and C. N. Lakshminarayana; Appl. sci. Res.A 3 (1953) 415.
Timoshenko, S., Strength of Materials, Vol. 2, McGraw Hill, N.Y., 1949.
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Srinath, L.S., Acharya, Y.V.G. Stresses in a circular ring. Appl. sci. Res. 4, 189–194 (1954). https://doi.org/10.1007/BF03184950
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DOI: https://doi.org/10.1007/BF03184950