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Stress analysis of thick-walled tube with step change in thermal expansion

Authors compare the finite-element method of solution for the problem with the results obtained by photoelastic experiment

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Abstract

The finite-element method of stress analysis is used to evaluate highly localized stress distributions in a thick-walled tube with a step change in temperature. Effect of gird size on stress calculated in the neighborhood of the temperature discontinuity is examined. A photoelastic analysis of the differential-thermal-expansion problem is also described. Comparison of the experimental and the calculated stress distributions shows good agreement. An approximate analysis which provides insight into the manner in which the thermal stresses develop is also included.

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Abbreviations

a, b :

inner and outer radii of cylinder

D :

\(Eh^3 /12 (1 - \nu ^2 )\)

E :

Young's modulus

f :

material fringe value

G :

shear modulus

h :

wall thickness of cylinder

M z , M o :

bending moment

n, n′ :

fringe orders

p, q :

principal stresses

Q z , Q o :

radial shear force

r, θ,z :

cylindrical coordinates

r m :

mean radius

t :

slice thickness

T :

magnitude of temperature step

α:

coefficient of thermal expansion

β4 :

Eh/4r m2 D

ν:

Poisson's ratio

ϕ:

principal-stress angle (isoclinic parameter)

References

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  3. Slot, T., “Photoelastic Simulation of Thermal Stresses by Mechanical Prestraining,”Experimental Mechanics,5 (9),273–282 (1965).

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  4. Slot, T., “Differential Thermal Expansion in Butt-Joined Tubes,”Technical Information Service Report 63GL86, General Electric Company, Schenectady, N.Y. (May1963).

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  5. Frocht, M. M., Photoelasticity,1,John Wiley and Sons,New York, N.Y. (1941).

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  6. Timoshenko, S. andWoinowsky-Krieger, S., Theory of Plates and Shells, 2nd ed., McGraw-Hill, New York, N.Y., 466–471 (1959).

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  7. Horvay, G., “Thermal Stresses in Rectangular Strips,” Proc. Sec. U.S. Natl. Cong. of Appl. Mech., 313–322 (June 1954).

  8. Slot, T., “Theoretical and Experimental Analysis of a Thermal Stress Problem in Tube Sheet Design,” Proceedings First International Conference on Pressure Vessel Technology (ASME), Delft, The Netherlands, 379–399 (Sept. 29–Oct. 2, 1969).

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Authors and Affiliations

  1. Structures and Materials Laboratory, General Electric Co., Knolls Atomic Power Laboratory, 12301, Schenectady, N.Y.

    A. Merend (Manager, Applied Mechanics) & T. Slot (Manager)

Authors
  1. A. Merend
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  2. T. Slot
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Merend, A., Slot, T. Stress analysis of thick-walled tube with step change in thermal expansion. Experimental Mechanics 12, 136–141 (1972). https://doi.org/10.1007/BF02328562

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  • DOI: https://doi.org/10.1007/BF02328562

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