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Inelastic column buckling of internally pressurized tubes

Experimentally determined buckling loads of internally pressurized, axially compressed tubes substantiate the predictions of the incrementaly theory of plasticity and cast further doubt on the use of the deformation theory

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Abstract

The incremental theory and the deformation theory of plasticity are used to analyze column buckling of internally pressurized tubes subjected to axial thrust, and the results are compared to the buckling loads determined in tests of annealed-aluminum tubes. By using stress-strain curves obtained from tensile tests of tubing samples, reliable predictions are obtained with the incremental theory. However, the results of the deformation theory are so conservative as to cast doubt on the usefulness of this theory for buckling analyses.

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Abbreviations

E :

modulus of elasticity

f :

plastic portion of strain in tensile test

I :

centroidal moment of inertia of cross section of tube

l :

length of flexible section of buckling specimen

l o :

length of rigid section of buckling specimen

P :

internal pressure

r :

radial coordinate inr, θ,z coordinates, or radius of end of specimen

R :

radius of cup

r i :

internal radius of tube

r o :

external radius of tube

T :

axial thrust

u :

displacement of column from straight line

z :

axial coordinate inr, θ,z coordinates

δ:

increment of following variable, or measured deflection

ε:

strain. Components are\(\varepsilon _\Upsilon ,\varepsilon _\theta ,\varepsilon _z \)

\(\varepsilon _\alpha \) :

strain at neutral axis in Shanley analysis of column buckling

\(\varepsilon ^P \) :

plastic portion of strain

θ:

tangential coordinate inr, θ,z coordinates

σ:

stress. Components are\(\sigma _\Upsilon ,\sigma _\theta ,\sigma _z \)

\(\sigma _\alpha \) :

stress at neutral axis in Shanley analysis of column buckling

\(\sigma _b \) :

bending stress in Shanley analysis of column buckling

\(\sigma _g \) :

generalized stress

References

  1. Shanley, F. R., “Inelastic Column Theory,”J. of the Aeron. Sci.,14,261–268 (1947).

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  2. Naghdi, P. M., “Stress-Strain Relations in Plasticity and Thermoplasticity,”Plasticity, Proc. 2nd Symp. on Naval Structural Mech., Ed. by E. H. Lee andP. S. Symonds, Pergamon Press, New York, 121–169 (1960).

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  3. Ilyushin, A. A., “The Elasto-Plastic Stability of Plates,” N.A.C.A. TM Number 1188 (Dec. 1947).

  4. Hill, R., The Mathematical Theory of Plasticity, Clarendon Press, Oxford, England (1956).

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  5. Alcoa Aluminum Handbook, Aluminum Company of America, Pittsburgh, PA (1967).

  6. Timoshenko, S. P. andGere, J. M., Theory of Elastic Stability, McGraw-Hill Book Company, New York (1961).

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Authors and Affiliations

  1. Bettis Atomic Power Laboratory, Westinghouse Electric Corporation, 15122, West Mifflin, PA

    John B. Newman (Senior Engineer)

Authors
  1. John B. Newman
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Newman, J.B. Inelastic column buckling of internally pressurized tubes. Experimental Mechanics 13, 265–272 (1973). https://doi.org/10.1007/BF02322722

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  • DOI: https://doi.org/10.1007/BF02322722

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