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Elastic Limit Analysis for Elliptical and Circular Tubes Under Lateral Tension

  • Research Article - Mechanical Engineering
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Abstract

The elastic limit analysis for elliptical and circular tubes under lateral force is conducted in the present paper, and elastic–perfect plastic material model is employed. An analytical expression for describing the elastic limit load of elliptical and circular tubes under lateral force is obtained. It shows that the critical load for elliptical and circular tubes under lateral force increases with the plastic yielding strength of the tube material, the ratio of the wall thickness to radius, the wall thickness and the length of the tube, as well as the degree of deviation from circular tube monotonously. The experimental results from available literature for both steel and aluminum tubes are cited to verify the proposed expression, and it shows that the expression reflects the loading capacity of elliptical and circular tubes quite well, which indicates the proposed expression is a reasonable formula.

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Abbreviations

mn :

Cross-sectional line at symmetric position of structure

P :

Tensile force

M 0 :

Bending moment on the cross section mn

U :

Strain energy of the one-quarter elliptical tube in loading

m 1 n 1 :

A cross-sectional line at general position of structure

\({\phi}\) :

Directional angle of a cross section m 1 n 1 with respect to the cross section mn

M :

Bending moment on the cross section m 1 n 1

b :

The semi-length of the shorter axis of the elliptical tube

a :

The semi-length of the longer axis of the elliptical tube

E :

Elasticity modulus of the tube material

I z :

Moment of inertia

ds :

Increment on the elliptical arc

R :

Radius of the corresponding circular tube

\({\zeta}\) :

Degree of deviation from circular tube

M e :

Plastic bending moment of a sheet

t :

Wall thickness of tube

l :

Length of tube or width of tube sheet

\({\sigma_{\rm s}}\) :

Plastic yielding strength of the tube material with elastic–perfect plastic property

P e :

Critical value of tensile force P

P Ce :

Critical load for a circular tube under lateral tension

\({t\cdot l}\) :

Cross-sectional area of the tube sheet

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Authors and Affiliations

  1. Institute for Energy Transmission Technology and Application, School of Chemical Engineering, Northwest University, Xi’an, 710069, China

    M. Zheng, Y. Zhao, H. Teng, J. Hu & L. Yu

Authors
  1. M. Zheng
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  2. Y. Zhao
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  3. H. Teng
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  4. J. Hu
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  5. L. Yu
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Correspondence to M. Zheng.

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Zheng, M., Zhao, Y., Teng, H. et al. Elastic Limit Analysis for Elliptical and Circular Tubes Under Lateral Tension. Arab J Sci Eng 40, 1727–1732 (2015). https://doi.org/10.1007/s13369-015-1655-4

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  • DOI: https://doi.org/10.1007/s13369-015-1655-4

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