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Research Papers

Estimation of Collapse Load for Thin-Walled Rectangular Tubes Under Bending

[+] Author and Article Information
D. H. Chen

Faculty of Civil Engineering and Mechanics,
Jiangsu University,
Zhenjiang 212013, China

K. Masuda

Faculty of Engineering,
University of Toyama,
Toyama 9308555, Japan
e-mail: masuda@eng.u-toyama.ac.jp

1Corresponding author.

Manuscript received October 11, 2015; final manuscript received December 1, 2015; published online December 21, 2015. Assoc. Editor: Nick Aravas.

J. Appl. Mech 83(3), 031012 (Dec 21, 2015) (8 pages) Paper No: JAM-15-1550; doi: 10.1115/1.4032159 History: Received October 11, 2015; Revised December 01, 2015

In two recent papers, the authors investigated the bending collapse load of rectangular tubes consisting of a perfectly elastoplastic material. From these investigations, it is found that the collapse may also occur due to the buckling of web in a rectangular tube under bending, when the tube has a cross section with a large aspect ratio of web to flange b/a. In order to evaluate the collapse load of such tubes under bending, the effective width concept given by Rusch and Lindner for a plate compressed with stress gradient was used to calculate the postbuckling strength of the tube web. However, in the solution of Rusch and Lindner, the plate is supported at only one longitudinal edge with the other longitudinal edge being free. This boundary condition is obviously different from that of the tube web. This paper complements the previous work by addressing the postbuckling strength of the web under stress gradients. The postbuckling strength of the web under stress gradients is also calculated using the effective width concept given in AS/NZS 4600 standard and North American specification (NAS) for a plate compressed with stress gradient and supported at both two longitudinal edges. Moreover, the web slenderness also affects the condition for reaching cross-sectional fully plastic yielding when the web is wider. A new method is proposed to predict the maximum moment considering the effect of web slenderness on the cross-sectional fully plastic yielding. The validity of the collapse load estimation is checked by the results of FEM (finite element method) numerical analysis.

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References

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Figures

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Fig. 1

Rectangular tube to which a pure bending moment is applied

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Fig. 2

Schematic representation of axial stress distribution used in Kecman's method: (a) Case 1: σbuc–a < σs; (b) Case 2: σs ≤ σbuc–a < 2σs; and (c) Case 3: σbuc–a 2σs

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Fig. 3

Comparison of Kecman's method and the FEM analysis

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Fig. 4

Axial stress distribution on cross section at the maximum moment: (a) t = 0.4 mm, a = 50 mm, b = 100 mm; (b) t = 0.5 mm, a = 20 mm, b = 100 mm; and (c) t = 1.2 mm, a = 50 mm, b = 150 mm

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Fig. 5

Schematic representation of axial stress distribution with considering the buckling at web when the maximum moment occurs: (a) Case 4: σbuc–a < σs and (b) Case 5: σbuc–a > σs

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Fig. 6

Plate subjected to compression and bending: (a) analyzed model and (b) axial compressive stress σx distribution on E–E cross section in (a)

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Fig. 7

Stress distribution of web when the ultimate load is reached for the tube used in Fig. 4(a): (a) comparison with Eq. (9) and (b) comparison with Eq. (18)

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Fig. 8

Stress distribution of web when the ultimate load is reached for the tube used in Fig. 4(b): (a) comparison with Eq. (9) and (b) comparison with Eq. (18)

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Fig. 9

Various possible buckling stress σbuc–b and stress ratios ψ with Eq. (17) satisfied

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Fig. 10

Flow chart of a new method proposed in the present study for predicting the maximum moment of tubes under pure bending

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Fig. 11

Prediction of the maximum bending moment Mmax for rectangular tubes with b/a = 1

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Fig. 12

Prediction of the maximum bending moment Mmax for rectangular tubes with b/a = 2

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Fig. 13

Prediction of the maximum bending moment Mmax for rectangular tubes with b/a = 3

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