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Research Papers

# Analysis of the Carrying Capacity for Tubes Under Oblique Loading

[+] Author and Article Information
Wei Wang

Department of Engineering Mechanics,
Tsinghua University,
Beijing 100084, China

Xinming Qiu

Department of Engineering Mechanics,
Tsinghua University,
Beijing 100084, China
e-mail: qxm@tsinghua.edu.cn

1Corresponding author.

Contributed by the Applied Mechanics Division of ASME for publication in the JOURNAL OF APPLIED MECHANICS. Manuscript received December 5, 2017; final manuscript received January 7, 2018; published online January 24, 2018. Assoc. Editor: A. Amine Benzerga.

J. Appl. Mech 85(3), 031010 (Jan 24, 2018) (6 pages) Paper No: JAM-17-1665; doi: 10.1115/1.4038921 History: Received December 05, 2017; Revised January 07, 2018

## Abstract

In this study, the plastic deformation mechanism of a fully clamped beam under oblique loading at its free end is analyzed. Supposing the cross sections are variable along the beam length, a characteristic length $L∗≡MP/NP$, defined as the ratio between fully plastic bending moment $MP$ and fully compression force $NP$, is employed to estimate the load carrying capacity of each cross section. By finite element (FE) simulations of the conical tubes, it is validated that if the initial failure positon locates in the middle of the beam, it will not change with the total beam length. Then, based on the analytical analysis and FE simulation, a progressive deformation mechanism triggered by bending, notated as progressive bending, is proposed for the first time. From the optimization result of maximizing loading force that the unit mass can withstand, the tubes with constant thickness are found to be better than tubes with graded thickness, when they are used as supporting structures. The multi-objective optimization for tubes with varying cross sections under oblique loading with different angles is also given. Then, two methods to improve the load carrying capacity of tubes are given: (1) to design the cross section of the tube, which is corresponding to let the critical loading force of all the cross sections be equal; (2) to optimize the initial failure point, so as to produce repeated failure modes.

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## Figures

Fig. 1

Fig. 2

The relationship between the initial failure position and the tube length

Fig. 3

Fig. 4

Different failure modes of a tube under compression at different angles

Fig. 5

The critical loading force corresponding to each tube cross section (θ=5 deg, α=30 deg, y¯≡y/L)

Fig. 6

The multi-objective solutions for different α (L = 600 mm, R0=20 mm, t0=2 mm)

Fig. 7

(a) The cross section of a structure and (b) four typical cross sections with equal area

Fig. 8

The tube has uniform critical force of different cross sections (L=100 mm, α=30 deg, R0=10 mm, t0=1 mm)

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