Research Papers

On an Elastic Rod Inside a Slender Tube Under End Twisting Moment

[+] Author and Article Information
Jen-San Chen1

Department of Mechanical Engineering, National Taiwan University, Taipei 10617, Taiwanjschen@ntu.edu.tw

Hong-Chi Li

Department of Mechanical Engineering, National Taiwan University, Taipei 10617, Taiwan


Corresponding author.

J. Appl. Mech 78(4), 041009 (Apr 13, 2011) (9 pages) doi:10.1115/1.4003708 History: Received June 17, 2010; Revised October 03, 2010; Posted February 23, 2011; Published April 13, 2011; Online April 13, 2011

In this paper, we study the deformation of a thin elastic rod constrained inside a cylindrical tube and under the action of an end twisting moment. The ends of the rod are clamped in the lateral direction. Unlike the previous works of others, in which only the fully developed line-contact spiral was considered, we present a complete analysis on the deformation when the dimensionless twisting moment Mx is increased from zero. It is found that the straight rod buckles into a spiral shape and touches the inner wall of the tube at the midpoint when Mx reaches 8.987. As Mx increases to 11.472, the contact point in the middle splits into two, leaving the midpoint floating in the air. As Mx increases to 13.022, the midpoint returns to touch the tube wall and the two-point-contact deformation evolves to a three-point-contact deformation. Starting from Mx=13.098, the point contact in the middle evolves to a line contact, and the deformation becomes a point-line-point contact configuration and remains so thereafter. In the case when the line-contact pattern is fully developed, it is possible to predict the spiral shape analytically. The numerical results are found to agree very well with those predicted analytically. Finally, an experimental setup is constructed to observe the deformation evolution of the constrained rod under end twist.

Copyright © 2011 by American Society of Mechanical Engineers
Your Session has timed out. Please sign back in to continue.



Grahic Jump Location
Figure 1

A clamped-clamped twisted rod constrained in a tube. Solid (B-C) and dashed (O-A and A-B) lines represent line contact and no contact with the tube wall, respectively. C is the middle point of the constrained rod.

Grahic Jump Location
Figure 2

l1 and l2 for the line-contact deformation when Mx is reduced from 35. It is observed that l2 approaches 0.5 when Mx approaches 13.098.

Grahic Jump Location
Figure 3

(a) The radial distance ρ=y2+z2 and (b) angle ϕ as functions of x when Mx=35

Grahic Jump Location
Figure 4

The relation between ϕ,x(0.5) and Mx. Energy method predicts that this relation is very close to a straight line Mx=43ϕ,x.

Grahic Jump Location
Figure 5

Distribution of the line-contact force q(x) when Mx=35

Grahic Jump Location
Figure 6

The relation between q(0.5) and Mx. Energy method predicts that this relation is close to q=(27/256)Mx4.

Grahic Jump Location
Figure 7

The point force RA when Mx changes from 8.987 to 20 in one-point (dotted), two-point (dashed), three-point (chained line in the inset), and line-contact (solid) deformations

Grahic Jump Location
Figure 8

The point force RB when Mx changes from 13.022 to 20 in three-point (dashed), and line-contact (solid) deformations. The range near Mx=13.098 is magnified and shown in the inset.

Grahic Jump Location
Figure 9

Three-dimensional and end views of the four deformation patterns when Mx is equal to (a) 9 (one-point contact), (b) 12 (two-point contact), (c) 13.05 (three-point contact), and (d) 35 (line contact)

Grahic Jump Location
Figure 10

Bending moment distributions for various end twisting moments

Grahic Jump Location
Figure 11

Shear force distributions for various end twisting moments

Grahic Jump Location
Figure 12

Photograph of experimental set-up

Grahic Jump Location
Figure 13

Relation between end displacement e and twisting moment Mx

Grahic Jump Location
Figure 14

Relation between the location of the first contact point l1 and twisting moment Mx

Grahic Jump Location
Figure 15

Relation between helix angle β and twisting moment Mx after line-contact deformation appears




Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In