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Problem:

enter image description here

A beam is said to be in pure bending if the bending moment in it remains constant throughout the length.

The problem asks to determine the bending moment in the wire. In the solution of the problem, the textbook uses the formulas which were derived for a beam in pure bending. So I believe the wire is in pure bending, but I don't understand how it is in pure bending.

How the wire is in pure bending?

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  • $\begingroup$ are you asking what forces/moments are applied to it that lead to pure bending? $\endgroup$
    – NMech ♦
    Feb 2, 2022 at 12:53
  • $\begingroup$ Yes, somewhat, and also how when those forces are applied the wire experiences pure bending. Before that , I'm not even able to visualize how bending moment will be developed in the wire, pure bending is an argument to ponder upon after that $\endgroup$
    – Harshit Rajput
    Feb 2, 2022 at 13:47

2 Answers 2

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The bending moment is there because the wire "bends" around the cylindrical drum. If there is bending of the wire there has to be a bending moment.

Regarding the pure bending moment first of all its an approximation (it is not accurate but its pretty good if you assume a very small d and neglect frictional forces).

The reason you can t happens because of the support conditions. e.g. if the applied force is the F like in the image below

enter image description here

then there is a bending and a shear force up to the point that the wire contacts the drum. Beyond that point the wire is resting on the cylinder (pretty much like a beam on elastic foundations). Therefore any shear forces are counteracted by the drum and therefore the wire is in pure bending.

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  • $\begingroup$ Ohh now I get it, I don't know for what reason I was always thinking about the wire being stretched by applying forces along it's axis. Now it makes sense. The transverse forces being cancelled out by reaction from the roller, yess it all makes sense, thank you. $\endgroup$
    – Harshit Rajput
    Feb 2, 2022 at 14:17
  • $\begingroup$ Is the shear force zero at every c/s of the wire, where it is in contact with the drum? I tried drawing the FBD of the part of the wire in contact with drum, and it says otherwise $\endgroup$
    – Harshit Rajput
    Feb 17, 2022 at 11:54
  • $\begingroup$ That really depends on the friction. If friction is present then the shear force will gradually diminish. $\endgroup$
    – NMech ♦
    Feb 17, 2022 at 11:55
  • $\begingroup$ and if the Friction is not present, then the SF will be zero at every section? $\endgroup$
    – Harshit Rajput
    Feb 17, 2022 at 12:01
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    $\begingroup$ So, as you said in the answer, this is an approximation of pure bending. Just like we can use the flexure formula which was derived for pure bending of beams, even for beams in non uniform bending, with reasonable accuracy. $\endgroup$
    – Harshit Rajput
    Feb 17, 2022 at 12:13
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A couple of easy ways of producing pure bending are:

  • Applying equal opposing moments at the two ends of the beam, and applying two equal concentrated loads symmetrically spaced.

Assuming one of the supports on the digrams is a roller.

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pur bending 1

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pure bending

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