Why is BC a Two-Force Member but not AE?

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Discussion Overview

The discussion centers around the classification of structural members in a mechanical system, specifically why member BC is considered a two-force member while member AE is not. Participants explore the implications of pin connections and the effects of applied loads on the members, addressing concepts related to forces, moments, and structural behavior.

Discussion Character

  • Debate/contested
  • Technical explanation
  • Mathematical reasoning

Main Points Raised

  • One participant questions the assertion that AE is not a two-force member, prompting further examination of the definitions involved.
  • Another participant explains that for a member to be classified as a two-force member, the forces must be colinear and along the axis of the link, suggesting that member ADE experiences shear and bending, which disqualifies it as a two-force member.
  • It is noted that since member BC has no applied load at point C and is only connected by pins at B and D, it cannot experience bending or shear, thus qualifying it as a two-force member.
  • One participant expresses confusion about the absence of a reaction force in the Y direction at D, arguing that the negative Y component of the force at E should create a reaction and moment on member BC.
  • Another participant counters that the negative component of the force at E does not necessarily need to be reacted at D and could be addressed at A, emphasizing that without a vertical force at D, no moment can exist about B for link CDB.

Areas of Agreement / Disagreement

Participants express differing views on the classification of member AE and the implications of forces and moments on the members. There is no consensus on the reasoning behind the two-force member classification, and the discussion remains unresolved.

Contextual Notes

Participants reference specific assumptions about pin connections and the nature of forces acting on the members, but these assumptions are not universally accepted or clarified, leading to ongoing debate.

Feodalherren
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Homework Statement


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Homework Equations

The Attempt at a Solution


Was trying to solve for the horizontal reaction at B. Why is BC a two-force member but not AE?
 
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Who says AE is not a two-force member?
 
Well, nobody but the solution says: CB is a two force member so the reaction at B only in the horizontal direction. Then the sum of the moments about A bla bla bla.
How can they know that there is no reaction in the Y-direction and why isn't the same true for A?
 
For a two force member, the forces are necessarily colinear and along the axis of the link. The link ADE supports shear and bending as well as the axial load, which is why it is not a two force member.
 
I think that's why you have to work out the reactions. Remember, the two bars appear to be pin-connected at D, so what kind of forces and moments can be applied here?
 
SteamKing: I agree that the members are pinned at D (that is the way I read the figure), and, by definition, a pin only transmits forces, no moments. Without working through the details, if we think about moments wrt A, it is evident that the load at E puts bending in the member ADE.

On the other hand, since there is no applied load at C, and there are only pins at B and D, there cannot be any bending in the member BDC. No bending implies no shear, and BDC must be a two force member.
 
I don't get that at all. It doesn't seem to make any intuitive sense to me. The force has a negative Y component so there should be a reaction force in the Y direction at D. That should create some moment on beam BC and also some reaction in it... I don't see the two force member.
 
@ Feodalherren: You have noted the negative component of the force applied at E and the fact that it must be reacted somewhere. But there is no reason it has to be reacted at D; it can be equally well reacted at A. If there were a vertical force component at D, then there would be a moment about B on the link CDB. There is nothing to react such a moment, so that moment cannot exist.
 

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