Short links? Weightless links?

[Stephen Bulking]

TL;DR Summary

In static force analysis for system in equilibrium, are short links and weightless links one and the same?

Hi! I am an engineering student. I have just started reading this book ENGINEERING MECHANICS by PEARSON and got a little confused between short links and weightless links. Please see the examples below and help me explain:
1) Are short links and weightless links the same but with different names? If they are not, how are they different?
2) Example 5.2 has an ordinary straight SHORT link with support reaction force acting along its axis. Example 5.13 has a two-force member link BD but it's still a SHORT link, how is the reaction force not directed along its axis? Is it because it's shaped differently? I know that since it's a two-force member the forces on link BD have to have the same line of action that is BD itself BUT does this override the reaction force that is supposed to act along the axis of the short/weightless link?

 

[Lnewqban]

I am not aware of any convention about short link or weightless link.
Any solid link that is pivoted at both ends should be able to transfer two types of forces: tension and compression.

Tension never has problems of stability or buckling, reason for which cables and ropes can be used for that application.

Compression can induce buckling of the link, especially if it is slender and/or heavy and horizontal: perhaps that is the reason behind those two adjectives for the links presented in the problems.

 

[Dr.D]

I think the idea is simply this:
1) a short link is not very long in the scale of other lengths in the problem
2) a massless link does not involve a gravity force on the link.

 

[Stephen Bulking]

I am not aware of any convention about short link or weightless link.
Any solid link that is pivoted at both ends should be able to transfer two types of forces: tension and compression.

Tension never has problems of stability or buckling, reason for which cables and ropes can be used for that application.

Compression can induce buckling of the link, especially if it is slender and/or heavy and horizontal: perhaps that is the reason behind those two adjectives for the links presented in the problems.

If I understand you correctly, you're saying these SOLID links are under compression. But that still doesn't answer the question as to why the reaction forces at the short link support act in different directions in the two problems, they should all be along the direction of the short/weightless link. The book says since link BD in example 5.13 is a TWO-FORCE MEMBER, the support reaction has to be in the 45 degree direction and NOT along the link, but this is contradictory with the previously introduced reaction support of the weightless link(see included figure, table 5.1)

 

[Stephen Bulking]

I think the idea is simply this:
1) a short link is not very long in the scale of other lengths in the problem
2) a massless link does not involve a gravity force on the link.

Yes, that is logical...so you're saying that these links are completely different and that their reaction support is also different? I guess that would make sense since technically, the book never introduced any link under the name "short link" while discussing reaction support(see included figure, table 5.1).

 

[Lnewqban]

If I understand you correctly, you're saying these SOLID links are under compression. But that still doesn't answer the question as to why the reaction forces at the short link support act in different directions in the two problems, they should all be along the direction of the short/weightless link. The book says since link BD in example 5.13 is a TWO-FORCE MEMBER, the support reaction has to be in the 45 degree direction and NOT along the link, but this is contradictory with the previously introduced reaction support of the weightless link(see included figure, table 5.1)

Not exactly.
Link BD of example 5.13, working solely under tension, could be a string or a rope, and could have any lenght.
The direction of the forces is not a function of the shape or length of the linkage member.

A real very heavy link introduces vertical additional forces due to its weight, which are transferred to the pivots.
If L-shape link BD weigths one ton, each of the pivots should "feel" about half a ton vertical force in addition to any force created by the mechanism.

Note that diagram b) of example 5.2 is incorrect regarding right end of linkage (compare to picture of machine).

 

[Dr.D]

the book never introduced any link under the name "short link" while discussing reaction support(see included figure, table 5.1).

The word "short" is simply an adjective modifying "link." This is the opposite of a "long link."

 

[Stephen Bulking]

Not exactly.
Link BD of example 5.13, working solely under tension, could be a string or a rope, and could have any lenght.
The direction of the forces is not a function of the shape or length of the linkage member.

A real very heavy link introduces vertical additional forces due to its weight, which are transferred to the pivots.
If L-shape link BD weigths one ton, each of the pivots should "feel" about half a ton vertical force in addition to any force created by the mechanism.

Note that diagram b) of example 5.2 is incorrect regarding right end of linkage (compare to picture of machine).
View attachment 277410

I think I got it, thanks to "The direction of the forces is not a function of the shape or length of the linkage member.", but please check if I really get it right...
I could replace the L shaped link BD with a straight rope or link that connects B and D, which would totally agree with table 5.1 for the case of weightless link/cable in terms of reaction support. Please tell me I got it right :)

 

[Lnewqban]

You do.
Don’t worry much about these concepts; with more experience, and as you study more complex mechanisms, it will be easier for you to properly evaluate forces at pivots and linkage members.

 

[Lnewqban]

As you can intuitively see in this picture, the boom of the crane works under compression, reason for which truss structure makes it more stable and more resistent to buckling under heavy load.
The wire-rope works under tension, and that type of load makes it self-stable.

Compared to the magnitude of the load, the weight of the wire-rope is not important and we could consider it to be a “weightless link”.
The boom is heavier, and it would impose its weight on the crane-boom pivot as an additional vertical force, besides the compression force that is natural to this mechanism.
None of those links are “short”.

 

[Dr.D]

The image posted in #10 has a classic error in the way that things are drawn at B.

Does the cable with tension T act over the pulley or at its center? Does the weight of the suspended load at on the rim of the pulley or at the pivot? Is that centerline on the boom actually a second cable supporting the suspended load? If that centerline is a cable, does it act at the pulley pivot, or over the top of the pulley?

Different versions of this same problem appear in many textbooks, and they are entirely misleading.

 

[Stephen Bulking]

You do.
Don’t worry much about these concepts; with more experience, and as you study more complex mechanisms, it will be easier for you to properly evaluate forces at pivots and linkage members.

Ok thanks a lot.

 

[Lnewqban]

Ok thanks a lot.

You are welcome

Improving image of post #10 with a real machine.
The four wire-ropes to the extreme right hold the boom and normally attach to the axis of the pulleys at top.
In this case, two additional wire-ropes, closer to the boom, go around those pulleys and end up in a hook each.
Note that each wire uses a different drum inside the housing, next to the engine.

 

[Stephen Bulking]

As you can intuitively see in this picture, the boom of the crane works under compression, reason for which truss structure makes it more stable and more resistent to buckling under heavy load.
The wire-rope works under tension, and that type of load makes it self-stable.

Compared to the magnitude of the load, the weight of the wire-rope is not important and we could consider it to be a “weightless link”.
The boom is heavier, and it would impose its weight on the crane-boom pivot as an additional vertical force, besides the compression force that is natural to this mechanism.
None of those links are “short”.

View attachment 277440

Wow man, this is a great example on the "weightless link/cable". Totally changed my way of thinking about the word "weightless link": it's weightless relative to the boom. And yeah none of these links are short, the "weightless link" is even longer than the heavy boom.