# Need to know about chains?

Hello guys,

My question is about how chains and their links work. We know to old saying that a chain is only as strong as its weakest link. Regarding links, assume a 1000lb. weight is suspended by one oval shaped steel link. Each of the ends of the oval link, with one end to the hook and the other end to the weight, are holding in tension 500lbs, 1000lbs or another amount of weight?

Thinking about it another way, for the same 1000lb weight, if now suspended by a chain of 10 links of the same types of links, is the 100lbs evenly distributed to the 10 links where each link is holding 100lbs plus the weight of the additional links below it? If so, then the more links there are in the chain, the more weight (tension force) the chain can hold. Correct or does it not work out that way?

Please clarify. Thanks,

Bretina

## Discussions

I was thinking about what you said about carbon fiber. I've seen it but haven't played with it yet. Is it like fiberglass fibers in that the fibers can be very long ( for use as a cable)? If so are they flexible or brittle? And is using it dependent on surrounding it in a resin? How much tension force could say, a 1 or 2mm OD cable of it hold? What about the price as compared to steel?

Would graphene be another option to consider as a cable?

BTW: Is it possible the set the site to alert me by email when I get a reply to a post? If so how is that set - I don't see the option?

Thanks so much! Those are great answers and now I understand how a chain works. I may want to go with a cable now but in the end, whichever is used, the entire length of the part in tension takes the 100lbs, even if it's sectioned of as with links, once they are all connected, it's the same thing, right?

So, in the case of a suspending a 1000lb kettle ball with two handles, if chain inks were connected evenly to each handle and suspended by separate hooks, then each chain would be holding 500lbs. But if both chains, each connected to one handle but are entwined together, and hung by one hook then just the hook link takes the 1000lbs and all the other links are individually 500 lbs. Right?

You are correct and on your way to become a mechanical stress engineer.

Have you heard about the

Space Elevator?The elevator works like a tether_ball with a straw for an elevator.

The ball is a synchronous orbiting space station dangling a chain of carbon fiber

down to sea level. Carbon fiber is used because a steel chain or cable of the

satellite height length would break right away because of its own length

would get too heavy and tear the metal apart !!!

Carbon fiber is a flexible, much lighter material, and far stronger then any metal chain.

For chains under tension, the tension is roughly constant throughout the chain.

That is to say if you look at any link in the chain, there is a pair of forces

Tand -Tpulling on that link in opposite directions.Supposing you have a chain with ten links, with its bottom link (link 1) attached to a 1000 lb weight, and its top link (link 10) connected to a sturdy hook on the ceiling. Also suppose these links are made out of mithril, or some other magical material, so the links themselves are weightless, but still very strong.

The chain is tensioned in the vertical direction, since the hook on the ceiling is pulling it up, and the weight on the bottom link is pulling it down. Looking at the force balance for each link:

Link 1 feels a 1000 lb downward force from the 1000 lb weight, and a 1000 lb upward force from link 2.

Link 2 feels a 1000 lb downward force from link 1, and a 1000 lb upward force from link 3.

Link 3 feels a 1000 lb downward force from link 2, and a 1000 lb upward force from link 4.

Link 4 feels a 1000 lb downward force from link 3, and a 1000 lb upward force from link 5.

Link 5 feels a 1000 lb downward force from link 4, and a 1000 lb upward force from link 6.

Link 6 feels a 1000 lb downward force from link 5, and a 1000 lb upward force from link 7.

Link 7 feels a 1000 lb downward force from link 6, and a 1000 lb upward force from link 8.

Link 8 feels a 1000 lb downward force from link 7, and a 1000 lb upward force from link 9.

Link 9 feels a 1000 lb downward force from link 8, and a 1000 lb upward force from link 10.

Link 10 feels a 1000 lb downward force from link 9, and a 1000 lb upward force from the hook on the ceiling.

The situation is only slightly different for using a heavy steel chain, whose links happen to weigh exactly 1 lb each. In that case:

Link 1 feels a 1000 lb downward force from the 1000 lb weight, 1 lb downward due to its own weight, and a 1001 lb upward force from link 2.

Link 2 feels a 1001 lb downward force from link 1, 1 lb downward due to its own weight, and a 1002 lb upward force from link 3.

Link 3 feels a 1002 lb downward force from link 2, 1 lb downward due to its own weight, and a 1003 lb upward force from link 4.

Link 4 feels a 1003 lb downward force from link 3, 1 lb downward due to its own weight, and a 1004 lb upward force from link 5.

Link 5 feels a 1004 lb downward force from link 4, 1 lb downward due to its own weight, and a 1005 lb upward force from link 6.

Link 6 feels a 1005 lb downward force from link 5, 1 lb downward due to its own weight, and a 1006 lb upward force from link 7.

Link 7 feels a 1006 lb downward force from link 6, 1 lb downward due to its own weight, and a 1007 lb upward force from link 8.

Link 8 feels a 1007 lb downward force from link 7, 1 lb downward due to its own weight, and a 1008 lb upward force from link 9.

Link 9 feels a 1008 lb downward force from link 8, 1 lb downward due to its own weight, and a 1009 lb upward force from link 10.

Link 10 feels a 1009 lb downward force from link 9, 1 lb downward due to its own weight, and a 1010 lb upward force from the hook on the ceiling.

For the case in which the chain has weight, the links closer to ceiling are under slightly more tension, since they must support the big 1000 lb weight and the weight of the chain in links below them.

Like Steve said each link carries the entire load. It might be easier to visualize it if you think of a chain that has only one link. That link's limit determines how large a load it can support. If now you add a second identical link, at which time it actually becomes a chain, that link must support the load of the first and the weight on the first now includes the load and the weight and of the second link as well. Keep adding links and the same is true for each link that comes after it. If there is one link that is inferior in some way and it cannot support the load then the chain fails. Each link stands or fails on its own, each is independent of the others. Now if you keep adding links and the chain becomes very long then the weight on the first link becomes much greater since it has to bear the weight off all the other links and the load as well. If all the links are equal in their support ability it will be the first link that fails when the load becomes to great because it is the one that supports all the rest. This failing of a chain is the reason that they have limited use. A cable however does distribute the load between each strand. With a cable each strand runs the entire length and as such each one can carry its full load. Put together they add all their capacities together PLUS gain additional strength due to the structure of the cable itself. If one strand of a cable fails the rest can continue to provide support unless the load is to great for it overall. That is why suspension bridges are supported with cables and not chains. (Generally, but not absolute) If you are talking about a chain hanging then what happens is the opposite of what you were thinking, its capacity becomes less the longer it becomes because it has to support itself in addition to any load.

The whole chain is holding 1000 lbs, if we assume the weight of the chain is negligible.

In answer to your question, No, EACH link is carrying 1000lbs, not splitting the load between them.

Only MULTIPLE chains, in parallel would share load.