Understanding Turnbuckle Rotation: Solving for Shortening in a Multi-Rod System

[chetzread]

Homework Statement

in this problem , it's not clear that whether the shortening of 1.5mm is for which rod , there are 3 rods in the diagram and forces applied at which part to cause the rotation ... ...

Homework Equations

The Attempt at a Solution

Can somenoe explain about it ? if the forces is applied at rod Ef , then rod EF will shorten , and both rod AB and rod CD will either undergo shortening and lengthening , right ? [/B]

 

[CWatters]

in this problem , it's not clear that whether the shortening of 1.5mm is for which rod

The problem statement says..

Determine the forces in the rods if a turnbuckle on rod EF undergoes one full turn

So it's clear that rod EF is the one being shortened. This will change the tension in the other two rods.

 

[chetzread]

The problem statement says..
So it's clear that rod EF is the one being shortened. This will change the tension in the other two rods.

Is it a must that when the rod EF is shorten, then the rod AB and CD will extend?? I am confused...

 

[CWatters]

Yes. If you shorten EF then AB and CD must get longer/extend. The total length (vertical component of BF) remains constant.

 

[chetzread]

Yes. If you shorten EF then AB and CD must get longer/extend. The total length (vertical component of BF) remains constant.

The 0.0015 is the total length? I m confused ...

 

[CWatters]

Perhaps forget I mentioned the total length. You can't work it out because the rods "overlap".

I'm struggling to read the worked answer in the image. Can you post an enlargement?

 

[chetzread]

Perhaps forget I mentioned the total length. You can't work it out because the rods "overlap".

I'm struggling to read the worked answer in the image. Can you post an enlargement?

 

[CWatters]

OK the way to visualise this is to imagine that the rods have been assembled with no tension to set the initial length. Then they are disconnected and the lower rod is shortened by 1.5mm (0.0015m). Then the rods are reconnected. That requires the combination of rods to be stretched 1.5mm.

There are two rods at the top and one at the bottom so the 1.5mm is divided unequally between the top rods and the bottom rod. That's why they have an equation/sum that adds up to 0.0015m.

They also have another equation that relates the tension in the top two rods to the bottom rod. That's arrived at by noting that the system is in static equilibrium so the net force on beam is zero.

Now they have two equations and two unknowns.