Resultant vectors in cable and beams

[Femme_physics]

I know that when I have cable connected, the resultant vector of each cable will point at the direction of the angle it's connected in.

http://img26.imageshack.us/img26/8454/wiresn.jpg

BUT, suppose we switch all these cables to rigid body structures like beams. I cannot make the same assumption (to my understanding), is that correct?

HERE, for instance, I make the assumption that Tbc is pulling the direction of its angle. If these were beams, and not cables, I cannot make such an assumption can I?

http://img36.imageshack.us/img36/4784/wires2.jpg

 

[I like Serena]

Suppose Tbc is not pulling at its angle.

Can you set up an FBD for section BC?

 

[Femme_physics]

Wait, in which case? Beams or cables? Because in cable cases it must!

 

[I like Serena]

Wait, in which case? Beams or cables? Because in cable cases it must!

Does not matter.
Pick one.
Just look at the external forces that act on section BC, whether it be beam or cable.

What is the sum of the forces?
What is the sum of the moments?
They should both be zero.
What does that tell you?

 

[Femme_physics]

That it doesn't matter whether it's cable or beam?

 

[I like Serena]

Huh...

EDIT: Uh no, if Tbc is not along the cable or beam, it will always start moving or rotating.
Since the construction is supposedly static, Tbc has to be along the cable or beam.

 

[Femme_physics]

Yes, of course, but the point it the value of the forces stays the same regardless of the fact that in case it's cables and in the other it's beams?

 

[I like Serena]

Short answer: in this case there is no difference between cables and beams.

But there's really no need to make an assumption about what the direction is.
Draw an FBD of just one section and you can deduce what the direction is.

 

[Femme_physics]

I agree, that's the best way... :)

HOWEVER, I do think I am getting to conceptual understand WITHOUT calculations and I'd like to demonstrate it by words.

The beams will act the same as ropes because

1) All forces are acting in the pins
2) All forces are pointing downwards with gravity in the y direction (no X component)
When you have beams, with forces pointing down from

So there is nothing to differentiate beams from ropes in this case because all the beams are IN TENSION, in fact, like the ropes.

Aha, I got it!

Tell me I'm not brilliant huh? :D

 

[Studiot]

Tell me I'm not (huh?)brilliant huh?

OK

You are not brilliant.

Actually it is the fact that the joints (rings) act as hinges that make the beam solution the same as the cable one.

Joints at the end of beams can be (partly) rigid and transmit moments, in which case the beam solution would not be the same.

Cable joints cannot be rigid.

 

[Femme_physics]

OK

You are not brilliant.

Actually it is the fact that the joints (rings) act as hinges that make the beam solution the same as the cable one.

I figured that's "one of the reasons".

Joints at the end of beams can be (partly) rigid and transmit moments, in which case the beam solution would not be the same.

You're right. Cables don't transmit moments, that makes the big difference here. :)

I guess if I'd have calculated I might have seen it for myself, but I'd like to have reached there by words for a change,...if you'd excuse me for that. I appreciate your help :)

 

[Studiot]

Just a bit of terminology for you.

Structural members that do not carry moments or transverse loads. ie are only subject to axial forces and are only loaded at their ends are called

Compression - struts

Tensions - ties

Structural members that may carry transverse loads and may be loaded at any point are

Cables and chains tension only. No compression or moment.

Beams can carry tension, compression and moment.

 

[I like Serena]

I guess if I'd have calculated I might have seen it for myself, but I'd like to have reached there by words for a change,...if you'd excuse me for that.

No need to calculate, but it does help to draw a picture (an FBD of a section). ;)

 

[Femme_physics]

Thanks, you two :)