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# Bracing structures - stability

## Bracing structures - stability

(OP)
How do you go about calculating the horizontal deflection in a braced structure by hand? Sorry if this seems a really dense question - I've never had to calculate it by hand before but I can't get a FEM model to work properly and I'm confused.

I have attached a picture of the problem -> http://imageshack.us/photo/my-images/718/horizforcebracedstructu.png/ The blue dots indicate moment releases - suppose the frame is stabilised 'into the page' by already given means. If anyone can work it out using guidelines in BS5950 then that'd be even better, though I know a lot of you chaps are American.

The British Codes give lots of advice as to what limits to work to but when actually calculating the deflection using elastic analysis there's no help and I can't find any reference material which will help me either! Grr.

Regards,

A very stupid feeling NJonesUK.

### RE: Bracing structures - stability

(OP)
The brace is the diagonal member at the end.

But yeah, that is exactly the kind of info that I'm looking for. Where did it come from?!! Why isn't it printed in every structural steel document ever?!!

### RE: Bracing structures - stability

Yea, I am having a hard time seeing how that brace really works. Why doenst FEM work right?

### RE: Bracing structures - stability

I thought that was the deflected shape of the system.

I don't think that brace is going to work.  That is probably why you are having problems with the computer model.  I think you will need a column on the far left side to get the system to work, otherwise you need to make a frame out of it (fix the connections).

### RE: Bracing structures - stability

That diagonal isn't a brace in my view.

### RE: Bracing structures - stability

too many hinges - mechanism - collapse.

### RE: Bracing structures - stability

You can also use virtual work to find the deflections. delta = SUMM(nnL/(AE)) where n is the force in a member with a unit load applied for the shear. Once you get the hang of it, it only takes a couple of minutes. Look in any structural analysis book for the skinny.

### RE: Bracing structures - stability

Ir's not a braced frame, it is a rigid frame, it relies on the bending of the beam to resist horizontal movement. The diagonal and the column act together to make a weird fixed end, the diagonal and the column providing the force couple that is a moment in the beam.

Michael.
Timing has a lot to do with the outcome of a rain dance.

### RE: Bracing structures - stability

(OP)
Perhaps my terminology was off, but yeah, you use the bending in the beam to stabilise the structure and the diagonal member takes the compression that comes as a result of any horizontal loading. Tension in the vertical member, therefore - as you said you get a 'weird moment' in the top member.

### RE: Bracing structures - stability

I grabbed a copy of the braced frame deflection calcs SteelPE had uploaded. I was going to put it in my work folder for future use as it would be handy.

Just to be sure all was okay, I tried to prove the K-brace formula. However, I am getting a factor of 4 difference in the last term.

I uploaded the proof and if anyone has a minute, can you see an error in my proof?

thanks all

### RE: Bracing structures - stability

fancy-
If you apply P=1/2 to each end of member 3 and break member 3 into two members with length L/2. The force (n) in each member is 1/2, (n) squared is 1/4, multiplied by L/2 = L/8, sum both members = L/4, which corresponds to the second part of the equation. I'm not sure if that is the correct way to do it, but it matches the equation.

### RE: Bracing structures - stability

nac,

Yup, that looks correct and works out well. Funny thing, when you think about it, if P is applied to on side only, then all of P end up in the braces and nothing on the last half of the beam.

thanks again

### RE: Bracing structures - stability

You can solve this easily by hand using statics. The applied force "P" is horizontal so it can only be resisted by the horizontal component of the brace. Using the geometry of the brace, you can find the tension force in the brace. The vertical component of the brace force must be equal and opposite to the force in the adjacent column. This gives you a couple moment in the beam at the end.

### RE: Bracing structures - stability

Nix the last part about the force being equal and opposite in the adjacent column. I forgot about the right side post contribution. But you should still be able to get at the answer with statics. Good luck.

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