Solving for reactional forces in a Tower 1

[Gouthamm]

I have Tower Assembly, it has four columns and cross Bracings. As the columns of the Tower are fixed at the bottom, I was wondering if the assembly can be considered as a Statically indeterminate structure. If so, being a Mechanical Engineer I am clueless about how to solve for the reactions forces and moments at the bottom and resolving the force.
can someone please suggest how to solve this ?
Please find the attachment

http://files.engineering.com/getfil...-c232-46b2-8d37-c76c0979625e&file=Capture.PNG

 

[Once20036]

The braces will be much more rigid than the moment connections, and I would consider the moment to be zero.

 

[jayrod12]

Agree with Once, If it's a braced structure, ignore the fixed-base. Treat it as pinned-base and it's much easier to analyze. The bonus of that, generally the anchorage and foundations are easier for pinned-base frames compared to fixed-base frames.

 

[SteelPE]

Also, if your frame and members are all symmetrical then you can but some simplifying assumptions (each brace would receive 1/2 of the lateral load etc). This doesn't help you with your specific problem, but makes it east to look at the other members in the frame.

 

[Gouthamm]

@jayrod12 , thank you for the suggestion. considering it as a pin joint still leaves me with four unknown reactions. Which means my structure is not yet a determinate one! Is there any other way out of this?

 

[jayrod12]

You're going to have to provide a sketch of your situation and the applied loading. Then we can comment more directly on analysis method. There's likely a simplifying assumption we can make to solve the problem.

 

[Gouthamm]

I have attached a link along with the post. Please do check.
Here is the link:

http://files.engineering.com/getfile.aspx?folder=221fb92d-c232-46b2-8d37-c7

That is my exact situations while viewing the tower from front.

 

[jayrod12]

Link didn't work. Try renaming the file, don't have any spaces or additional punctuation in the file name.

 

[Gouthamm]

I have re-upoloadit. Please do check.

 

[andriver]

if you have purely vertical forces acting at the columns, your reactions are just going to be those forces ie 10...

 

[Gouthamm]

This is a service limit condition. I real time, will have to consider horizontal force due to wind and seismic analysis is also needed! so I guess, it will be a little more than just vertical loads, isn't it?

 

[jayrod12]

I would be treating the bracing as tension only. That way it is determinate. You would only have one brace active at any one time.

 

[ukbridge]

If I had to do a hand-check of this type of problem in a pinch, I'd probably consider two cases based on the assumption that the base is pinned:

(1) 1st Diagonal Brace only
(2) 2nd Diagonal Brace only

Then I'd simply take the average of the two forces in the diagonals. In practice I'd resort to a simple FE model with bar/beam elements as appropriate, and examine the deflected shape/check reactions and axial forces are reasonable.

Good luck!

 

[Gouthamm]

@ukbridge, I am supposed to code these mechanical equations and unfortunately, equations obtained from FE model analysis does not fit into my code.
Thank you

 

[Gouthamm]

jayrod12, my only concern as of now is solving for the reactional forces while considering the horizontal force due to wind.

 

[jayrod12]

I can sketch something up later. But my comment above will provide an upper bound solution. Only look at 1 brace resisting in tension, neglect the 2nd brace for the analysis.

And if you're coding the equations can't you just make a proper stiffness matrix and have it do the FEA analysis for you?

 

[Gouthamm]

Unfortunately no! We dont do that kind of coding. Actually it's a Design Automation we are working on. Thank you for your advice. Please do sketch up when you are free.

 

[jayrod12]

See attached. The colour coordination didn't come through as nice as it did on paper. But you should be able to follow it.

As ukbridge indicated, it may also be prudent to check the bracing as compression bracing as well, one way or the other the simple solution is to pretend like one of the braces doesn't exist, and that there is zero moment transfer at any of the connections. We operate with these assumptions all the time.

 

[rb1957]

i guess i see it different to jayrod ...

for the load shown, member 1 is in bending (SS beam), members 2 and 3 in compression, member 4 has zero acting.

curiously if you have 4 and 5 (ie both diagonals) then 1 could be a beam-column, and members 4 and 5 would be reacting load, and there'd be equal and opposite horizontal reactions at the ground.

if there is a lateral load applied, then the member 4 would react this, and the load in members 2 and 3 would change. If a lateral load applied with members 4 and 5 then you could assume that the load is reacted either ...
a) equally by both members 4 and 5, or
b) only by the tension loaded diagonal, or
c) only by the compression loaded diagonal.

another day in paradise, or is paradise one day closer ?

 

[jayrod12]

Fh is the lateral load.

As I said, there are a few different ways people would analyze it. My way is not the only way, nor is it necessarily the easiest. But it does work and I'm comfortable with it. Perhaps my sketch doesn't fully give my whole intent. I was thinking of the bracing as tension only. Therefore the member 1 would be in bending and compression. The bracing only sees tension (and self weight bending) and the columns only compression.