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Solving for reactional forces in a Tower

Solving for reactional forces in a Tower

Solving for reactional forces in a Tower

(OP)
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/getfile.aspx?folder=2...

RE: Solving for reactional forces in a Tower

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

RE: Solving for reactional forces in a Tower

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.

RE: Solving for reactional forces in a Tower

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.

RE: Solving for reactional forces in a Tower

(OP)
@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?

RE: Solving for reactional forces in a Tower

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.

RE: Solving for reactional forces in a Tower

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

RE: Solving for reactional forces in a Tower

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

RE: Solving for reactional forces in a Tower

(OP)
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?

RE: Solving for reactional forces in a Tower

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.

RE: Solving for reactional forces in a Tower

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!

RE: Solving for reactional forces in a Tower

(OP)
@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

RE: Solving for reactional forces in a Tower

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

RE: Solving for reactional forces in a Tower

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?

RE: Solving for reactional forces in a Tower

(OP)
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.

RE: Solving for reactional forces in a Tower

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.

RE: Solving for reactional forces in a Tower

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 ?

RE: Solving for reactional forces in a Tower

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.

RE: Solving for reactional forces in a Tower

none so blind as those who will not see ...

(missed your very large Fh !?)

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

RE: Solving for reactional forces in a Tower

I'd definitely go with Jayrod's solution; he also provides a very pertinent point that you/we may have missed ,namely that the "real" answer is really down to how the thing is going to be fitted/connected together. Some other things to think about:

1) Is the column a true "fixed" connection to the top "beam"? Or has it been designed as a simple connection permitting rotation?
2) Is everything going to node out, or will there be additional local moments exerted due to joint eccentricities?
3) How are you going to deal with the design of the connections (which can often be the critical case) if everything's welded together?
4) How many different load patterns are there going to be - if theres a lot it sounds like you're going to have to make a very complicated spreadsheet if you're implementing some kind of analysis which deals with statically indeterminate trusses like http://www.sut.ac.th/engineering/Civil/CourseOnlin...
5) Will the provision of an extra brace outweigh the additional fabrication cost, for what may be a frame using modest standardised hot rolled sections.

If you absolutely insist on analysing it to the extent you want to, download a free frame analysis package like 2D frame and do it for a test-run. Ideally it should be a portable program so whoever else has to use it doesnt have to install the program also! Examine the output/datafile and with a bit of tooling you can use Excel and a few concenate functions to get excel to generate a handy script with little/no knowledge of programming.

I think the above idea is much better than programming your own spreadsheet; it will be less prone to errors and will be far more flexible than a spreadsheet could ever be for this type of thing. I don't think I've used a spreadsheet that doesn't have an error in it somewhere, and I don't think this project will be any different.

I think very often as structural engineers we're expected to produce perfectly working, validated spreadsheets; in reality we're not software engineers and don't have all day to make test cases and see if theres any errors in it somewhere.


RE: Solving for reactional forces in a Tower

...couldnt help myself, but as a final final option you could produce some simple graphs (and thus equations) using a 2D analysis package to help calculate the reactions in each member such as those in the Steel Designer's Manual, for a unit load. You could even vary the stiffness of the bracings as an addition parameter if you wish. This would also be beneficial I think for a graduate to learn the hard way that bracing isn't very efficient at certain angles! (Not that I think you're a graduate :) )

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