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2D frame analysis using Cross method

2D frame analysis using Cross method

2D frame analysis using Cross method

(OP)
Helo all! smile
Im new here so be gentlesmile
Please look at the picture
[URL=http://imageshack.us][IMG]http://img262.imageshack.us/img262/3895/2dframely4.jpg[/IMG][/URL]

For calculating bending moments diagrams of beams in an 2d frame simplification like this one is used.
This way you get higher  moments over the support and in the mid spam since your sistem is not framed.
My question is how would you get right diagrams for columns?
Can Cross method be used for the entire 2D frame (like in the picture) when calculating by hand, or you have to use another simplification for geting column diagrams?
Thanx in advance!

RE: 2D frame analysis using Cross method

I am unable to open your sketch. Try to post the sketch in some other way.

RE: 2D frame analysis using Cross method

(OP)
Anyone? sad

RE: 2D frame analysis using Cross method

Yes, moment distribution can be used to analyse the whole frame.

RE: 2D frame analysis using Cross method

(OP)
I got different result on this problem.
http://www.freeimagehost.eu/image/3d34201277662
If you can notice on the right the results where obtained using cross program.
When I calculated by hand, I got results same as the cross program has, but they quite differ from the ones got from our standard 3d analyze&design program we use here.
Can some do the same egsampe in their application and just verify wich results are correct and wich are not.
Thanx!

RE: 2D frame analysis using Cross method

(OP)
...but they are two differnt system...so ofcoures the results would be differnet...stupid of me...
But how else can I calculate this using Cross method?
Or Cross method cant be used when structures is subjected to lateral loads?

RE: 2D frame analysis using Cross method

SnapSpace,
I'm not real clear about what your question actually is.
If you are trying to use Hardy Cross's Moment Distribution to comparing a rigid frame to a continuous beam that is "flattened out" with a ridid frame that is subjected to sidesway you are comparing very different structural systems. I suggest that you get out your indeterminate structures text and review the section with a title something like "frames subject to sidesway". With Moment Distribution it is basically a two step process with the first step done with all joints fixed against rotation and with translation prevented. Then the moments & shear from the artificial force at the top of the frame that prevented translation is distributed to obtain the actual moments & shears.
I'm sure that your text book will do a better job of explaining this than my post has done.

RE: 2D frame analysis using Cross method

Do you need a frame in this situation or can it all be pinned?

I usually dont use fixed frames unless they form part of the lateral system.

csd

RE: 2D frame analysis using Cross method

The difference between a frame and a continuous beam is the frame is subject to sideway and additional moments are required for stability. You are comparing apples and oranges. They are not the same.

Try comparing a frame, not subject to sideway, with a continuous beam.

RE: 2D frame analysis using Cross method

I finally managed to open the sketch.

I am assuming that all the connections are rigid. Then for approximate analysis- for lateral-

It is common to assume pin at the mid height of columns and mid length of beams. Find out the axial forces in the columns depending on their distances from the cg of the structure. Find out the moments.

For gravity loads, if the joints are rigid-

It's common to assume pins at both ends of a beam about .1L to .145L from the ends. 'L' being the span length.  Slove for the moments. Remember any unbalanced moment will go directly into the column.

RE: 2D frame analysis using Cross method

oldPaperMaker is correct.  The differece here is sidesway.

Mike McCann
McCann Engineering

RE: 2D frame analysis using Cross method

(OP)
Shin25 can you post a sketch pleasesmile

RE: 2D frame analysis using Cross method


I am unable to post any sketch. But, you probably can check in any good structural analysis book and look under approximate analysis methods.

For most of the structures, exact analysis is can be supplemented with appropriate approximate methods. Remembers that for an approx. method the number of assumptions needs to be equal to DOI (degree of indeterm.) of a structure.

For an example, if DOI = 4, the assumptions need to be = 4.

RE: 2D frame analysis using Cross method

You CAN use moment distribution to solve for the moments in the frame--but don't use those approximate continuous beams; use the actual frame.

shin25 describes the best approximate solution for something like this--the portal method.  Once you define where moments are equal to zero (the inflection points), the frame becomes determinate.

But why not use a computer analysis program?  It will give you joint deflections as well.

DaveAtkins

RE: 2D frame analysis using Cross method

(OP)
Can someone confirm if I got the proceedure right, please.
I know that you people have mastered this, but Im a student and unfortunalty, still trying to learn something that our staff hasnt learned ussad

http://img86.imageshack.us/img86/9410/crosshq7.th.jpg

RE: 2D frame analysis using Cross method

(OP)
Bay lenght is 6,00m and frames height is 5,00m

RE: 2D frame analysis using Cross method

(OP)
O.k. this was wrong.
I found the right waysmile
Will get back to you guys after Im done with practicingsmile

RE: 2D frame analysis using Cross method

(OP)
I take this question back!
Blushed like hell!

RE: 2D frame analysis using Cross method

mmmm.... I'm so familiar with that kind of approach when frame is subject to lateral load and gravity load... the common practice is that, first, you analyze the frame separately with lateral load alone using portal method, and secondly, analyze the the continuous beam using moment distribution method with the assumption of continuous beam in the right sketch you posted... then in designing for example concrete or steel... you will combine the loads or stresses you get from separate analysis and that will be your basis in the design....

I hope I answered your question...

That's the common practice here when analyzing frame, If some one know more precise analysis can you give us some tips???

RE: 2D frame analysis using Cross method

Lateral load analysis with moment distribution is quite tedious- first, the frame has to be analysed as if it is fixed from lateral movement, second, the frame has to be re-analysed allowing lateral displacement and the moments from the first step has to be corrected.



RE: 2D frame analysis using Cross method

(OP)
Anyonesad

RE: 2D frame analysis using Cross method

(OP)
Can someone recommend me a good book on this subject, please.

RE: 2D frame analysis using Cross method

SnapSpace,
1.If you are located in a city that has a university with a college of engineering I suggest that you call the civil engineering department, ask to talk to a professor that teaches structural engineering and ask him for his recommendations for books about indeterminate structures.
2.If that resource (#1, above) is not available then go to Google, type in "books about indeterminate structures", read the reviews and order one that appears to meet your needs.
3. The book that I used as an undergraduate is probably out of print now.
4. If you have not taken an undergraduate course in strength of materials then you will probably have a very difficult time teaching yourself how to do an analysis of indeterminate frames that are subject to sidesway.

RE: 2D frame analysis using Cross method

(OP)
Can this 2 problems be solved with Cross method?
http://img118.imageshack.us/img118/8826/forcewb7.jpg
I tried with force method and theres no problem, but I dont know how to start it with Crosssad
Can anyone give me an hint please.

RE: 2D frame analysis using Cross method

This isn't really the place for hw help.  However, if you are really stuck and need help, then you need to tell us exactly what you've done so we can find your error.  Those last two posts have been especially lazy.  You've obviously neglected the carry over moments in symmrr9.  forcewb7 can be done by dividing into two members for the top - the force is conveniently given perpendicular to the members, so it should be straightforward.

RE: 2D frame analysis using Cross method

I didn't look too closely, but you managed to solve "crosshq7", yes?  So, "forcewb7" really isn't much different.

Your mistake in "fixedbeamsz1" is that you are neglecting the columns.  When you include the whole picture, you will see that the "ratio" for 1-2 and for 3-2 is not zero.  Thus, at nodes 1 and 3 there will be distributed moments.   This will also result in carry-over moments from 1-2 to 2-1 and from 3-2 to 2-3.  You have to continue this cycle until the carry-over-moments are negligible.  Didn't you do this, at least for a few cycles, for "crosshq7"?  Again, I didn't look too closely at that one...

Also, I don't know what is the significance of your tabulating 4/EI*L...


It's going to get even more cumbersome when you have to consider joint translations, as others in this thread have mentioned.

I recommend the book by Hsieh and Mau; it is cheap on Amazon.

Hope that helps

RE: 2D frame analysis using Cross method

(OP)
Forget the frame.
Im talking about only this problem:
http://img45.imageshack.us/img45/5764/fixedbeamsz1.jpg
where you have a beam thats fixed at both sides and its like an roof structure (angled).
You can see my calculation there, and also see that the final result are moments of 10,32kNm wich are far from the real solution.
By looking at the picture can you tell me where I did wrong.

RE: 2D frame analysis using Cross method

there is a joint translation/deflection at node 2.
you can convince yourself that a unit translation at the end of a beam creates moments analagous to the case of "antisymmetry" (if you've covered modified stiffness in your studies).

So you have to consider those moments, in terms of the node 2 deflection.  You can use moment distribution as always, but considering fixed-end-moments as usual PLUS those from the deflection.  In the end, you can solve for the deflection by simply including equilibrium (sum forces in y dir = 0), then you have all of your moment values.

I recommend using modified stiffness "ratios".
Also, that book I mentioned covers this.

RE: 2D frame analysis using Cross method

(OP)
Please, can you write this down, like I did.
I kinnda need this in a hurry, and if I order the book it would take about 3 weeks to arrive.
Please

RE: 2D frame analysis using Cross method

forget the comment about modified stiffness for your prob.

-6*E*I*D/L^2 is the moment on both sides of a beam subjected to end displacement D.

g'luck, sir

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