Direct Stiffness Method works for Simple Unbraced Frame, but does not for Braced Frame 1

[kabindrabhattarai]

Hi everyone!

I am trying to develop a spreadsheet that calculates reaction forces for a simple braced frame using direct stiffness method. I did the regular process of

Calculation of stiffness matrix in local coordinate
Calculation of stiffness matrix in global coordinate
Calculation of global stiffness matrix
Calculation of reaction forced from known values

My problem is that my spreadsheet calculated right reaction forces for unbraced frames. It does not calculate right reaction forces for braced frame though. Is Direct Stiffness Method limited to unbraced frames only? I didn't think so but I feel like I have reached a road block can't find out why. Please help.I can upload the spreadsheet if you all want me to.

 

[SteelPE]

I had to Google Direct Stiffness Method to figure out what you were talking about. From what I can see, you are basically solving the structure using a matrix so, it shouldn’t matter if the frame is braced or unbraced.

Do your reactions satisfy equilibrium?

 

[BigInch]

I assume you mean a "knee braced" frame, in which case the cross top beam and the columns are continuous across the brace connection points and carry moments as generated by the brace's point loads. The braces themselves are pinned end. Your matrix must consider the continuity of the beam and columns.

you must get smarter than the software you're using.

 

[kabindrabhattarai]

@SteelPE, bracing or unbracing would affect the reaction force wouldn't it? Because it changes the overall stiffness of the structure. What do you mean when you say "satisfy equilibrium"? The reactions are equal to the sum of the loads. Is that what you meant?

@BigInch, my brace is a full vertical cross brace i.e. it goes from the top of one column to the base of the other column. My matrix does consider the presence of brace as well and as far as I know it should be correct as well.

I have attached that spreadsheet with this post for you all to look at. That you so much for your views. Please let me know your thoughts.

 

[SteelPE]

kabin,

Yes, by equilibrium, I mean the sum of the loads in any direction should equal 0 in the end. Yes, loads are attracted to stiffness, therefore reactions will be greater where the members have more stiffness. However, you should be able to come really close to the reactions in concentric brace frames buy using statics.

Sorry, I don't really want to go through your spreadsheet as it has been 10+ years since I have had to do this type of work (when I was at uni) and it would take me a while to decipher.

 

[JAE]

Is this work for class? Are you a student?

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[kabindrabhattarai]

SteelPE, This is a statically indeterminate structure. So the reactions cannot be calculated by just using statics. That is why I am having to use this direct stiffness method.

JAE, I am not a student. I am trying to develop this spreadsheet so that anybody can figure out the approximate weight of steel needed to support a specified load without having to use a structural analysis software.

 

[WinelandV]

kabindrabhattarai,

In your matrices, it appears that you're only accounting for the flexural stiffness of all the members, but your brace (especially with the shape chosen) is going to carry axial forces - you need to account for the axial stiffness of the brace to get the forces correct in your members. Please note that I only spent 5 minutes looking at your spreadsheet, so if I missed where it's accounted for, I apologize.

 

[bookowski]

Direct stiffness method would solve any system braced or unbraced, this is how all of our software programs are working. Doing this in Excel is very ambitious unless you only want it to deal with a very specific configuration/condition. I'm sure it could be done - but why not just get a simple software program.

 

[kabindrabhattarai]

winelandv, I have taken the axial stiffness of the braces into account. I probably could have ignored and nullified the flexural stiffnesses of brace but I left it in there as those are so little and are not changing the global stiffness matrix by very much.

bookowski, our support structure condiciton/configuration does not change much. I am doing it in excel so that any one without prior structural experience can get an approximate steel weight values.

 

[Archie264]

Congrats on undertaking that project. It can be (and has been) done; see the following link. (And no, you don't have to pay for the course to get the course material or spreadsheet. Just scroll to the bottom of the page and click on the links.) Good luck...

http://www.cedengineering.com/courseoutline.asp?cid=240

 

[SteelPE]

kabind

While I understand that you have two supports and 4 unknowns, I think any engineer would eliminate the horizontal component of the support w/o the brace attachment making the system statically determinant at that point no matter what the connection was at the top of the column. How else did they design building w/o computers 100 years ago.

 

[kabindrabhattarai]

Archie264, thank you for the information. I will look into that in detail and see if that helps.

SteelPE, I did not understand you. When you say elimination of the horizontal component of the support, which support are you referring to? Are you talking about the top beam sitting on top of the two columns? Please elaborate a little bit further.

 

[IDS]

At the risk of overloading you with information, you might like to have a look at:

http://newtonexcelbach.wordpress.com/2014/01/22/frame-analysis-with-excel/

The link is a series of blog posts on frame analysis in Excel, starting with simple on-sheet solutions, through to 2D and 3D program using VBA or compiled solvers that will deal with structures of just about any complexity.

The stiffness method should certainly cope with a braced frame, so there must be an error in your formulation somewhere. Unfortunately I won't have much time to look at it today, but if I do find anything I'll let you know.

Doug Jenkins
Interactive Design Services

http://newtonexcelbach.wordpress.com/

 

[JAE]

What do you mean when you say "satisfy equilibrium"?

Yikes!

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[IDS]

From a quick look at the spreadsheet, I see you have lengths in feet but section properties in inch units. For the stiffness matrices and load vectors you need to use consistent units throughout, including for bending moments.

Doug Jenkins
Interactive Design Services

http://newtonexcelbach.wordpress.com/

 

[kabindrabhattarai]

Thank you very much Doug. That was it. Just an unit error. I got the code working and have launched it too. The stresses and deflections that I am getting are right on with structural calculation software.

I really appreciate you all helping me out on this project.