## Frame Analysis with Excel – 3, Continuous beam or frame

Continuing from Frame Analysis with Excel 2 – Single inclined beam

The spreadsheet for a single inclined beam presented in the previous post has been modified to deal with up to six continuous horizontal or inclined beams.  Examples of a 5 span beam and a four member portal frame have been compared with a frame analysis in Strand7 and show near exact agreement.

The procedure used in the new spreadsheet is:

• The stiffness matrix for each beam is generated as before.
• The beam matrices are combined into a global matrix, adding coefficients for the beams meeting at each node.
• The stiffness matrix for active freedoms is extracted from the complete global matrix
• This matrix is inverted using the Excel Minverse() function
• The inverted matrix is matrix multiplied by the applied nodal actions, giving the nodal translations and rotations.
• The complete stiffness matrix is multiplied by the complete nodal deflection vector, giving the net load for each freedom.
• Reactions at the fixed freedoms are found by deducting the applied loads from the net loads.

Formation of the global matrix for beams 1 and 2 of a continuous beam are shown below:

Global Stiffness Matrix

Screenshots below show Strand7 models for a 5 member continuous beam, and a portal frame, and comparisons of the Strand7 analysis and the spreadsheet output:

Strand7 continuous beam analysis

Continuous beam results

Strand7 Portal Frame Analysis

Portal Frame results

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### 30 Responses to Frame Analysis with Excel – 3, Continuous beam or frame

1. Tomasz says:

Great thing to learn matrix method for continous beam or frame analysis. I used Mathcad for this type of computations (involving matrixes) before but it looks Excel aided by VB programming works well.
Thanks, Tomasz

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• Vijay says:

Hi,
Don’t know whether you still follow this post, if so, could you please share any mathCAD files on continuous beam you may have.

Thanks

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2. Mahesh says:

I am not able to give input for 3 beam portal. Explain, how to reduce your programm for 3 member portal frame.

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3. Mahesh says:

In 3 member portal if the last dof is constrained then your programm is giving error. check

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4. dougaj4 says:

Mahesh

Yes, the program crashes if the last node is fixed against rotation. I have fixed the problem and added a 3 member portal frame example to the download file:

http://interactiveds.com.au/software/Beam3.zip

Note that the beam3 spreadsheet was intended mainly for educational purposes, and was set up so the matrices etc are all visible on the spreadsheet. There is a frame analysis spreadsheet at:

http://interactiveds.com.au/software/Frame4.zip

which is much more versatile, and should be easier to use for problems other than the provided example.

Thanks for the feedback.

Doug

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• Amir says:

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5. dougaj4 says:
6. susant patra says:

Hi Doug,

Sorry about too many questions. I was comparing program beam2 (theta = 45deg) with program beam3(with number of beams=1 and theta=45deg). However, the reaction forces do not match.

I looked at the stiffness matrix. Both beam2 and beam 3 give same result. however, the inverse of active matrix in beam 2 and beam 3 do not match.

I would appreciate your help.

Regards,
Susant

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7. susant patra says:

Hi Doug,

Sorry about my previous e-mail. I traced the problem to BC mismatch.

Regards,
Susant

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8. dougaj4 says:

Susan – no such thing as too many questions 🙂

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9. Srikrishna Koduri says:

Hi,
I have used your Beam3 Spreadsheet Utility (Beam3 Excel File) for Frame Deflection & Reaction Forces Analysis.
We found it is very helpful for solving continuous beam problems for deflection analysis.
1. We are finding it difficult while giving requisite inputs in “Input – Worksheet in the Beam3 Excel File”,
e.g., while giving theta value its mentioned that it is w.r.t X axis. i.e, whether, it must be 0 to 360 (or) +180 to -180(Direction of the theta).
So, Please provide the user manual for that spreadsheet.
2. In the explanation given by you about the spreadsheet, you have shown the figure of a deformed inclined continuous beam.
But, Nothing is visible as such in the spreadsheet when we have computed one analysis in the Beam3 excel file.

3. And also, With known Inputs, when we have Recalculated, “KGi”and “Node- def” Worksheets in the excel file are not displaying any results (showing Formula Error “#Num!”). Image files attached for your reference.

I am unable to attach figure here which clearly explains my problem.
My interest is to change the support position and observe the deflection in various cases.

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10. dougaj4 says:

Srikrishna – there is no “user’s manual” but if you look at the portal frame example in the download file, and also look at my response to Mahesh above, it should answer your questions. The angles in this example are shown as +- 180 degrees, but substituting 270 degrees for -90 degrees will also work. If you have more questions please feel free to ask.

If you would like to e-mail the spreadsheet that is not working to dougaj4 at gmail, I will have a look at it.

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• srikrishna says:

Hello!
We have queries regarding the use of Frame4.xlsb Utility.
Objective : Deflection analysis of Continuous Beam – with 5 Span using Frame4.xlsb.
Problem Description :
Beam Type/ Span/ Support/ Load Description are followed.
Beam Type : Continuous Beam
No. of Spans : 5 (Five) Only
Span Length : 40 mm (Equal Span Lengths for all 5 Spans)
Support : Fixed at Left & Right Ends and Rollers at Intermediate Supports.
Type of Load : UDL (Uniformly Distributed Load)
UDL-1 : Start Point 30 mm from Left End and End Point 90 mm from Left End.
UDL-1 Load : 3.2 N/mm
UDL-2 : Start Point 110 mm from Left End and End Point 170 mm from Left End.
UDL-2 Load : 3.2 N/mm
Input Parameters for Worksheet “Input 1” :
Area of cross section(A) : 450mm2
Moment of inertia(I) : 337mm4
E : 210000N/mm2
Property is same for the all the spans.

Query:
1. I would like to understand how to input loading conditions in Worksheet “Input 2”:
“For distributed loads specify length from the ends of the start and end of the load, and the load intensity at the start and end”.
2. Deflection Plot Images for the Subjected Continuous Beam Analysis when solved using above input parameters.
3. Frame4.xlsb file with above input parameters.
Please provide needful support.
Regards

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11. dougaj4 says:

I have responded to this by e-mail.

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12. raezur says:

Do you have a speradsheet for continuous beam analysis that includes settlement?

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13. soco says:

how to retrun a result from the function “FEMact” to selected range in the sheet

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• dougaj4 says:

I have added a page to the blog menu with links to posts on using array functions and using UDFs:
The example on UDF is also a more recent continuous beam spreadsheet, which you might find useful. Also search the blog for Frame4 and 3DFrame, or look in the Download by Category page for the most recent versions of my frame analysis spreadsheets.

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• soco says:

i will review that 😀

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14. soco says:

thanks!
after review the code there is 2 mistakes :
first : the ref book eq for fixed end moment for triangular load is not correct that show be noticed in the code ref F.L (….) show be ur code is F.L/2 (….)
second :
in
‘ Fixed end moments due to distributed loads
show be Tload2 = DistLoads(i, 4) * DistLoads(i, 5) / 2

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• soco says:

ref :Partial Uniform Distributed Load (Formulas from Reinforced Concrete Designer’s Handbook, C.E. Reynolds and J.C. Steedman)

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• dougaj4 says:

soco – Thanks for taking the trouble to work through the code and report back.

I agree with your second point, and I have now fixed that (I will upload the corrected version later today).

I didn’t follow your first comment, and the corrected code now gives correct results for a triangular distributed load.

Note that the Frame3 spreadsheet was only intended to demonstrate the application of the stiffness method to continuous beams and portal frames. For practical use the later spreadsheets provide more input options, and much more useful output data. The latest versions are:
Continuous beam: http://interactiveds.com.au/software/ConBeamU.zip
2D Frame analysis: http://interactiveds.com.au/software/Frame4.zip
3D Frame analysis: http://interactiveds.com.au/software/3DFrame.zip

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15. Many yrs ago during my graduate work I took a course MM of Structual analysis. Thank you for this reminder. The professor was from Germany, Anton Wegmueller. Somewhere I have his notes, still after 40 yrs. he started with the single beam. I sweated during that course, but did well.
Mike

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