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Offline Ernesto  
#1 Posted : 02 May 2015 10:16:28(UTC)
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I've attached a file to generate the Compression and Bending Interaction diagram for rectangular sections, using ACI 318-11.

Any SI and US customary units work, but the results are in kN-m, which can be switched manually if you know where to look.
The rebar area and location column vectors can be made larger or smaller with no effect to the algorithm, So any number of steel layers can be used.

Future work: Expanding on this to include Biaxial Bending using the Reciprocal Load method. I had done this previously with MathCAD, and am currently working on a version for smath. I am having trouble getting it to be done without human input at certain points, but will keep working on it.


Please upload any improvements done to this file and post if any mistakes are found or if you have any suggestions.

Updated: Automatic scaling of the plot has been implemented. Also previously the section was treated as compression controlled, now the transition from compression controlled to tension controlled is taken into account.

Edited by user 20 June 2015 17:53:07(UTC)  | Reason: Not specified

Ernesto attached the following image(s):
interaction diagram.PNG
thanks 1 user thanked Ernesto for this useful post.
on 20/06/2015(UTC)
Offline RFreund  
#2 Posted : 02 May 2015 15:35:54(UTC)
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Ernesto,

Very nice! Thanks!

Here is one thought I have when creating calculations. With your current setup you can really only use this one calculation on one page, right? Otherwise you would get into trouble of overwriting variables. I have been trying to take the calculation like you have created and turn it into a large function. This way you can use this for multiple beams on a single smath "page" (meaning a single .sm file). I think this is much more efficient especially if trying to print multiple beams/pages. But maybe there is a different way and even using function you have to be careful how you name your variables (the # symbol at the end of the variable seems to be a popular way to do it on smath).

Anyway thanks for posting.
Offline mkraska  
#3 Posted : 02 May 2015 16:10:03(UTC)
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I have reproduced the diagram in Maxima Draw2D with automatic scaling (except for the x ticks, which are hardwired). Also, I parametrized the usage of units in the plot. One might even use radiobutton list regions for unit selection and having appropriate dynamic labels in the diagram.
File Attachment(s):
P-M-Interaction_Kr.sm (183kb) downloaded 240 time(s).
mkraska attached the following image(s):
N-M.PNG
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Offline Ernesto  
#4 Posted : 02 May 2015 22:34:23(UTC)
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RFreund: I'm also playing around with making it a larger function, but still along the same lines as I currently have it. Just making the functions dependent on more variables. I still want to keep it clear where each step comes from without making it so overly complicated where someone may get lost following it. This way I can add bending in the y-axis more easily. Which would lead me to my next step of incorporating the Reciprocal Load Method for checking biaxial bending and compression. Hopefully I will get around to doing that soon. I will post it once I get everything working correctly in biaxial bending.

I am wary of making a sheet that does multiple beams on the same sheet, as that takes away from the clarity of the calculations. This is another challenge of itself, scaling these things up in a way that someone else can follow what you are doing to audit your calculations. My objective is not to make a black box where things magically appear, but clear steps where other engineers can easily verify my work.


mkraska:
Thanks for taking the initiative with the plot! The scaling looks great. I don't have any experience with the Maxima Draw2D and am carefully checking out your code to see what I can get out of it.

Thanks again!
Offline RFreund  
#5 Posted : 03 May 2015 23:31:31(UTC)
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Ernesto: Yes that is the 'rub' I suppose. I started using Smath to create very clear/comprehensible calculations. Now that they are clear I am trying to turn them into a black box (or so it seams), which would be more geared towards production. However, the advantage is that there is the option to view the "code" behind the black box. In any case good work!
I have the motivation to create a more general "rigorous" axial and biaxial bending function but just don't seem to have the time.
Offline RFreund  
#6 Posted : 20 June 2015 04:29:01(UTC)
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Ernesto:
I'm curious how you chose (h.x * 1.4) * 0.005m for the interval of iteration?

Offline Ernesto  
#7 Posted : 20 June 2015 18:08:20(UTC)
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RFreund: I updated the file just now with the reasons described in the first post.

I actually increased it to (h.x*1.6)*0.005m. I chose the interval (0.005m) just so the plot wouldn't look sluggish for small sections. Another way to do this is based on the percentage of the section size so there would be the same number of data points for small sections as large sections, this would probably be more efficient but didn't think of it at the time Fool .

The range for the iteration (1.6) was chosen from trial and error, trying different section sizes and verifying if the range was adequate (if all the data points required to complete the plot were generated) , while at the same time keeping the range as small as possible to save on computing time.

I was thinking about what you said before about checking various columns in one sheet. One way I was playing with is to have one sheet for one section size, but used in multiple column locations so there would be different loads to check, and plotting those points to see if they are in the envelope or not. But with the X-Y plot I'm using, I haven't figured out a way to differentiate those points with one another (with labels or in the legend). (see attached image).

Edited by user 20 June 2015 21:33:40(UTC)  | Reason: Not specified

Ernesto attached the following image(s):
Capture.PNG
Offline RFreund  
#8 Posted : 04 July 2015 02:17:47(UTC)
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Thanks for the Response Ernesto.

You know, another nice feature would be if there was a way to check if the point falls within the curve, then return an "OK" or "NG" or something along these lines. Of course it is easy enough to visually compare but it would still be neat.

I've attached a spreadsheet which is for masonry shear walls, but they use a close range liner interpolation technique it seems.
File Attachment(s):
Axial_and_Flexure.xls (135kb) downloaded 171 time(s).
Offline Davide Carpi  
#9 Posted : 04 July 2015 11:25:16(UTC)
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To accomplish the task you can use the even-odd rule.

Attached an example.

Edited by user 04 July 2015 15:43:14(UTC)  | Reason: Not specified

File Attachment(s):
Check.sm (16kb) downloaded 95 time(s).
Davide Carpi attached the following image(s):
2015-07-04 14_52_08-SMath Studio Desktop - [Check.sm_].png
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Offline Joe_Jones  
#10 Posted : 18 July 2019 16:59:52(UTC)
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Hi,

I need a compression and bending interaction diagram for my master's dissertation. I have downloaded the file and input the values of my column into the smath sheet. However. when i recalculate the page, it does not update the diagram.

How do i update the diagram to match up with my input data?

Any help would be appreciated.

Offline uni  
#11 Posted : 18 July 2019 18:15:57(UTC)
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With X-Y Plot

P-M-Interaction_Kr.sm (49kb) downloaded 69 time(s).
Russia ☭ forever
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Offline jinwon  
#12 Posted : 21 October 2019 05:21:04(UTC)
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Originally Posted by: uni Go to Quoted Post
With X-Y Plot
P-M-Interaction_Modify.sm (61kb) downloaded 12 time(s).
P-M-Interaction_Kr.sm (49kb) downloaded 69 time(s).


The smath sheet you provided is very useful.

I have a question.

1) An error occurs when the length of the column becomes longer.

ex) hx = 4000 mm



2) I want to find n value that satisfies Pnx = pu.

when I use the solve() function, an error occurs.

Is there a way to fix it?

how can find n value ?

Please refer to the attached sheet
Offline Razonar  
#13 Posted : 21 October 2019 07:47:56(UTC)
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Hi.

Originally Posted by: jinwon Go to Quoted Post

I have a question.

1) An error occurs when the length of the column becomes longer.

ex) hx = 4000 mm



The formulae for apply is valid only for certain ranges. You can see that the surface is outside the required range (by the norm), so, the SMath error actually is irrelevant: what it's important is the red in the worksheet:

q1.gif

Originally Posted by: jinwon Go to Quoted Post


2) I want to find n value that satisfies Pnx = pu.

when I use the solve() function, an error occurs.

Is there a way to fix it?

how can find n value ?



Solvers are unstables, except maybe for al_nleqsolve. But here, and similar cases, you can implement always your own solver:

q2.gif

Best regards.
Alvaro.
Offline Jean Giraud  
#14 Posted : 21 October 2019 15:24:53(UTC)
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Originally Posted by: jinwon Go to Quoted Post
when Iuse the solve() function, an error occurs.Is there a way to fix it?

... more solvers in there.

Solve Dichotomy.sm (20kb) downloaded 14 time(s).
Solve roots Newton-Raphson.sm (52kb) downloaded 16 time(s).
Solve roots_solve RootSecant (1).sm (105kb) downloaded 16 time(s).

Offline jinwon  
#15 Posted : 23 October 2019 03:18:16(UTC)
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Originally Posted by: Jean Giraud Go to Quoted Post
Originally Posted by: jinwon Go to Quoted Post
when Iuse the solve() function, an error occurs.Is there a way to fix it?

... more solvers in there.

Solve Dichotomy.sm (20kb) downloaded 14 time(s).
Solve roots Newton-Raphson.sm (52kb) downloaded 16 time(s).
Solve roots_solve RootSecant (1).sm (105kb) downloaded 16 time(s).



Thank you for your answer.
Have a nice day.
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