Very impressive for sure. :d

Davide: here comes the same in green :-)

Ioan: Doubleclick on any object on the canvas gives you numeric control. This is handy for forces (x co-ordinate and lenght are relevant) and supports. For beams and distributed loads, the endpoints have to be specified indirectly via x co-ordinate of the midpoint and by width.

Another way to apply numeric control is to edit the values of N between preprocessing and solving.

As to the hinges: They can be done by having 2 nodes at the same position and linking their vertical displacement by an additional equation (zero lenght beam element with zero bending stiffness)
I thought of representing this by a black circle. In the preprocessor, this requires quite some added lines, in the FEA function I see no problems.

Another DOF per node is required only if you want longitudinal displacements and/or arbitrary beam orientation, which currently is beyond my ambitions and also beyond what can be done with the modeller region. I see no way to draw an oblique line except to provide some more symbols and scale them accordingly. But then-how to make oblique triangles and rectangles...

Andrey, do you have an idea, how I can avoid having separate force symbols for up and down directions or left and right moments or left and right triangular distributed loads? Is there a way to flip the symbols interactively?
If not, I would mess up the template palette (at least four more symbols are needed: hinge, up force, left and right moment).

I experience strange snap to object behaviour in the modeller region. If I drag a corner, then sometimes the opposite corner is not fixed, making it nearly impossible to create a triangular load with the same extension as the underlying beam (which should be trivial with normal snap behaviour).

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beam.sm (104 КиБ) скачан 108 раз(а).

Wrote

The use of an fictive link member of zero length and zero stiffness gives indeterminacy in the stiffness matrix (EI/L=0/0) o_o . Or, maybe you see a trick to avoid this

I simplified a bit, working on the implementation...

Update:
- everything provided as callable functions with description strings
- Solver output modified for more flexible postprocessing
- hinge element implemented (using an element with zero bending stiffness and a penalty for coupling the displacements)

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beam1.sm (121 КиБ) скачан 88 раз(а).

Wrote

?
While you're at it, what about - some fixed loads and a convoy (mobile) loads ? with animation and filters ?

My daughter would say "Ta mère". It was a nice two day's distraction but now I run out of promising ideas as for how to do further progress with reasonable effort.

Except for this one. I modified the stuff a bit but take care, the cloud is not really stable. I found the following restrictions so far:
- no context menu access
- no access to object properties in the modeller region
- no chance to input new area regions (this totally messes the sheet)

I had to remove Davide's convenience stuff to run the program in the cloud.

In principle, the file should be Viewer-proof but I just get a crash if I launch the exe.

You can put another rectangular load on top of the structural weight and move it around to see, where it creates the largest moment ->model. Not really animated but yet interactive.

Wrote

If I'm not wrong, the right translation in your language for the equivalent answer is: "Deine Mutter".

Yes. In the sense of having nothing else to contribute, at least for the moment ;-)

One more update:
- up and down forces
- left and right moments
- table of nodal results (including support reactions)
- sign of shear and moment line changed (positive direction for shear and moment is upwards in the diagram)
The stuff is uploaded as example. It can be opened in the cloud version, you won't see, however, the table of nodal results because it uses the table region plugin by Davide.

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Cool

There'a an easy way to setup the diagrams conventions? Usually I use the shear as in your last example and the positive moments on the tension side...

i.e. the Signs conventions panel of Ftool

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Wrote

There'a an easy way to setup the diagrams conventions? Usually I use the shear as in your last example and the positive moments on the tension side...

Setting the signs is easy. Have a look at the function BeamPost().

The convention used in the final example is that which I use for teaching.
External forces correspond to steps in shear and distributed loads change the shear curve in the direction they are sketched.
The shear line gives the slope of the moment line. This facilitates easy sketching of the lines without non-obvious sign conventions.
the drawback is that the positive direction in M and Q diagrams is opposite to the positive direction for external loads and displacement.

Example updated.
- Non-zero displacement constraints (y position of triangles is evaluated)
- Solver crashes due to non-invertible systems avoided by connecting orphan nodes with low
stiffness beams
- Instructions added
The code should be fairly stable now (impossible to crash by whatever senseless model layout). Please report any issue.

Don't ask me why, but now BeamFEA.sm runs in the viewer.

I uploaded it as application to the gallery (table of nodal values is missing, because the exe is compiled on server side without external plugins.

If you want an executable with table, then save the example as exe and you are done.

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@Martin

First of all, awesome job. Very Impressive. I'm sure I will have more questions in the near future as I try to incorporate this.

Regarding the Getmax function we talked about in post 33 when I use this in a blank page it works fine, but when I use it in a page that must define a variable or something along these lines, I receive an error message "variables should be defined for argument-functions"
Is there a way to make sure this doesn't happen? Or maybe you can shed light on the reason for the error message?

Thanks!

Wrote

Regarding the Getmax function we talked about in post 33 when I use this in a blank page it works fine, but when I use it in a page that must define a variable or something along these lines, I receive an error message "variables should be defined for argument-functions"
Is there a way to make sure this doesn't happen? Or maybe you can shed light on the reason for the error message?

Can you provide a minimum working example of the error?
In BeamFEA.sm, intermediate values between nodes are considered to be element solutions and provided by the solver (element results)
The min/max check is done by the function absmax() in the postprocessing environment.

Martin, first of all I would like to say that your implementation of Modeller and FEA simply blew my mind - I had no idea that something like this is possible with the Smath Studio. As a practicing structural engineer I find it very useful to be able to do a quick continuous beam analysis without firing up SAP2000 or SFrame. I will start experimenting with formulas and modeller myself; I do not however believe I will come up with something even remotely close in complexity to your code.

For what it is worth I have few comments:

- I really like the approach you took in the 1st iteration of your BeamFEA,
when you displayed Shear, Moment and Displacement curves separately - it is quite
useful to tell demand at any given point just by looking at plot. I have tried
(partially successfully) to modify your document to recreate those plots

- Is there away to set X-axis and Y-axis "ticks" to a reasonable minimum value
automatically? It will make output chart easier to read.

- It is also quite useful to plot the distributed load (q) so one can see all the demands imposed on a beam (force and moment from table, q from plot). I have tried to implement this but got stuck plotting piecewise function using Draw2d().

- When scaling EI it makes more sense (visually) to make EI proportional to (beam depth)^3

- I believe it is not possible but anyway.. Can you define geometry of modeller region non-interactively? Say you want 3 span beam with UDL=5 and Point load / moment. Is it possible to tell modeller region what to display instead of dragging objects about?

Again great work - just made me want to learn the Smath Studio even more.

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BeamFEA (2).sm (235 КиБ) скачан 95 раз(а).

Oxel - good suggestions. Also if we could incorporate units, that would really be great. Even if they are preset units.


Martin - sorry I did not notice your reply. I've attached the simple beam function. I believe my issue is when X is defined on the page. Then I receive an error.

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Simple Beam Function - Error.sm (70 КиБ) скачан 85 раз(а).

Wrote

- I really like the approach you took in the 1st iteration of your BeamFEA,
when you displayed Shear, Moment and Displacement curves separately - it is quite
useful to tell demand at any given point just by looking at plot. I have tried
(partially successfully) to modify your document to recreate those plots
- Is there away to set X-axis and Y-axis "ticks" to a reasonable minimum value
automatically? It will make output chart easier to read.]

Separating the diagrams could be done in a single modeler region or in separate regions, just by slightly modifying the postprocessing function.
I dropped the Maxima draw based approach because I do not see acceptance of that way of plotting in the SMath community. However, nice to see that you took the pain to create some plots.

As to the ticks: in Draw2D that is easy, in the modeller region one would have to implement this from scratch. And I don't know how to create text annotations in the modeller, I am waiting for Andrey to reveal this secret.

Цитата

- It is also quite useful to plot the distributed load (q) so one can see all the demands imposed on a beam (force and moment from table, q from plot). I have tried to implement this but got stuck plotting piecewise function using Draw2d().

q is the second column of the element result matrix, see attachment. I had to fix a bug but now it works correctly.

Цитата

- When scaling EI it makes more sense (visually) to make EI proportional to (beam depth)^3

I agree.

Цитата

- I believe it is not possible but anyway.. Can you define geometry of modeller region non-interactively? Say you want 3 span beam with UDL=5 and Point load / moment. Is it possible to tell modeller region what to display instead of dragging objects about?

Actually it is very easy. You just have to create a matrix similar to the modeller output (limited to the first 5 columns) and select this as predefined template in the context menu. In the attached example I added a second modeller region, which reflects all the actions you do in the input region. You can see how the control matrix is affected and how it has to be designed for a particular system.

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BeamFEA2.sm (249 КиБ) скачан 111 раз(а).

Wrote

Oxel - good suggestions. Also if we could incorporate units, that would really be great. Even if they are preset units.


Martin - sorry I did not notice your reply. I've attached the simple beam function. I believe my issue is when X is defined on the page. Then I receive an error.

Just change X to X# in your function. Then it works (unless you define X# outside the function).
As to the units - that should be possible to implement, actually, the solver should be unit-proof. Thus, just pre- and postprocessing need to be adapted.

Here is a version with separated plots. Would that be preferrable to a single plot with multiple curves?
Note that the maximum values are essentially maximum absolute values.

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BeamFEA.sm (171 КиБ) скачан 126 раз(а).

IMO, the latest version is preferred (separated plots). Although knowing the maximum negative and maximum positive can also be helpful. Idealy Max Positive, Max Negative and user defined location.

I would encourage anyone who continues to modify the program to post updates here as it would be interesting to see.
When I get some free time I would like to incorporate units and possibly change some of the input so that loads could be defined above and put into a matrix and then shown in the modeller (I think that is what Oxel was saying).

I was thinking of starting another thread, either analysis of concrete beam-column, or cantilevered retaining wall or a beam comparison calculator.... In any case should I start another thread in the questions forum or somewhere different?