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I have organized my worksheet somewhat now, and collected only the relevant parts for my specific problem at the top. The other stuff that although it displays the power of SMath - it's not relevant for this workbook, is gathered at the bottom.

Something mysterious, it does not download *.sm, only some sort of "Chrome" document.
Nothing to see, that's OK unless I can help more.

Cheers, Jean

That is certainly strange. When I try to download the file it opens just fine.

Maybe it's the use of the Scandinavian alphabet it the filename that's causing this.

Hopefully this works

Staaltemperaturer ved brann.sm (739 KiB) downloaded 77 time(s).

Wrote

Hopefully this works

Works fine, thanks.

Hi guys,

I'm back again with more headaches I'm hoping you can help me with.

The last time I wanted (we succeeded ) to make a calculation for the temperature development of UNPROTECTED steel sections during fire.

This time I want to make a similar calculation for PROTECTED steel sections. Most of the work that was done on the last sheet is reused. However, the expressions for temperature development this time seems (to my eyes) to be a bit trickier. In the sheet I have pointed out where I am stuck. The image shows the example I am trying to follow.

Any help on this is greatly appreciated. :d


Best regards,

Hans Kristian.


File not found.File not found.

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I'm back again with more headaches I'm hoping you can help me with.

Hello ! Hans
Will be back on that soon ... cheers.

Appreciated Jean!

I have added some graphic illustrations to highlight what is going on with some of the variables..

Best regards,

Temperaturforlop i isolerte stalkonstruksjoner ved brann.sm (415 KiB) downloaded 52 time(s).

Wrote

I have added some graphic illustrations to highlight what is going on with some of the variables..

All the graphs down to the DE solvers work fine ... but
======== the suite of 6671 is not compatible with 6179 ========
Simply disastrous that dn_GearsBDF 6179 is not compatible 6671.

The suite 6671 looks correct, sorry for this handicap.
Maybe more collab will terminate checking.

Cheers Hanski ... Jean

Temperaturforlop i isolerte stalkonstruksjoner ved brann page2.sm (57 KiB) downloaded 44 time(s).

... going back to your original 6671, the suite looks ok.
Not sure if I understand the meshing of the solvers from
the stacked "res"... missed something in there.

See you Norway ! ... Jean

Temperaturforlop i isolerte stalkonstruksjoner ved brann [Suite 6671].sm (478 KiB) downloaded 48 time(s).

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... going back to your original 6671, the suite looks ok.

... just a comment: "ainterp" is a very unique/specific cubic interpolator.
From applied analysis, it ranks from best to pure crap.
Your DE solvers are so dense, "linterp" is sufficient.

Jean

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I have added some graphic illustrations to highlight what is going on with some of the variables..

All the graphs down to the DE solvers work fine ... but
======== the suite of 6671 is not compatible with 6179 ========
Simply disastrous that dn_GearsBDF 6179 is not compatible 6671.

The suite 6671 looks correct, sorry for this handicap.
Maybe more collab will terminate checking.

Cheers Hanski ... Jean

Temperaturforlop i isolerte stalkonstruksjoner ved brann page2.sm (57 KiB) downloaded 44 time(s).

Jean,

I must be missing something.. I tried to downgrade to suite 6671, and dn_GearsBDF still tells me it cannot calculate.

I don't understand why the DE cant handle e^ø. Or have I constructed the DE wrong?

Best regards,

Wrote

... going back to your original 6671, the suite looks ok.
Not sure if I understand the meshing of the solvers from
the stacked "res"... missed something in there.

See you Norway ! ... Jean

Temperaturforlop i isolerte stalkonstruksjoner ved brann [Suite 6671].sm (478 KiB) downloaded 48 time(s).

I'm not following you.. what do you mean?

Best regards,

Wrote

Jean,

I must be missing something.. I tried to downgrade to suite 6671,
and dn_GearsBDF still tells me it cannot calculate.

I don't understand why the DE cant handle e^ø. Or have I constructed the DE wrong?

The books style are very difficult to put it executable.
Your DE setup looks quite correct: proof the first one works
but the 2, 3, 4 "Division by 0". It must have to do with the
meshing of the Solver. It does not like something in there.
Should work in your latest 6671.
I simply reconstructed piece wise, simplified, on my 6179.

See U tonight ... Jean

Temperaturforlop i isolerte stalkonstruksjoner ved brann page2 fixed.sm (269 KiB) downloaded 51 time(s).

You mean you downgraded 6179

Wrote

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Jean,

I must be missing something.. I tried to downgrade to suite 6671,
and dn_GearsBDF still tells me it cannot calculate.

I don't understand why the DE cant handle e^ø. Or have I constructed the DE wrong?

The books style are very difficult to put it executable.
Your DE setup looks quite correct: proof the first one works
but the 2, 3, 4 "Division by 0". It must have to do with the
meshing of the Solver. It does not like something in there.
Should work in your latest 6671.
I simply reconstructed piece wise, simplified, on my 6179.

See U tonight ... Jean

Temperaturforlop i isolerte stalkonstruksjoner ved brann page2 fixed.sm (269 KiB) downloaded 51 time(s).

You mean you downgraded 6179

Jean,

I can not get it to work in my current version of Smath.

Is it possible another solver has to be used? One of the Runge-Kutta versions maybe?

You are quite right though, the fact that the first of the four equations work on your sheet suggests that it should work. However, that values in the solution you posted is quite wrong... Not quite sure why that is though, has to be something with the input.

I'm quite curious as to what the workaround/solution to this project will be. Looking forward to seeing what you will come up with

Best regards,
Hans Kristian

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Jean,

I can not get it to work in my current version of Smath.

Is it possible another solver has to be used? One of the Runge-Kutta versions maybe?

You are quite right though, the fact that the first of the four equations work on your sheet suggests that it should work. However, that values in the solution you posted is quite wrong... Not quite sure why that is though, has to be something with the input.

I'm quite curious as to what the workaround/solution to this project will be. Looking forward to seeing what you will come up with

Hanski,

A bit of headache
Those solver may fails ... guess the cause "Division by zero".
You should have the first segment running as the picture.
Just to show how difficult it could be, read the ODE Yuk.

Jean



Temperaturforlop Compactum.sm (60 KiB) downloaded 43 time(s).

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A bit of headache

Forgot to add: possibly a piece wise Finite Differences
will do. Just a matter of setting it correctly. That will
not "divide by zero " !

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Jean,

I can not get it to work in my current version of Smath.

Is it possible another solver has to be used? One of the Runge-Kutta versions maybe?

You are quite right though, the fact that the first of the four equations work on your sheet suggests that it should work. However, that values in the solution you posted is quite wrong... Not quite sure why that is though, has to be something with the input.

I'm quite curious as to what the workaround/solution to this project will be. Looking forward to seeing what you will come up with

Hanski,

A bit of headache
Those solver may fails ... guess the cause "Division by zero".
You should have the first segment running as the picture.
Just to show how difficult it could be, read the ODE Yuk.

Jean



Temperaturforlop Compactum.sm (60 KiB) downloaded 43 time(s).

Do you have a link to that text?

All the solutions works just fine if the last part e^ø(theta) is neglected. The DE solver can handle ø(theta) in the first part of the expression.

As a matter of fact, if the last part of the expression is altered to e^ø(t), the solver can handle that too. Of course the results are wrong, but it might suggest that the thing that the solver dislikes is the fact the e^ø is dependent on theta.


Is Mathcad able to handle this DE? Can anyone try to solve it there?


PS: I still cant get the original sol_1 to calculate in my version of Smath. It just tells med "Cannot calculate". If you get the error "Division by zero", maybe you can try to modify the IC's a little bit? From 600 to 595/605, from 735 to 730/740 etc.

Best regards,
Hans Kristian

File not found.File not found.


Edit:

Does sol_4 work for you? It should work considering Ca is constant for this solution.

Wrote

Just to show how difficult it could be, read the ODE Yuk.

... Oh ! it didn't upload.
17 solvers, only rkfixed responds at very specific 'N'

ODE Yuk.sm (27 KiB) downloaded 36 time(s).

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Is Mathcad able to handle this DE? Can anyone try to solve it there?

I doubt because rkfixed, Rkadapt are same.
The first segment maybe ? from the "Stiff option"
Good news is that the project has an elegant solution.
It consists in solving the Integral Equation
Will post it before bed time ...

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It consists in solving the Integral Equation

... maybe there is some applicable scaling factor ? ?



Temperaturforlop Compactum Copy.sm (48 KiB) downloaded 39 time(s).

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It consists in solving the Integral Equation

... maybe there is some applicable scaling factor ? ?



Temperaturforlop Compactum Copy.sm (48 KiB) downloaded 39 time(s).

Interesting! I will look into this later this evening!

But from the top of my head - the X-axis should represent time in minutes, not temperature.

Also, it took quite some time for the sheet to finish calculating.

Best regards,
Hans Kristian

Wrote

But from the top of my head - the X-axis should represent time in minutes, not temperature.

Also, it took quite some time for the sheet to finish calculating.

Best regards,
Hans Kristian

1. You can leave it in native 't'
2. the default Integration accuracy is 100, set it 50
it will have no influence in this application but much faster.
1.7 min in my 1.66 GHz laptop runs 225 greedy maths.
3. Does your version bracket t:=[0,5..600] ?
rather than Smath 6179 t:=0,5..600

Temperaturforlop Compactum Copy.sm (53 KiB) downloaded 43 time(s).