File not found.File not found.File not found.Hello
Sorry but I have a problem with Smath
Im looking for the neutral axis of a reinforced concrete section.
I wrote the integral equation in order to find the correct position..but there is something probably wrong becouse i have no output from the equation. Im able to find it in Mathcad.. and i don't understand where i'm making mistakes, maybe in the equation sintax?
Someone more expert than me can help?
The file is attached with the post.
Here there are even the pictures regarding the wrong equation

The file is not very linear and cute because is still just a draft. I will surely improve it!

Hi Ale. Don't worry, your worksheet is well composed. Unfortunately SMath does not have simple functions to find roots by purely numerical procedures, and for some reason I cannot implement al_nleqsol, but you can always resort to the basic algorithms.



Verifica pressoflessione retta.sm (319 KiB) downloaded 40 time(s).

Best regards.
Alvaro.

Greetings,

̶I̶ ̶̶t̶h̶i̶̶n̶k̶ ̶t̶h̶e̶ ̶̶m̶a̶i̶n̶ ̶i̶s̶s̶̶u̶̶e̶ ̶i̶s̶ ̶t̶h̶a̶t̶ ̶y̶o̶u̶ ̶a̶r̶e̶ ̶t̶r̶y̶i̶n̶g̶ ̶t̶o̶ ̶i̶n̶t̶e̶g̶r̶a̶t̶e̶ ̶"̶c̶a̶s̶e̶s̶(̶)̶"̶.̶ ̶ ̶B̶e̶l̶o̶w̶ ̶i̶s̶ ̶a̶ ̶s̶i̶m̶i̶l̶a̶r̶ ̶t̶h̶r̶e̶a̶d̶:
- https://en.smath.com/forum/yaf_postst23389_Boolean-condition-and-diff-issues.aspx


̶̶T̶h̶̶a̶t̶ ̶i̶s̶,̶ ̶fo̶r̶ ̶s̶t̶a̶t̶e̶m̶e̶n̶t̶s̶ ̶l̶i̶k̶e̶ ̶ε̶.̶c̶(̶x̶,̶x̶.̶c̶)̶:
̶[̶S̶P̶O̶I̶L̶E̶R̶]̶
y̶o̶u̶ ̶n̶e̶e̶d̶ ̶t̶o̶ ̶i̶n̶t̶e̶g̶r̶a̶t̶e̶ ̶e̶a̶c̶h̶ ̶e̶q̶u̶a̶t̶i̶o̶n̶ ̶se̶p̶a̶r̶a̶t̶e̶l̶y̶ ̶(̶y̶o̶u̶ ̶h̶a̶v̶e̶ ̶t̶h̶e̶m̶ ̶a̶l̶l̶ ̶c̶o̶m̶b̶i̶n̶e̶d̶ ̶i̶n̶t̶o̶ ̶(̶1̶)̶ ̶f̶o̶r̶m̶u̶l̶a̶/̶e̶q̶u̶a̶t̶i̶o̶n.


Formation of Integration utilizing cases() is not the/an issue.


May this be of Good Help;
- Kenny Lemens, P.E. ᵂᴵ

Hi!
Again me.
Verifica pressoflessione retta M+_R3.sm (1 MiB) downloaded 24 time(s).
Sorry if I bother you again, but i've got another problem related the graphical output of the obtained solution.
I'd like to see the M-N domain that should have this form (just the upper part of the of the domain show in the picture "Gelfi Domani").

My problem is that I'm not able to find the solution for more than one N. I tried several stuff and ideas but I didn't find the correct way.

Someone has got the solution to find the neutral axis xi related to a range of Axial forces N (pic. "Neutral axis for multiple N")?


Additionally the domain is not complete in the last part, close to field 6 where the reinforced concrete sections are very brittle and totally compressed (pic "Assumption 1 and 2"), and where collaps happend for concrete failure.
Im pretty sure to have defined correctly the assumption until fild 5 in order to define concrete stresses and steel bars stresses, but the last part is surely wrong.



Someone know how to find the solution to that problem?

Thank you in advance!!!

Hi. For the first question, this is a way to define a family of functions h(x) for a parameter i that can be manipulated later.


Verifica pressoflessione retta M__R3.sm (1 MiB) downloaded 26 time(s).

For the second question, from the point of view of numerical calculation, equalities do not exist, so it is very difficult to decide when x = H, since what can actually be detected is x-ε < H < x+ε or x ≈ H with the new operator '≈'. But then you also have to verify that other operations, such as the integral, detect that value. A generic way to do it is with the Dirac delta, but the drawback is that it is not a function, but a distribution, and it is not easy to implement it.

In other words, you have to implement a numerical model and verify that you get the desired values, or use other software, like Maple and the piecewise function, for example.

Best regards.
Alvaro.

Credo che la costruzione dei domini M-N risulti più semplice con il metodo che veniva insegnato quando la velocità e la capacità dei calcolatori era inferiore. In sostanza si fissano delle coppie di valori di deformazione al lembo superiore ed al lembo inferiore (o all'altezza dell'armatura più tesa). Tali valori sono scelti proprio prendendo i valori che delimitano i 6 campi di rottura più alcuni punti interni (alcuni valori tipici si possono ricavare da alcune pubblicazioni ma sono sostanzialmente a scelta e più coppie consideri e migliore sarà la rappresentazione). Diventa subito facile calcolare l'asse neutro dalle due deformazioni (come hai fatto per x2, x3 ...) e le deformazioni in tutte le altre armature. Dalle deformazioni ricavi le tensioni entrando nelle curve dei materiali. Infine dall'equilibrio alla traslazione e alla rotazione ottieni (anche usando l'integrale come hai fatto tu nell'equazione dell'asse neutro; ma in questo caso l'asse neutro è fissato) una coppia di valori M e N da usare per tracciare il diagramma. Ripeti per tutte le coppie di deformazione fissate.
sergio

I believe that the construction of the M-N domains is easier with the method that was taught when the speed and ability of the calculators was lower. In essence, couples of deformation values ​​to the upper flap and lower flap are fixed (or at the height of the more tense bar). These values ​​are chosen precisely by taking the values ​​that delimit the 6 rupture fields plus some internal points (some typical values ​​can be obtained from some publications but they are substantially choice and the more couples consider and the better the representation will be). It immediately becomes easy to calculate the neutral axis from the two deformations (as you did for X2, X3 ...) and the deformations in all the other bars. From the deformations revenue the tensions by entering the curves of the materials. Finally from the balance to the translation and rotation you get (also using the full as you did in the equation of the neutral axis; but in this case the neutral axis is fixed) a pair of values M and N to be used to trace The diagram. Repeat for all deformation pairs fixed.