Solving symbolically a system of equations with boundary values

[ptc-5524048]

Hello, I´m new to Mathcad Prime 3 and haven't find a solutión on internet or here

What I´m trying to do is to solve simbolically g ‘ ‘ (x) = M where M =P2*x-P3

The answer should be, P2 = 12 EI/L^3, P3 = 6 EI/L^2, c2 = 1, and c1 = 0.

g ' (x) = (P2*x^2)/2 - P3*x + c1

Then solving for g ’ (x=0) = 0 wich gives me c1=0 and solving for g ’ (x=L) = 0 wich gives me P3 = P2*L/2

g (x) = (P2*x^3)/6 - (P3*x^2)/2 + c1*x + c2

Then replacing P3 in g (x), solving for g (x=0) = 1 wich gives me c2=1 and solving for g (x=L) = 0 wich gives me P2 = 12 EI/L^3

Is there a way that Mathcad do this with find function? or something else that is like placing equations, then placing boundary value conditios and get an answer?

I attach a sheet with averything i have tried

thanks.

JAC

[ptc-5524048]

Sorry g ' ' (x) = M / EI or EI* g ' ' (x) = M

[Werner_E · Accepted solution]

As it seems you are searching a symbolic solution, you would have to use the symbolic "solve" (see if the attached sheet helps).

In contrary to Mathcad 15 and below we unfortunately cannot evaluate a solve block symbolically in Prime.

To avoid the red errors from the numeric processor, you would have to add all unknown variables as arguments of the functions (see also attached file)

[ptc-5524048]

thank you!!! awsome

[ptc-5793717]

Hello, I'm also new to mathcad, and I'm having a similiar problem with a bit more complex beam.

I'm trying to calculate and plot the deflection (by quadruple integration) for this beam:

and after trying several different approaches I'm forced to ask for help 🙂

When I'm trying to calculate the deflection for each part of the beam separatly it works well, but as soon as i try to do it for all 16 boundary values it just stops cooperating. I suspect that I'm making some dumb error somewhere, but I just can't find it.

and btw. Sorry for any errors in this text. I'm not a native english speaker.

[AndyWesterman]

Looking at the output from the 1st of the solve blocks,

you have :

since i=6m & p=10kN*m from the picture these appear to be contradictory.

There may be an error in the problem definition - you will need to check all the input equations.

I have tried to understand the relationship between the 4 parts that you have , but it is not easy to see what the conditions should be.

Can you explain what the various symbols represent?

e.g. w(x) displacement , w'(x) velocity, w''(x) acceleration, w'''(x) ???

there are also fixed conditions that you want to meet & these again are not too obvious from the picture at the top of the sheet.

Can you list what these should be?

Regards

Andy

[ptc-5793717]

The idea is to get the direct determination of the elastic curve from load distribution.

w'''(x) - shear equation

w''(x) - bending moment equation

w'(x) - slope equation

w(x) - deflection equation

The picture at the top shows the beam with results for moment, shear and deflection.

It is taken from "Robot stuctural analysis". Plots that i want to get should look exactly like those on the picture.

1 support is fixed. (no rotation, has moment, no deflection)

1 beam (7m EI1)

1 hinge (no moment, can deflect) (loaded with 15 kN)

2 beam (6m EI1)

2 support (can rotate, carries moment, no deflection)

3 beam (7m EI1)

2 hinge (no moment, can deflect)

4 beam (6m EI2) (loaded with 10 kN/m)

3 support (can rotate, no moment, no deflection)