Hi,

I have a problem with N/m (Newton per meter) unit in SWMath Studio. Here's my input and output:

a := 3 m
α := 0,01443
β := 0,1259
q := 60000 N/m
E := 210000000000 Pa
t := 0,05 m
ν := 0,3

D := (E*(t^3))/(12*(1-(ν^3))) = 2,2482*10^6 J
y := α*((q*(a^4))/D) = 0,0312 m^2
M := β*q*(a^2) = 67986 J
σ := (6*M)/(t^2) = 1,6317*10^8 m Pa

Now the problem is with output units. D should be in Pa*m^3, y should be in m, M should be in N*m and σ should be in Pa. It seems that the input of q units causes these problems. I type it as 'N/'m but it seems that it's not recognized properly. Am I doing something wrong ?

Much easier to doctor with the *.sm document attached !
Same problem as before, as it looks.

I state that what Jean wrote is important.
This seems to be the solution for plate in flexion; I don't know which manual (Bares ???) you got this solution from but I see at least two potential errors:
1) 1-v ^ 3 ----> 1-v ^ 2 (irrelevant for the unit of measurement problem)
2) q = 60000 N / m ---> 60000 N / m ^ 2

sergio

Wrote

Now the problem is with output units. D should be in Pa*m^3, y should be in m, M should be in N*m and σ should be in Pa. It seems that the input of q units causes these problems. I type it as 'N/'m but it seems that it's not recognized properly. Am I doing something wrong ?

As stated above there is a problem with dimensions (f.e. if M should be Force x Length then the equation of σ misses a length on the denominator if you want a tension [F]/[L]^2 as output)

You can type the desired output unit in the rightmost placeholder (see examples here); doing this you can see that D and M they have your expected units while γ σ not.

Thank you all for replies. Indeed, that's a plate bending problem. The equations and coefficients are taken from "Theory of Plates and Shells" by Timoshenko (table 47). I attached the .sm file to this post.

PompelmoTell is right, it should be 1-ν^2 instead of 1-ν^3, I made a mistake while rewriting this. I also thought that q should be in N/m^2 instead of N/m but in such case M would have incorrect units: M=β*q*a^2=(N/m^2)*(m^2)=N while it should be in N*m. On the other hand, with q in Pa the units of σ and y are correct, only M is wrong.

Plate bending.sm (7 KiB) downloaded 34 time(s).

No it's not wrong: it should be read as N * m / m (this is how the bending moments in the plates are measured)
sergio

So the moment should be in (N*m)/m = N in this case ? Seems right because in the Notation section at the beginning of Timoshenko's book it is said that M means "bending moment per unit lenght of sections of a plate perpendicular to x axis". Thank you very much.

Wrote

So the moment should be in (N*m)/m = N in this case ? Seems right because in the Notation section at the beginning of Timoshenko's book it is said that M means "bending moment per unit lenght of sections of a plate perpendicular to x axis". Thank you very much.

Yes. Also, you can set the result unit as N*m/m if you want and will not cause any issues SMath-side.

What about making the system silent, i.e: in silent units ?