Torsion differential equation
Torsion differential equation
(OP)
hey everyone,
i have a channel beam under a linearly varying torsional moment
my question is:
given the torsion differential equation written as:
phi''[x] - [E*Jw/(G*Jt)]phi''''[x] = -[mx/(G*Jt)]
how must it be written for a load like the one in the attached figure?
in other words, what "mx" should i use? or should i divide the beam in half? i've tried several things but the solutions came out "suspicious" every time.
i have a channel beam under a linearly varying torsional moment
my question is:
given the torsion differential equation written as:
phi''[x] - [E*Jw/(G*Jt)]phi''''[x] = -[mx/(G*Jt)]
how must it be written for a load like the one in the attached figure?
in other words, what "mx" should i use? or should i divide the beam in half? i've tried several things but the solutions came out "suspicious" every time.






RE: Torsion differential equation
RE: Torsion differential equation
I like to debate structural engineering theory -- a lot. If I challenge you on something, know that I'm doing so because I respect your opinion enough to either change it or adopt it.
RE: Torsion differential equation
Why?
the case i'm studying is torsionally fixed at both ends (phi = 0) and in two separate scenarios it can be warping fixed (phi' = 0) and warping free (phi'' = 0)
i've tried to divide it in half considering phi(0)=phi'(0)=0 and phi'(L/2)=0 but the results were not good
RE: Torsion differential equation
Be careful with torsional fixity. It requires rotation restraint and warping restraint. Regardless of your boundary condition at the real supports, torsional fixity can be assumed at L/2 in a half span model.
I like to debate structural engineering theory -- a lot. If I challenge you on something, know that I'm doing so because I respect your opinion enough to either change it or adopt it.
RE: Torsion differential equation
RE: Torsion differential equation
I like to debate structural engineering theory -- a lot. If I challenge you on something, know that I'm doing so because I respect your opinion enough to either change it or adopt it.
RE: Torsion differential equation
But that's just something that quickly popped into my head, I'm no solid mechanics expert.
RE: Torsion differential equation
That is, unless this is a existing member that you are trying to make work/pass under a new load.
RE: Torsion differential equation
it'd react the same way if if were a constant moment (ie zero-some-zero twist) ... the amount of twist is likely to be higher for the tapering torque.
another day in paradise, or is paradise one day closer ?
RE: Torsion differential equation
another day in paradise, or is paradise one day closer ?
RE: Torsion differential equation
I divided the beam in half and at L/2 applied warping fixity (but free rotation) so now i just have 3 boundary conditions
for the left part:
phi'[x] - [E*Jw/(G*Jt)]phi'''[x] = Tm (2 (1 - b) x/L + b)/(G*Jt), phi[0] = 0, phi'[0] = 0, phi'[L/2] = 0
and for the right part:
phi'[x] - [E*Jw/(G*Jt)]phi'''[x] = -Tm (2 (1 - b) (L - x)/L + b)/(G*Jt), phi[L] = 0, phi'[L] = 0, phi'[L/2] = 0
where b is T0/Tm.
The results now seem plausible but i don't know for sure if they are correct
what do you guys think about this?
RE: Torsion differential equation
it is a very easy way to accommodate difficult functions. I'm not sure how it shakes out for torsional functions, but for beam functions it works quite well.