Tek-Tips is the largest IT community on the Internet today!
Members share and learn making Tek-Tips Forums the best source of peer-reviewed technical information on the Internet!
-
Congratulations TugboatEng on being selected by the Eng-Tips community for having the most helpful posts in the forums last week. Way to Go!
Torsion - AISC Design Guide 9 Formulas for Graphs? 3
- Thread starter DAVE9999
- Start date
JoshPlumSE
Structural
The Steel Construction Institute produces a similar guide titled Design of Members Subject to Combined Bending and Torsion. It has an appendix with all the solutions to the differential equations.
If you want to do it by hand, then I believe the solution will always have the form:
Phi = Phi_h + Phi_p
Phi = twist angle
Phi_h = homogeneous solution to differential equation
Phi_h = A*Sinh(Lambda*z)+B*Cosh(Lambda*z) + C
Phi_p = Particular solution
Phi_p = C1 + C2*z+C3*Z^2 + ...
You need to set the values of the constants base on the known conditions (i.e. when z = 0, z = L... sometimes even z = 0.5*L).
If you want to do it by hand, then I believe the solution will always have the form:
Phi = Phi_h + Phi_p
Phi = twist angle
Phi_h = homogeneous solution to differential equation
Phi_h = A*Sinh(Lambda*z)+B*Cosh(Lambda*z) + C
Phi_p = Particular solution
Phi_p = C1 + C2*z+C3*Z^2 + ...
You need to set the values of the constants base on the known conditions (i.e. when z = 0, z = L... sometimes even z = 0.5*L).
BTW, Josh is correct also.
Beware that the non-homogeneous equation has t(z) on one side. This is the *internal* torque, not the applied torque as indicated in DG9 Eq. 3.2, etc.
It takes a while to solve for the particular solution. I solved one of these manualy a couple of weeks ago for a case outside DG9 and it took about 5 pages by the time I correctly solved for Phi_p. Took me about 3 tries before I made it through without a goofy mistake. Not easy for someone who doesn't solve ODEs like this on a routine basis. Selection of Phi_p is also not trivial because some problems require what they call the "modification rule" to the method of undetermined coeff.
Beware that the non-homogeneous equation has t(z) on one side. This is the *internal* torque, not the applied torque as indicated in DG9 Eq. 3.2, etc.
It takes a while to solve for the particular solution. I solved one of these manualy a couple of weeks ago for a case outside DG9 and it took about 5 pages by the time I correctly solved for Phi_p. Took me about 3 tries before I made it through without a goofy mistake. Not easy for someone who doesn't solve ODEs like this on a routine basis. Selection of Phi_p is also not trivial because some problems require what they call the "modification rule" to the method of undetermined coeff.
-
2
- #5
- Thread starter
- #6
- Thread starter
- #7
I posted the solution yesterday, but my posting was deleted from the thread. Attached is a solution to case 3 for a concentrated torque. No one has checked or verified this solution, so be cautious.
As a side note, someone out there is deleting my postings. This has happened at least a half dozen times. It is very disconcerting to have a posting deleted without ever learning why. It would be helpful if, when someone red flags a post, that the reason got passed on.
As a side note, someone out there is deleting my postings. This has happened at least a half dozen times. It is very disconcerting to have a posting deleted without ever learning why. It would be helpful if, when someone red flags a post, that the reason got passed on.
- Thread starter
- #9
That is strange why your posts are deleted. I agree, if someone is deleting it, they should explain why, that is poor communication!
Thanks for posting the solution. I agree with the solution but when z=0, I get ?'=0 (on paper and in mathcad) and that doesn't match up with what you show on page 11: a flange stress due to St.venant torsion of 4.53ksi (so ?' must not be zero) as well as in the AISC Design guide example.
What am I doing wrong to come up ?'=0 when z=0?
Thanks for posting the solution. I agree with the solution but when z=0, I get ?'=0 (on paper and in mathcad) and that doesn't match up with what you show on page 11: a flange stress due to St.venant torsion of 4.53ksi (so ?' must not be zero) as well as in the AISC Design guide example.
What am I doing wrong to come up ?'=0 when z=0?
- Thread starter
- #11
i couldn't get the file upload to work, i have a pdf of my mathcad file and when i hit upload it wouldn't work
i was getting the same formula you had for ?'and I agree, ?' shouldn't be zero from the graphs
your formula for ?' looks like it would be zero when z=0, what do you get for ?' when z=0?
i was getting the same formula you had for ?'and I agree, ?' shouldn't be zero from the graphs
your formula for ?' looks like it would be zero when z=0, what do you get for ?' when z=0?
- Thread starter
- #14
I get the 'page cannot be found' window when i try uploading but i got it working now (thanks HeeeyDave), i was mixing up location of the torque and the location of the stresses
thank you (again) for your help, hopefully i will have this working now
thank you (again) for your help, hopefully i will have this working now
-
1
- #16
Sorry to resurrect an old thread, but the solutions to the derivatives for all cases were provided in an Engineering Journal article in 2002 that can be downloaded here:
- Status
Similar threads
