Torsion - AISC Design Guide 9 Formulas for Graphs?
Torsion - AISC Design Guide 9 Formulas for Graphs?
(OP)
I am working on a Mathcad file for calculating torsional stresses. Looking at AISC Design Guide 9, is there a way to calculate the values in the graphs in Appendix B instead of looking at the graph to come up with the values?
Thank you
Thank you






RE: Torsion - AISC Design Guide 9 Formulas for Graphs?
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).
RE: Torsion - AISC Design Guide 9 Formulas for Graphs?
RE: Torsion - AISC Design Guide 9 Formulas for Graphs?
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.
RE: Torsion - AISC Design Guide 9 Formulas for Graphs?
RE: Torsion - AISC Design Guide 9 Formulas for Graphs?
RE: Torsion - AISC Design Guide 9 Formulas for Graphs?
RE: Torsion - AISC Design Guide 9 Formulas for Graphs?
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.
RE: Torsion - AISC Design Guide 9 Formulas for Graphs?
Thanks for posting the solution. I agree with the solution but when z=0, I get Θ'=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 Θ' must not be zero) as well as in the AISC Design guide example.
What am I doing wrong to come up Θ'=0 when z=0?
RE: Torsion - AISC Design Guide 9 Formulas for Graphs?
RE: Torsion - AISC Design Guide 9 Formulas for Graphs?
i was getting the same formula you had for Θ'and I agree, Θ' shouldn't be zero from the graphs
your formula for Θ' looks like it would be zero when z=0, what do you get for Θ' when z=0?
RE: Torsion - AISC Design Guide 9 Formulas for Graphs?
I'd be glad to help you.
Post your formula
RE: Torsion - AISC Design Guide 9 Formulas for Graphs?
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RE: Torsion - AISC Design Guide 9 Formulas for Graphs?
thank you (again) for your help, hopefully i will have this working now
RE: Torsion - AISC Design Guide 9 Formulas for Graphs?
I think you are using α = 0, and I do not think that is correct buddy !!!
RE: Torsion - AISC Design Guide 9 Formulas for Graphs?
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