# Low-speed shaft bending moments - LSSTipMys and LSSTipMzs

Hello everybody,

I wish you all the best, success and especially healthiness. I am starting with the first question in this year

I would like to know, how FAST is calculating the bending Moments LSSTipMys and LSSTipMzs on the lowspeed shaft?

My equations (see my attachment) are missing something, because i have a littlesome offset.

Best regards
Kemal

Dear Kemal,

I see a few problems with your equations:

• You havenâ€™t stated which FAST/ElastoDyn outputs deltaM_y# refer to, but Iâ€™m assuming you mean RootMyc#.
• If I am right about the first bullet, then I agree with the first terms on the right-hand side. But in ElastoDyn, blade 3 is ahead of blade 2, which is ahead of blade 1, so, the azimuth angle of blade 2 is psi+120 deg and the azimuth angle of blade 3 is psi+240 deg; you have the signs swapped.
• In addition to RootMyc#, the blade-root pitching moments (RootMzc#) will contribute to the nontorque loading of the shaft whenever there is nonzero precone.
• The hub mass and inertia will also contribute to the nontorque loading of the shaft.

I hope that helps.

Best regards,

Hi Jason,

you are right I mean RootMyc. I will check that with your azimuth angles. Do you have a formula for me which includes RootMzc, hub inertia and â€¦? I am asking because I am comparing Bladed and OpenFAST and all bladeloads are identical except the Moment about z. The lowspeed shaft loads Fx, Mx, Fz are also identical. And I want to know how can it be, that My#shaft, Mz#shaft and Fy#shaft have offsets. I hope you can give me the equations for the loads which are different.

Best regards
Kemal

Dear Kemal,

It would not be trivial to write this equation down in closed form (it would take many lines). I donâ€™t already have it written down in the form you seek. The equation would be simplified if PreCone = 0 and HubCM = 0.

From my prior list, I also forgot to include the contribution of the in-plane and out-of-plane blade-root shear forces to the nontorque loading of the shaft.

Best regards,

Hi,
well then, do you have maybe a paper or a book in mind, where it is described?

Best regards Kemal

Dear Kemal,

The equations implemented in FAST/ElastoDyn are documented in the â€śUnofficial FAST Theory Manualâ€ť, discussed in the following forum topic: http://forums.nrel.gov/t/fast-theory-manual/1322/1. But while the equations for LSSTipMys and LSSTipMzs are stated here, they are stated in terms of local variables, not spelled out explicitly in terms of the blade-root loads.

Best regards,

Thanks!