Dear Conor,
Just to be clear, the OC3-Hywind specifications report (nrel.gov/docs/fy10osti/47535.pdf) gives the Young’s modulus (E) of the tower as 210 GPa; however the yield strength (sigma_yield = E*epsilon_yield, where epsilon_yield is the axial strain at the yield strength) is not given in that report. I misread your post and was simply using your value. You’ll have to make your own assumptions on sigma_yield for your own purposes.
Here are the basic equations for LUlt for a thin-walled circular cross section (from basic stress equations and tau_yield = G*gamma_yield, where G is the shear modulus and gamma_yield is the shear strain at the yield strength; you’ll have to assume your own value of tau_yield):
Transverse shear: Lult = tau_yield * A/2
Axial loading: LUlt = sigma_yield * A
Pure bending: LUlt = sigma_yield * I/y
Torsion: LUlt = tau_yield * J/r
where:
Outer diameter: D_o
Inner diameter: D_i
Maximum radius: y = r = D_o/2
Area: A = pi/4 * ( D_o^2 - D_i^2 )
Area transverse inertia: I = pi/64 * ( D_o^4 - D_i^4 )
Area polar inertia: J = 2 * I = pi/32 * ( D_o^4 - D_i^4 )
I hope that helps.
Best regards,