Flapwise/Edgewise Stiffness Calculation


I’m interested in calculating the Flapwise/Edgewise Stiffness for an aerofoil cross-section. However I’m not entirely confident about the formula. In the FAST user guide the definition for stiffness are :

FlpStff = ∫∫ E (x, y) x^2 dxdy
EdgStff = ∫∫ E (x, y) y^2 dxdy

I would like to know how do the formulas changes for uni-directional material (Ex not equal Ey), can it be :

FlpStff = ∫∫ Ex (x, y) x^2 dxdy
EdgStff = ∫∫ Ey (x, y) y^2 dxdy

or is it totally different?

Thanks for your time.

Dear Terence,

Yes, I suppose you can say that.

However, please bear in the mind that the existing blade model in FAST effectively assumes an isotropic material. For composite blades with anisotripic material, FAST will miss a lot of terms. See the following forum topic for more information: http://forums.nrel.gov/t/coupled-blade-modes-in-fast/314/1.

The new finite-element blade model that we are developing (mentioned briefly in the post above) is capable of modeling highly flexible composite blades, including:

*Full geometric nonlinearity
*Bending, torsion, shear, & extensional DOFs
*Anisotropic material couplings
*Sectional offsets
*Initially curved/swept blades

Best regards,

Hello Jason,

Thanks for your reply. I’m trying to reverse engineer the stiffness and inertia cross-section data given in the pdf ‘Definition of a 5-MW Reference Wind Turbine for Offshore System Development’. I know that Brian R. Resor from Sandia actually did it and I have the pdf as well, however I just would like my own code to play with. Unfortunately I must do something wrong because my results do not quite agree with the other ones. I’m pretty confident for the inertial calculations because I validated the results against SolidWorks however I’m not so sure about stiffness.

The formulas are :

FlpStff = ∫∫ Ex(x, y) x^2 dxdy
EdgStff = ∫∫ Ey(x, y) y^2 dxdy

taken with respect to the elastic center. First, that is not clear for me, I tried finding information about how to calculate it but I’m still confused about the different denominations such as elastic axis, neutral axis, elastic center and shear center. I calculate the elastic center, similarly to the center of mass with density, by integrating the elastic modulus time distance over the area.

xe= ∫∫ Ex(x, y) x dxdy
ye= ∫∫ Ey(x, y) y dxdy

I then calculate the FlpStff and EdgStff with respect to the chord axis and then use the parallel axis theorem to transfer the results into the elastic center.

Does this seem correct?

Thanks for your time.


I checked the reference by Lindenburg for the blade structural data interpolation given in ‘Definition of a 5-MW Reference Wind Turbine for Offshore System Development’’ but the FlpIner and EdgIner are not given in the original pdf. Did you calculate those separately?


Dear Terence,

The distributed flapwise and edgewise inertias of the NREL 5-MW turbine blade were derived from the distributed mass and radii of gyration values reported in Appendix A of Ref. [17] from the NREL 5-MW specifications report.

Hopefully someone who knows more about cross sectional analysis than I do can comment on your approach to calculating the flapwise and edgewise stiffness.

Best regards,


I have created a shell FEM model of a wind turbine composite blade in Calculix. I would now like to calculate blade properties to use in ElastoDyn. Is there a suggested way to approach this? Calculating edgewise & flapwise stiffness and structural twist needed in ElastoDyn does not seem like a straightforward task and I was not able to find an adequate reference for the moment.

Thanks in advance to whom might reply,


Francesco Papi

Dear Francesco,

The flapwise and edgewise stiffness are defined by cross-sectional integrals, as documented in the old FAST User’s Guide (drive.google.com/file/d/1d_-vRR … sp=sharing), as well as in the following forum topic: http://forums.nrel.gov/t/downscaling-nrel-5mw-structural-properties-blade-and-tower/2479/1. The structural pretwist specifies the orientation of the principal flapwise and edgewise axes of bending.

I hope that helps.

Best regards,

Dear Jason,

I’m trying to simulate the NREL 5 MW blade model considering the “bend-bend-twist” modes. Following the work of Hodges and Dowell, I found two section constants (B1 and B2)are needed:

B1 = double integral of E(x,y) * (x^2 + y^2)^2 * dxdy
B2 = double integral of E(x,y) * y * (x^2 + y^2) * dxdy


FlpStff = double integral of E(x,y) * x^2 dxdy
EdgStff = double integral of E(x,y) * y^2 dxdy

However, it seems that B1 and B2 are unknown without knowing the elastic modulus E(x,y) and the structurally effective portion of the blade cross section. As the detailed structure of the blade is confidential. I wonder if it is possible for you to get these constants (as a function about z) ?


[1] Hodges DH, Dowell E. Nonlinear equations of motion for the elastic bending and torsion of twisted nonuniform rotor blades. TN D-7818, National Aeronautics and Space Administration;Washington, US; 1974.

Thanks for your time.
Best regards,

Dear Bowen,

I’m not familiar with your reference or equations, and I’m not sure I understand your question. The NREL 5-MW baseline blade does not have composite material coupling like bend-twist coupling. So, if you want that, you’ll need to modify the blade design anyway.

But if this is useful to you, the composite layup of the NREL 5-MW baseline blade has been reversed engineered by Brian Resor of Sandia National Laboratory, as discussed in the following forum topic: http://forums.nrel.gov/t/structural-design-of-the-wind-turbine-blade/271/18.

Best regards,