What are angle goal strength units?

[Vigardo]

Dear experts,

I´ve prepared a simple example KangarooTest.gh (51.9 KB) to figure out what units are used in the Strength input of the Length(Line) and Angle goal components. It consist of two lines initially at 90º with one anchor point in common (point “0”). By selecting None, One or Two in the Value List component from the yellow group, you can switch between three models, i.e. fix either no point, point “1” or point “2”, respectively.

For the Length(Line) goal it is evident that the Strength input corresponds to the stiffness constant of a simple linear spring with the units in [Newton/meter]. You can check in the gray group panels that the Strength input value is recovered by dividing the Force by the Length increment for all models.

For the Angle goal I´m a bit confused. Shouldn´t the Strength input correspond to a torsional stiffness? In the white group, I divide the Momentum by the angular increment in radians and I obtain a smaller torsional stiffness than expected. For example, feeding 100 to the Strength input of the Angle goal component, a value of 68.66 is recovered upon dividing the Momentum by the angle increment.

Would you help me to find what are the units of the Angle goal Strength input? I must be missing something key in my derivation… Thank you very much!

[DanielPiker]

Hi @Vigardo,
Does my earlier answer here help?

How to consider Moment of Inertia as BendStrength in the Bend component

Hi René, The Angle goal is calculated using the approach described in: https://www.researchgate.net/publication/223069750_Tensegrity_spline_beam_and_grid_shell_structures With the ‘Strength’ input taken as the value of EI. For units you just have to be consistent across all the goals you use (such as when calculating EA/L for the strength of the Length goal). So generally I use metres, pascals, newtons. You can read the code which runs inside the component here: https://github.com/Dan-Piker/…

[Vigardo]

Thanks for your quick response Daniel, it is highly appreciated!

In the Angle goal example file, I´ve checked that the Strength input is stored into a variable called EI. In addition, I´ve performed a couple of tests without success… KangarooTest2.gh (38.9 KB)

In Test A, I´ve tried a couple of formulas from the reference you´ve suggested (“Tensegrity spline beam and grid shell structures” by S.M.L. Adriaenssens, M.R. Barnes (2001)), but now I obtain 68.8…, a result very similar to the Strength calculated in previous post.

R = L / (2·sin(da) )
M = EI/R
EI = M·R = 68.8…

Where:
L → Beam Length [m]
M → Momentum [N·m]
da → Angular increment [rad]

In Test B, I used the maximum deflection (w) formula for a cantilever beam and a point load (from the classic Euler-Bernuolly Beam Theory), but now I find either 45.87… or the same result as before (i.e. 68.8…) depending on whether I divide by 3 or 2, respectively.
w = P·L^3 / 3EI

Solving for EI:
w = M·L^2 / 3EI
w = L·da
da = M·L / 3EI
M/da = 3EI/L
EI = L·M/3da ← Using this eq.

Where:
P → Transverse force [N]
M → Momentum [N·m] M = P·L
L → Beam Length [m]
da → Ang. increment [rad]
ka → Torsional stiffness [N·m/rad]

Did I use the correct formulas in Adriaenssens and Barnes 2001? Should I use the Shear formulas instead (eq. 6 of the ref.)?
Sa = 2·EI·sin(da) / la·lc <------- (Eq.6)
Sb = 2·EI·sin(da) / lb·lc

If so, how should they be used to get back the EI and cross-check the Strength units input for Angle goal? Sorry for my ignorance, but the paper is a bit difficult for my expertise Thanks again!