# In Nx BeamView output working fine?

Dear experts,

I´ve prepared a simple 5 m pole example to play around with the different Karamba3D analysis types as well as with cross-section optimization component. MyBeamTest.gh (80.6 KB)

Using the BeamView component and first order analysis (Th.I), the expected Nx and Mz results are obtained (see Fig.1) for the example load case (20 kN force along +y axis and 10 kN force along -z axis.

Fig.1 Using Th.I analysis

However, in the second order analysis (Th.II) the Nx forces are significantly deviating from the expected -10 kN result (see Fig.2).

Fig.2 Using Th.II analysis

I figured out that this behavior would be related to the projection of the 20 kN transverse force along the local element system of reference, but the deviation from the vertical axis seems too small to produce around 0.42 kN effects. Note that Gravity forces were not considered.

Do you agree? Am I missing something?

PS: I´m using Karamba3D 2.0.0 - build 210212 WIP for RHINO 6

Dear @Vigardo,
the value of the normal force Nx and the shear force Vy are influenced by the rotation of the cross-section (see the example MyBeamTest_cp.gh (75.9 KB)).
The formula for the normal and shear force are these:
V = R * cos(phi+phiV)-NIIr * sin(phi+phiV)
N = NIIr * cos(phi+phiV) + R * sin(phi+phiV)
Here phi is the angle of rotation of the cross section due to displacements and phiV the rotation due to imperfection. R and NIIr are the transverse and normal force with respect to the undeformed configuration.
Details can be found in “Baustatik, Theorie I. und II. Ordnung, Rubin/Schneider, 3rd edition, p. 124, Werner-Verlag, ISBN 3-8041-3084-4, 1996”. The book is however written in German.
– Clemens

Thanks Clemens for the accurate answer!

I did the math for an even simpler example (just one beam element) and I found that the results are very feasible. My intuition failed in the previous one , Karamba is Ok, as usual…