2. Benchmark solution

2.1. Calculation method used for the reference solution

The reference solution is determined using a finite element calculation where the ten beams are modelled using ten multi-fiber Euler beam elements. The forces in each of the beams are subsequently homogenized in the manner of the skeleton assembly element. For the efforts, we therefore have:

\(N=\sum _{i=1}^{Np}{N}^{i}\) \({V}_{y}=\sum _{i=1}^{Np}{V}_{y}^{i}\) \({V}_{z}=\sum _{i=1}^{Np}{V}_{z}^{i}\)

For beam moments:

\({M}_{x}=\sum _{i=1}^{Np}{M}_{x}^{i}\) \({M}_{y}=\sum _{i=1}^{Np}{M}_{y}^{i}\) \({M}_{z}=\sum _{i=1}^{Np}{M}_{z}^{i}\)

For grid moments:

\({M}_{\mathit{gx}}=\sum _{i=1}^{Np}{F}_{z}^{i}{Y}^{i}-\sum _{i=1}^{Np}{F}_{y}^{i}{Z}^{i}\) \({M}_{\mathit{gy}}=\sum _{i=1}^{Np}{N}^{i}{Z}^{i}\) \({M}_{\mathit{gz}}=-\sum _{i=1}^{Np}{N}^{i}{Y}^{i}\)

where Fx is the normal force, Vy and Vz respectively the shear forces, Mx (MGx) the torsional moment and My (MGy) and Mz (MGz) respectively the bending moments of beams (grids). Np = 10 because the modeling is carried out using ten beams.

2.2. Benchmark results

The reference result is given by the calculation on the beam bundle with imposed assembly kinematics.