3. Modeling A#
3.1. Characteristics of modeling#
Imposed displacement loads (ui, θ i) are imposed on the beam bundle (displacement calculated by introducing common link grid rotations and girder rotations) in order to reproduce the kinematics used in the skeleton element (U, θ, ohm):
\({u}_{x}^{i}={U}_{x}\left(x\right)-{Y}^{i}{\omega }_{z}\left(x\right)+{Z}^{i}{\omega }_{y}\left(x\right)\)
\({u}_{y}^{i}={U}_{y}\left(x\right)-{Z}^{i}{\omega }_{x}\left(x\right)\)
\({u}_{z}^{i}={U}_{z}\left(x\right)+{Y}^{i}{\omega }_{x}\left(x\right)\)
\({\theta }_{x}^{i}={\theta }_{x}(x)\)
\({\theta }_{y}^{i}={\theta }_{y}(x)\)
\({\theta }_{z}^{i}={\theta }_{z}(x)\)
with:
U x |
U y |
U y |
U z |
†x |
Ω x |
Ω y |
oh y |
oh y |
U z |
U z |
1 |
1 |
1 |
0.1 |
0.1 |
0.1 |
0.1 |
0.1 |
0.1 |
0.1 |
0.1 |
Note that the rotation of the grids is taken to be equal to that of the beams.
3.2. Results#
Stress tests at the node (X=0) of the skeleton element:
Node 1 |
Reference value |
Calculated value |
Precision (in%) |
Reference value |
Fx |
-2337344934.27 |
-2337344934.27 |
|
|
Vy |
-152304411.85 |
-152304411.85 |
|
|
Vz |
-159844234.21 |
-159844234.21 |
|
|
Mx |
-1.0 |
-1.0 |
|
|
My |
78665480.05 |
78665480.05 |
|
|
Mz |
-77408842.98 |
-77408842.98 |
|
|
Mgx |
-275203516.45 |
-275203516.45 |
|
|
Mgy |
-201061929.83 |
-201061929.83 |
|
|
Mgz |
-1834690109.7 |
-1834690109.7 |
|
|