3. Modeling A#
3.1. Characteristics of modeling#
We use a POU_D_EM model.
3.2. Characteristics of the mesh#
Longitudinal mesh of the beam:
We have 3 knots and two elements (POU_D_EM).
The concrete part of the cross section of the beam is meshed (DEFI_GEOM_FIBRE/SECT) while the steels are given directly in the form of 4 point fibers in DEFI_GEOM_FIBRE/FIBRE.
Two meshes of the concrete part are tested for load case 1. The fine mesh consists of 120 fibers and the coarse mesh consists of 16 fibers:
Note:
The problem being \(\mathrm{2D}\), a single fiber in the width could seem sufficient (multilayers), but this would lead to zero terms in the stiffness matrix (the natural inertia of the fibers not being taken into account) and to an error when solving the system of equations.
3.3. Tested sizes and results#
3.3.1. Charging case 1#
Reference |
|
Arrow |
|
(fine mesh) |
2.2735 10—3 |
Arrow |
|
(coarse mesh) |
2.2735 10—3 |
Sharp effort |
|
(supports \(A\)) |
5000 |
Bending moment |
|
(Middle) |
1.25 104 |
The calculations are carried out without taking into account the inherent inertia of each fiber. The results show that it is nevertheless not very useful to take it into account because the difference between a coarse mesh and a fine mesh is not obvious. The mesh of the section does not have to be very fine to have accurate results (in terms of elasticity). |
|
Option EFGE_NOEU used to calculate the generalized efforts at the nodes averages the generalized efforts of all the elements connected to the node. In our case, we have 2 superimposed beam elements (one for concrete, one for steel), so the calculated forces are divided by 2. If we add the force values per element (EFGE_ELNO) of the concrete element and the steel element, we find the theoretical values. |
Note:
If we do an arrow calculation by taking \(O\) (half-height) as the reference axis instead of the elastic center (COOR_AXE_POUTRE), the relative error on the arrow is 0.2% (because here the elastic center is practically halfway up (see 1.2.1) .
We also test the volume distribution of the component SIXXdes fields SIEF_ELGA and SIGM_ELNO as well as the volume of the concrete beam.
3.3.2. Charging case 2#
Reference |
|
Arrow |
|
(fine mesh) |
7,900 10—4 |
3.3.3. Charging case 3#
Reference |
|
Elongation |
5.00 10—3 |
Efforts |
0.00 |