1. Reference problem#

1.1. Geometry#

_images/1000039A0000154A0000054548BF3DCEC0A40115.svg

Figure 1.1-a

\(\mathrm{7,5}m\) length straight beam.

Section features:

This is the \(U\) beam shown [Figure 1.1-b].

_images/Object_1.svg

Figure 1.1-b : Section of the beam in \(U\)

\(h=200\mathrm{mm}\)

\(b=273\mathrm{mm}\)

\(e=\mathrm{8,2}\mathrm{mm}\)

For [bib1] we have the following data:

\({I}_{y}={I}_{z}=\mathrm{5,022}{10}^{-5}{m}^{4}\)

\(\mathrm{ZGC}=\mathrm{221,5}\mathrm{mm}\)

From the geometry of the section, we calculate:

\(S=\mathrm{6,117}{10}^{-3}{m}^{2}\)

\({J}_{x}=\mathrm{1,28}{10}^{-7}{m}^{4}\)

1.2. Material properties#

Young’s module:

\(E=2.07{10}^{11}\mathrm{Pa}\)

Poisson’s ratio:

\(\nu =\mathrm{0,3}\)

Density:

\(\rho =7850\mathrm{kg}/{m}^{3}\)

1.3. Boundary conditions#

Boundary condition:

Problem plan: \(\mathrm{DZ}\) and \(\mathrm{DRY}\) stuck.

Knots \(A\) and \(B\) supported: \(\mathrm{DX}\) and \(\mathrm{DY}\) blocked

The eccentricity is taken into account using the LIAISON_DDL operand of the AFFE_CHAR_MECA command.

The degrees of freedom are always in \(G\), and eccentricity is taken into account by: \(\mathrm{DY}(G)=\mathrm{DY}(C)+\mathrm{GC}\wedge {\Theta }_{x}\)