1. Reference problem#

1.1. Geometry#

Problem plan

_images/10000000000000F3000000E2E694AF03FC638AA8.png

Beam

Length

Moment of inertia

\(\mathrm{AB}\)

\({l}_{\mathrm{AB}}=\mathrm{4m}\)

\({I}_{\mathrm{AB}}=\frac{64}{3}{10}^{-8}{m}^{4}\)

\(\mathrm{AC}\)

\({l}_{\mathrm{AC}}=\mathrm{1m}\)

\({I}_{\mathrm{AC}}=\frac{1}{12}{10}^{-8}{m}^{4}\)

\(\mathrm{AD}\)

\({l}_{\mathrm{AD}}=\mathrm{1m}\)

\({I}_{\mathrm{AD}}=\frac{1}{12}{10}^{-8}{m}^{4}\)

\(\mathrm{AE}\)

\({l}_{\mathrm{AE}}=\mathrm{2m}\)

\({I}_{\mathrm{AE}}=\frac{4}{3}{10}^{-8}{m}^{4}\)

\(G\) is in the middle of \(\mathrm{DA}\).

Another characteristic of beams that are not used for calculations: the beams have a square cross section.

\(\begin{array}{}{A}_{\mathrm{AB}}=16{10}^{-4}m\\ {A}_{\mathrm{AD}}=1{10}^{-4}m\\ {A}_{\mathrm{AC}}=1{10}^{-4}m\\ {A}_{\mathrm{AE}}=4{10}^{-4}m\end{array}\)

1.2. Material properties#

Isotropic linear elastic material: \(E=2.{10}^{11}\mathrm{Pa}\)

1.3. Boundary conditions and loads#

  1. Point \(C\): articulated \(({u}_{C}={v}_{C}=0)\).

_images/10000000000000E3000000CBC004F62C5F77025D.png

Punctual force in \(G\): \(F=-{10}^{5}N\)

Force distributed on the beam \(\mathrm{AD}\): \(p=-{10}^{3}N/m\)