1. Reference problem#

1.1. Geometry#

_images/1000000000000179000001369BF8DBD499E24E3F.png

Gantry geometry \((m)\):

  • \(l=20\)

  • \(h=8\)

  • \(a=4\)

Quadratic moments of beams \(({m}^{4})\):

  • Sections \(\mathrm{AD}\), \(\mathrm{EB}\): \({I}_{1}=5.0{E}^{-4}\)

  • Sections \(\mathrm{DC}\), \(\mathrm{CE}\): \({I}_{1}=2.5{E}^{-4}\)

The gantry consists of beams with symmetrical sections, so that \(\mathrm{IY}=\mathrm{IZ.}\)

Only the flexural energy is taken into account, because the beams are very slender. This is why the other beam cross-section characteristics do not come into play.

1.2. Material properties#

Isotropic linear elastic material: \(E=2.1\mathrm{E11}\mathrm{Pa}\)

1.3. Boundary conditions and loads#

Articulated \(A\) and \(B\) post legs.

Loading

Nodal strength in \(C\):

\(Fy=–2000N=F1\)

Nodal strength in \(D\):

\(Fx=–10000N=F2\)

Moment in \(D\):

\(\mathrm{Mx}=–100000\mathrm{N.m}=M\)

Force distributed over section \(\mathrm{DC}\):

\(Pz=–3000N/m\)