# I Beam Under Remote Force¶

## Overview¶

The aim of this test case is to validate the following functions:

- remote force

The simulation results of SimScale were compared to the analytical results derived from [Roark]. The meshes used in case (A) and (C) were created with the fully-automatic-tetrahedralization tool on the SimScale platform. The meshes used in case (B) and (D) were created locally.

## Geometry¶

The I-beam is \(L\) = 1 m long. The geometry of the cross section is shown below.

B | 0.06 m |

H | 0.08 m |

b | 0.04 m |

h | 0.06 m |

## Analysis type and Domain¶

**Tool Type** : Code_Aster

**Analysis Type** : Static

**Mesh and Element types** :

Case | Mesh type | Number of nodes | Element type |
---|---|---|---|

(A) | linear tetrahedral | 5761 | 3D isoparametric |

(B) | linear hexrahedral | 5757 | 3D isoparametric |

(C) | quadratic tetrahedral | 37486 | 3D isoparametric |

(D) | quadratic hexrahedral | 20749 | 3D isoparametric |

## Simulation Setup¶

Material:

- isotropic: E = 205 GPa, \(\nu\) = 0.28

Constraints:

- Face A is fixed

Loads:

- A remote force \(F\) = 1000 N in a distance of 1 m is applied to face B

## Reference Solution¶

A remote force can be substituted in a parallel force \(F_0\) with the same magnitude and a momentum \(M_0\). This momentum can be calulated with the direction of the force and the distance \(d\). In this example the connection line between the force and the point of attack is perpendicular to the force and therefore the momentum \(M_0\) can be calculated as stated in equation \(\eqref{ref1}\).

The equation \(\eqref{ref2}\) used to solve the problem is derived in [Roark] with a superposition of the momentum and the force.