# Problem 16: Static Load on a Truss Structure

## Model Description

Model location: <altair>\utility\mbd\nlfe\validationmanual\model4.mdl

This model consists of a truss structure composed of seven straight beams of a 0.01m*0.01m cross section as shown in Figure 1 below.

A load of 2000000N and 1000000N is applied in the downward direction at point A and B respectively.

## Multibody Model

Each beam member is modeled using a single NLFE beam element in MotionSolve. Gravity is turned off for this model. The truss is attached to the ground via revolute joint at point C and via Inplane joint at point E. The joints between the beams are all revolute joints.

- $A$
- 1 m2
- $\rho $
- 7860 kg/m3
- $E$
- 2.1 x 1011 N/m2
- $\nu $
- 0.3 (Poisson ratio)

**Beam****Theoretical Axial Stress N/m2**- AB
- 1500 x 103
- BC
- 5250 x 103
- AD
- 2500 x 103
- DB
- 2500 x 103
- BE
- 3750 x 103
- EC
- 8750 x 103
- DE
- 3000 x 103

This model is simulated with an end time of 5 seconds, for a quasi-static analysis.

## Numerical Results

Figure 3 below depicts the final state of the truss structure under the load. The contours depict the axial stresses in each beam member (ignoring the local values at the joint locations).

**Beam****Numerical Axial Stress N/m2**- AB
- 1505 x 103
- BC
- 5255 x 103
- AD
- 2501 x 103
- DB
- 2501 x 103
- BE
- 3749 x 103
- EC
- 8752 x 103
- DE
- 3001 x 103

## Conclusion

The NLFE model with 7 BEAM12 elements show close agreement to the theoretical results for this case.

Beam | Theoretical Axial Stress N/m2 | Numerical Axial Stress N/m2 | % error |
---|---|---|---|

AB | 1500 x 103 | 1505 x 103 | 0.33 |

BC | 5250 x 103 | 5255 x 103 | 0.1 |

AD | 2500 x 103 | 2501 x 103 | 0.04 |

DB | 2500 x 103 | 2501 x 103 | 0.04 |

BE | 3750 x 103 | 3749 x 103 | 0.03 |

EC | 8750 x 103 | 8752 x 103 | 0.02 |

DE | 3000 x 103 | 3001 x 103 | 0.03 |

The results presented use the default solver settings present in MotionView.