# 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.

The load of 2000000N and 1000000N is applied in the negative Y direction at points A and B. The following material properties are used for the NFLE beam:
$A$
1 m2
$\rho$
7860 kg/m3
$E$
2.1 x 1011 N/m2
$\nu$
0.3 (Poisson ratio)
For the above values, the theoretical axial stress (force/area) in each of the beam members is:
Beam
Theoretical Axial Stress N/m2
AB
1500 x 103
BC
5250 x 103
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).

The axial stresses are written to the H3D file and their contours can be visualized in HyperView as shown in Figure 3. The numerical values of these axial stresses are summarized below.
Beam
Numerical Axial Stress N/m2
AB
1505 x 103
BC
5255 x 103
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.