# Problem 13: Hollow Circular Beam under a Twist Load

## Model Description

Model location: <altair>\utility\mbd\nlfe\validationmanual\model1.mdl

This model consists of a straight cantilever beam of a hollow circular cross-section. The beam is subjected to a torsion load at its endpoint as shown in Figure 1 below.

- Twist angle
- $\theta =\frac{Tl}{GJ}$
- Shear strain
- $\gamma =\frac{\theta r}{l}$

- $l$
- Beam length
- $r$
- Beam radius.
- $J$
- Polar moment of inertia about the beam axis.
- $G=\frac{E}{2\left(1+\nu \right)}$
- Shear modulus
- $E$
- Young's modulus
- $\nu $
- Poisson ratio

## Multibody Model

The cantilever beam is modeled using 10 NLFE beam elements in MotionSolve. NLFE beam elements with a hollow tube section are used by specifying an inner and outer radius. The cantilever beam is fixed to the ground by a fixed joint. Gravity is turned off for this model.

θ = 0.026686*rad*

## Numerical Results

The multibody model described in the previous section is run for an end time of 5.0 seconds. The output request is plotted below.

## Conclusion

The NLFE model with 10 NLFE beam elements shows close agreement to the theoretical results for this case.

Beam Theory | Numerical | % error | |
---|---|---|---|

Twist Angle | 0.026686 rad | 0.026690 rad | 0.02 % |