# SS-V: 5030 Reactions at the Ends of Axially Loaded Plastic Bar

Test No. VNL04 Find reactions at the fixed ends and maximum displacement of a bar axially loaded beyond plasticity.

## Definition

Bar dimensions are 10 x 10 x 200 mm. Distance between loaded point and left end A=50 mm. Strain-stress curve of the bar material is defined by the power law:

- $K$
- Strength coefficient
- $n$
- Must be in the range [0,1]
- $n$ =0
- Material is perfectly plastic.
- $n$ =1
- Material is elastic.

**Properties****Value**- $K$
- 530 MPa
- $n$
- 0.26
- Poisson's Ratio
- 0

The study was performed for the following load F values: 30000 N, 47000 N, 55000 N, and 60000 N. These loads cover the full range of elastic-plastic response of the bar.

## Reference Solution

One-dimensional analytical reference solution is described here.

The length of the bar does not change under the load.

or,

- $\epsilon 1$
- Tensile strain at the left span of the bar.
- $\epsilon 2$
- Compressive strain at the right span of the bar,
- $N$
- Reaction force at left end of the bar.
- $R=F-N$
- Reaction force at the right end of the bar.
- $A$
- Bar cross-section area

From this equation you can find the reaction at the left end of the bar.

and $R=F-N$ at the right end.

## Results

Force F [N] | SOL Reference, Reaction [N] | SimSolid, Reaction [N] | % Difference |
---|---|---|---|

30000 | 17128 | 17635 | 2.96% |

47000 | 26834 | 26993 | 0.59% |

55000 | 31401 | 31694 | 0.93% |

60000 | 34256 | 34546 | 0.85% |