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:

$\sigma =K{\epsilon }^{n}$

Where,
$K$
Strength coefficient
$n$
Must be in the range [0,1]
$n$ =0
Material is perfectly plastic.
$n$ =1
Material is elastic.
The material properties are:
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,

Where,
$\epsilon 1$
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 at the right end.

Results

Bar was modeled as a 3D solid with immovable ends. Axial force F could not be applied precisely at the solid bar axis, so four line spots were created at the bar sides and total load F was uniformly distributed over the spots (Figure 3).
The following table summarizes the reaction force 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%