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

Test No. NVL04 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:(1)

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

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.(2)

From this equation you can find the reaction at the left end of the
bar.(4)

$$N=F/\left(1+{\left(a/b\right)}^{n}\right)$$

and $R=F-N$ 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

18151

5.97%

47000

26834

27146

1.16%

55000

31401

31788

1.23%

60000

34256

34591

0.98%

Typical von Mises stress distributions are shown in Figure 4 and Figure 5. The distribution has high gradients at load
application lines; yet the reactions values correlate to the 1D solution because the
reactions are applied far from the active force.