SS-V: 5050 Pure Bending of a Plastic Beam

Definition

Figure 1.

Beam dimensions are b x h x L.

Material of the beam is rigid plastic with the strain-stress curve (Figure 2).

Figure 2.

The study was performed for the following moment $M$ values: 776.893 N*m and 847.518 N*m

Reference Solution

Plastic beam bending theory assumes that there are two zones in the beam material: plastic zone at the outer layers of the beam and elastic core at the beam centerline.

Figure 3. Corresponding stress distribution for material without hardening

Where, $b$ is the beam thickness.

Results

The theory of bending of plastic beams is based on hypothesis of flat cross-sections which remain flat during deformations. In order to emulate this basic assumption as close as possible the problem was modeled as an assembly of two solids. One solid represented the beam itself with material properties defined by the curve (Figure 2). Another small solid was attached to the beam end and was set as an absolutely rigid body (Figure 4). The rigid solid was loaded with the moment $M$ and it served as a moment transfer element.

Figure 4.

It should be mentioned that SimSolid 3D solution does not have sharp boundary between elastic and plastic zones as it is in simplified beam bending formulations. This makes difficult direct comparison; however, the elastic zone approximate sizes are in good correlation.

Figure 5. Stress X at M=776.893 N*m

Figure 6. Stress X at M=847.518 N*m

Figure 7. von Mises stress at M=776.893 N*m

Figure 8. von Mises stress at M=847.518 N*m

Figure 9. Residual von Mises stress after unloading at M=776.893 N*m

Figure 10. Residual von Mises stress after unloading at M=847.518 N*m