SS-V: 5060 Separate Beams
Test No. VNL07 Find total or partial beam separation/slippage depending on the applied loads.
Definition
Two similar beams with dimensions 10 x 10 x 100 mm are in contact (Figure 1).
- Properties
- Value
- Friction Coefficient
- f=0.15
- Modulus of Elasticity
- 2.1e+11 Pa
- Poisson's Ratio
- 0.3

Load Case | Fx, [N] | Fy, [N] |
---|---|---|
1 | 0 | 1 |
2 | 0 | 0.9 |
3 | 0.3 | 0 |
4 | 0.31 | 0 |
5 | 0.29 | 0 |

Results
- Case 1:
Figure 3. Figure 4. Consider the equilibrium of the upper beam. If Fy =0, then force N is equilibrated by the reaction force in contact. As Fy grows, the beam deforms, and the contact separation starts at its right end and expands to the left. Ultimately, the contact fully separates and contact area degenerates into a line (point A in Figure 3). The value of force Fy which results in full separation can be found from moments equilibrium equation.
∑M(A)=P*(L2)− Fy*L=0This ultimate value is Fy =1 N.
SimSolid result for this value of Fy is shown in Figure 5. Full separation occurred and the contact occurs only along the single edge which causes stress concentration at the beam corner.Figure 5. - Case 2:In this load case, force Fy =0.9 N is not sufficient to cause full separation of the contact (Figure 6).
Figure 6. - Case 3:
Figure 7. Figure 8. In this load case, normal separation does occur because there is no detaching force - Fy =0. Shear force Fx tends to cause beam slippage which is resisted by friction forces distributed over the contact area. In equilibrium the force projectes onto the horizontal axis:
F−Fx=0Where, F is total friction force.
Maximum total friction force is:
F=f∗PTotal slippage (or total tangential separation) starts when Fx ≥ f*P . When Fx < f*P , only partial slippage is possible. Maximum total friction force is Fmax=0.15*2=0.3 N .
The result for Fx =0.3 N is shown in Figure 9. Full slippage develops in contact area, but left lower edge of the upper beam is still almost coincides with the edge of the lower beam.Figure 9. - Case 4:In this load case the shifting force Fx is increased to 0.31 N. The force exceeds the maximum friction force and the upper beam not only deforms but also starts moving as a rigid body.
Figure 10. - Case 5:In this load case the shifting force Fx is decreased to 0.29 N in order to not exceed the maximum friction force. Only partial slippage occurs in this case. There is a clear "sticking" contact area at the left end of the beams.
Figure 11.