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# Validation Case: Elongation of a Solid Tapered Bar

In this case, a tapered steel bar of square cross-section is fixed at one end and a tensile force is applied at the other end. The aim of this FEA analysis is to determine the maximum deflection in the bar and the axial stress at the middle of the bar.

The FEA model and the resulting comparison of the simulation results against the analytical calculations validates the use of following conditions for linear mechanical static analysis in Solve:

• Restraint

## Geometry:

Download the geometry here or use Onshape to access the geometry used for this analysis:

## ### Material:

• Structural Steel
• Young’s Modulus (E) = 200 GPa
• Poisson’s Ratio (ν) = 0.3

### Physics:

• Restraints (Fixture)
• Face1 ( PQRS)
• -10,000 N on Face2 ( ABCD)  ## Meshing:

OnScale Solve generated the mesh automatically and the meshing statistics, at the time of writing this document,  are as follows:

Mesh Quality: Very Fine

Cells: 6909

Vertices: 1680

## Reference Solution: The axial deflection is given by: where E is the Young’s Modulus (1)

The stress at any point x along L is given by: where A(x) is the cross-sectional area at distance x along L (2)

For the current geometry the values are follows:

dA = 50 mm

dB = 25 mm

L = 200 mm

P = 10,000 N

E = 200 GPa ( Young’s Modulus of Structural Steel)

## Results Comparison

The table below compares the values obtained using the analytical methods described above and the FEA analysis performed using OnScale Solve.

Result Quantity Analytical OnScale Solve
Maximum axial deflection (μm) 8 8.06
Normal Stress at mid-length (MPa) 7.11 7.16 