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# Validation Case: Flange Under Bolt Preload

This validation case belongs to structural analysis, with the case of a pipe flange under the effect of bolt preload. The aim of this test case is to validate the following parameters:

The simulation results from SimScale were compared to test case results presented in [SSNV228]$$^1$$.

## Geometry

The geometry used for the case is shown below:

It represents a quarter section of a pipe bolted flange pair. The bolt shaft is simplified as a cylinder, as well as the nut. The model includes the pipes sections, flanges, a bolt, nuts, washers, and a gasket.

## Analysis Type and Mesh

Tool Type: Code Aster

Analysis Type: Non-linear Static

Mesh and Element Types:

The mesh was computed using SimScale’s standard mesher algorithm.

## Simulation Setup

Material:

• Elastic Modulus $$E =$$ 200 $$GPa$$
• Poison’s ratio $$\nu =$$ 0.3

Boundary Conditions:

• Constraints:
• XZ plane symmetry faces $$d_y =$$ 0 $$m$$
• YZ plane symmetry faces $$d_x =$$ 0 $$m$$
• Symmetry plane on pipe end faces
• Contacts:
• Bonded contact between the pipes and flange necks
• Bonded contact between the flange faces and washers
• Bonded contact between the washers and nuts
• Bonded contact between the nuts and bolt shaft
• Physical contact between the flanges and seal ring
• Bolt preload of 3393 $$N$$
• Pressure on internal pipe, flange and seal faces $$P =$$ 1e-6 $$Pa$$, ramped from zero to maximum value

## Reference Solution

The reference solution is of the numerical type, as presented in [SSNV228]$$^1$$. It is given in terms of the mean stress on the bolt shaft:

$$\sigma_{bolt} = 30\ MPa$$

## Result Comparison

Comparison of the axial bolt stress $$\sigma_{ZZ}$$ at a point data result control item located on the bolt shaft with the theoretical solution is presented below:

Illustration of the deformed shape and stress distribution on the flange under bolt preload condition is presented in Figure 3, while the overall distribution of the axial stress on the bolt $$\sigma_{ZZ}$$ is presented in Figure 4: Figure 4: Stress contour plot for $$\sigma_{ZZ}$$ $$(SIZZ)$$, showing the distribution of the axial stress in the bolt. Stress concentrations can be seen varying from the reference value of 30 MPa.