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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:

  • Bolt preload boundary condition

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


The geometry used for the case is shown below:

flange bolt preload geometry model
Figure 1: Only one quarter of the flange, corresponding to one bolt is modeled.

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:

Mesh TypeNumber of
Element Type
Standard2085921st Order Tetrahedrals
Table 1: Mesh details

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

tetrahedral mesh flange bolt preload validation case
Figure 2: Finite elements tetrahedral mesh used for the simulation generated with the standard algorithm

Simulation Setup


  • 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
  • Load:
    • 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:

\(\sigma_{ZZ}\) \((SIZZ)\) \([MPa]\)30.262430.00.87 %
Table 2: Results comparison and computed errors

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:

stress contours developed due to bolt preload flange
Figure 3: Deformed shape and stress contour on the bolted flange.
stress on bolt in preload
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.


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Last updated: January 14th, 2021

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