Systematic investigation of stresses in concentrically clamped bolted joints using the finite element method

In this paper, the systematic investigation of the stresses occurring in a rod bearing cap bolted joint is carried out by considering a concentrically clamped rod bearing cap bolted joint.  The aim of this study is to develop a 2D finite element model to determine occurring stress in bolted joints during all cases of bolted joint and to compare VDI-Directives.  For this aim, the bolt load and part load are analytically calculated based on the axial load.  The assembly stress, working stress, and alternating stress are calculated and simulated based on the  introduction of a load factor $n$.  A 2D finite element model is developed.  For this aim, the global stiffness matrix $[K]$ is obtained and the boundary conditions and load (such as force $[F]$ and moment $[M]$) are applied.  By solving algebraic equations of the system in terms of nodal displacement $\{u\}$ and $\{\theta\}$, we obtain assembly stresses $\sigma_v$, working stress $\sigma_B$ and alternating stress $\sigma_a$ in each element of the structure.  The finite element equations for the bolt are established.  The assembly stress, working stress, and alternating stress are calculated using the developed finite element model.  The analytical calculation results and finite element calculation results are compared and are found to be highly similar in terms of the assembly stress, working stress, and alternating stress.  Increasing the stiffness rate of the bolt causes the increase of the bolt load and alternating stresses; in contrast, increasing the stiffness rate of the clamp causes the decrease of the bolt load and alternating stresses.  The stiffness of the bolt should be as low as possible to reduce the maximum bolt load and stress of the bolt cross-sections.  However, the stiffness of the clamped part should be as high as possible.  Additionally, increasing the load introduction factor causes the increase of the bolt load.  Thus, for concentrically bolted joints,  increasing the load introduction factor causes the increase of the assembly stress and alternating stress.

bolted joints
assembly stress
working stress
alternating stress
finite element
  1. Pedersen N. L., Pedersen P.  Bolt–plate contact assemblies with prestress and external loads: Solved with super element technique.  Computers & Structures. 87 (21–22), 1374–1383 (2009).
  2. Chakhari J., Daidié A., Chaib Z., Guillot J.  Numerical model for two-bolted joints subjected to compressive loading.  Finite Elements in Analysis and Design. 44 (4), 162–173 (2008).
  3. Fares Y., Chaussumier M., Daidie A., Guillot J.  Determining the life cycle of bolts using a local approach and the Dang Van criterion.  Fatigue and Fracture of Engineering Materials and Structures. 29 (8), 588–596 (2006).
  4. Venkatesan S., Kinzel G. L.  Reduction of Stress Concentration in Bolt-Nut Connectors.  Journal of Mechanical Design. 128 (6), 1337–1342 (2005).
  5. Bhonge P. S., Foster B. D., Lankarani H. M.  Finite Element Modeling and Analysis of Structural Joints Using Nuts and Bolts.  Proceedings of the ASME 2011 International Mechanical Engineering Congress and Exposition.  Vol. 3: Design and Manufacturing. Denver, Colorado, USA. November 11–17, 2011. pp. 73–83.
  6. Kim J., Yoon J.-C., Kang B.-S.  Finite element analysis and modeling of structure with bolted joints.  Applied Mathematical Modelling. 31 (5), 895–911 (2007).
  7. Piraprez E.  The effect of prying stress ranges on fatigue behaviour of bolted connections: The state-of-the-art.  Journal of Constructional Steel Research. 27 (1–3), 55–68 (1993).
  8. Friede R., Lange J.  Loss of Preload in Bolted Connections Due to Embedding and Self Loosening.  In SDSS' Rio 2010 Stability and Ductility of Steel Structures, edited by E. Batista, P. Vellasco, and L de Lima, 287–294 (2010).  Rio de Janeiro, Brazil.
  9. Stephen J. T, Marshall M. B., Lewis R.  Relaxation of contact pressure and self-loosening in dynamic bolted joints.  Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science. 231 (18), 3462–3475 (2016).
  10. Gong Hao, Liu Jianhua.  Some factors affecting the loosening failure of bolted joints under vibration using finite element analysis.  Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science. 232 (21), 3942–3953 (2017).
  11. Poljak S., Bašt'ovanský R.   Vibration Resistance of High Speed Assembly Secured Bolted Joint with Nut DIN 985.  Modern Methods of Construction Design. 299–305 (2014).
  12. VDI-Richtlinien 2230: Systematische Berechnung Hochbeanspruchter Schraubenverbindungen Zylindrische Einschraubenverbindungen.
  13. Haberhauer H., Bodenstein F.  Maschinenelemente. Springer (2009).
  14. Wittel H., Becker M.  Roloff/Matek Maschinenelemente Aufgabensammlung.  Wiesbaden, Vieweg&Sohn Verlag/Fachverlage GmbH (2005).
  15. Kabus K., Decker K.  Maschinenelemente Formeln.  Carl Hanser Verlag (2009).
  16. Moaveni S.  Finite Element Analysis Theory and Application with ANSYS.  New Jersey, Prentice Hall (2003).
  17. Chandrupatla T. R., Belegundu A. D.  Introduction to Finite Elements in Engineering.  New Jersey, Prentice Hall (2002).