Linear three-dimensional finite element analysis (FEA) was performed on bolted pressure vessel joints to determine maximum stresses and stress concentration factors in the bolt head fillet as a result of the prying action. The three-dimensional finite element models consisted of a segment of the flanges containing one bolt, using cyclic symmetry boundary conditions. The flanges were each 20 mm in thickness with 901.7 mm inner diameter. The outer flange diameter was varied from 1021 to 1041 mm in steps of 5 mm. The bolt circle diameter was varied from 960.2 to 980.2 mm in steps of 5 mm. The bolts used were 16-mm-dia metric bolts with standard head and nut thickness. The threads were not modeled. The internal vessel pressure was 0.6895 MPa (100 psi). Stress concentration factors in the bolt head fillet were calculated, and they ranged from 3.34 to 4.80. The maximum stress in the bolt as well as the stress concentration factors in the bolt head fillet increase with an increase in bolt circle diameter for a given outer flange dimension. Keeping the bolt circle diameter constant, bolt stress and stress concentration factors in the bolt head fillet decrease with increase in outer flange diameter. The maximum stresses in the bolt were also calculated according to the American Society of Mechanical Engineers (ASME) Boiler and Pressure Vessel Code and the Verein Deutscher Ingenieur (VDI) guidelines and compared to the results observed through finite element analysis. The stresses obtained through FEA were larger than those predicted by the ASME and VDI methods by a factor that ranged between 2.96 to 3.41 (ASME) and 2.76 to 3.63 (VDI).

ASME Boiler and Pressure Vessel Code, 1998, Section VIII, Division 1, Appendix Y.
VDI 2230, 1986, Part 1, “Systematic Calculation of High Duty Bolted Joints: Joints with One Cylindrical Bolt,” VDI, Dusseldorf, Germany.
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Srinivasan, G., 2000, “Bolt Head Fillet Stress Concentration Factors in Cylindrical Pressure Vessels,” M.S. thesis, University of Missouri-Rolla, Rolla, MO.
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Lehnhoff, T. F., and Bunyard, B. A., 1999, “Bolt Thread and Head Fillet Stress Concentration Factors,” ASME PVP-Vol. 398, Recent Advances in Solids and Structures, pp. 103–108.
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