On the Applicability of the Loading Parameter Φ in Pinned Connections with Relevant Initial Clearance

In pinned connections, the presence of an initial clearance increases the lug stress concentration with respect to a neat fit configuration. By employing a recently proposed loading parameter Φ valid for plane models, the applied load and initial clearance effects on the stress concentration are normalised for a straight-shanked, round-ended, longitudinally loaded pin-lug connection of fixed outer to inner radius ratio. Results are obtained with a Mitchell-type, Fourier series solution and with commercial Finite Elements. The applicability of the loading parameter Φ to pinned connections with small to relevant initial clearances is explored. Two preliminary design charts are presented, which quantify the lug stress concentration factor versus the loading parameter Φ for two lug geometries defined by inner to outer radii ratios of 0.376 and 0.77.

References

[1] R.B. Heywood: (1952) Designing with photoelasticity, Chapman&Hall, London.

[2] G.S. Wang: (1994) Stress analysis for a lug under various conditions. J. Strain Analysis. Vol. 29, 7-16.

[3] H.H. Chen and K.M. Marsheck: (1988) Effect of clearance and material property on contact pressure in two-dimensional conforming cylinders. Mech. Mach. Theory, Vol. 23, 55-62.

DOI: https://doi.org/10.1016/0094-114x(88)90009-2

[4] M. Ciavarella and P. Decuzzi: (2001) The state of stress induced by the plane frictionless cylindrical contact. I. The case of elastic similarity. Int. J. Solids Structures, Vol. 38, 4507- 4523.

DOI: https://doi.org/10.1016/s0020-7683(00)00289-4

[5] M. Ciavarella A. Baldini, J.R. Barber and A. Strozzi: (2006) Reduced dependence on loading parameters in almost conforming contacts. To be published in Int. J. Mechanical Sciences.

DOI: https://doi.org/10.1016/j.ijmecsci.2006.03.016

[6] A. Strozzi, A. Baldini and M. Nascimbeni: (2006) Maximum equivalent stress in a pin-loaded lug subject to inclined loading, To be published in J Strain Analysis.

DOI: https://doi.org/10.1243/03093247jsa150

[7] J.H. Mitchell: (1899) On the direct determination of stress in an elastic solid, with application to the theory of plates. Proc. London Math. Soc., Vol. 31, 100-124.

[8] S. Timoshenko and J.N. Goodier: (1970) Theory of elasticity. McGraw-Hill, N. Y.

[9] E.G. Coker and L.N.G. Filon: (1957) A treatise on Photo-elasticity. Cambridge University Press.

[10] H. Reiβner and Fr. Strauch: (1933) Ringplatte und Augenstab. Ingenieur-Archiv, Vol. 4, 481505.

DOI: https://doi.org/10.1007/bf02079967

[11] R.W. Soutas-Little: (1973) Elasticity. Dover, N. Y.

[12] J.R. Barber: (2002) Elasticity. Kluwer, London.

[13] Strozzi, A., and De Bona, F. (2005) Hoop stresses in the con-rod small end. J. Automobile Engineering, Vol. 219, 1331-1345.

DOI: https://doi.org/10.1243/095440705x34973

[14] A.L. Schlack and R.W. Little: (1964) Elastostatic problem of a perforated square plate. ASCE Engng Mech. Div., Vol. 90, 171-187.

[15] D. Shilkrut and E. Ben-Gad: (1985) Elastic stress concentration phenomena in an axially stressed rectangular plate with a central circular hole and other related problems. J. Appl. Mech., Vol. 52, 216-219.

DOI: https://doi.org/10.1115/1.3169001

[16] D. Shilkrut, A. Uziel and S. Gruntman: (1987) Elastic stress concentrations in a square plate with a large hole under axial loading. J. Strain Analysis, Vol. 22, 55-61.

DOI: https://doi.org/10.1243/03093247v221055

[17] A.K. Rao: (1978) Elastic analysis of pin joints. Computers & Structures, Vol. 9, 125-144.

[18] M.D. Bird and C.R. Steele: (1992) A solution procedure for Laplace's equation on multiply connected circular domains. J. Appl. Mech., Vol. 59, 398-404.

DOI: https://doi.org/10.1115/1.2899533

[19] Y. Katznelson: (1968) Harmonic analysis, Wiley, N. Y.

[20] T.J. I'A. Bromwich: (1947) An introduction to the theory of infinite series, Macmillan, London.

[21] T.A. Driscoll and B. Fornberg: (2001) A Padé-based algorithm for overcoming the Gibbs phenomenon. Numerical Algorithms, Vol 26, 77-92.

[22] M.D. Greenberg: (1978) Foundations of applied mathematics, Prentice-Hall.

[23] S.P. Timoshenko: (1922) On the distribution of stresses in a circular ring compressed by tow forces acting along a diameter. Phil. Mag. , Vol. 44, 1014-1019.

DOI: https://doi.org/10.1080/14786441208562578

[24] A.A. Cannarozzi: (1980) On the resolution of some unilaterally constrained problems in structural engineering. Comp. Methods Appl. Mech. Engng, 24, 339-357.

DOI: https://doi.org/10.1016/0045-7825(80)90069-9