Abstract
This paper presents the historical development of methods used for the study of torsional stresses in shafts. In particular, the paper covers both analog methods, especially those based on electrical analogies proposed circa 1925, and numerical methods, especially finite difference methods (FDM), finite element methods (FEM) and boundary element methods (BEM).
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Ajovalasit A, Nigrelli V, Pitarresi G, Virzì Mariotti G (2013) Torsional stress concentrations in shafts: from electrical analogies to numerical methods. IFToMM workshop on history of mechanism and machine science, University of Palermo, 21st–22nd Nov 2013. Proceedings published by Edizioni Scientifiche e Artistiche, Naples 01/31/2014. ISBN: 9788895430843
Ajovalasit A, Nigrelli V, Pitarresi G, Virzì Mariotti G (2014) On the history of torsional stress concentrations in shafts: from electrical analogies to numerical methods. J Strain Anal Eng Des 49:452–466
Barone G, Pirrotta A, Santoro R (2011) Comparison among three boundary element methods for torsion problems: CPM, CVBEM, LEM. Eng Anal Boundary Elem 35(7):895–907
Beadle CW, Conway HD (1963) Conducting-sheet analogy for stress concentrations in twisted structural sections. Exp Mech 3(8):198–200
Biezeno CB, Koch JJ (1933) Über einige Beispiele zur elektrischen Spannugs-bestimmung. Ingenieur—Archiv 4:384–393
Brebbia CA (1980) The boundary element method for engineers. Pentech Press, London
Chen F, (1993) Solution of torsional problems by BEM. Transactions on modelling and simulation, vol. 1, WIT Press
Cranz H (1933) Experimentelle Losung von Torsions Aufgaben. Ingenieur—Archiv 4:506–509
Darılmaz K, Orakdogen E, Girgin K (2007) Torsional rigidity of arbitrarily shaped composite sections by hybrid finite element approach. Steel Compos Struct 7:241–251
Den Hartog JP, McGivern JG (1935) On the hydrodynamic analogy of torsion J Appl Mech 2(2):A46–A48
Ely JF, Zienkiewicz OC (1960) Torsion of compound bars-a relaxation solution. Int J Mech Sci 1(4):356–365
Fessler H, Rogers C, Stanley P (1969) Shouldered plates and shafts in tension and torsion. J Strain Anal 4(3):169
Fuerst A, Sprysl H (2000) Determination of polar moment of inertia and stress concentration of shafts under torsion load with arbitrary cross section. Int Ser Adv Boundary Elem 8:109–116
Giordano G (1940a) Ricerca delle tensioni in alberi soggetti a torsione. apparecchiature per la determinazione sperimentale di esse negli alberi di rivoluzione. Tecnica Italiana, febbraio 1940
Giordano G (1940b) Coefficiente di forma per alberi con un risalto soggetti a torsione. Tecnica Italiana, aprile 1940
Giordano G (1940c) Fattori di forma per alberi con variazione di diametro soggetti a torsione. Tecnica Italiana, maggio 1940
Griffith AA, Taylor GI (1917) The use of soap films in solving torsion problems. Proc Inst Mech Eng 1917:755–809
Griffith AA, Taylor GI (1918) The application of soap films to the determination of the torsion and flexure of hollow shafts. Technical report of the advisory committee for aeronautics1917; vol. 392
Henshell RD (1975) A survey of the use of the finite element method in stress analysis. In: Stanley P (ed) Computing development in experimental and numerical stress analysis, Applied Science Publishers, London, pp 1–19
Hetényi M (ed) (1950) Handbook of experimental stress analysis. John Wiley, New York
Higgins TJ (1945a) Analogic experimental methods in stress analysis as exemplified by Saint-Venant torsion problem. Proc SESA II(2):17–27
Higgins TJ (1945b) Stress analysis of shafting as exemplified by Saint-Venant torsion problem. Proc SESA III(1):94–101
Huth JH (1950) Torsional stress concentrations in angle and square tube fillets. J Appl Mech 17(December):388–390
Isakower RI, Barnas RE (1977) Torsional stresses in slotted shafts. Mach Des 49(21):100–103
Jacobsen LS (1925) Torsional stress concentrations in shafts of circular cross section and variable diameter. Trans ASME 47:619–641
Jawson MA, Ponter RA, (1963) An integral equation solution of the torsion problem. Proc R Soc London 275(A):237–46
Kobayashi AS (ed) (1987) Handbook on experimental mechanics. Prentice Hall, Englewood Cliffs
Leven MM (1949) Stresses in key ways by photoelastic methods and comparison with numerical solution. Proc Soc Exp Stress Anal 7(2):141
Manzella G (1939) Determinazione sperimentale delle tensioni torsionali in aste prismatiche. Tecnica Italiana, marzo 1939
Manzella G. (1940a) Sullo scarico delle tensioni torsionali prodotte da incassi circolari negli alberi. Tecnica Italiana, marzo 1940
Manzella G (1940b) Influenza del grado di cavità sul coefficiente di forma di alberi con tagli di chiavetta. Tecnica Italiana, aprile 1940
Matthews GJ, Hooke CJ (1971) Solution of axisymmetric torsion problems by point matching. J Strain Anal 6(2):124–133
Nigrelli V (1994) Alberi con colletto soggetti a torsione: determinazione dei fattori di forma con il metodo degli elementi di contorno—XXIII Convegno Naz. AIAS, Cosenza, 1994
Nigrelli V, Virzì Mariotti G (1995) Stress concentration factor in collar and shouldered shafts in torsion. Eng Anal Boundary Elem 16:71–77
Nigrelli V, Virzì Mariotti G, (1996) Fattori di concentrazione delle tensioni in alberi con colletto soggetti a trazione o a flessione—Organi di Trasmissione, Maggio 1996, pp 160–165
Nigrelli V, Virzì Mariotti G (1997) Stress concentration factor in collar and shouldered shafts in traction or in bending. Eng Anal Boundary Elem 20:245–252
Pedersen NL (2010) Stress concentrations in keyways and optimization of keyway design. J Strain Anal Eng Des 45(8):593–604
Peterson RE (1953) Stress concentration design factors. John Wiley & Sons, New York
Peterson RE (1974) Stress concentration factors. John Wiley & Sons, New York
Prandtl L (1903) Zur Torsion von prismatischen Staben. Physikalishe Zeitscrift 4:758–759
Sharpe WN (ed) (2008) Handbook of experimental solid mechanics. Springer, New York
Shumas FJ, (1949) The effect of a slot on the stresses and rigidity of a shaft subject to pure torque. Thesis dissertation, University of British Columbia (http://hdl.handle.net/2429/41237)
Thum A, Bautz W (1934) Die Ermittlung von Spannungsspitzen in Verdrehbeanspruchten Wellen durch ein elektrisches Modell. Verein Deutscher Ingenieure (VDI) 78:17
Timoshenko S, Goodier JN (1951) Theory of elasticity, 2nd edn, McGraw-Hill, New York
Virzì Mariotti G (1992) BEM applications on an external problem, comparison with both theoretical and finite element results and observations on divergence strip. Eng Anal Boundary Elem 10(3):267–271
Waner NS, Sokora WW (1953) Stress concentrations for structural angles in torsion by the conducting sheet analogy. Proc SESA XI(1):19–34
Young WC, Budynas RG (2002) Roark’s formulas for stress and strain, 7th edn. McGraw Hill, New York (Chapter 10)
Zienkiewicz OC (1979) Numerical methods in stress analysis—the basis and some recent paths of development. In: Holister GS (ed) Developments in stress analysis, vol. 1, Applied Science Publishers, London (Chapter 1)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2016 Springer International Publishing Switzerland
About this chapter
Cite this chapter
Ajovalasit, A., Nigrelli, V., Pitarresi, G., Mariotti, G.V. (2016). Determination of Torsional Stresses in Shafts: From Physical Analogies to Mathematical Models. In: Sorge, F., Genchi, G. (eds) Essays on the History of Mechanical Engineering. History of Mechanism and Machine Science, vol 31. Springer, Cham. https://doi.org/10.1007/978-3-319-22680-4_19
Download citation
DOI: https://doi.org/10.1007/978-3-319-22680-4_19
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-22679-8
Online ISBN: 978-3-319-22680-4
eBook Packages: EngineeringEngineering (R0)