New Design Formulae for Safety and Precision in the Fatigue Engineering of Mechanical Components and Structures

Year : 2026 | Volume : 16 | Issue : 01 | Page : 6 24
    By

    Nori VSN Murthy,

  1. , Independent Research Scientist, , India

Abstract

This paper introduces two new formulae, termed the Nori Fatigue Formulae, for determining the maximum allowable fatigue stress in mechanical components and structures with significant stress concentrations. These formulae will eliminate the usage of code-sensitive safety factors along with other factored values from the entire mechanical design engineering work, ranging from a safety pin to spacecraft. The first formula gives the maximum allowable fatigue stress in tension, and the second formula gives the maximum allowable fatigue stress in shear. These formulae are established by methodically using all the vital mechanical properties of steel—ultimate tensile strength (T), yield strength (Y), reduction of area (R), and elongation (E)—as obtained from the engineering stress–strain curve generated by the globally standardized tensile testing. This framework enables effective utilization of the vast amount of tensile- test databases already available worldwide, particularly reduction of area and elongation, for computing the maximum permissible fatigue stress of a given material in the given condition and application. Consequently, the proposed approach eliminates the need for generating additional experimental data, which often entails substantial investments of time and financial resources. Such a unified approach, previously unavailable, is essential in view of the divergent design philosophies and design factors adopted across international design codes, standards, and handbooks over time. To make this paper more comprehensive, several new formulae are provided in the Appendix-A for use in various design situations routinely encountered. Also provided additional applications for the formulae offered in the first two papers. Thus, this paper fully encompasses the previous two papers of this new-design-formulae series.

Keywords: Allowable stress, design stress, maximum permissible stress, maximum allowable fatigue stress, maximum working stress, maximum safe stress, design factor, factor of safety, safety margin, failure stress.

[This article belongs to Trends in Mechanical Engineering & Technology ]

How to cite this article:
Nori VSN Murthy. New Design Formulae for Safety and Precision in the Fatigue Engineering of Mechanical Components and Structures. Trends in Mechanical Engineering & Technology. 2026; 16(01):6-24.
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Nori VSN Murthy. New Design Formulae for Safety and Precision in the Fatigue Engineering of Mechanical Components and Structures. Trends in Mechanical Engineering & Technology. 2026; 16(01):6-24. Available from: https://journals.stmjournals.com/tmet/article=2026/view=235800


References

  1. C. Roberts-Austen, An Introduction to the Study of Metallurgy, 1st Edition, Charles Griffin and Company, Exeter Street, London, 1891.
  2. E. Shank, A critical survey of brittle failure in carbon plate steel structures other than ships, report serial no. SSC-65, BuShips Project: NS-731, prepared for National Council’s Committee on Ship Structural Design, Advisory to Ship Structure Committee, Division of Engineering and Industrial Research, National Academy of Sciences, National Research Council, Washington, D.C, December 01, 1953.
  3. Lloyd Brownell and Edwin H. Young, Process Equipment Design, ISBN No. 0 471 11319 0, John Wiley & Sons, 1959.
  4. Weibull, Fatigue Testing and Analysis of Results, Pergamon Press, London, 1961.
  5. George E. Linnert, Welding Metallurgy, Volume I&II, Third Edition, published by American Welding Society, USA, 1965.
  6. Horace Grover, Fatigue of Aircraft Structures, Naval Air Systems Command, BMI, 1966.
  7. John W. Fisher, Karl H. Frank, Manfred A. Hirt and Bernard McNamee, Effect of Weldments on the Fatigue Strength of Steel Beams, Report No. 334.2, Lehigh University Institute of Research, National Cooperative Highway Research Program, National Academy of Sciences, September 1969.
  8. Merhyle Franklin Spotts, Design of Machine Elements, ISBN 10: 0132005506, ISBN 13: 9780132005500, Prentice-Hall,

Inc., NJ, 1971.

  1. Technical Report on Fatigue Properties, SAE J1099, SAE Information Report: 197502, Issued on: 1975-02-01, February,
  1. Joseph Edward Shigley, Mechanical Engineering Design, 1st published date: March 1, 1972, McGraw-Hill, Inc., ISBN 0- 07-056881-2, 1977.
  2. M. Lakhtin, Engineering Physical Metallurgy and Heat Treatment, Mir Publishers, Moscow, USSR, ISBN: 81-239- 0602-1, 1979.
  3. Jack Collins, Failure of Materials in Mechanical Design – Analysis, Prediction and Prevention, John Wiley & Sons Inc., 1981.
  4. L. Bernstein and V. A. Zaimovsky, Mechanical Properties of Metals, Mir Publishers, Moscow, Item Number. 114158115322, 1983.
  5. Stephen P Timoshenko, History of Strength of Materials with a brief account of the history theory of elasticity and theory of structures, 61187611, 1983.
  6. Donald J Wulpi, Understanding How Components Fail, American Society of Metals, USA, ISBN 10: 0871701898 / ISBN 13: 9780871701893,
  7. C. Boyer, Fatigue Testing, Atlas of Fatigue Curves, ASM International, USA, 1986.
  8. David Ullman, Mechanical Design Failure Analysis, 1st Edition, Marcel Dekker Inc., 270 Madison Avenue, New York 10016, USA, ISBN 0-8247-7534-1, 1986.
  9. Robert B. Ross, Handbook of Metal Treatments and Testing, Second Edition, Chapman and Hall Ltd., London, ISBN: 0412313901, 1988.
  10. George Dieter, Mechanical Metallurgy, SI Metric Edition, No. 789KHL987654 McGraw-Hill Book Company, London / New York, 1988.
  11. Fatigue Resistance of Steels, Bruce Boardman, Technical Centre, ASM Handbook, Volume 1: Properties and Selection: Irons, Steels, and High-Performance Alloys, ASM Handbook Committee, p 673-688, 1990.
  12. Walter Schlitz, A History of Fatigue, Engineering Fracture Mechanics, 0013-7944(95)00178-6, Vol. 54, No. 2, Elsevier Science Ltd, 1996.
  13. Nori VSN Murthy, A Hardenability Test Proposal (provides a new hardenability evaluation methodology/ theory with new specimen designs, new hardenability definition and terminology), ASM Heat Treating Society, Proceedings of the 2nd International Conference on Quenching and the Control of Distortion, Cleveland, USA, pages 123-131, Nov. 4-7, 1996.
  14. Fatigue and Fracture, ASM Handbook, Volume-19, ASM International, USA, ISBN: 978-0-87170-385-9, Product Code: 06197G, 1996.
  15. Francis G. Pascual and William Q. Meeker, Estimating Fatigue Curves with Random Fatigue-Limit Mode, Digital Repository, Iowa State University, 1997.
  16. David G. Ullman, Oregon State University, The Mechanical Design Process, Second Edition, The McGraw-Hill Companies, Inc., 1997.
  17. Nori VSN Murthy, Noriq – An Universal and Ideal Quenchant, ASM International, Proceedings of the 1st International Automotive Heat-Treating Conference, 13-15 July, Mexico,
  18. O. Ritchie, Mechanisms of fatigue-crack propagation in ductile and brittle solids, International Journal of Fracture 100: 55–83, Kluwer Academic Publishers, 1999.
  19. Hugo Bachmann, Problems relevant to poor ductility properties of European reinforcing steel, 0524, 12WCEE- 2000, February 4, 2000.
  20. David Roylance, Stress-Strain Curves, of Materials Science, MIT, Cambridge, MA 02139, USA, August 23, 2001.
  21. Sergio Oller, Omar Salomon and Eugenio Onate, Thermo-Mechanical Fatigue Analysis Using Generalized Continuum Damage Mechanics and The Finite Element Method, International Journal for Numerical Methods in Engineering, Corpus ID: 106405063, 2001.
  22. Information Bulletin, No. IB01-005, Alberta Boilers Safety Association, Alberta Municipal Affairs, ABSA: D1207842.DOC.1, November 15, 2001.
  23. Failure Analysis and Prevention, ASM Handbook, Volume-11, ISBN electronic: 978-1-62708-180-1, ASM International, USA, 2002.
  1. E. Totten, M. Howes, T. Inouse, Handbook of Residual Stress and Deformation of Steel, ASM Handbook, ASM International, 2002.
  2. J. Findlay and N. D. Harrison, Why Aircraft Fail, Materialstoday, ISSN:1369 7021, Elsevier Science Ltd, November 2002.
  3. William Becker, Principles of Failure Analysis, Ductile and Brittle Fracture, Course: 0335, ASM International, www.asminternational.org, 2002.
  4. Nori VSN Murthy, A Quenchant Discovery Breeding Many Inventions, Proceedings of the 4th International Conference on Quenching and the Control of Distortion, pp 243-246, CHTS, Beijing, China, May 20-23, 2003.
  5. Review of the Margins for ASME Code Fatigue Design Curve – Effects of Surface Roughness and Material Variability,

U.S. Nuclear Regulatory Commission, Prepared by O. K. Chopra, W. J. Shack, Prepared for Division of Engineering Technology, NRC Job Code Y6388, NUREG/CR-6815, ANL-02/39, Published: September 2003.

  1. George Totten, Kiyoshi Funatani, LinXie, Handbook of Mechanical Alloy Design, ISBN: 0-8247-4308-3, Marcel Dekker, Inc., USA, 2004.
  2. EN: 13445, Unfired Pressure Vessels, Background to the rules in Part 3 Design, Issue 2, 20 August, Union de Normalisation de la Mécanique, 2004.
  3. Dennis Moss, Pressure Vessel Design Manual, 3rd Edition, Gulf Publishing Co. an imprint of Elsevier, MA 01803, 2004.
  4. George Totten, Kiyoshi Funatani, Lin Xie, Design issues to prevent failures, Handbook of Metallurgical Process Design, ISBN: 0-8247-4106-4, Marcel Dekker, Inc., New York, 2004.
  5. Anand and D. M. Parks, Defect-Free Fatigue, Supplementary Notes, 2.002 Mechanics and Materials II, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, Spring 2004.
  6. Principles of Structural Design, edited by F. Chen and E.M. Lui, CRC Press, FL-USA, ISBN: 0-8493-7235-6, October 31, 2005.
  7. S. Manson and G.R. Halford, Fatigue and Durability of Structural Materials, ASM International, ISBN: 0871708256, 2006.
  8. W. Eischen, Fatigue and Fracture Mechanics, ASME Short Course, Eastern NC Section, Dept of Mechanical and Aerospace Engineering, NC State University, Saturday, April 21, 2007.
  9. Mishima, , Kang, M., Aono, Y., & Noguchi, H. (2007), Method for the evaluation of mode I fatigue crack growth rate of pre-strained materials, International Journal of Fatigue, 29(9-11), 1737-1743, 2007.
  10. William Segui, Steel Design, Fourth Edition, Thomson Canada Limited, Ontario, Canada, ISBN 13: 0-978-0- 495- 24471-4, 2007.
  11. Henry Pusey and Paul L Howard, An Historical View of Mechanical Failure Prevention Technology, sandV.com, 2008.
  12. Bahram Farahmand and Kamran Nikbin, Predicting fracture and fatigue crack growth properties using tensile properties, Science Direct, Engineering Fracture Mechanics, Volume 75, Issue: 8, pp 2144-2155, 2008.
  13. George Totten, Fatigue Crack Propagation, Advanced Materials & Processes, Volume 166, ASM International, May 2008.
  14. Fatigue, Chapter 14, Elements of Metallurgy and Engineering Alloys, Product Code: 05224G, ASM International, asminternational.org/bookstore, 2008.
  15. C.F. Canale, R.A. Mesquita, G.E. Totten, Failure Analysis of Heat-Treated Steel Components (#05113G), ASM International, September 2008. Specification for Structural Joints Using High-Strength Bolts, Research Council on Structural Connections (RCSC), Chicago, USA, December 31 2009.
  16. Jack A. Collins, Henry Busby and George Staab, Mechanical design of Machine Elements and Machines, 2nd Edition, ISBN-10: 0470413034, John Wiley & Sons, Inc., 2009.
  17. ASME Boiler and Pressure Vessel Code (BPVC), American Society of Mechanical Engineers, July 1,
  18. Gregory A. Fett, The Limitations of Fatigue Testing, Society of Automotive Engineers (SAE) Technical Paper 2010-01- 1908, 2010.
  19. Bhat and R. Patibandla, Metal Fatigue and Basic Theoretical Models, A Review, Alloy Steel – Properties and Use, Dr.

Eduardo Valencia Morales (Ed.), Available from InTech Europe, University Campus STeP Ri, Slavka Krautzeka 83/A, 51000 Rijeka, Croatia, ISBN: 978-953-307-484-9, www.intechopen.com, 2011.

  1. Van Hooreweder, D. Moens, Rene Boonen, Jean-Pierre and Pal Sas, Analysis of fracture toughness and crack propagation of Ti6Al4V produced by selective laser melting, Advanced Engineering Materials, Volume 14(1-2), pp 92-97, DOI: 10.1002/adem.201100233, 2012
  2. C. Campbell, Fatigue and Fracture – Understanding the Basics, ASM International, USA, ISBN: 978-1-61503- 976-0, 2012.
  3. Miyuki Yamamoto, Research and Development of Fatigue Issues for Railway Steel Products and Future Prospects, Nippon Steel & Sumitomo Metal Technical Report 105, Dec 2013.
  4. Chaminda Bandara, Sudath C. Siriwardane, Udaya I. Dissanayake, and Ranjith Dissanayake, Fatigue Strength Prediction Formulae for Steels and Alloys in the Gigacycle Regime, International Journal of Materials, Mechanics and Manufacturing, Vol. 1, No. 3, August 2013.
  5. Nori VSN Murthy, Calculate Allowable Stress, Quit Factor of Safety (provides formulae for design of components and structures where fatigue and stress-raisers are not design considerations), 27th ASM Heat Treating Society Conference of ASM International, pages: 29-35, Indianapolis, USA, ISBN: 9781632666802, Sept. 16-18, 2013.
  6. J Robert Sims, ASME HPHT (High Pressure High Temperature) Standards, BSEE Domestic and International Standards Conference, Offshore Standards Update, 2014.
  7. API Recommended Practice 2A-WSD for Planning, Designing and Constructing Fixed Offshore Platforms- Working Stress Design, 22nd Edition, Product No. G2AWSD22, November, 2014.
  8. R. Shives and J. A. Bennett, The Effect of Surface Reactions on Fatigue Failure, public release by National Institute of Standards and Technology (NIST), USA, National Bureau of Standards Report No. 9488, NBS Project No. 3120414, October 9, 2015.
  9. Nori VSN Murthy, Formulae for Safe Design Against Fatigue Failures, Part-I (this paper provides formulae for safe fatigue-design of the components and structures with insignificant stress-raisers), 23rd IFHTSE Congress of ASM International, held at Savannah, Georgia, April 18-21, 2016.
  10. Design and Evaluation of Steel Bridges for Fatigue and Fracture, Federal Highway Administration, U.S. Department of Transportation, Reference Manual, NHI Course No. 130122, Publication No. FHWA-NHI-16-016, December 2016.
  11. Stephen Armah, Preliminary Design of a Power Transmission Shaft under Fatigue Loading Using ASME Code, American Journal of Engineering and Applied Sciences, DOI: 10.3844/ajeassp.2018.227.244, 2018.
  12. John Ramsey, Calculating Factors of Safety and Margins of Safety from Interaction Equations, NASA/TM- 2019- 220153, September 2019.
  13. Petroleum Safety Authority, DNV GL AS Oil & Gas, Norway, Bolted Joints, Study on bolt incidents, Report No.: 2018- 5333 Rev. 3, Document No.: 119G52PN-23, Report prepared by: Hartvigsen and Tore, 15 January, 2019.
  14. Richard Byne, TEMA Standard, Tenth Edition, www.tema.org, 2019.
  15. Guidelines on Fatigue Design Assessment of Ship Structures, by Indian Register of Shipping, March
  16. Shane Turcott, Bolt Failures–Why Learn to Recognize Mechanical Failure Modes, Publisher: Society for Maintenance & Reliability Professionals, Atlanta, GA 30342, USA, June 2021.
  17. Design for Fatigue, Chapter 12, Steel Bridge Design Handbook, Original Author Dennis Mertz, Revision Author Michael
  18. Grubb, American Institute of Steel Construction, AISC Publication No. B912-22, February 2022.
  19. Yasmin Musa, Khalid H. Tantawi and Omar Tantawi, Analysis of Bolt Failure Locations for Predictive Maintenance, Proceedings of the International Conference on Industrial Engineering and Operations Management, 14th Annual International Conference on Industrial Engineering and Operations Management, Dubai, United Arab Emirates (UAE), Publisher: IEOM Society International, USA, DOI: 10.46254/AN14.20240311, Published: February 12, 2024.
  20. Corigliano and F Frisone, University of Messina, Italy, On the Fatigue of Ship-Structures under Wave Loads, ISSN: 2754-4982, Journal of Civil Engineering Research & Technology, Volume 6 (5): 1-7, 2024.

Regular Issue Subscription Review Article
Volume 16
Issue 01
Received 13/12/2025
Accepted 05/01/2026
Published 09/01/2026
Publication Time 27 Days


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