Advertisement

Medical and biological engineering

, Volume 9, Issue 5, pp 479–493 | Cite as

An experimental stress analysis of the neck of the femur

  • J. F. Williams
  • N. L. Svensson
Article

Abstract

The paper is concerned with the experimental analysis of the distribution of stress across the neck of the femur (thigh bone). The case considered was that of a man supported on one leg, a position which imposes maximum static load on the femur. The frozen stress method of three dimensional photoelasticity was adopted as the means of solution. A procedure was devised for correcting the results obtained from a homogeneous photoelastic model to apply to the case of bone which was considered to be composed of two main regions, a hard shell and a softer core. The bending and axial stress components so determined show a distribution which can be predicted by an engineering analysis but the shear stress distribution is not so satisfactory.

Furthermore, additional weight has been added to the theory that bone growth occurs in response to applied stress.

Keywords

Femoral Neck Femoral Head Shear Stress Distribution Cortical Shell Thigh Bone 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Nomenclature

Aα,Aβ

Cross-sectional areas of α and β regions of the neck cross-section

A, B, α′, β′

Constants describing the shape of the idealized neck cross-section

Eα,Eβ,Em

Modulus of Elasticity for α and β regions of neck and of model

P*,Q*,M*

Axial force, shear force and bending

P′, Q′, M′

moment

wα,wβ,w

Cross-sectional width of α and β regions of neck and of model cross-section at any depth

x, y, z

Co-ordinate axes

μα,μβ,μm

Poisson's ratio for α and β regions of neck and of model

σα,σβ,σm

Direct stress components in α and β regions of neck and in model

τα,τβ,τm

Shear stress components in α and β regions of neck and in model

θ, ϕ

Polar co-ordinates

Sommaire

Le mémoire s'occupe de l'analyse expérimentale de la force à travers le col du fémur (l'os de la cuisse). Le cas considéré était celui d'un homme soutenu par une jambe, une position qui impose un maximum de fardeau statique sur le fémur. La méthode de force fixée de photoélasticité à trois dimensions a été adoptée comme moyen de solution. Un procédé a été conçu pour corriger les résultats obtenus d'un modèle photoélastique homogène pour être appliqué au cas de l'os qui était considéré d'être composé de deux régions principales, une couche extérieure dure et un centre plus mou. Les constituantes de l'effort d'inclinaison et axial, déterminées ainsi, montrent une distribution qui peut être prédite par une analyse technique mais la distribution de force appliquée n'est pas tellement satisfaisante.

En outre, un poids additionnel a été ajouté à la théorie qu'une croissance de l'os se produit comme une réaction à la force appliquée.

Zusammenfassung

Der Bericht befasst sich mit der experimentellen Verteilungsanalyse von Spannungen über dem Hals des Oberschenkels (Schenkelbein). Der in Betracht gezogene Fall war der, eines auf einem Bein gehaltenen Mannes, einer Stellung, welche dem Oberschenkel maximum statische Belastung auferlegt. Die Spannungsgefriermethode von dreidimensionaler Photoelastizität wurde als Lösungsmittel angenommen. Ein Verfahren wurde für die Korrektur der, aus einem homogenen photoelastischem Modell erhaltenen Ergebnisse in Bezug auf den Fall des Knochens entworfen, welcher, aus zwei Hauptregionen bestehend, betrachtet wurde, einer harten Hülle und einem weichen Kern. Die so bestimmten Biege- und axialen Spannungskomponenten weisen eine Verteilung auf, welche mit einer technischen Analyse vorausgesagt werden kann, die Schubspannungsverteilung ist jedoch nicht so zufriedenstellend.

Ausserdem kommt zusätzliche Schwere zu der Theorie, dass Knochenwuchs als Reaktion auf angewandte Spannung erfolgt.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Amba Rao, C. L. (1956) The suitability of Araldite D resin in photoelastic investigations.Br. J. appl. Phys. 7, 229.Google Scholar
  2. Backman, S. (1957) The proximal end of the femur.Acta Radiol. Suppl. 146.Google Scholar
  3. Bechtol, C. O., Ferguson, A. B. andLaing, P. G. (1959)Metals and Engineering in Bone and Joint Surgery. Williams & Wilkins, Baltimore.Google Scholar
  4. Evans, F. G. (1957)Stress and Strain in Bones. C. C. Thomas, Springfield.Google Scholar
  5. Evans, F. G. andLebow, M. (1952) The strength of human compact bone as revealed by engineering techniques.Am. J. Surg. 83, 326.CrossRefGoogle Scholar
  6. Fessler, H. (1957) Load distribution in a model of the hip joint.J. Bone Jt Surg. 39B, 145.Google Scholar
  7. Frocht, M. M. (1948)Photoelasticity, Wiley, New York.zbMATHGoogle Scholar
  8. Hirsch, C. andBrochetti, A. (1956) The weight-bearing capacity of structural elements in femoral necks.Acta orthop. scand. 26.Google Scholar
  9. Koch, J. C. (1917) The laws of bone architecture.Am. J. Anat. 21, 177.CrossRefGoogle Scholar
  10. Milch, H. (1940) Photoelastic studies of bone forms.J. Bone Jt Surg. 22, 621.Google Scholar
  11. Paul, J. P. (1964) Bioengineering studies of the forces transmitted by joints—engineering analysis.Biomechanics and Related Bio-Engineering Topics (Ed.R. M. Kenedi). Pergamon, Oxford.Google Scholar
  12. Pauwels, F. (1951) Uber die Bedeutung der Bauprinzipien des Stutzund Bewegungsapparates fur die Beanspruchung der Rohrenknochen.Acta Anat. 12, 207.CrossRefGoogle Scholar
  13. Robinson, R. A. (1954) Electron micrography of bone.Trans. 5th Conference on Metabolic Inter-relations (Ed.E. C. Reifenstein). J. Macy Jr. Foundation, New York.Google Scholar
  14. Timoshenko, S. (1934)Theory of Elasticity, p. 290. McGraw-Hill, New York.zbMATHGoogle Scholar
  15. Timoshenko, S. (1957)Strength of Materials, Vol. 1, p. 217. Van Nostrand, New York.Google Scholar
  16. Williams, J. F. (1964) A stress analysis of the proximal end of the femur. Thesis (M.Eng.Sc.), University of Melbourne.Google Scholar
  17. Williams, J. F. andSvensson, N. L. (1968) A force analysis of the hip joint.Bio-Med. Engng 3, 365.Google Scholar

Copyright information

© International Federation for Medical and Biological Engineering 1971

Authors and Affiliations

  • J. F. Williams
    • 1
  • N. L. Svensson
    • 2
  1. 1.Department of Mechanical EngineeringUniversity of MelbourneMelbourneAustralia
  2. 2.School of Mechanical and Industrial EngineeringUniversity of New south WalesAustralia

Personalised recommendations