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Abstract
Classic beam theory is frequently used in biomechanics to model the stress behaviour of vertebrate long bones, particularly when creating intraspecific scaling models. Although methodologically straightforward, classic beam theory requires complex irregular bones to be approximated as slender beams, and the errors associated with simplifying complex organic structures to such an extent are unknown. Alternative approaches, such as finite element analysis (FEA), while much more timeconsuming to perform, require no such assumptions. This study compares the results obtained using classic beam theory with those from FEA to quantify the beam theory errors and to provide recommendations about when a full FEA is essential for reasonable biomechanical predictions. Highresolution computed tomographic scans of eight vertebrate long bones were used to calculate diaphyseal stress owing to various loading regimes. Under compression, FEA values of minimum principal stress (σ(min)) were on average 142 per cent (±28% s.e.) larger than those predicted by beam theory, with deviation between the two models correlated to shaft curvature (twotailed p = 0.03, r(2) = 0.56). Under bending, FEA values of maximum principal stress (σ(max)) and beam theory values differed on average by 12 per cent (±4% s.e.), with deviation between the models significantly correlated to crosssectional asymmetry at midshaft (twotailed p = 0.02, r(2) = 0.62). In torsion, assuming maximum stress values occurred at the location of minimum cortical thickness brought beam theory and FEA values closest in line, and in this case FEA values of τ(torsion) were on average 14 per cent (±5% s.e.) higher than beam theory. Therefore, FEA is the preferred modelling solution when estimates of absolute diaphyseal stress are required, although values calculated by beam theory for bending may be acceptable in some situations.
Original language  English 

Article number  20120823 
Journal  Journal of the Royal Society Interface 
Volume  10 
Issue number  79 
DOIs  
Publication status  Published  2013 
Keywords
 Beam theory
 Biomechanics
 Crosssectional asymmetry
 Curvature
 Finite element analysis
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Dive into the research topics of 'Finite element modelling versus classic beam theory: comparing methods for stress estimation in a morphologically diverse sample of vertebrate long bones'. Together they form a unique fingerprint.Projects
 1 Finished

Structural Evolution across multiple time and length scales
Withers, P., Cartmell, S., Cernik, R., Derby, B., Eichhorn, S., Freemont, A., Hollis, C., Mummery, P., Sherratt, M., Thompson, G. & Watts, D.
1/06/11 → 31/05/16
Project: Research