Abstract
Classic beam theory is frequently employed 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), whilst much more time-consuming to perform, require no such assumptions. This paper 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 analysis is essential for reasonable biomechanical predictions. High-resolution computed tomographic (CT) scans of eight vertebrate long bones were used to calculate diaphyseal stress due to various loading regimes. Under compression, FEA values of minimum principal stress (σ_min) were on average 142%(±28% SE) larger than those predicted by beam theory, with deviation between the two models correlated to shaft curvature (2-tailed 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% (±4% SE), with deviation between the models significantly correlated to cross-sectional asymmetry at midshaft (2-tailed 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% (±5% SE) 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.