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Vertebrate long bone strength (implications for dinosaurs)

From: Ben Creisler

A new paper. The pdf is free:

Charlotte A. Brassey Lee Margetts, Andrew C. Kitchener, Philip J.
Withers, Phillip L. Manning and William I. Sellers (2013)
Finite element modelling versus classic beam theory: comparing methods
for stress estimation in a morphologically diverse sample of
vertebrate long bones.
Journal of the Royal Society Interface10 (79): 20120823
doi: 10.1098/rsif.2012.0823

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 time-consuming 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. High-resolution 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 (σmin) 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 (two-tailed p =
0.03, r2 = 0.56). Under bending, FEA values of maximum principal
stress (σmax) and beam theory values differed on average by 12 per
cent (±4% s.e.), with deviation between the models significantly
correlated to cross-sectional asymmetry at midshaft (two-tailed p =
0.02, r2 = 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 τtorsion
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.


Science magazine Science Shots online news mentions how this study may
apply to dinosaurs:


"The strategy might be especially useful in reconstructing animals
that are extinct, such as dinosaurs. Overestimating the strength of a
dinosaur's leg bones by ignoring the effects of bone curvature may, in
turn, mean overestimating how much weight those bones could have
supported. Turns out, large dinos like Tyrannosaurus rex and the
lumbering sauropods might have been somewhat slimmer than previously