ZOOL 30010 Functional Morphology

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ZOOL 30010 - Functional Morphology Lectures
Tuesday 10.00-10.50 Thursday
10.00-10.50 Practicals Thursday 15.00-17.00
(start week 24th) Assessment exam (60), pracs
(30), comp (10) Gareth Dyke Room
103A gareth.dyke_at_ucd.ie Lecture slides
http//www.ucd.ie/zoology/lecturenotes/index.html
Course Text Pough et al. (1999) Vertebrate
Life Recommended Reading (for various chunks) -
I will provide references and handouts Young
(1984) The Life of Vertebrates Hildebrand (1985)
Functional Vertebrate Morphology, Harvard Uni.
Press.
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Crack-stopping and toughness of Haversian bone
at the functional level, osteon is the fibre
unit will determine how the bone breaks
cement layer is equivalent of embedding matrix
Haversian bone functions to prevent bone
breakages deflecting cracks around the cement
layer energy of the crack is dissipated around
the cement layer
crack propogation
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Variation in mechanical properties there is
little variation in the mechanical properties of
different bones among different mammals or
within different bones in different parts of the
skeleton Currey (1984) mechanical properties
of a cow femur vs. red deer antler v.s tympanic
bulla of fin whale but these structures are
all used in markedly different ways Property Fe
mur Antler Bulla Youngs M 13.5 7.4 31.3 Bend
ing S 247 179 33 Fracture W 1710 6190 200 De
nsity 2.06 1.86 2.47
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Variation in mechanical properties femur -
used for weight support and locomotion needs to
be stiff, strong and tough accelerated and
retarded in the step cycle (unlike other limb
bones) energy proportional to mass, hence
density decrease density lowers energy but
decreases stiffness compromise density
antlers - structures shed each year competitive
interactions etc etc dont need to be that
strong and tough compromise density vs.
weight tympanic bulla - bony capsule that
houses the ear apparatus high density to
maximise contrast with surrounding
water correlated with sound reflection
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Juvenile bones points so far pertain to adult
(mature) bone immature bone - young animals -
compact bone primary osteons, stonger in
tension and compression than that made from
secondary osteons low Youngs Modulus far more
resilient than adult bone can absorb far more
strain energy than can adult bone young
animals less likely to break bones loaded
beyond failure, tend to bend rather than break
green stick fracture patterns But this is not
always the case in young animals e.g., neonate
deer - very stiff indeed ungulates can
run very soon after birth
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Skeletons as columns and beams a vertebrate
skeleton (like any engineering structure) is
composed of columns and beams how are bones
loaded? how are they adapted to deal with these
loads? columns vertical load-bearing
structures loaded in compression position
of load on a column determines shape stress
conditions
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Stresses in beams (1) when a beam is loaded
the top edge (usually dorsal surface) will be
in compression and the bottom (ventral) will be
in tension compressive stress is negative
whereas tensile forces are positive neutral axis
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Stresses in beams (2) neutral axis - there are
no stresses at the centre of a beam loaded in
bending, so there is no need to have any material
there conversely, stresses are maximal at the
edges, so this is where most of the material of
the beam will be concentrated bending in one
direction only (beam under a roof), engineers
I-bean two directions box beams
multidirectional loading tubular
structure bicycle frames lamposts vertebrate
bones tubes are also stiffer as well as
stronger when compared to rods of the same
overall mass
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I-beams, box beams and tubes
where are these seen within a vertebrate skeleton?
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Stresses in beams (3) stress at any point in
the material of a beam is directly proportional
to its distance from the neutral axis stress
also varies with the cross sectional shape of the
beam this expressed as shape-second moment of
area (not the same as second moment of
inertia) beam - equation 2nd moment of area
(I) of a rectangular beam I wd3/12 where
w width of the beam d depth
thin-walled tube (of radius r and thickness
t) I pr3t
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Why are tubes stronger than rods? intuitively,
a tube with largest possible diameter will place
the material as far as possible from the
neutral axis, where it would be most needed to
resist bending loads rods compress loading
forces because they of uniform internal
thickness this is a compromise however - as
the diameter of a tube increases, the relative
thickness of material on the outside will
decrease there is less material to take the
load under these conditions, composite
materials (bone, wood) become vulnerable to
buckling - bending occurs causing material to
bend and then to fail as a tube becomes
progressively thinner, a point will be reached
when advantage of large diameter to decrease
stresses at the surface is outweighed by the
tendancy for the tube to fail through buckling
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Buckling long thin tubes (as well as rods and
beams) fail in buckling as their lengths become
arched consider a drinking straw compressed
against a table this will fail in the middle
and be destroyed bowed to one side and
collapsed Euler Failure Leonhard Euler
(1707-1783) tubular structures can fail by
Euler Buckling whether loaded as beams or as
columns load S at which a column or beam will
fail by Euler Buckling S n2 (EIIL2) Where
E Youngs Modulus of material L length I
second M of Area
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Expanding Euler Buckling for a thin walled
tube, recall that I pr3t where r
radius of curvature t thickness
therefore S (pEr3rt)/L2 hence if S is
high, Euler Buckling can be avoided raising S
is most efficiently achieved by increasing the
radius of a tube, since this term will be
cubed next most effective strategy would be to
decrease the radius as then S would be squared
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Poissons ratio its effect on bone strength
pull on a rubber band, it stretches becoming
elongated in the direction of the tensile
stress - it also becomes narrower strain in
direction of main stress is referred to as
primary strain (PS) lesser strain, at right
angles to primary strain is secondary strain
(SS) experiments have shown that ratio between
PS and SS is constant ratio called
Poissons Ratio S. D. Poisson (1781-1840)
this has no units (simple ratio of strain) one
is compressive and the other tensive (opposite
polarities) should be negative conventionally
recorded as positive PS recorded as I/L and SS
recorded as w/W hence PR (w/W)/(l/L)
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How bones are loaded from the perspective of
bearing the weight of an animal, it would make
sense if limb bones were held vertical and loaded
in compression, as simple columns this is
the case in elephants, sauropod dinosaurs
maximise weight supporting role of limbs - solid
rather than hollow columnar limb bones limbs
are referred to as graviportal this is in
contrast to many quadropedal animals that carry
their limbs at an angle limbs are referred
to as cursorial when limbs are totally vertical
when viewed from the front, erect