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BIOMECH - Bending: Trusses (what happens in a cantilever? (in a long…
BIOMECH - Bending: Trusses
what happens in a cantilever?
there isnt just longitudinal stresses
loads can be held by a combination of tension wires and compression rods
in a long cantilever, the central material is put into alternate tension and compression -> SHEAR
the other function of the central material is :. to resit shear
in a cantilever, shear can also be resisted by solid material, in this case stress is maximum at the neutral axis
since a beam in 3 point bending is equivalent to two cantilever placed end to end, this will also but put into shear
consequences of shear in beams
some structure which have no shear stiffness may not behave like a conventional beam at all but as lots of separate beams
books or deck of cards
fish fins have tension and compression rods and a separating material, but except for the join at the tip, no shear stiffness
relative longitudinal movements of the plates is possible at their base, causing bending
some structures which have low shear strength may fail in shear
shear failure in hollow trees
because rays dont grow transversely, tree trunks have low shear strength through the centre, which becomes a problem when they become hollow
shear stress is raised by a factor of 3 when thickness falls to 0.3xRadius
consequently the trunk can split down its length and then becomes much weaker in bending
fibre orientation and rigidity
some structure are arranged with the stresses
some fibre-reinforced structures such as lianas have helical fibres
these structures have greatly increased bending compliance because fibres can shear past each other and matrix shear and stretch just like in ropes
trusses
beams don't have to be made of solid material. trusses consist of alternating tension and compression members
e.g. bridges and roof trusses
biological trusses
trusses are seen commonly in the necks and tails of animals
the bodies of ungulates are also said to resemble trusses
alike to trusses diagram, B
excellent trusses also includes the hip region of dinosaurs
have ossified ligaments
flatter structures such as plate bones and leaves may also resemble trusses
in the horse ischium, the trabeculae seems to run along the lines of stress produced by bending
plate structures that are really flat have problems raising the second moment of area high enough
many leaves are strengthened by midribs which show dorsoventral asymmetry
the fibrous upper tissue resists tension, parenchyma at the bottom resist compression
other plates structures may be stiffened by corrugation
sedge leaves and insect wings
the peaks and troughs can be strengthen by thickening, forming solid and even tubular veins
in the leading edge of damselfly wings the shape is maintained by angle brackets, while the membrane prevents shear by acting as a stressed skin
a flat plate can be given asymmetrical bending strength by making it channel-shaped
it is much easier to bend upwards than downwards because bending upwards flattens out its section
grass leaves and many petioles of other plants are channel shaped, which helps support then against gravity
butterfly wings are positively cambered
