what does string weights and dome structures have in common and how
do they relate to the ancient engineering marvels we can see around the
world we all know that dome structures have
produced some of the most beautiful gravity defying structure that we can see
around and they've been utilized for engineers
for thousands of years this is beautifully illustrated by
brunelleschi's dome on top of the sant maria de fiore in florence
while the physics behind how this dome stands up is no longer up for
debate but how brunelleschi was able to construct
his dome is and it has stumped engineers for many
years that is at least up until now where researchers from Princeton and from
the university of Bergamo able to mathematically prove how
brunelleschi was able to construct his dome
this gives us great insight behind the physics of how brunelleschi was able to
construct his dome and teaches us some lessons that can be
learned to even modern engineering today let's find out a little bit about
brunelleschi dome how it relates back to some string and some
weights and what the researchers at princeton
and the university of Bergamo actually found my name is Brendan
I am a structural engineer based in australia and i produce videos
around engineering and how to progress to your career faster
so if you do like that type of content please subscribe so now let's get into
it the efficiency behind shell structures
is due to them primarily utilizing the compressive force of a material
this provides engineers the structure that is both thin
lightweight and very efficient and engineers have been utilizing this
for over 5000 years with the oldest known shell structure dating back to 3000BC
... in old mesopotamia in an old burial
vault uncovered there it can also be seen
throughout all of ancient rome through many of the arches such as the
roman aqueducts or even in the colosseum and seen
throughout all the renaissance of italy with their
amazing churches that was constructed and even in barcelona where Gaudi
made some magnificent structures none other than the sagrada familia
there are also very many modern day structures as well
such as the sydney opera house and the JFK terminal
in the usa shell structures can also make many forms
such as domes barrel vaults arches and even warp surfaces you can even form
shell structures from folded plates however all these structures have a very
similar feature they have the flow of force primarily in
the compression action so if we take a bit of material it's
quite simple for compressive forces especially like a column
just transmit straight through however this shape
doesn't form the beautiful arches that we see in dome and shell structures
which form a curve so how were the ancient engineers able to do this
it's quite simple and quite ingenious and all they needed was a bit of string
so if we take a bit of string we can see we take that same compressive force it
curls up into a ball it doesn't compress like the object
we've just seen it has no bending capacity either as you
can see we can curve it around quite easily
however if we take the two points and we pull them together
we can see it forms a perfect arch so now if we flip this shape upside down
we can now take that same force in compressive actions
it's quite ingenious and quite simple what they also found out as well
if you add a bit of weight to that string
then take that same shape you can see the shape has slightly changed
the shape has changed based on the weight that's applied to it
this is beautifully illustrated by the Sagrada Familia produced by Gaudi in
Barcelona where he produced a complex string model
with weights that equated to the weight of his
towers of his cathedral this tower was so complex
that engineers had to go to the aerospace industry where they were
utilizing FE analysis to design their planes this
was actually the birth of FE analysis for structural engineers today
and all Gaudi needed back in the day to design his tower
was some weights and some string isn't that quite simple and quite
ingenious now let's get back to brunelleschi's dome
this dome is one of the largest masonry domes around the world
standing at over 52 meters tall with a diameter of 44 meters
it's truly monumental and really hard to understand the true scale of it
without actually seeing it and brunelleschi was able to construct this
dome without the need of temporary supports
and any temporary support structure was made out of timber back in the day
there was not enough timber in europe to be able to support this structure
for Brunelleschi to be able to construct this he had to crack
130 year code to even build this dome so what he produced was truly ingenious
it even stumped engineers today brunelleschi's dome is actually a twin
dome structure so it has an internal structural dome
plus an external facade that we see from the outside there's actually a
skeleton built with inside that dome as well
to solve the spreading problem brunelleschi had a series of horizontal
chains that wrap around the dome much like the
straps around a barrel to tie it together these horizontal
chains form a octagon shape around the dome
brunelleschi also included a series of vertical ribs
around the corners of the hexagon all curving towards the center
point of the dome as you can see from some of these videos
the scale of it is truly monumental and the fact that they're able to
construct it without the need of any temporary timber supports
is truly amazing while the physics behind
this dome was always hypothesized no one was actually able to prove
how brunelleschi was able to do it until up until now
what the university researchers at Princeton and the university of Bergamo
were able to do was mathematically prove the physics behind it
So how were they able to do this what the researchers did
was they built up a model of the dome in pieces
in a method called a discrete element modelling where they built each element
on top of each other and they found something truly amazing
so what the researchers found out was to do with the way the dome was
constructed the dome has is a series of
vertical bricks radiating around the dome as it's been
built up known as Loxodrome with a series of
horizontal bricks known as a Plate Bande so as the Loxodrome radiates around the
dome it allows them to lock in the Plate Bande horizontal bricks and wedge
them together effectively keeping them in compression
so this makes the dome self-sustaining as it's been constructed
so what brunelleschi did was truly ingenious
he had to crack over 130-year code to better do it as well
this was later built on to a double Loxodrome
later throughout the renaissance where they had
these Loxodrome crisscrossing around each other essentially forming a
crisscross around the whole dome so it's likely that later engineers
built upon brunelleschi's original idea of this Loxodrome
to make even more impressive structures and all they needed
back in the day was some string and some weight
to produce their masterpieces isn't it quite simple
and quite ingenious it even pushed some of the complex analysis software that we
have now so is there any other structures you'd
like to cover in detail if you do please comment below or do you want me
to go more in detail about shell structures
and truly understand the magnificence of what they are
and if you did like this video please like comment and subscribe
it helps get this video out to more people so i look forward to seeing you
in the next episode bye