there's really only one thing that you need to know when you're analyzing structures
and it is now seriously I will get to it shortly but it does cover every aspect of analysis whether
you're doing slab design beam design column design composite decks those local connection designs and
even just local transfers and the simplicity will make you realize how elegant and efficient you can
make designs by just following this one rule this one mechanical aspect is the fact that load always
travels to the stiffest path first that's all it is oh really it doesn't matter whether it's a beam
column or wall this is because it's embedded in the way structural mechanics behave so the load
will travel along that route until that route either breaks or becomes softer now breaking
the element that's pretty easy to understand the load tries to go along it the element can't
resist it it breaks it finds a new path well becoming softer what does that actually mean
now it all stems from newton's third law that every reaction has an equal and opposite reaction
linking back to that structural mechanics the fact that any structural element to take load needs to
have an equal and opposite reaction so for a beam or slab to take the load back to the supports
it needs to deflect if we bring back to that beam analogy just so we've got multiple beams lined up
and for whatever reason the stiffest form over that doesn't allow it to deflect we push down on
it the load will share between those beams now if those beams are a varying stiffness it's all
about the deflection that's going on upon it the load will go onto the beams and share it between
the stiffnesses of each of those beams so the stiffest beam it needs the most force for it to
deflect will take the biggest load and the softest beam will take the least now if we're moving up a
little bit more into this analogy just say we've got beams and we've separated them with floor
joists the load applies down upon it the floor just deflects the deflection of that floor joist
helps spread the load between the different elements in the structure so of course that
one in the middle which can take the biggest load because the balancing force of the beam will have
the highest load because the deflection from both the beam and the floor joist is forcing the load
to go there where the outer beams which have a softer connection because of the way they're
loaded up from the floor joist will take least load but it's a combination of both the beam stiffness
and the floor joist stiffness depending on the load spread between the three elements
so if we're going into something even a little bit more complex we start to look at the behavior of
slabs and how two-way actions work so if we're looking at the way the load spread is a really
good analogy is yield line so we have a series of columns on a floor plate how is the load going to
spread between them the easiest way is going to be which is going to be the shortest path
for the least deflection there's an easy way by using yield line so yield line takes 45 degree
angles from each of the supports until they make a crossing point at which point then we'll draw the
straight line until we get to the other end so we have a combination of triangles
and really rectangles the triangle area is where the slab is behaving in two ways the
stiffest path is for that load to go down towards the column strip which is between the columns
and back towards the column and likewise on the other end it goes down towards the column strip
that's along the bottom and back there but in the middle where I've got the straight line the slab
is really behaving one way as it's only going up and down similar to a one-way slab so we can see
where we've got two-way action and where we've got one way by this simple methodology now this can
be even expanded further quite often when you're looking at load rundowns and tributary on columns
you just draw pure rectangles wherever load doesn't really flow that way it's always going
to the shortest path possible and quite often our columns are not in a symmetrical grid which
would form those rectangular load distributions they're normally quite random as they need to be
in walls or where their other elements are so when we're looking at circles and just drawing
rectangles about the load paths we can either be over or underestimating the loads on these areas
so we're applying back to that stiffest path first means that the load needs to travel the shortest
distance to get towards those columns and this is where you start to look at voronoi diagrams
now basically what a voronoi diagram is it looks at each of those column grids and starts to draw
a circle progressively bigger from each of them and when it intersects with one of the other
circles it's when it starts to draw a line so you can see by drawing lots of very nice shapes from
those random column grids you can get to quite unique tributary areas that are loaded on each
of those columns it's all about the stiffest path first but what even complicates it even further
is the fact that the columns themselves need to shorten to take load and this is called elastic
shortening or PL on EA if you need to calculate it so P is the force that's applied to the column
l is either length or height E is its young's modulus and A is the area so if we combine both
the stiffness of the slab and the softness of the columns we can have a slightly variation of
where that load's going so for example if you're surrounded by stiff columns with one soft column
in the middle the stiffer columns around the outer edge will take more load than that central
softer column so this is quite critical when you're looking at load distributions and where
they're going especially around walls columns are typically more highly stressed as they're a single
element where wall is normally a longer element and it gets from that same applied load it will
deflect less as it deflects less it's more likely to attract greater loads on top of it so we also
need to be careful when we're distributing forces that we're not creating great differentials and
sometimes we need to balance the forces between the columns that are adjacent walls now that we've
covered some basics of the gravity forces and how this applies in these areas how about lateral
stability surely it's different well it's not really any different just the load is coming from
a different direction when we think about a slab we do simplify back into a strut and tied terms
where we've got feeders and collectors to try and transfer the load back to the cause sometimes
people may argue that we can create any form of diagrams it doesn't really matter how we form
that up but why do there is some load path there however there is going to be a more efficient
path and it's always going towards that stiffest direction so you need to look at which is going
to be the stiffest shortest path for the load to get back to the elements that you're looking at
yes you could form up any diagram and maybe it might work however have you had to break the
other one that is stiffer for this load path to exist and if that low path is broken has it still
allowed you to form the load path that you've come up with if you don't really know where it's going
and got lots of elements on the floor that make up where the force needs to go you can throw it
into an FEA software and apply a load and look at where your tension and compression forces are
applying to the structure and you'll see you'll be following more of a flexible action but before you
just go and grab that FEA software and go I know the answer I'm going to go straight towards it
make a guess of where you think the loads are going to go and approximate and overtime
you'll get better you more understand structural mechanics it's all about improving your knowledge
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there getting back to low paths and how the lows transfer in a lateral sense there's also confusion
about which alums are going to take which load as you may have multiple elements in your structure
so you may have a shear wall here core wall over here or just bracing frames in certain locations
the load distribution is all about that stiffest path first so just say they're all in the same
location pushing in the same direction the load should be based on how much each element deflects
and how much force it requires so we've got the lateral force over here that's trying to push
against the structure it's a balancing about how much each element will take so that some of the
element deflections over here is the same but it also equals that lateral force and that's how it
distributes the load now there's a little bit more complexity here as sometimes the slab will deflect
you may have rotation so elements that are further out may better resist more load because they will
deflect relatively less based on that rotation to the slab when it's transferring the loads
does need to elastically shorten so to some extent elements that are further away may take slightly
less load as there's some elastic shortening occurring before the load actually gets there
well how about big transfer structures so we've got a big long wall multiple point loads on the
top coming down to two supports now when you look at it it may be quite simple you're just drawing a
strong tie diagram all the way up to the top and you've got a little tie at the bottom due to the
size of those angles it's not quite that simple because when we look at structural mechanics and
how the behavior of this wall actually occur the load will spread so if the load can spread it will
and the spreading of that load will be roughly at 45 degrees as the load from the top wants
to spread down and get to equilibrium the wall so you've got an even stress roughly along the whole
length of that wall until which point it will come down to the bottom and spread back out to
those two supports so your tension ties if you do that really big long strut may have been a little
bit conservative so you may need a little bit more load in there so something you may have also been
missing so we've got the tension tight at the bottom which is quite obvious from the strut and
tie but the load is also spreading at the top so potentially there's also tension tight at the top
for the load to spread out to get to equilibrium so if you're just thinking about a simple strut
and tire you may have missed that tie at the top as we're saying the lows diverging there's
a tension tight developed from the divergence of that load so not only does the load diverge
out causing a tension tie at the top but that divergence is also calling a spreading action
that needs to be resisted in the wall that's calculating that bottling action and how much
force we need to resist it as it's spreading out this divergence of load is also why you see local
failures from bearing as we're saying that load always needs to diverge so the load comes down
onto an element and is trying to diverge out to come to that equilibrium point this is why you get
local failures and bearing just below the surface as the load comes down as trying to diverge
out you get potentially local splitting failures and this is what a bearing failure will be
if you're looking to progress your career faster in structural engineering i'll do a link to my 10
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