Load Paths & Tributary Area for Beams Video Lecture - Civil Engineering (CE)

hey guys the objective of this video is
to look at loath parts going from slab
joists to get others to columns we're
then going to be looking at tributary
area for beams and then we're going to
be defining and looking at one-way and
two-way slabs and the major difference
between the two so just to start off
with we're gonna have a typical
structure like this okay so it normally
has a slab notice that slab is then
supported by joists so these joists over
there which are then supported by
girders so we have a girder here and a
girder at the back over there and then
these girders will be supported by
columns alright so this place lab joist
girder column now we're gonna break this
down into each of those components and
talk about the load path so the first
thing is the slab now obviously a
portion of the load from the slab is
going to go to the joist now what we do
is we're going to start with a slab over
here alright now this is a top-down view
so if I show you what we have we have
Joyce Joyce Joyce and slab so there's
Joyce Joyce Joyce in our slab and we
need to distribute this loading in the
slab into some of the choices now we
called that the tributary area okay the
tributary area is the area of the slab
which goes into particular beams okay so
the blue over here in the blue over here
so if I were drawing 3d I hope it's
quite obvious that this middle joist is
gonna take a portion of the middle
section of the snap say that portion
there this joist over there I will take
that portion and this joist over there
will take that last portion okay so we
just divided up so say this was 10
meters we would call this the distance
from there to there five meters and the
distance from there to there as five
meters we then split that in two so that
would be 2.5 2.5 2.5 and 2.5 and this
joist would take two point five plus two
point five so five meters and these two
joists would take 2.5 meters of the slab
there okay so I hope that's quite
obvious going to be doing examples where
we actually do all this but I just hope
it's quite intuitive for now that the
distribution of the slab will be taken
in this type of pattern for the joists
okay so this some of the loading in the
slab is
to be transferred to the joists and if
we look from above it's gonna look
something like this where this middle
mill joist there takes this amount in
the mountain red and needs to enjoy this
end joist takes this amount of slab and
blue and this n joist there takes this
amount of slab in blue there okay and
then we can distribute all the slabs
into those joists so if we were to take
a typical joist so say one of these
joists here it's gonna look something
like that
alright we're gonna get a UDL so this is
an area load which is something like kPa
and we're gonna have a UDL which is
gonna be say kilonewtons per meter all
right from this slab those joists are
then supported by girders all right so
if we look at the girders then we're
going to be getting three point loads
from those joists so those joists let's
have you do is we're gonna find the
reactions on either side of those joists
so we have one two three joists hitting
this girder so the point load point load
point load all right all point loads and
then from all those point loads of the
joist we can work out the point loads in
the columns okay so that's going to be
the load path on the process you go
slabs two joists two girders and then
two columns I hope that the actions of
area loads kilonewtons per meter UDL and
point loads are quite obvious how you do
that once again this is just breaking it
down we're going to be looking at
example later on with numbers to make it
a bit to put it into a bit more
perspective but I just want to give you
a bit of perspective behind this okay so
that's all for what we call for this
type of structure where it's quite
obvious that the slab is supported by
Joyce Joyce on girders girders on
columns this is where it becomes a bit
trickier let's say we have a system like
this tell me zoom out a bit so this
system we have colonies girders joists
slabs just like before except now the
girders and the joists are in the exact
same plane as each other alright so in
the previous one it was quite clear that
the joists and girders went separate
planes joist arm was at both girder but
in this one the girder and the joist
both feed directly into the column okay
so this is a bit different so the lower
path on what goes on is going to be a
bit different and it's governed by
something
to determine when it sorry to to workout
the low path we need to determine if
this behave this slab behaves as a
one-way or two-way slab so let's look at
what that means now sorry for a two-way
slab pretending that we're looking at a
section pretend there's a column here
now and a column here now and this is
closed off okay so we're looking at this
portion over here where we have two
joists and girders on either ends
okay so just closing this off we're
putting a girder there a column there in
a column there alright so looking down
on that type of structure we have this
type of system so we need to determine
how this acts for a two-way slab what
happens is is that the distribution of
the slab feeds directly into the joist
and girder so it'd look like this so now
we have a square section it's gonna go
the lows gonna go there there there and
there it's called two-way because it's
going in two directions a rectangular
shape would look like this where these
angles feed off at 45 degrees forming
trapeziums and triangles once again to
because it's going in two ways however
like we've said it could also be
potentially behave like a one-way slab
so one way slab is exactly how we saw
before it's this type of structure but a
one-way slab can still happen
in this type of structure as well we're
gonna see what defines a one-way two-way
slab but for a one-way slab the load
just goes from the slab in one direction
to that beam there in that beam there
sorry we need to determine whether it
behaves like a one-way or two-way slab
so it behaves like a one-way slab if the
aspect ratio is greater than two the
aspect ratio is l2 and l1 where l2 is
the long length and l1 is the short
length so of that ratio the long length
the short length is greater than 2 we
can say it behaves like a one-way slab
just intuitively solid if your slab is
really really long it's gonna behave
more like a one-way slab if you had slab
is shorter like this it's gonna behave
like a two-way slab so let's talk a bit
about how we go in this void process now
so just to quickly show you what happens
in a one-way slab as we've said it goes
slab
McCollum okay so this can't exist it
exists in this structure for sure and a
potentially can't exist in this
structure if you can show that the
aspect ratio is greater than 2 all right
if the aspect ratio is less than 2 then
it behaves like a two-way slab in a
two-way slab the action is slab a
portion of that slab goes to joist and a
portion goes to girder and then they
both feed into column in contrast to a
one layer ago slab joist quor'toth
column okay so this is very linear
direct whereas to a slab a portion of
the slab loading goes into joist and a
portion of the slab loading goes into
girder and then they both go into column
I hope that's quite clear the difference
between the two sorry this is for slab
this is how we would spit out the slab
so we've seen one way slab that was this
thing when we looked over here so we're
gonna ignore this for now they're
looking now for to a slab we're gonna
see how these actions impact on the
joist and girders okay so for the joists
in girders looking at this square one
first if we take say that one over there
you can see we have a triangle loading
pattern all right so it looks a bit like
this this triangle in red we called this
point there W max the maximum UDL point
this little L is the distance from the
edge to these midpoint and this big L is
the total distance okay so that's for
the square for the rectangular slab on
this beam there we have a trapezium and
in this beam here we have triangle all
right so we have the triangle again it's
the same situation over there and then
for the longer beam this one we have a
trapezium and we call this the maximum
distributed load W max now what we need
to do is these are quite complicated
loading patterns triangles and rotations
so we use this formula to convert these
complicated loading patterns the
triangle and the trapezium into just
normal rectangular you do score W - the
formula is this W - equals W max with W
max in a triangle those points there the
maximum values and W max new trapezium
is just where it flattens out equals 1 -
4 + 3
to L is the distance from the edge to W
Mac so in triangles it's from there to
there from trapeziums it's from there to
there so that will distance there on L
the total distance the total length of
the beam squared okay and that gives us
the W - the equivalent rectangular UDL
so we're going to be using this formula
quite a bit we're going to see an
example later on using this formula as
one to introduce it now and then once we
work out all that we can find we can
find the load in the columns based on
this okay so the main thing I want you
to get out of this video at the end of
the day is just this summary over here
alright for a one-way slab the load path
goes slab joists girder column and for a
two-way slab it goes slab and a portion
of that's taken by joist a portion of
that taken by girder and then they both
feed into the column okay and just by
diagram this is a one-way slab case
because it's directly supported by
joists and then good on okay this one it
could be one way or it could be two-way
slab you have to work out based on the
aspect ratio if it's one-way slab you
just use this load pattern this this
load pattern if it's two-way slab you're
going to be using this load pattern with
this type of distribution okay with this
type of stuff anyway we're gonna be
doing two examples in this this topic
where we're going to be looking at both
one ways and two-way slabs separately so
example one is using one-way slab
example two is with two-way slab so I
recommend you check them both out anyway
guys hope that helps and we'll see you
in the next video