OK.
So we have dealt with structures that have fixed and built in and that was the very first type of example
we looked at than in the last lecture.
We looked at structures that have PINI ends.
Now the last variation that we're gonna consider in this lecture is a structure that has a cantilevered.
And and and what what different things is that introduce into the analysis process.
So we're gonna take the exact same structure we had before except we're going to move support c to the
left by three meters and that will generate an extremely dry cantilever after the right hand side of
support.
See that's the structure you see in front you same as before.
We've just shifted the support.
It was a cantilever on the right.
So right let's think about this.
What do we know though destruction before we even begin.
Before we start thinking about a moment distribution were one thing we know is the moment at sea we
can say right at the outset what the moment at sea will be.
So let's let's just go with that for a second so before we start before we start we know with the final
moments at sea we know the final moments.
At sea.
Excellent.
Okay.
So what is that.
Well what I want when we're saying there.
Well if I was to cut the structure immediately to the right of sea and I have my 25 kill and Noon's
per meter we're at that.
See that's e in cutting I reveal an internal bending moment.
See and the bending moment diagram.
We all know this stage will look like this X.
OK.
So m c is equal to 25 times three times one point five which is one one two point five meters.
OK.
Sort of thar I ever start thinking about MoMA distribution or any kind of analysis like that we can
say something about the structure and use what we know happens.
And in that scenario where we know something at the start it tends to influence demand distribution
procedure because we have to carry that knowledge.
True that procedure and it will make slight modifications to that procedure along the way.
And that's exactly what we saw happened and example.
So what do what does this knowledge mean for our analysis.
Well what we're going to say is during the analysis no moment is going to be it is going to get distributed
into C E.
So we work with duckula to distribute and moments in to that section of structure between CMG because
we already know what the modes are.
So that's the first thing we're going to say during the analysis.
During the analysis no moment no moments will be distributed.
Into You see it.
So that has implications for our stiff misses and for our distribution factors.
So what we will say is joint sea is going to be balanced at the beginning of the analysis.
Okay.
So on a balanced like the very start and it will receive no further carry moment.
So joint C joint C will be balanced at the beginning.
The analysis
and will receive will receive no further moment no further carry over.
Moment can no further carry over it.
Great.
So we we we've here a couple of things here.
So let's now see how they play out.
True.
Our usual analysis procedure.
So the first thing we're always going to start off with is the stimuluses stiffness.
So if I think about mamber a b the man or the member a.b..
Well it's continuous at support B because the structure continues to support C and so there's rotation
resistance Provider B there's no rotation resistance provide that aid.
And so it shouldn't be any surprise that K A B is the lesser of the two options and it's equal to 3
B.
All right.
Okay.
And then just plug the numbers in Again we usually assume each is constant so we don't need to think
too much about that.
So we're just gonna.
In fact we forget about the year.
And we just have three over L which is 3 over 8 which is Point 3 7 5.
Now let's think about kbc What's going on here.
Rates of kbc before I say worries us think about.
We have.
The structure to be the structure continues already supported to be to the left and joins aren't two
to joint effort or to support.
And so there will be rotational resistance will be provided a joint base.
That's fine.
Now what's happening at sea level at sea.
We have a role our destruction does continue on past sea.
It doesn't connect to anything.
Okay it's a cantilever it's free.
So that means don't.
There is no rotational resistance provided by the structure continuing past sea.
OK it does continue past because it doesn't connect or join anything it doesn't provide any resistance
or rather the structure to the right of C is providing no rotational resistance.
And so there is no swap with say here is the cantilever.
The counselee it provides no rotational resistance at sea.
No rotational resistance.
SI OK.
So that's the exact same having I can't leave it there.
We may as it is the exact same we may as well.
For the purposes of the stiffness of the sea we may as well just have a pin dent.
Because a pinned end provides exactly the same rotation of resistance.
Are we known as having a cantilever at sea.
All right so the stiffness is again the lesser of the two options three e.
Or else which gives us not point four to nine.
Where in this case is seven meters are right at now.
Now you may be thinking what about the stiffness of sea.
Well it's not required.
There is no stiffness required because we will have a distribution factor for sea equal to zero.
So we don't need to go working out while a stiffness is.
So no not required.
The cars the cars no moments.
Won't be distributed will be distributed.
To see he.
Excellent.
OK.
Right.
Jumped straight on into a distribution factors distribution factors.
Now what have we got.
Well this proceedings first for joy be annually it receives exactly as before.
So the distribution factor for EPA is the stiffness of the would be a point 3 7 5 or the of the stiffness
is which was one point seventy five plus now point four to nine which is not for seven.
And then the distribution factor for B.C. is simply not to be worn minus point for seven because remember
the distribution factor for all members distribution factors for each member meeting at a joint most
adduct what.
So I can't sure caught it say one mine it's not 4 7 which is not quite like 3 OK.
Super.
Now the distribution factor for C B is one could say that straight away it's worn because Annie and
rebalancing moment apply to joints C has gotta only be distributed in cheap member at CB because remember
the bending moment is in let's see the bending moment in the cantilevers baked in from the start he
can't change so we can't distribute.
And he further moment into it mamber see.
And so the distribution factor at that joint see must be essentially saying.
Telling us that all of the only applied balancing has to wait to see and no moment is distribution factor
for C E equal zero because the cantilevering armed is baked in at the very start.
It's not gonna change our rate and Soledad is the distribution factor is dealt with.
We move from that straight onto fixed end moments as he ends.
Okay so the fixed end moments for a B and B are exactly as we had in the previous lecture.
We had our props cantilever model so fixed and moment a B was zero as the P and end and the fixed end
moments for B.
Based on our cross counselee Ramadhan we were SOL previously was plus 150 and now we can't think about
the C.
So what would happen.
Member of B C let's just sketch it out.
We had joined B was locked.
Remember dealing with fixed end moments.
Now so where dealing with the locked off structure of the structure with the relevant joint locked.
So we hanner you dear girl.
That was B.
That was C..
Now remember the structure flying after the right of C.
It's flying out and connecting to anything so it's not providing any rotation resistance and so I can
very simply say that that is like having a AP self determining the extant moment.
I determine based on Croft carnally.
So what will I say.
Quick note here.
This simple.
Simple support assumed.
Remember.
C is free to rotate after the joint is balanced.
Based on our Based on our proft counselee remodel but uses using the fixed and moment for ABC is egal
T minus W L squared over 8 which is equal to minus 1 5 3 point 1 and the fixed and mom would receive
B is zero.
Excellent.
So now we can go we've got to extend it.
We can go straight into our table and process the distribution.
We noticed that joint B is ever balanced.
Now it's only had a balance by a relatively small amount so you need to add a positive three point warn
killiney meters and we're going to distribute that 47 percent of it into B and 53 percent of it into
B.C. So when we do that it results in as adding a plus one point for six.
And to be a side an A plus one point six for on the b.c side.
So that's joint B now balanced.
Now we go and look at our cantilever on the right hand side of that joint joint see we are a cantilever
among the 1 1 2.5 or rather in negative 1 1 2 point 5.
Now that needs to be balanced by a plus one or 2.5.
So we do that one.
One two point five and that cantilever joint is fairly balanced and we can leave it alone.
We're not going to distribute any moments over to that joint So when we look at our carry over section
we note that joint a is a pain and so the carry over it to appear and support will be zero.
We said that we carry no further moment over to the cantilevered support at sea.
So we have no moment carried over here but what we do have is 50 percent of the moments that we have
applied to balance walk joints.
50 percent of that will be transferred back over to joint B and so we'll end up with a fifty six point
two thighs.
So this is the first time that we've seen what we were referred to as a multi iteration distribution
and we're going to get into these in more detail in the next lecture.
But for now the focus of this lecture is just her arm dealing with this cantilevering And so what.
I'll just say for now is we're on balancing joint B again with that carry over moment which means that
we're going to have to go in and balance it out.
So don't worry too much about the day the any further detail than that because as I say we're gonna
tackle at the next lecture.
So for now let's just go in and rebalance up joint B.
So we got a balanced deal.
So we need to add inagua Fifty six point two fives that's going to be a minus 26 point four four and
a minus twenty nine point eight war.
Okay.
And we know again there is no moment carried over to opin support.
A.
And so again we have zero carried over here and we know we're carrying zero moment over to join C as
well because of that count of the hour.
That means that we basically finished we can go no further with balanced up all of our joints.
And so we can sum up our final moments.
So if we if we so we'll build on each call what do we have.
We have zero at the pin support a as we would expect.
We have one hundred and twenty five point 0 2 at joint B and we have a negative one to five point 0
2 on the right hand side.
Well it actually adds up to a point or one but that's just a rounding error in the difference.
So joint B is balanced as we would expect and we know agency is also balanced.
So we've got a plus 1 1 2 point five on a negative 1 1 2 point five.
So that's our distribution and I mean that's that's that's how we handle scantly ran and you've also
seen a little bit of a preview and into multi iteration moment distributions.
So at this stage it's a good idea to just some of what are the effects of the cantilevering and hadiza
cantilever and influence our mom distribution process.
Summary of cantilevering effects.
So the first thing that will say is the distribution factor for a cantilever is zero.
So what that really means is once we've balanced our cantilever there is no further moments transmitted
internat cantilevers section of the structure.
And so the distribution factor for a cantilevers 0.
The next thing that we have to keep in mind is that a cantilever support receives no carry over a moment.
And that's what we've seen happening in that table no carry over moment is carried over to that continues
support after we've got it balanced or we leave it alone.
So that's the second point.
Okay.
The third point that we're gonna have to keep in mind is that the stiffness of any member gets adjacent
to a cantilever and does spinning and be one of them.
So in when we're dealing with beams so the stiffness of any member that's adjacent to a cantilever is
gonna be three over L.
And the fourth point is he fixed in moment for any member that is adjacent to a cancer lever are determined
based on a proper cantilever model.
Okay so where did we see that it's to scale back up because that tends to be an arbitrary.
So look at this this one here right we've got that member of B.C. It's adjacent to the cantilever And
so the fixed end moment for that substructure are determined based on this prompt cantilever model and
that's all cars that extend moment that cantilevers support for the adjacent member was to be zero.
So they are the four main things that you're going to want to keep in mind when you're dealing with
and structure that has a cantilever in it in case that a distribution factor for the cantilever is zero.
The cantilevers support it receives no carry over moments the stiffness for a member adjacent to a cantilever
is going to be 3i over L and the flixton moments for the member adjacent to a Qantas lever are based
on the proper cantilever.
Okay.
So at this point we are ready to go and determine the span moments the reactions on the sheer force.
Now this proceed in exactly the same way that you've seen before.
So what I'll do is and summarize our solution here.
What you need to go and make sure that you can arrive at this same solution yourself.
So confirm the following complete solution.
Okay so that is summarize complete solution.
We have our reactions complete sheer force diagram and our complete pandemonium diagram.
Really you've only got half of the story told by the time you finished the distribution you still have
quite a bit of leg work to do to go from that distribution Mormon distribution which has given you the
support moments to this complete picture which has all of the shear forces all of the moments including
span moments and the reactions.
So you got to make sure that you can go that extra step and get yourself to this stage.
So now what I want to do in the next video is take a deep dive into the multi iteration distribution
and just talking it in a little bit more detail.
But what's going on in these mortie iteration distributions you've seen a sneak preview of it here in
this example.
What we'll do.
You're now in the next lecture.