OK.
So one of the first things that we have to think about before we get too deep into the analysis of frames
is lateral stability so that stability refers to the frames ability the frame or structures ability
to resist lateral loading.
So we're used to applying vertical loads to beam structures.
That's what we've done so far.
But when we get into frame structures which are much more like full buildings we have to start taking
about lateral loading and a classic example of lateral loading with the wind loading So the wind is
blowing against a building that building has to be able to resist that wind loading and ultimately transmit
down to the foundations of the structure.
And the way it does that is true it's lateral stability system saw Adonis flesh out a couple of different
ideas a couple of different points around lateral stability and sway of structures.
And that's gone and he was much better placed to tackle Momi distribution in our as for frame structures
So a starrett off was started off by thinking about a very very simple case of a frame structure.
Okay so just two columns connected together way.
Okay so let's imagine we have a very simple structure and we apply a very simple horizontal load.
P Now what's gonna happen to that structure the natural thing is going to be for it a structure to deflect
or sway or rack is another term for it to the right hand side.
Okay so I only get something in the simplest case with something like this.
Okay.
So that did that dashed line as a deflected shape essentially.
So what we're going to see is a lateral deflection which we're going to call Delta capital Delta.
Now what's happening here.
The load is coming on pea and it's causing a dis sway deflection Delta and that's really all happening
because the vertical columns are deflecting but we also have flex in these joints here case which is
a combination of flex in.
These joints.
And bending.
Mainly in the columns vertical members the columns and was the flex and these joints and burning in
the columns that allows.
Structure to sway.
So if those joints if let's just label them b and c..
So if the joints the structural joints at bnc Saw way the beam is bolted into the columnist's effort
to steel structure if that joint is sufficiently stiff you're going to reduce that sway deflection doubt
that would you still don't get some sway because the vertical calms were banned.
And you're going to get a sway as a result of that so we will put the classic solution to this.
Well there are two classic solutions to this which we'll just talk about a little bit briefly.
The first one which you're probably familiar with is called bracing or cross bracing.
So if I have a structureless again just get this structure.
So one way I can stop this structure deflecting to the right is by putting in a cross brace and case
on it start off with thinking about a crossmember here that would ultimately be intentioned.
So this top member here is gonna go into compression to resist that external load.
P That joint B.
And then as a result of that we'll get a tensile force developing in this tension member.
Okay so this is a tension member or rather there's tension in that mamber And so we typically refer
to that as a tie case.
Now that's one way we can deal the other way as well would be to put in a compression member and that's
just a day agnel mamber going the opposite direction.
Okay.
So now this day I can remember it goes directly into compression.
And typically we call compression membranous strong.
So our compression movement of providing lateral stability is often called strokes.
So those will be some of the simplest ways that we can we can't counteract that lateral sway that will
be induced in the structure due to horizontal external loading.
Now where do you see this you very often see this in your are your classic steel framed car power structure.
I drive into one every single day and I see this.
Never shred the structure so let's imagine I'm just drawn a rough schematic of a multi-storey steel
frame car park and you will very often see that the end bays are one of the days.
Has this arrangement of cross members or something like this.
And very often they will be members that are slender.
Okay.
And so what that tells us is that they're not going to resist compression will they go on or resist
tension.
And that's why they're crossed all solved the wind blows in this direction.
This one goes into tension.
But if the wind came from that direction well then that would go into.
So you have.
That's where they've crossed over like that so that's where you typically see this type of lateral stability
system that's just the first point you really draw in here.
I'm talking about these lateral stability systems.
That's what a lateral stability system is.
One example of one steel cross bracing in a structure.
Now another very common type of lateral stability system is a what's what's often referred to as a propping
type system whereby we have our structure connected to a much much stiffer structure.
Okay so what would that look like schematically.
So we talked about that.
What do we got.
So let's imagine we don't want to pull cross bracing in.
OK.
Maybe our structure has big windows in this here.
For some reason we can't accommodate mamber running diagonally across the face of the structure.
What we might do when a load comes on we might build an adjacent structure and some structure beside
that is much stiffer than our structure.
And when I say stiffer I mean flex surely it's stiffer it's harder to cause it to bend or deflect laterally
so we'll join our structure to that structure with some compression mamber.
So Force P comes on.
We get the tug member here going into compression and that compression force is directed straight across
into you are stiffer structure here.
So what's happening here is we're propping We're propping.
Half a stiffer a stiffer structure case or think we're only seen this before because you definitely
if you've looked at any building sites of any real scale you'll definitely have seen this.
And it's common in reinforced concrete structures very very common.
I have a nice graphic that was released.
Have you visualized this so common in reinforced concrete.
Or C structures.
All right.
So let's bring in saltness going to help us visualize this a little bit better.
OK.
So what do we got here.
We're looking at.
Let's forget about the bottom photograph for a second and then just look at this top schematic diagram
so we're looking at a cross section through a concrete frame structure.
And in that concrete frame structure we have this element here which we're calling a readout referred
to as a core concrete core.
And what is often hour in buildings is the lift cause or the lift shafts that lift shaft is acting as
a vertical cantilever.
So it's got a big it's got a big foundation structure down here.
And what's happening is lateral wind loading is coming after the structure.
The floors are going into compression So the floor play to the floor slabs are going into compression
and they're transmitting lateral loading directly into not vertical core structure.
And so before we move over to the right or it's at this picture what we're looking at here is essentially
a vertical cantilever that's bending over to the right in response to that lateral wind load.
Now obviously the degree of bending that I've sketched on here and the dashed lines is drastically exaggerated.
The reality is that the flexural rigidity of that vertical core structure or the degree to which that
that will bend is very very very small honking.
And so what we're really saying here is that the lateral the ability of that core to resist lateral
loading is much much much greater than the combined effect of all of these Collum to been connections
and their ability to resist the lateral loading.
And what we see at the bottom diagram or in the photograph is what it looks like in real life.
So this is a real concrete structure that's being built it's actually built.
Now this was taken during the construction phase.
And what we see here is we see these core structures here called courteille Core 3 there.
They are those vertical cantilevers.
And what you're going on what you would see is there would be a floor there's the bottom floor being
put in here that the other floor put in here another floor put in here and another one.
Look here.
OK.
And those floors are going to be propped off of these vertical core structures.
They're going to act or behave like this stiff points or stiff rigid point in the structure that are
gonna stop it from deflecting laterally so that is their stability system based around propping off
of much stiffer structures.
So the picture the diagram there kind of wraps up that story quite nicely so that's the second type
of lateral stability system so very simply schematically we can represent it like this where we have
our frame structure that are left propping the compression crop over our straws against this very very
stiff core structure.
So that is system number two.
We've got propping.
And then just to recap this number one was based around cross bracing or putting an additional day Agnon
members that experience in axial force Martin in which an actual force develops.
OK.
This was probably worth putting in just a couple of notes on this.
The concrete shafts.
Concrete shafts or cores are significantly significantly
stiffer.
Are we in bending at me or harder to bend.
They're significantly stiffer in bending I suppose to say axial stiffness which is a good point actually.
It's the axial stiffness of that compression member and that tension mamber that are going to be the
defining characteristics when it comes to how much this structure will sway.
And I'll get onto that now in a couple of minutes.
But for us straughter a compression member were concerned about their actual stiffness which for a propping
type stability system like we have here it's the flexural stiffness of the flexural rigidity of that
cantilever that we're interested in.
Right so let's get back on topic here.
So the concrete shaft is significantly stiffer in ending than.
Combined.
If that well I'll call Ms.
And leam two column connections.
That means.
And therefore the cause resist because they're stiffer.
They resist much more lateral loading much much more lateral loading the loads you can think about the
load being attracted to the stiffest members and because the cause is so much stiffer they attract the
majority of the lateral loading so they resist much or rather much as you say much of the lateral loading.
Okay so the quarries are acting as a vertical cantilevers now.
So we have looked at two stability systems.
Now what would a third one be.
Another option
would be think see if you can think about how else would we stabilize laterally stabilize the structure.
Starbury can matter frame again.
K. So what we could do is not optimal from a lateral sway point of view but we could reinforce these
joints.
We could make those joints very very stiff Okay.
And in doing so were making it harder for the angle between the vertical member and the horizontal mamber
to change.
Okay.
So currently the angle between those two members is approximately 90 degrees.
And if I reinforce that joint that joint what I'm doing is I'm making it harder for that angle to change
and if you remember back up to the top diagram I deflected structure had an angle greater than 90 degrees
here and an angle less than 90 degrees here so the angle was changing as a result of this way.
Well obviously if I stiffness those joints and make it harder for that for those two angles to change
I make it harder for that structure to sway to the right hand side.
And you typically see this type of lateral stability system in what are often called Portal frames.
Okay so let's just put in a quick note on this and say we could reinforce we could reinforce the beam
to cullom Connections.
To resist.
Bending moments generated at these locations.
The ending was generated at these locations.
What does that look like in reality.
Well what you'll very often see em I've drawn a very simplified version of it here.
What you'll very often see is big industrial type buildings so big steel framed buildings or hangers
very often have a shape.
Something like this.
You see here big big industrial sheds or aircraft hangers.
They're the big steel elements.
And let's imagine that's gonna go.
And let's drop them a little bit more fleshed out.
Oh yes we're used to seeing salt in like that.
Now the bit I'm interested in is to reinforcing that happens in katusa help reduce sway and that's going
to be.
And additional piece of steel the goals and they are called Haj and we have another piece of steel that
goes in there.
And people very often have what's called an apex Harge goes something like this.
In piece of steel section goals there.
What are you doing with those.
You're essentially providing a larger lever am because these will be bolted connections.
We're getting a little bit off topic here but what your sense you're doing is you're increasing the
lever.
L A N through which you can generate a bending moment at that location.
So what I worry really boils down to is you're reinforcing that location and the strokes you are making
it's stiffer and therefore reducing the degree of sway that you'll see in response to lateral loading.
So those are a different more common types of stability systems of course you can mix and match and
then add in there you know different combinations of these different stability systems.
So really what we're going to do now is get down to the crux of it.
And the reason I have explained is defensibility systems for you is because we're going to categorize
them into two groups.
So let's just do a summary here right.
So what have we got.
We have in terms of lateral stability systems what are we up right.
Well we had one was cross bracing.
We saw out at the start cross bracing.
Okay.
Another one was a prop in and that was the concrete core.
Sol those were you were vertical cantilevers.
And the third type system which we just introduced was the portal frame or a moment frame the portal
because it looks like some kind of a portal.
Am also often referred to as a moment frame because it resists lateral sway purely by developing bending
moments within the frame.
Now the whole point of explaining all of these different systems to you added in the factor that's really
interesting is that they divide up into two different categories like cell these ones.
Cold no sway frames no sway also often referred to as brace frames because there were actively bracing
the frame.
You saw an active measure like a cross power elements or propping structure.
And then we had these guys down here which are called sway frames.
Sway frames or structures.
Okay so in the next lecture go on it dig in a little bit more in to why the top ones are nons way and
the bottom ones are sway.
And what that means for us in terms of our moment distribution analysis.