Okay so in the last lecture we just about introduced this 80 year old sway frames and not sway frames.
We said that frames that were cross braced or frames that were propped against more and much more which
stiffer structures they were referred to was nahm sway frames.
And that portal frames or frames that had no act do of if you like.
No active measures to resist sway.
Those were portal frames or moment frames.
Now so the question arises why why are some sway and some not sway.
Well the way to answer this is to first heed both what would have to happen to enhance way frame in
order for it to sway right.
These frames that we categorize as Narn sway would have to happen for those things to sway in response
to loading.
So let's start off with thinking about our cross braced structure.
So we have our cross braced structure here we got a tension tie in there that we are a member Aday agamemnon
I will go into tension response to the load P being applied now.
What would sway look like will sway would look something like just giving a rough rough indication here.
Now with a critical point here is that the diagonal member would need to look something like this.
We get deflection swayed a flexion Delta.
What you gonna see happen here is an error remember our bracing member must get longer.
And if it was braced in the opposite direction and pressure mamber would have to get shorter.
So really what we're saying here is we need to get longer and we know for an actually loaded ma'am.
Remember subject.
Axial load the change in length delta of that member is equal to the loading applied to the member times
its length provided by the Young's modulus for the material the member is made of times the cross-sectional
area.
Okay so whats this telling me in order for the sway for the frame here to sway in response to load P
the diagonal bracing member most get longer.
So we have to do is make sure we put in a member that is big and off I can effectively limit or eliminate
lousily speaking eliminate that lateral sway delta.
Okay so I can reduce it to a such a small value that it's insignificant.
Okay so I can really reduce that sway.
Now let's take those.
The other case of proper structure arrowroot non sway type structure.
Okay what the sway looks like in this case.
Flats way to occur.
This big diff.
Let's assume it's a big stiff concrete frame or a concrete core.
Now one of the band.
OK.
That thing that corps is acting like a vertical cantilever case was like having Incans leverich coming
out of the ground.
The point all apply in the end.
And you're going to get a deflection in order for sway to happen it has to deflect.
Well the prop structure is very stiff.
And so what we say here is the proper structure arrived with the proper instruction to proper structure.
Most band.
Wood It's very stiff.
I promise you this will eventually get back to it will get back to moments distribution and hours as
a lamarck's Sensors in.
Now how would I bend if that's if that's a cancel lever.
Okay so which p.
The deflection of the tippled that cantilever and coat which is also capital Delta or sway is going
to be equal to p l cubed over three e r.
Okay so.
So the only thing that we can change is the second moment of area of the cross section of that cantilevering.
Okay so Provi lay made that corer structure such that it has a high enough value.
K we can effect essentially reduce that lateral sway to such a small value that is negligibly small.
Okay so what I'm trying to say here is were boat of D non sway type structure as I as the engineer have
it within my power to very very easily reduce the magnitude of that sway to a very small number.
Okay and that's why we're calling them non sways structures.
And then how does that compare to a sway structure.
So but for a sway frame for a sway for an in one way dealing with.
So let's imagine our joints here are reinforced rigid joints etc..
We are not going to get a change in angle between the vertical and horizontal members at the joint.
So what would happen weedier we'd have a load coming on and the Sway is gonna be Larry's legal here
and by the degree to which those vertical elements bend.
We get a much larger square source saying here is the sway in this case.
The sway is largely largely governed or determined governed by the flexibility.
The columns.
So it's these vertical columns bending that is really what's giving rise to that lausch delta that allows
sway.
So that left that those columns are gone in the flat.
Much more than a prod or braced structure.
So so in order for me to reduce this way I have to start pulling in very very stiff CALM's very stiff
vertical columns and it very quickly becomes uneconomical.
So to try and reduce a large lateral deflection or allow swayed deflection by increasing the Fletcher
rigidity of the vertical column members that quickly becomes one economical case and so we tend to have
to accept large or swayed reflections in structures like this where there is no cropping structure.
There's an old cross bracing element.
Okay salt now.
Before we start thinking about why this matters to your squat We're gonna.
Justine Bird is one or two things about headway recognize sway vs. a non sway frame.
Well it's pretty it's very straightforward actually so this was showing a quick heading here.
How to recognize how to recognize and non sway versus a sway frame.
Well it's it's it's pretty it's pretty obvious.
So let's think about I see with this respect.
Well the first thing is if I have a lateral support or support providing resistance to sway it's very
obvious you know sway Fran.
So the first thing to look for is a support providing a support providing resistance to sway that will
be the first thing that tells you this is not a sway time frame.
This is a braced Frane so schematically in terms of our structural analysis type sketches that are very
often represented.
If I had a brain structure let's say I arrived let's say I had a structure that was propped against
a much stiffer structure after a right hand side here and it's it was a low P coming on here.
Let's put in some pins as our supports rardin drying on an additional structure there.
The right hand side I would there.
I would probably just draw on a support here and what that's telling me is I am getting a propping force
developed in that support at that joint.
OK so this is my reaction or cropping force.
So if your frame is such that you can you can see it's supported in a way that you can see lateral sway
won't be allowed because of the way to support of said Orb.
Well then it's a braced frames and that's a reaction or cropping.
Force developed.
Okay so that's a braced ring or there are other common other common examples would be let's imagine
not a very common type of structure that you'll see analyzed as something like this.
Art in C in the analysis of reinforced concrete columns.
So when you're you when you're designing a reinforced concrete column you'll very often take out a section
of the structure are referred to as a source structure around the column so you can look at what's happening
to the structure around the column that your interest is.
Let's say I'm interested in this column here.
Well I might want to know what's the been at framing into the top that column on either side and so
I'll draw those because here don't influence the bending moment that will develop in the column that
I'm interested in the stiffness of those beams.
Getting a little bit off topic but anyway the point is you'll often see a frame structure like this.
Now that as I draw on here that there thing to use is that a year and this is that sway frame are in
enhanced way freeing.
Forget about the loading let's just pretend feebly f a middle loading on for a second.
Is that a Swayer in anyway frame.
Well the answer is that a sway frame because an E loading and lateral loading will allow which can can
cause structure to deflect to the right.
So you're very likely to see if any lateral loading comes on or even unsymmetrical vertical loading.
Very likely to see this structure sway to the right hand side or indeed perhaps the left hand side which
would mean that.
You'd have something like that sort of thing would sway through right now.
If I under your other hand changed that support instead of a roller.
Imagine it was at pin area that deflected shape.
If that was a pin that all of a sudden becomes a non sway frame because now I can develop a cropping
reaction force at that support.
Okay so.
It's very important to look at your support conditions and that will help you identify whether you're
dealing with a sway frame or a non sway frame the other teams look out for is symmetry.
Okay so what we mean by this symmetry.
So a symmetrical frame.
It's a magical frame.
I mean the structure is symmetrical with symmetrical loading.
It's a magical loading.
Okay.
So if I have that situation I have a frame that is symmetrical I have loading that is also symmetrical
on that frame.
That frame will not sway.
What if either of those two conditions are not mesh SOL.
If the frame itself the structure is not symmetrical and or the loading is not symmetrical Well then
we will have a sway induced if there's no propping force developed.
So what does that mean graphically.
You can think about that.
So let's draw a symmetrical frame.
Something like this.
Given some simple pins.
That's a symmetrical frame.
It's magical about a vertical sanyal line.
Now if I did this and I stuck salt an answer the right hand side there counselee relevant.
It's no longer symmetrical right.
So now it's symmetrical.
And if I add some symmetrical loading.
Imagine a point load right down the line of symmetry.
Well then I'm going to get a deflected shape which is Isle's or symmetrical.
And if the deflected shape symmetrical by definition I can't have any sway.
So that is a metrically loaded symmetrical frame.
And that is a non sway frame.
Excellent.
Right now what's the opposite to that.
If I had the exact same frame.
So let's deal with this case.
The same frames were symmetrical friend and I shift that point lodged to the right or to the left.
All of a sudden that thing is gonna want to sway.
It had to have some lateral deflection.
Unless I provide a prop in force.
So now let's say we had P shifted to the left.
Well now all of a sudden this is gonna to happen.
This is a safe ring.
Okay so that's the order thing to watch out for so you're looking out when you're analyzing frame when
you're given at the one solver you look not for the first time you're looking at white as support conditions
and will they stop it from swaying or will they allow it to sway.
And you're also looking for symmetry gaudier to most of the shortcuts to allow you to determine if this
thing is going to sway or not sway ondar loading.
Oh case solved.
Now finally why does all of this matter when you're just interested in using moment distribution.
So we have to categorize our frames as sway and non sway because it influences worried alters the procedure
of air for moment distribution analysis.
And why is that the case.
So let's try on another a little heading here right so we are looking at the influence of the influence
of everything we've disclosed in this election in the previous lecture on moment distribution.
So why do I care.
Well for the following reason.
For.
And no harm's way for any case were friend that will not wait for in harms way.
Friend in moments are induced by moments.
Inge used by what.
Well moments will be induced by the external loads
and that is exactly the same as what you've seen for beams.
A loading comes on and the frame sways.
Okay so that you'll be happy.
Here is a standard a standard moment distribution analysis we can go straight into analysing a non sway
frame using no more than the tools and techniques that we've developed for beeves we can shoot Australian
and get to work.
So that's got the added slight added complication comes into play when we're dealing with sway frain
solve.
And so for a strayer's for a sway frame.
Moments are generated.
Orange used by what.
How could that possibly be different from a dance waif ring.
Thank you.
That Warren moment and juist boy.
Well I was the external loading external load exactly the same as an arm's way Frank.
Also we have additional moments induced by the lateral sway of the frame itself.
So we have moments induced by the lateral sway of the frame.
Okay how was that possible.
In regard to how it's possible.
But the whole point here is that that involves a two stage analysis a two stage which we might dig into
and you'll be an expert on where the end of this course.
Well at this stage are we going to say is that that involves a two stage moment.
Distribution analysis.
Okay excellent.
So let's briefly just a.
Not to keep you in suspense.
How does sway induce a moment in the frame and it's pretty straightforward actually.
So very briefly we lift the curtain and just talk briefly about sway induced Hmongs sway induced modes.
So consider We'll sort of abstract this and just think about a beam all on it's OK.
So so of these I say Beam it's just if let's remember what a fixed support at edar end came so so horizontal
no less straight as a dashed line.
So we'll draw a dashed line here to indicate the initial position of this beach.
We'll give it a support on the left that remains in the same place.
Sure.
And we'll say that this beam does the following.
Experiences.
Som sway.
So the support on the right hand side that was on here has now experienced a sway which we're calling
Delta.
OK.
So let's try on some labels Let's call that a let's call this down here B OK.
So let's see we're going to have an inflection point there so that's going to have tension on the bar
on that tension on the top.
Now I'm not going to get into the derivation of this because we don't really need to but the whole point
here is if I forget about held sway occurred imagine that that sway was simply imposed on this bean.
OK.
So something came externally and took a hold of the support B and pulled it vertically down.
OK I think that would mean that would induce an additional moment in this structure.
So we get a moment here at a because obviously the structure is bending it as tension on the top here
and tension and tension on the bottom over here.
So there is a bending moment in that member.
And so we look at the moments on either end the magnitudes of the moment on year round going to be the
same.
So the fixed end moments fixed and moment from a to b.
Anticlockwise So it's going to be a negative six e a Delta over L squared.
And then the fixed and moments from B back to a has the exact same magnitude.
It's anticlockwise minus 6 E.
Delta over hell's squared.
Okay.
So the whole point mazare would want a say on it.
The sway itself the fact that the frame has swayed case of the sway of the structure the sway of the
structure.
Inducers induces moments.
Which we must consider moments which we must hear.
Okay.
And more we will dig into that a little bit later in the two stage process.
More towards the end of the course.
So that's really all we want to say it was sway vs. sway way friends but we need to do now is just roll
up our sleeves and sort of dig into a few example questions over the next few lectures.
So we'll draw a line under this one for now.