OK.
In this world example what we want to do is take this frame which we've analyzed previously as a proper
frame and we want to take the proper way and analyze it as a sway frame.
So the usual story we want reactions sheer force diagram bending one diagram and a qualitative deflected
shape.
Okay so from our previous analysis this is what we did.
We looked at that frame with a prop at c and the charmant propping force of eleven point seven a.m.
and.
Now or as I said in the in the previous example.
In these videos we're going to focus on the stage to analysis.
So the stage 2 and hours is basically involves taking that frame and working out what are the moments
that are generated due to the sway.
So what that means is taking our frame and then applying the reverse of that propping force.
So essentially cancelling out that propping foresaw what we need to do now is analyze a frame.
We're a force P like that which is in the reverse direction to propping force.
So those two frames will give me the total set of bending moment for the frame I am interested in which
is this frame so we can go ahead and continue with the stage to analysis.
Which involves imposing an arbitrary sway Delta prime and then back calculating to calculate p prime
which would cause the algieri sway.
So visually what that would be is as follows.
Okay so in applying that arbitrary sway force p prime we induce a sway deflection down Delta cry.
Now the key thing to note here is that we're going to get bending moments in those vertical mambas.
So if I was to lock joint B and joint C and work out what the sway moments are we would get a set of
arbitrary sway or obituary's fixed end moments.
So locking
joints B and C..
So the fixed end moment.
Remember that's a that's B with locked joint B and so we've isolated joint.
So f e e n be a.
Remember a prime and there to indicate that this is simply an arbitrary fixed and moment and it's going
to be the usual.
Moving on to mamber seedy.
So we've worked out a fixed end Mormons or rather our outrage to extend momus that arise due to our
arbitrary sway Delta prime before we go ahead and do a more distribution based on these arbitrary fixed
end moments.
Were gonna just produce a set of fixed and Momos that are a little bit easier numerically to handle
in our distribution.
Because personally I'm not a big fan of working with fractions So I'm just gonna tidy up these fixed
end moments.
So what do we have that could condensed down in to a 10.
Well in fact 1 1 4 and for.
I'm going to multiply that across a tangent just yet bigger numbers to work with in my distribution.
So that will be 10 10 40 and 40.
The key thing is that the relationship in terms of magnitude is maintained between all of the fixed
and Mormans of said Norm and umbrage often times now.
So these are much easier numbers to perform.
Our mono distribution with.
So now we can go in and we can do a Mormon distribution for this frame with those arbitraged extend
moments.
Okay so that finishes out the moments distribution based on a set of arbitrary fixed and moments and
now the next phase is to work.
What is P prime that our arbitrary sway force that would cause Delta prime and all we really have to
do is consider the shear that is developed at the top of member at a b and at the top of member at c
d.
Because the combination of those two shear forces are equal to that p prime that propping or sway force
an arbitrary sway force.
So let's look at member a.b first to determine the shear at the top of that element.
So taken some of the moments about coins so that I can determine VB lower.
Phoebe lower is equal to three point three one five kill in heathens in the direction shot.
Moving on to mamber seedy.
Okay.
Taken someone along it's about point D again just following the exact same exact same procedure.
B c lower seventeen point eight three.
And so the.
P prime or the arbitrary sway force p prime is equal to three point 3 1 5 plus seventeen point eight
3.
And so he prime is equal to twenty one point 1 5.
Killen heads.
Now we can go straight on and work at a sway factor lambda equal to the actual propping force.
While there is an arbitrary sway force which is eleven point seven eight over twenty one point 1 to
5.
So in this case lambda is equal to northpoint.
5 5 7.
So remember keep thinking yourself what all of these different things are.
What lambda is is the is de factor factor by which I have to scale the Arab literary stage two moments
in order to determine the actual stage two modes.
Because there is a linear relationship between the sway force applied to a structure and the moment
that is generated within the structure.
As a result of that sway force.
So we can go ahead and wrap up the or summarize rather different stage moments in a table and then add
them up to determine the final set of sway moments which is simply just the stage one added to the stage
too.
So taking the stage one moment from our previous analysis.
Stage two moments.
As a total set of moments is obtained by superimposing the moments induced by external loading armed
to the moments that are generated by sway.
Okay so that Dan concludes the moment distribution analysis again.
The next step from here is to use freeway diagrams to determine all or known shear forces and span moments
were necessary.
And to summarize that analysis in sheer force diagram dendy Moment diagram and our deflected shape.
So we picked those up in the next video.