OK.
So in this work example we're going to look at a frame that we have looked at Previously we've only
made one small change.
And that is we've changed our support at points.
Each will roll up support so in doing so we've turned this into a sway Frank.
Now the convenient thing for us is that because we've looked at this frame as a propped frame previously
that means we've carried out a stage one analysis.
So in this video and in the following videos we can concentrate on the stage to analysis which is the
sway moments analysis.
So the first thing to do really is to summarize some key results from a stage 1 analysis.
So if we turn support from RAW into a pin we would generate a cropping force and as I said we've done
that previously so we can just summarize here the propping force that we were generated and we can call
that P equal to twenty three point five seven kill innocents.
Okay so from our stage 1 analysis that is dropping force that develops at that point.
Okay now we can summarize our stage one moments.
Summary of Dan's app from previous analysis.
So now we're ready to move onto the stage to analysis and stage 2 you'll know from our previous lectures
is where we apply in our arbitrary amps way down to prime.
So we will impose Delta prime and back calculate.
People like.
So what does it look like for this particular frame.
So we're imposing a lateral sway Delta primes.
What that's got to do is it's gonna cause the Verch gang members in this structure to deflect.
And if they're deflecting it means a bending moment is being generated within the members.
So that visually is what we're doing with this stage to analysis applying Delta pricing.
So Delta prime in juice is fixed and Mormons are arbitrary fixed and moment within the vertical members
of this structure.
And that's an axiom that would focus on.
So looking at member e see.
Noting that we have locked joint B.
Okay.
So now we can look at mamber B.
So we noticed that it is pimm that day.
And so the fixed end moment that will develop at B will be s e n prime B to A.
That will now equal negative because it anticlockwise and will beat three be Delta prime or elsewhere
which is going to be 9 squared because it's 9 meters high so it's minus 3 or aisy warn me.
I doubt prime.
Now we can reduce those fixed hand moments down into more manageable numbers to use within our mommer
distribution.
So we are say we're going to produce more convenient.
Fixed and Mormons are arbitrary fixed and moments such as are moments.
So we go six I'm automatically cancelling out the E idle to prime because remember it is the relative
values or relative magnitudes of these Mormons were interested in.
So the e I doubt a prime can happily cancel out.
Okay so the simplest thing I can think of to do here is to have a common denominator of 25 times.
One.
Okay.
And so we can reduce that down to for 86 for 86 and minus 75 it really doesn't matter what number is
you've arrived at after condensing these mommies down was the relative magnitude and signs between them
maintained.
So just reinforced that we'll say relative values only are important.
Now we can go ahead and do a distribution with these habitué fixed and moments.
Okay so these are our arbitrary stage 2 moments.
Now we need to determine what the propping force are arbitrary propping force p prime would be or in
this case for stage 2 analysis that's our arbitrary sway force that induced Delta prime.
So considering free body diagrams to determine what is the shear at the top of member at a b and at
the bottom of member b.c.
OK.
So we can take some of the moments where point A true deal the unknown sheer force that we're after.
Okay so it's eighteen point three three kill any evidence in the direction shaar moving onto member
ABC.
So I'd say the sooner the moments about point C to determine v.b. Opera remember we're focussing only
on what we have slightly have to in order to determine the propping force p prime or the sway force
P crime in this case.
So the B or birth is equal to one to eight point seven eight.
Kill any guidance in the direction shaar.
And so the arbitrary sway force p prime is gonna simply be the summation of those two shear forces.
So the eighteen point three three remember a B at the top of member a B plus the one to eight point
seven eight at the bottom of member CB
one 1 4 point one 1 kill in humans.
Okay now we can go ahead and work out our sway factor.
Remember the sway factor is that factor by which we scale the arbitrary stage to moments in order to
get the actual stage to Mormons or the actual mom is generated by the real sway within the structure.
Bammed is p o p prime.
Okay.
And so lambda in this case for this frame is not a point worn 6.
Okay so now let's go ahead and scalar arbitrary stage two moments by lammed up to get the final stage
two moments and then we can see those final stage to moment to stage one moment and then at the final
set of bending moments for our structure.
Ssali stage all moments at the moments that are generated as a result of the external loading.
The stage to moment at the moment an hour generated due to the sway of the frame.
And those are the arbitrary stage two moments scales by the sway factor lambda.
And so the final moments for these sway frame our justI stage 1 and Stage two moments added together.
Okay so that moralez wraps up that stage to analysis.
The next step after this would be to consider free body diagrams and to flesh out the summary diagrams
for for our structure so that's our bending moment diagrams sheer force diagram and our qualitative
deflected shape so we will leave those until the next video.