Okay so we're going to go step by step through one more fairly simple structure just to demonstrate
the ideas involved again and the different the different stages to the analysis process.
So we have here in order to sway friend.
So it's similar to the last frame except for the fact that one man with the member on the left a shorter
and the one on the right.
So this is gonna accentuate the sway of this particular frame.
So again if we lay out a principle of superposition and how it applies to this analysis we could summarize
that with the following two diagrams.
So we're going to represent that structure by the superposition of two different structures which will
analyze the structure we're interested in is going to be the same as and try and try and flesh this
idea out yourself before watching media of what to structures.
Could you draw that would give you the same influence the same effect as that complete structure above.
So we start off by looking at a product version of the structure.
And so we're going to propert stop it from swaying by putting a roller at supports C or at junction
C and that will allow us to develop a propping force which we will call P and that's standard analysis
for us.
So that is the analysis of a prompt or a nice way frame.
And from that analysis we will get our arm one moments but we've altered the structure that we were
asked to investigate.
We've altered by adding in a support at sea and so we need to superimpose on to that structure or to
add to that structure the moment from a second structure whereby we cancel out the effect of that propping
up propping force though is the superposition of that structure plus this one.
OK.
So hopefully now it by now you can see that by determining the bending moments am worn and the bending
moment too and superimposing are adding those moments together we will end up with the bending moment
diagram for the actual structure where interestingly in the sway frame again for the purposes of completeness
and demonstration.
I'll go through the stage with analysis and suggest that you pause the video here and complete the stage
worn in hours.
As for this frame.
So again our rattle should fairly quickly because we've seen plenty of these explained.
Now at this stage.
So the first thing I'll do is establish for the stage one analysis.
My structural differences.
And in the normal way we'll establish our fixed and moments or lock in joint B.
And locking joints.
B and C.
OK.
Hopefully in managed to get down a fair bit.
Too many hiccups.
We can now jump straight into the distribution.
Okay.
So again we just label these up these are Stage 1 moments now.
We want to determine what is the actual propping force P And again like we did in the last example we're
only gonna consider the free body diagrams that we absolutely have to in order to determine what that
propping forces that really means we're going to focus on every body diagram from Ambre a.b and member
C D.
And look at the sheer force at the top or the sheer force that develops internally at the top with both
of those mamber is because it's true analyzing those shear forces which we that we can work out the
propping force p.
So let's look at member B C on its own first.
So we want to determine propping force p.
So let's say that some of the moments of their points.
It sure is going to be seventeen point two for kill any patterns in into direction sharne.
And now we can move over it.
We consider it member of c.d.
Taking against some of the moments there.
Points.
The sheer force the sea lower as he was at three point zero five conclusions in the direction show.
OK.
And again we can go and take a closer look at what's happening at the joint see and point B.
So let's.
What I'm saying here is let's consider let's consider the force transmitted
across those joints across joints B and C..
So we know the propping force the line of action of that propping force acts through member of DC.
So really what were trying to do here is are trying to work at what is the axis of force in that member
because it's that that will be the propping force.
So.
When we worked at our shares in the bottom of that Kosh we had seventeen point two for at top of member
a b and we had at the opposite direction three point zero or five at the top of member Cedi which meant
on the opposite side of those cuts we would have the shear same magnitude but in the opposite direction.
Three point zero five and 17 points to four.
OK.
So that meant that the net force in B.C. The net force in member B C was equal to seventeen point two
for which rememberer was a force to the right.
Minus three point zero thigh which was a force to the left which gave me a net force of fourteen point
one nine killens acting to the right.
Right.
So if that's the axial force in that mamber that really means that the propping force must be restraining
that propping force is resisting that.
So there's a force a fourteen point one nine Clinton's acting on member of DC and if there was nothing
there to restrain a member B C would shift over to the right so therefore it is the logic that you use
or explain to yourself to reason this out there for the propping force.
The propping force that resists swayed to the right is fourteen point one nine Clinton's to the left.
So that's your stage worn analysis complete.