Okay so and this worked example we noticed at E.
It is again constant.
And we noticed that we have a patient support.
So this is again not going to be a sway frame.
So we want to determine as usual our reactions are for sheer force diagram before bending moment diagram.
And we'd also like a qualitative deflective deflected shape.
So we followed the standard procedure.
Now at this point and work at work at our stiffness is first.
Okay.
And again we can look at our distribution factors.
Not wait six seven over three point seven which is not a point to win one excellence and that's stiff
mrs. annot distribution factor has worked out.
We can move now straight RG were fixed end moments.
So again we're locking each of these internal joints against rotation and we are determining what is
the fixed end moment what is the moment that would develop at that newly lock's joint.
So considering accountancy ramonet first we're looking at mamber a B.
So by inspection our fixed end moment for b.a. will simply be plus 50 KILLIN it in meters or K within
our TO member of Peacey.
So of these fixed end moment for ABC would be minus P L or 8.
Which is minus thirty seven point five kilometres which means that the fixed and moment for C B is equal
to plus PLO rate which will be Plus thirty seven point five.
Q In 18 meters.
Okay.
And then we can look at member C D.
So these fixed and moment for saeedi it's going to be minus that counterclockwise 3 p l 16 which would
end up being minus eighty four point three eight killer meters.
Okay.
So the last member that has external loading applied to wash and so therefore the last member for which
we have to consider fixed and moments is C F vertical member C F.
So f e m c f will b w l squared over 12 positive because it's a clockwise moment.
And that will end up being 20 times six square or 12 which will beat 60 killiney meters and then obviously
the corresponding trickster extend moment on the bottom F C will be minus 60.
OK so we can now jump straight into the moment distribution table.
So this is a good example this question is a great example of one that really does rely heavily on having
a table to keep track of everything.
So we're just gonna lay this table out.
OK so we've got a table Ledo distribution factories are in and are fixed and momentary And so the best
way to approach this now once you get table established is to have the table open in front of you but
also have a picture of your structure or a diagram of your structure.
As well because we're going to have to refer back to our structure when it comes to working out where
our transfer moments need to go because it's not going to be immediately obvious from our table because
for example we will have carry over moments like call a joint death and then go over to joint E.
And so we're OK on it.
The best way to for us to recognize or to see that is not by looking at the table but actually by looking
at the structure.
OK.
So let's go and do our first set of distributed moments.
So what do we have joint.
B We have a positive 50 and a minus thirty seven point five.
So that means we need a minus six point twenty five added to be an A minus six point twenty five added
to B.C. in order to balance or joint B.
Okay now balancing joint see we are going to need a minus four point one three minus four point one
three minus two point seven and minus two point seventy seven.
Okay.
Now it's time to do a carry over.
So we need to carry 50 percent of our moment.
B E S L M P E which is six point twenty five fifty per cent get carried over to the fixed support at
E.
So that is going to be let me see three point one 3 but that gets carried over to this location so I
know I'll put an arrow in here just to signify that it is a carry over moment.
So essentially happening is work taking 50 percent of this and we're carrying it over to this location
on the table so that's not immediately obvious.
We're looking at a table.
It is obvious by looking at the picture of our structure and so that's why we need boalt references
here.
So we have minus three point one three we're going to need to carry frahm 50 percent of the moment b
c always joined C so that's gonna be a negative three point one three.
That's there.
We have from C back over to be.
So that's going to be a minus two point seven.
Which is that hairy over there.
And where what where else are we going to carry you.
We're not going to carry any moment to to support you because it's a pain and we all carry any moment
over to support.
DB That's also opinions.
The only other carry over mould we have is the 50 percent from C down to F so that's going to be minus
one point 319.
And I've just noticed that is in the wrong location.
That should be down here minus three point one three.
OK so that's the first set of distributed moments and carry overs.
We are going to just repeat the process again and rebalance.
The error bars moments at joint B and joint C..
And we want to finish on a distribution and not a carry over because we want to finish with our joints
balanced so Ill do one more balancing distribution round.
So now our joints are balanced.
If we were to go ahead and do not around carry over moments we'd unbalance our joints.
But the degree to which we'd on balance dome is actually very very small and so it's not worth that
to it.
On balance.
Join us again so we'll call the distribution finish and simply some of the moments at each join to get
our final moments.
OK.
So that wraps up the distribution part of the question.
The next stage is to go and consider a free body diagrams.