So at this point I have all the information required to work out the sheer force diagram the bending
moment diagram drawing the reactions and also determine a quality to have deflected shape based on the
bendy diagram.
So while I'm going to do now is just go and sketch out each one of those diagrams.
OK.
So starting on the sheer force diagram Well this uses everything that we have already seen when developing
sheer force.
So there is nothing nothing new.
Just because it's a frame so you DL will cause the sheer force to go from zero linearly increasing to
the negative value of 30 so we'll call that minus 30.
We have the horizontal reaction.
The bottom here bringing the sheer force again we're following the loads across the structure.
So we have that eight point nine six as the horizontal reaction that remains unchanged as we rise up
until we hit the point load coming on of 25 kalnins which causes the sheer force to step into the right
where a total value of 25 bringing it to a value of minus sixteen point zero four on the right hand
side and that continues on changed all the way up to the joint at the case.
That's two with the members dealt with.
It's probably a good idea just to carry through a central line here so you know which liner presents
the structure.
Okay now let's deal with the vertical mamber of both the joint.
Well very easily again the reaction is going to a sheer force of the base is gonna act to the left and
rise up.
On changed until our reaction or joined are at point C means a ship fast back in and the value is seven
point five 3 0 K.
Now we have the shear on the right hand side.
The joint stepping over value of twenty six point four seven and coming down linearly due to the UCL
reaching a value of minus thirteen point five three.
That was twenty six point four seven.
Right now we can start to think about the bending moment diagram so we show our previous analysis have
basically we've worked out the the magnitude of the bending moment at the significant location so let's
span locations and also at joint's locations and support locations.
But the sheer force diagram will help us when we are trying to determine how the bending moment varies
between those discrete locations.
So again this is really relying on a lot of what we have developed previously in our mastering sheer
force and bending what would ibram Course restirred out here in a moment at a pinch sport is zero.
We worked it span moment here was 40 at the point load was a value of forty point three two and the
the straight line are Radi line running parallel to the structure.
Tells me the sheer force eyebrowed that is that this line here that tells me that the bending moment
diagram is an incline straight line inclined with respect to the centreline of the structure.
I'll keep saying the slope of the benchmark diagram was constant in that location and the constant slope
needs an incline straight line so that is a value of forty point three now.
The fact that the sheer force changes from a positive value of a point ninety six immediately to a negative
value of minus sixteen point of 5 means the slogan the bending moment diagram also changes sign so that
tells me I have a peak which means that the bending moment now steps down in this direction and I worked
out that the bending moment at the underside of joint B was thirty one point eighty six.
So that's going to mean the bending moment does this front forty point three to up to thirty point eight
thirty one point eighty six thirty one point eight.
Six are right then.
Now let me see.
Let's deal with cantilever.
Now if I look at the sheer force diagram in this cantilever region I see that sheer force changes linearly.
That means the slope of the bending moment diagram changes linearly which means the bending more diagram
is a curve so it's going to start at zero it's always going to be zero.
Freehand of cantilevering unless as an externally applied moment when it's gone a curve from 0 with
the slope increasing which means that the curve is getting steeper and steeper because the slopes increasing
the sheer force increases ok to soane value which we worked out to be 45.
We said our counsellor moment was 45 kalinich metres.
Let's look at the farside the horizontal man was the right of B.
And again we said that the moment on the right hand side was fifty one point seventy five.
Our analysis gave us this and the inclined straight line of the sheer force around tells me that the
bending moment diagram is in fact curve.
We know that any experience is a local max roamin at soane value at some location and we work at that
location as been two points 7 1 meters 2 Win 7 1.
We know the bending moment here is zero.
The sheer force diagram starts off at a value of twenty six point four seven and decreases as we move
at a right.
That means the slope of the bending moment diagram is at a maximum right a joint B and the slope is
decreasing as we move to the right.
So what that means is it's getting shallower is shallower as we move to the right so it's going to go
down and shallower shallow or shallower.
It's going to experience its local maximum here and it's going to curve back up because we know one
has to finish at zero and so that's our bending moment.
I grant you right let's draw on our value of eighteen point three worn in this location.
And that just leaves the vertical mamber above B.
Well we worked out the bending moment down here as being twenty five point would one draw that 25 point
one as the value of the bending moment there.
And we know the value on the opposite end was half of that which has twelve point five six and we know
it must change linearly because the sheer force diagram is a is a straight line parallel to the axis
of the structure.
That means the benchmark diagram is a curved line rather a an incline straight line not a curve it's
an incline straight line an incline with respect to the axis of the structure.
Usually it is not a very good incline straight line.
Looks like that all right.
So that is complete bending moment diagram.
Now one thing that we've not tried to do is we've not previously tried to work.
What would the deflected shape of that structure be.
Well how would it how would it how would it how would it deflect.
Basically in response to loading and that is a fairly a fairly logical thing to try and work.
Particularly for a frame structure.
Cause there's a lot going on in terms of deflection.
So we're gonna use the bending moment diagram to help us to help us trying to terman how the structure
deflects.
So we're going to start off by drying the structure again.
This gives us a good opportunity to draw on our reactions.
OK so when we're trying to draw deflect that shake what we're really doing is we're combining information
from two sources we're looking at the loading on the structure that will inform a little bit what's
going to happen.
But the order a big source of information is the bending mode diagram the benwell diagram is really
what's going to tell us how this structure is going to deflect.
So you'll remember that we always drew our bending moment diagram.
Are we always drive any moment diagram on the tension face and case so that means when I look at this
bending moment diagram appear whatever side of the bending moment diagram is drawn on.
So for example in this region here the bending moment diagram was drawn on the bottom of the structure
as opposed to the top.
Well that's telling me that the bottom of the structure is in tension and that tells me that informs
me on the shape of the structure in that region because I know.
Most structure at most passed through that point.
It was also through at Support point and has to pass through that support point.
Now I know that the cantilever is going to experience tension across the top because that's where the
that's where the bending moment diagrams draw.
And so the cantilever is going to do something like this with the we can see it's logical and we look
at the loading on the cantilever.
It's gone is a flect down is going to curve down like so.
When something like this.
Now so the sense you were having is were having some sort of anticlockwise rotation of joint B.
We then if did this the joint We rotate anticlockwise.
Well then the vertical mamber arising from joint B was stacked arfe heading off in this direction.
And that's that's confirmed for us by our Any one the diagram which tells us that the left hand side
would be the left hand side is experiencing tension and can only change his detention on the right hand
side when we get closer to the support at the top.
So it's gonna have something like this shape kind of like this so it's tension tension tension and then
we passed through an inflection point or a point of zero moment which is given why this location here.
And we switch to tension on the inside.
So we're going to have an inflection point here Tension tension on the outside.
Then tension on the inside.
And for a casserly over we have tension on the top for the whole thing the cancellara.
Right now we can consider it the right hand side of the structure.
Well it has to start off because our joint be rotated counterclockwise by some amount.
The structure starts off heading off like this.
So we have tension on the top initially and very quickly at this point disrobed.
The structure has zero bending moment which means we have an inflection point and we switch to tension
on the bottom.
So were going to have something like this and tension on the bottom all the way until the support over
here.
So we saw inflection point here tension on the top to the left and tense tension on the bottom to the
right of that inflection point and then we can consider the last member and again the structure kicks
so to the right hand side here.
So we have something like this.
So there is an inflection point here.
So we have tension on the left.
Pastorius point of zero moment which is this point here.
And then we have tension on the right hand side all the way down to we get back to the pinza Court.
So that is a shot that is essentially the where you combine information about the loading on the structure
and the bending moment diagram for the structure.
You combine those two sources of information and you're able to come up with what is essentially a sketch
a qualitative sketch or why you think the deflection in the structure is going to look like and that
can be a really really useful thing as an engineer to be able to.
To be able to show it that kind of a sketch so that more or less rubs off.
We have we've we've we've finished analyzing that frame and in these last three diagrams we've completely
summarized our analysis we are a sheer force diagram complete bending moment diagram and then a diagram
of the structure noting all of the what were originally or non reactions first outwardly indetermined
structure.
And we've also gone and added a nice little extra there which is a quality of deflected shape for our
structure so that more or less wraps up this will.