Hello, everyone, we continue talking about Mohr circle and the several conditions.
Case 1, 2, 3 and 4.
But we will have a close look.
As we are going to see one by one for case #1, we have Ix>Iy.
Ixy is positive.
While we were drawing the Mohr circle, we take one point Ix and we go down for the Ixy value.
We get this point A, for which the coordinate .
is (Ix,Ixy).
Both they are positive and then we look at another point
the coordinate both (Iy,
,-Ixy)
Coming upwards because we are using our axis is Ixy downward for the positive direction.
We join them together then we get the center point O, in reality, the x -axis is represented by the line
OA, while the Y -axis is represented by the line OB
and Mohr circle is twice the value of θ than the actual value.
For example if we have X and Y like this the angle in between is 90 degrees is represented by 
Mohr circle twice the value of the angle.
if θp is 60 It means that we are representing it by,120 , but it is also very important.
Notice, in the actual angle if we are going in the clockwise clockwise direction
while for the mohr  circle, we are going from X-axis to the y-axis  in the anti-clockwise direction in the reverse
manner to the actual axis.
If OA represents the x-axis and OB represents the y-axis then the O.C. will represent always the
major axis direction because of that major x-direction we have the maximum value Imax.
And for the line OD it represents a minor direction for which we have the Imin
when we are going from the X-axis  towards the major axis we are going in an anti-clockwise direction
having this angle as to 2*θp .
On the contrary, we will go in the  actual view from the X -axis in the clockwise direction and by the amount
=(1/2*2 θp) the half of the 2 θp  which will be θp.
This is u or the major direction and for the minor direction it will be perpendicular to it
and having an angle 90 degrees in the anti-clockwise direction.
Again we will have a look at case number #2, for the case#2 .
We have Ix>Iy and Ixy having a negative value.
How  we have drawn it?.
We came to the Ix horizontal and we come up.
Then we get the point that has a coordinate of (Ix,-Ixy) , then we extend this a line
and we join to another poin,t the other point having coordinate (Iy, and 
reverse value of Ixy 
In that case it will be positive.
This line intersect like before in the center point.
We call it O, then the x -axis.
If the line joining between the center of the circle to the point  having 
(Ix,-ve value of Ixy)
This is the X-axis, on the other hand the Y -axis is represented by the line from the center of the circle to
the points that have Iy and positive value _ve value of Ixy
Again we are going here from x-axis y-axis  in a clock wise.
That action was a total angle of 180.
In reality, we are going from X to y in an anti-clockwise direction and half the value of 180
which means it is 90 degree.
Again we will proceed from the X-axis to the major axis.
This is a major axis , for the line OC
we are moving from the X-axis in the direction of the major axis  X in the clockwise fashion and the angle
is considered to be (2θp) then in reality.
Again we are moving anti-clockwise from the X-axis was have the value of 2θp that which means it
is coming θp.
If we remember we have joint in order to get the direction we have joint taking that point  
to the
point and we say it is the direction of the major-axis, which again it is correct.
Once we get the major x-direction we take 90 degrees in the anti-clockwise and then we get the minor
axis direction.
Again we proceed to case #3 for case number #3, we have Ix l
Ixy is positive, how do we draw the circle?.
We have selected Ix value in the horizontal direction and since Ixy was positive we go down, then
we get that point and on the other hand, the other point we have Iy.
And the reverse sign of the (Ixy).
In that case will be negative.
And coming upwards, we join this line.
Then we get the center of the circle as a point O,
This is the X-axis from O to the point that have (Ix, Ixy positive value).
Now regarding y it is from that point to the other point that have (Iy, the reverse of Ixy)
which is negative moving from the X-axis to y-axis  in the Mohr circles in the
anti clockwise fashion.
And this angle 180.
In reality this is the x and y we are moving anti clockwise 90 degrees.
Again this is the major axis direction from O to the point that has a maximum value of I, 
the moment of inertia
While we are moving from the X-axis as we agree.
We move in the anti clockwise manner.
Then, in reality, we will move in the clockwise direction with a value of the angle which is θp
to the half of the anti clockwise angle.
That's why this is a major axis and this is the minor axis and in order to get the direction, we join from
that point is the point of the minimum value to the point of Ix and Ixy value.
And that was our direction that is matching this θp direction.
In the original view, the last case we have Ix 
How we get that point ? we go horizontally Ix.
And coming up because of coming up with that represents a negative value of my Ixy.
Then we have that point, on the other hand.
The other point we go Iy and going down.
Why.
Because Ixy is of a reverse sign it would become positive.
We join these two lines we get the center of the circle as point O, this line.
Joining from O to the point having Ix andIxy represents the x-axis and the other line extension of
that line represents the Y-axis and this line from O to the maximum amount of Ix represent the Major
axis,  my direction from the X-axis to the major axis.
We are moving clockwise direction and this value is 2θp, in  reality, we have to move anti-clockwise
half of this value which means that is θp and we will get the U.
Which is major axis and anti-clockwise by 90 degrees, we get the B which is minor axis .
These are all the cases that we have discussed earlier.
And we have established the relation between Mohr circle and the actual views regarding the x and y and
U and V.
Thanks a lot and see you.
Goodbye and take care.
