cause any moment because their line of action goes through the point in

the center of our engineering member.

But we do have M sub Rx in the i direction

plus the moment reaction in the y direction and the j direction,

and plus the moment reaction about the z axis in the k direction.

Plus then we have the two moment, if I'm looking at the outer side,

if I'm looking at the right hand side here of my cut, I have

the moments due to these two forces, which we're going to use as R cross F.

R is the distance from the point about which we're rotating out to

the line of action of the forces, and so R will be, in this case,

we're going out 800 millimeters in the z direction or the k direction.

And then we're gpmma go up 200 millimeters in the j direction.

And we're going to cross that with the forces acting at that point,

which are 2000 in the i direction plus 4,000 in the K direction.

And all that has to equal 0.

If you do that math and match components, you get M,

moment reaction about the x axis plus 800,000 In the i direction,

plus moment reaction about the y axis plus

1,600,000 all in the j direction.

Plus moment reaction about z,

-400,000, all in the k direction equals zero.

I match components, I get M sub

Rx equals -800,000

Newton millimeters.

M sub Ry equals -1,600,000 Newton millimeters.

And finally M sub Rz equals

400,000 Newton millimeters.

And so, here are the total results.

Those are my force reactions.

And those are my moment reactions.

Okay now with those force reactions and moment reactions,

we're going to get various loading conditions at Point A.

And so let's start with torsion.

And so for torsion if I take this cut, and this is difficult, so

you may have to try to take a piece of pool noodle or whatever and

look at this, but we're looking in this direction at this cut.

We see that the moment reaction in the Z direction is 400,000, do it in

millimeters and so by the righthand rule that's going to be this direction.

And so if I draw a cross section looking back out in this direction,

I'm going to have my moment of reaction about

the z axis is shown there in that direction.

Here is my point A, right at the top.

And we have our axis.

Up is y, and if I'm looking back in this direction,

then I'm going to get this axis is x.

And so let's first calculate the stresses due to torsion out at point A.

And try to do that on your own, and then come on back.

We know that the shear stress due to torsion is going to be,

if you review back to my Mechanics and Material part two course,