And this is obviously not quite the scale, but I'll do my best.
The slope of the moment diagram is equal to the value of the sheer,
which is constant all the way along and it's positive, so
we're going to have a constant slope from here to here, that's a straight line.
Now in going from point E to this point where we have zero sheer,
the area is a triangular area that's equal to 3,125.
It's positive shear, a positive side of the shear diagram.
So that means we're going to go up another 3,125,
where we will be up to 15,125.
And there we're integrating a ramp, so that's going to be a parabola shape.
So our slope goes from some positive value to a value of 0.
So we are going to go positive up to a value of 0.
That should be a parabola type shape, so I'll label it as a parabola.
And finally, in going from that point to the end of the beam,
or the pinned part of the beam, we have a area under the shear
curve to be -15,125 which means we're going to drop down 15,125,
which brings us back to 0, which again it always should.
That's a good way of checking yourself.
In this case, again, we're integrating a ramp and so
that's going to give us the parabola.
So if I draw that in here, goes like that as a parabola and,
We've completed our moment diagram.
So now I have a complete depiction of both the shear force and
the moment anywhere along this beam.
I don't have to cut it in several different places to find
out what the shear in the moment is at each of those places.
I know it all the way along and so Like I said in my earlier module,
I noticed that the critical values for shear at -10,000 over here,
11,000 here, 11,000 over here, a little less in between,
the values where I'm going to have the most moment and
we're going to have to be critical in designing the member to hold those loads.
Are here at point C at the roller where we have a value of -30,000 pound feet.
And we have a positive value of 15,125 but
this section over here is where we're experiencing the largest moments.
So, very, very helpful diagram.
It'll be very, very useful As you proceed in future courses in
designing beam members and mechanics of materials.
Okay, just like playing a piano,
the way that you get good at engineering problems is to practice.
It's a skill base thing and so you have to practice.
Over and over again and I've got some worksheets for you to work out.
I always like to tell my on campus students that it's easy to watch
me do the problems because I've been doing them for several years now.
But just to watch me doing and
not practice on your own is not a good way of learning.
The analogy is my oldest daughter used to be able to run an 18,
30, a 5k race which is very good and so
I could watch her all day long but I couldn't get that fast.
I'd have to practice and practice and practice.
And when I practiced I couldn't get below 20 minutes for a 5k but
I got better by practicing.
So that's what you need to do with these problems Here is a worksheet with
a simple beam with a roller on the left and on the right a loading situation.
I've got the solutions to all of these worksheets in the module handouts so
you can check yourself out.
This is a cantilever beam situations with an applied moment on the left hand
side and an applied force in the middle.
And then finally another cantilever beam.
And you can neglect the weight of the beams in all of these worksheets and
just use the applied loads that I've shown.
So now we've completed the four modules from my earlier course in applications and
engineering mechanics which covered the topics of shear force and
bending moment diagrams.
And they'll be Very important, and useful,
as we continue to solve problems in being bending.
So, we'll pick up again next time.
Dr. Wayne Whiteman, PESenior Academic Professional
