Today we are going to finish up that Bending Moment Diagram that we started

last class and so this is where we left off and so at this point D.

We're now looking at the change in the moment between point D and point E.

That's equal to the Area under the sheer curve.

The area under this rectangular portion of the sheer curve is positive 15,000.

And so we're going to go from a value of minus 3,000 up to a value of 12,000.

And

this is obviously not quite to scale, but I'll do my best.

The slope of the moment diagram is equal to the

value of the shear which is constant all the way along.

And it's positive, so we're going to have a constant slope from here.

To here, so that's a straight line.

now in going from point E to this point where we

have shear, zero sh, shear, the area is a

triangular area. That's equal to three point 3,125,

it's positive eh, shear or positive side of the shear diagram.

So, that means we going to go up another 3,125 or it

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're going to go positive up to a value of 0.

That should be a parabola, parabola type shape.

So I'll label it as parabola.

And finally in going from that point to the end

of the be, the beam, or the pinned part of

the beam, we have a area under the sheer curve

to be negative 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 a parabola. So if I draw that in here, it goes like

that as a parabola and we've completed

our moment diagram. So now I have a, 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 to share 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, I, I, I,I

notice that the critical values per share is 10,000 over minus 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 e, e, e, e, we're

[UNKNOWN]

to be critical in designing the member to hold those loads, are here at point

eh, C at the roller, where we have a value of minus 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, will be, very

very useful as you proceed in future courses

in designing beam members and mechanics of materials.

just like playing a piano, the way that

you get good at engineering problems is to practice.

It's a skill-based 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, for several years now.

but just

to watch me doing and not practice on your own, is not a good way of learning.

I, I, the analogy as I, my oldest daughter used to be able to run an,

I could watch her all day long, but I couldn't get that fast.

I'd have to practice and practice and practice.

And even when I practiced, I couldn't get

[LAUGH]

below 20 K 20 minutes for a five K. But, but I got better by practicing.

And so that's what you need to do with these problems.

here's the worksheet with a, a simple beam with a

roller on the left appear on the right a loading situation.

I've got the solutions to all of these

in the module handouts, you can check yourself out.

this is a can

[UNKNOWN]

being situation with an applied moment on the left

hand side and an applied force in the middle.

and then finally a, 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 after these series of modules, you should be pros at at

doing shear force and bending moment diagrams and we'll pick up next

module with structures that are supported by cables.