Module 6 – Shear Force and Bending Moment Diagram Examples

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Mechanics of Materials III: Beam Bending

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Georgia Institute of Technology

Mechanics of Materials III: Beam Bending

204 оценки

This course explores the analysis and design of beam bending problems. Prerequisite Knowledge: You will need to have successfully completed my earlier course “Mechanics of Materials I: Fundamentals of Stress and Strain and Axial Loading” in order to be successful in this course ------------------------------------------------- The copyright of all content and materials in this course are owned by either the Georgia Tech Research Corporation or Dr. Wayne Whiteman. By participating in the course or using the content or materials, whether in whole or in part, you agree that you may download and use any content and/or material in this course for your own personal, non-commercial use only in a manner consistent with a student of any academic course. Any other use of the content and materials, including use by other academic universities or entities, is prohibited without express written permission of the Georgia Tech Research Corporation. Interested parties may contact Dr. Wayne Whiteman directly for information regarding the procedure to obtain a non-exclusive license.

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Shear Force and Bending Moment Diagrams

In this section, we will review sketching shear force and bending moment diagrams.

Module 5 – Bending Moment Diagrams6:40

Module 6 – Shear Force and Bending Moment Diagram Examples6:02

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Dr. Wayne Whiteman, PE
Senior Academic Professional
Woodruff School of Mechanical Engineering

[MUSIC]

Welcome to Module 6 of Mechanics of Materials Part III on Beam Bending.

Today's learning outcomes are to finish up sketching the bending moment diagram for

a multiforce member and we refer back again to my earlier course,

Applications in Engineering Mechanics.

Today we're 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 this sheer curve is positive 15,000.

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 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.

[MUSIC]

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