Module 16: Elastic torsion of straight cylindrical shafts – angle of twist

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Mechanics of Materials II: Thin-Walled Pressure Vessels and Torsion

253 classificações

Georgia Institute of Technology

Mechanics of Materials II: Thin-Walled Pressure Vessels and Torsion

253 classificações

This course explores the analysis and design of thin-walled pressure vessels and engineering structures subjected to torsion. ------------------------------------------------ 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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Elastic Torsion of Straight Cylindrical Shafts

In this section, we will learn how to analyze and design for elastic torsion of straight cylindrical shafts.

Module 15: Elastic torsion of straight cylindrical shafts – maximum shear stress9:41

Module 16: Elastic torsion of straight cylindrical shafts – angle of twist4:19

Module 17: Elastic torsion of non-prismatic cylindrical shafts – maximum shear stress10:15

Module 18: Elastic torsion of non-prismatic cylindrical shafts – angle of twist5:20

Conheça os instrutores

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

[SOUND]

[MUSIC]

Welcome to module 16 of Mechanics of Materials part II.

Today's learning outcome is to solve for

the angle of twist when we have elastic torsion of a straight cylindrical shaft.

And we started this problem last time, we had a steel bar,

we modeled it as being maybe a drive shaft for a real world example.

And we determined the maximum shear stress in the structure and

now we want to determine the angle of twist

of the free end out here with respect to the fixed end which is on the right.

And so how would you go about doing that?

And what you should say is, well we did the theory for that.

We found the angle of twist was equal to the torque over the length

divided by the modulus of rigidity and the polar moment of inertia, J.

And so we found the torques in each of the sections last time,

so we'll look at the angle of twist In each section one at a time.

We also found j, and we need g which is the modulus of rigidity.

And I'd like you to go ahead and research what is a reasonable value for

the module of rigidity for steel.

And what you should come up with is most references

most deals around 80 giga pascals or

80,000 mega pascals is a pretty good number.

All right, so here's our angle of twist formula.

We have our torques in each section we have our J now and we have an assumed G.

Let's first look at the angle at twist of point B with respect to A.

So I've got the angle of twist of B with respect A.

So from A to B is equal to the torque in A to B is,

5.25* 10 to the 5th,

Newton millimeters.

The length from A to B is 800 millimeters.

We said that G was equal to 80, that's the module's rigidity.

The 80,000 megapascals or newtons per millimeter squared.

Since megapascals and newton per millimeter squared are the same.

And we had J which was 56,150

millimeters to the 4th.

And if I run those numbers I get 0.0935 and

all the units cancel out.

It's dimensionless or in terms of an angle, we'll call it radians and

since the twist, the torque is to this direction.

We're going to go ahead and say that,

the angle twist is in that direction which would be the positive Z direction.

I want you to go back and do the same thing now for the section,

the twist of c with respect to b, and then c with respect to d,

and then add them all together and let's see what we come up with.

And so from b to c, we have this value.

And from B to C, if I hold out B and look at C,

that's going to twist it in the negative Z direction.

And then finally from C to D I have 0.0267 if I look at just that section.

D with respect to C is going to twist in the positive z direction and

if I add those all together plus minus plus I get 1.035

radians in the positive z direction.

And that's the angle of twist of the free end

with respect to the fixed end over here on the right.

And so that's how you do the problem.

And that completes this section, this module.

[SOUND]

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