Loading...

PPT – Moments of Inertia PowerPoint presentation | free to view - id: 1a9af0-M2E1O

The Adobe Flash plugin is needed to view this content

View by Category

Presentations

Products
Sold on our sister site CrystalGraphics.com

About This Presentation

Write a Comment

User Comments (0)

Transcript and Presenter's Notes

Moments of Inertia

- ????????????????????????????
- Centroid ?????????????????????????????????????????

?????????????????? - ??????????????????????????????????????????????????

??????????????????????????????????????????

- ???????????????????????
- Stress within the beam varies linearly with the

distance from an axis passing through the

centroid C of the beams cross-sectional area - s kz
- For magnitude of the force acting
- on the area element dA
- dF s dA kz dA

- Definition of Moments of Inertia for Areas
- Since this force is located a distance z from the

y axis, the moment of dF about the y axis - dM dF kz2 dA
- Resulting moment of the entire stress

distribution applied moment M - Integral represent the moment of inertia of area

about the y axis

- Moment of Inertia
- Consider area A lying in the x-y plane
- Be definition, moments of inertia of the

differential plane area dA about the x and y axes

- For entire area, moments of
- inertia are given by

- Moment of Inertia
- Formulate the second moment of dA about the pole

O or z axis - This is known as the polar axis
- where r is perpendicular from the pole (z axis)

to the element dA - Polar moment of inertia for entire area,

Parallel Axis Theorem for an Area

- For moment of inertia of an area known about an

axis passing through its centroid, determine the

moment of inertia of area about a corresponding

parallel axis using the parallel axis theorem - Consider moment of inertia
- of the shaded area
- A differential element dA is
- located at an arbitrary distance
- y from the centroidal x axis

- The fixed distance between the parallel x and x

axes is defined as dy - For moment of inertia of dA about x axis
- For entire area
- First integral represent the moment of inertia of

the area about the centroidal axis

- Second integral 0 since x passes through the

areas centroid C - Third integral represents the total area A
- Similarly
- For polar moment of inertia about an axis

perpendicular to the x-y plane and passing

through pole O (z axis)

Moments of Inertia for an Area by Integration

- Example 10.1
- Determine the moment of
- inertia for the rectangular area
- with respect to (a) the centroidal
- x axis, (b) the axis xb passing
- through the base of the
- rectangular, and (c) the pole or
- z axis perpendicular to the x-y
- plane and passing through the
- centroid C.

- Solution
- Part (a)
- Differential element chosen, distance y from x

axis - Since dA b dy

- Solution
- Part (b)
- Moment of inertia about an axis passing through

the base of the rectangle obtained by applying

parallel axis theorem

- Solution
- Part (c)
- For polar moment of inertia about point C

???????????????????????????????????

- Example 10.5
- Compute the moment of
- inertia of the composite
- area about the x axis.

- Solution
- Composite Parts
- Composite area obtained by subtracting the circle

form the rectangle - Centroid of each area is located in the figure

- Solution
- Parallel Axis Theorem
- Circle
- Rectangle

- Solution
- Summation
- For moment of inertia for the composite area,

- Example 10.6
- Determine the moments
- of inertia of the beams
- cross-sectional area
- about the x and y
- centroidal axes.

- Solution
- Composite Parts
- Considered as 3 composite areas A, B, and D
- Centroid of each area is located in the figure

- Solution
- Parallel Axis Theorem
- Rectangle A

- Solution
- Parallel Axis Theorem
- Rectangle B

- Solution
- Parallel Axis Theorem
- Rectangle D

- Solution
- Summation
- For moment of inertia for the entire

cross-sectional area,

About PowerShow.com

PowerShow.com is a leading presentation/slideshow sharing website. Whether your application is business, how-to, education, medicine, school, church, sales, marketing, online training or just for fun, PowerShow.com is a great resource. And, best of all, most of its cool features are free and easy to use.

You can use PowerShow.com to find and download example online PowerPoint ppt presentations on just about any topic you can imagine so you can learn how to improve your own slides and presentations for free. Or use it to find and download high-quality how-to PowerPoint ppt presentations with illustrated or animated slides that will teach you how to do something new, also for free. Or use it to upload your own PowerPoint slides so you can share them with your teachers, class, students, bosses, employees, customers, potential investors or the world. Or use it to create really cool photo slideshows - with 2D and 3D transitions, animation, and your choice of music - that you can share with your Facebook friends or Google+ circles. That's all free as well!

For a small fee you can get the industry's best online privacy or publicly promote your presentations and slide shows with top rankings. But aside from that it's free. We'll even convert your presentations and slide shows into the universal Flash format with all their original multimedia glory, including animation, 2D and 3D transition effects, embedded music or other audio, or even video embedded in slides. All for free. Most of the presentations and slideshows on PowerShow.com are free to view, many are even free to download. (You can choose whether to allow people to download your original PowerPoint presentations and photo slideshows for a fee or free or not at all.) Check out PowerShow.com today - for FREE. There is truly something for everyone!

You can use PowerShow.com to find and download example online PowerPoint ppt presentations on just about any topic you can imagine so you can learn how to improve your own slides and presentations for free. Or use it to find and download high-quality how-to PowerPoint ppt presentations with illustrated or animated slides that will teach you how to do something new, also for free. Or use it to upload your own PowerPoint slides so you can share them with your teachers, class, students, bosses, employees, customers, potential investors or the world. Or use it to create really cool photo slideshows - with 2D and 3D transitions, animation, and your choice of music - that you can share with your Facebook friends or Google+ circles. That's all free as well!

For a small fee you can get the industry's best online privacy or publicly promote your presentations and slide shows with top rankings. But aside from that it's free. We'll even convert your presentations and slide shows into the universal Flash format with all their original multimedia glory, including animation, 2D and 3D transition effects, embedded music or other audio, or even video embedded in slides. All for free. Most of the presentations and slideshows on PowerShow.com are free to view, many are even free to download. (You can choose whether to allow people to download your original PowerPoint presentations and photo slideshows for a fee or free or not at all.) Check out PowerShow.com today - for FREE. There is truly something for everyone!

presentations for free. Or use it to find and download high-quality how-to PowerPoint ppt presentations with illustrated or animated slides that will teach you how to do something new, also for free. Or use it to upload your own PowerPoint slides so you can share them with your teachers, class, students, bosses, employees, customers, potential investors or the world. Or use it to create really cool photo slideshows - with 2D and 3D transitions, animation, and your choice of music - that you can share with your Facebook friends or Google+ circles. That's all free as well!

For a small fee you can get the industry's best online privacy or publicly promote your presentations and slide shows with top rankings. But aside from that it's free. We'll even convert your presentations and slide shows into the universal Flash format with all their original multimedia glory, including animation, 2D and 3D transition effects, embedded music or other audio, or even video embedded in slides. All for free. Most of the presentations and slideshows on PowerShow.com are free to view, many are even free to download. (You can choose whether to allow people to download your original PowerPoint presentations and photo slideshows for a fee or free or not at all.) Check out PowerShow.com today - for FREE. There is truly something for everyone!

For a small fee you can get the industry's best online privacy or publicly promote your presentations and slide shows with top rankings. But aside from that it's free. We'll even convert your presentations and slide shows into the universal Flash format with all their original multimedia glory, including animation, 2D and 3D transition effects, embedded music or other audio, or even video embedded in slides. All for free. Most of the presentations and slideshows on PowerShow.com are free to view, many are even free to download. (You can choose whether to allow people to download your original PowerPoint presentations and photo slideshows for a fee or free or not at all.) Check out PowerShow.com today - for FREE. There is truly something for everyone!

Recommended

«

/ »

Page of

«

/ »

Promoted Presentations

Related Presentations

Page of

Home About Us Terms and Conditions Privacy Policy Presentation Removal Request Contact Us Send Us Feedback

Copyright 2018 CrystalGraphics, Inc. — All rights Reserved. PowerShow.com is a trademark of CrystalGraphics, Inc.

Copyright 2018 CrystalGraphics, Inc. — All rights Reserved. PowerShow.com is a trademark of CrystalGraphics, Inc.

The PowerPoint PPT presentation: "Moments of Inertia" is the property of its rightful owner.

Do you have PowerPoint slides to share? If so, share your PPT presentation slides online with PowerShow.com. It's FREE!