@@Eagle_1174 Right. When you derive the sectional forces, the effective stiffness in terms of how the strain of the section changes with stress will come down to something involving x^2 with area. So, that turns out to be equivalent to the second moment of inertia as it is defined. The elastic modulus is also included in the bending stiffness. So, although those are true statements, the true stiffness of the beam is a combo of both in a sense. Only stating this to allow people to understand that for bending you need both for the full stiffness.
finally i found a video that talks about what it is....a lot of people teach how to calculate it but not what physical meaning of it.....thank you a lot
That’s the best example of demonstrating the moment of inertia! Helped me a lot in understanding. Loved the fact that you showed the difference in calculation and real life.
Hi sir, greetings from a student in India! Your videos are brilliant and really really helpful, thank you so much! This channel deserves to be a lot more popular 😊
Hi sir.....! Am from Sri Lanka & thank you very much for your service for an engineering student like me. your explanations are really simple instead of being too complicated. I keep watching you and learning from you instead of attending lectures.
I really really wish that you would continue making videos...Everyone can understand the theory, but the practical demonstration makes sure everyone understands and remembers WHEN and HOW to make use of it!
after 4 years of mechanical engineering , finally i understood the concept of ( capital i in beam equation ) thank you so much , you don't know how much difference that made in my life . please keep sharing you superior knowledge.
It's a capital I, and the shape that has the best value of capital I, looks like the letter I. Makes it very easy to remember. Too bad the comments don't have a serif font where you can see it better.
Thank you for this professor. I do have to comment that there are times you MUST absolutely fight tradition. If people didn't fight tradition, slavery and women not allowed to vote may still have continued. As such, not calling them "two by fours" is just one step in the correct direction. Metric system is where it's at.
That really was smart teaching........I was stuck on this doubt of mine for quite some time now that why do we consider MOI for calc. of deflection in beam but you jst cleared this in 7 mins.....awesome
I understood that means stiffness. Can you relate the moment of inertia with the bending moment of equation i.e. M/I=σ/y with a suitable physical example ? Thanks in advance
It’s everywhere. Think of it as the stress at any point perpendicular to the axis of bending is no different than a thin fiber in tension or compression; at that point, the strain is the stress divided by elastic modulus. The strain in beam can ALWAYS be derived from the linear elastic and fully planar assumption where the section MUST rotate about some point (also known as the neutral axis) and maintain a linear profile. This rotation is proportional to a curvature radius and length of the beam with small changes along the radius (called curvature). It is then possible to relate the length and the dimensions of that section to the strain which then becomes integrated with definitions of E and I. Let me know if you would like me to show the entire derivation.
Can someone please explain how the squared distance from the centroid relates to the equation (which you have to multiply with the area to get the area moment of inertia)?
excellent video on the subject, principles and real-life demo. It would have been interesting to make the same beam with 1/4-inch-thick pine box beam glue up, same size as the pine board you are using and demo that also. I am sure the beam would hold you also. I would have been good to have measured the deflection and know your weight to have further understanding till you have broken the board. The video could of had a free body diagram, to define the 'design specification', review of the formulas, did the demos, talk a little fo tbe design requirements and safety margins would of completed the video for me! But well done, nevertheless.
I'm afraid not. The normal stress is My/I. If you substitute I=1/12*b*h^3, it works out that the stress at the top and bottom of the beam goes down as h^2
Hi Marius, EI is a stiffness expression that includes both material contribution and the contribution from the cross-sectional shape. I is the portion of the stiffness due to geometry - the cross-sectional shape.
I think that When the load is applied on the beam it acts perpendicular to the surface and try to bend the material along its surface. And the material shows stiffness (resistance to rigidity) towards it, and to calculate how much stiffness the beam or material shows we calculate it's moment of inertia. For the calculation of moment of inertia we need to know the cross-section of the element along a desired axis we want to find. Remember when we study in class 11, the moment of inertia with its parallel axis theorem. In there the cross-section can be of regular or any irregular shape. But in case if beams we have standard shapes. I hope that your doubt is cleared. Furthermore you can calculate the beam stiffness at any point of fibre by changing its axis. Any more questions..... reply me.! Keep learning and growing.! *The knowledge is aggregation of marginal gains*
Moment in general means quantity multiplied by distance to a reference point. First moment of area is area multiplied (or rather integrated) with distance to the centroidal axis. Second moment of area, squares this distance. A practical reason why we care about first moment of area, is the strength of a member against shear loads. Maximum shear stress is inversely proportional to the first moment of area, and thus the shear strength of a cross section, is based on the first moment of area. The first moment of area is also part of the algorithm for calculating the centroid.
most lecturers teach this topics on materials in civil engineering class,but they never give us the practical meaning of them.i graduated from civil engineering class in kenya but struggled to understand the practical aspect of things like moment of inertia till i started researching on youtube videos.
Stiffness due to geometry! That short sentence changed everything!
Stiffness due to geometry = Moment of inertia
Stiffness due to material property = Youngs modulus of Elasticity.
@@Eagle_1174 Right. When you derive the sectional forces, the effective stiffness in terms of how the strain of the section changes with stress will come down to something involving x^2 with area. So, that turns out to be equivalent to the second moment of inertia as it is defined.
The elastic modulus is also included in the bending stiffness. So, although those are true statements, the true stiffness of the beam is a combo of both in a sense. Only stating this to allow people to understand that for bending you need both for the full stiffness.
finally i found a video that talks about what it is....a lot of people teach how to calculate it but not what physical meaning of it.....thank you a lot
You're most welcome :-)
The is the first location I’ve ever seen explain in practical terms. This guy is awesome
@@purdueMET thanks I needed a practical example of this.
That’s the best example of demonstrating the moment of inertia! Helped me a lot in understanding. Loved the fact that you showed the difference in calculation and real life.
Hi sir, greetings from a student in India! Your videos are brilliant and really really helpful, thank you so much! This channel deserves to be a lot more popular 😊
Hi Stephen, I think so too ;-) Thanks very much for your encouragement.
Soooo clear. I love your explanation, my professor couldn't explained to me that simple concept. Muchas gracias.
Finally in the last year of my civil engineering degree, I got the concept.... Thank you sir..
Hi sir.....! Am from Sri Lanka & thank you very much for your service for an engineering student like me. your explanations are really simple instead of being too complicated. I keep watching you and learning from you instead of attending lectures.
I really really wish that you would continue making videos...Everyone can understand the theory, but the practical demonstration makes sure everyone understands and remembers WHEN and HOW to make use of it!
Great Video. I’ve wondered about this exact example for years. Thanks.
after 4 years of mechanical engineering , finally i understood the concept of ( capital i in beam equation ) thank you so much , you don't know how much difference that made in my life . please keep sharing you superior knowledge.
It's a capital I, and the shape that has the best value of capital I, looks like the letter I. Makes it very easy to remember. Too bad the comments don't have a serif font where you can see it better.
Possibly the best explanation on Area Moment of Inertia!...😍😍😍
Walking on that beam was a bit scary! 😂😂😂
That's why I mounted it so close to the ground :-)
This is the only video that made me understand the concept...Subscribed....Hope to learn more!!!!!!!
Great demonstration. And the way you explain theory is very detailed and easy to understand. Keep doing the good work!!!
I was looking for such a brief explanation...that's too good explanation .
Your lectures are awesome before this area moment of inertia was such a difficult concept for me thanks a lot
Crystal clear explanation with practical examples
Superb ! Like due to practical implementation shown here.
Thank you for this professor. I do have to comment that there are times you MUST absolutely fight tradition. If people didn't fight tradition, slavery and women not allowed to vote may still have continued. As such, not calling them "two by fours" is just one step in the correct direction. Metric system is where it's at.
Greetings from South Africa. Thank you for the brilliant explanations. I can tell that you have great passion for what you do.
Thanks very much. It's a real treat to be able to reach students around the world. Hearing from a viewer in South Africa is just great :-)
North Africa (Egypt) as well
Finally!!! A video which explains Inertia in SOM
It's really good... after watching lot's of video finally I got concept...
Thank you professor for showing us in the actual model👍🏽👍🏽
Absolutely Ur Explanation And Physical Meaning got me really feel it..Thanku
This really made me soooooo happy. Thank you so much for this Sir!
u r my favorite professor
How nice, thank you :-)
Thank you!
I'm a visual learner so that demonstration at the end really helped
I wish he was my prof. in college. Also as soon as I saw him writing with the left hand I knew he is smart.
Wow. That was a revelation for me. Thank you for sharing that with us.
You're most welcome. I'm glad the video was helpful :-)
been looking for this everywhere, excellent explanation. THANKK YOUUU
That really was smart teaching........I was stuck on this doubt of mine for quite some time now that why do we consider MOI for calc. of deflection in beam but you jst cleared this in 7 mins.....awesome
Great visual video, thank you!
I'm glad you like the video :-)
hello professor. Thanx for this amazing video, please keep making such videos in the near future.
Superior explaination !
This really helped solidify my understanding! Thanks a ton!
First time i got my head wrapped around "area" moment of inertia ! Finally able to visualize the difference it makes !
i was wondering why h^3 then experiment explained everything.
thank you very much.
This was a great video!
Thanks :-)
I understood that means stiffness.
Can you relate the moment of inertia with the bending moment of equation i.e. M/I=σ/y with a suitable physical example ?
Thanks in advance
It’s everywhere. Think of it as the stress at any point perpendicular to the axis of bending is no different than a thin fiber in tension or compression; at that point, the strain is the stress divided by elastic modulus. The strain in beam can ALWAYS be derived from the linear elastic and fully planar assumption where the section MUST rotate about some point (also known as the neutral axis) and maintain a linear profile. This rotation is proportional to a curvature radius and length of the beam with small changes along the radius (called curvature). It is then possible to relate the length and the dimensions of that section to the strain which then becomes integrated with definitions of E and I. Let me know if you would like me to show the entire derivation.
Oh my god, these videos are amazing!
Why in the case of twisting moment polar moment of inertia is consider ?
Thank you so much sir!
Thank you sir
It's best explanation about
Area moment of inertial
Perfect explanation.
Best teacher....
Good explanation❤
Very helpful video ❤❤
Amazing vids!! Greetings from Chile!!
Can someone please explain how the squared distance from the centroid relates to the equation (which you have to multiply with the area to get the area moment of inertia)?
When you said 48EI in the denominator of that expression did you mean (48•10ᴵ); as in 48 by ten base to the degree of the moment of inertia?
No
E = young modulus of elasticity
@@kunjanmushyaju3300 why didn't he just use Y like a civilized person?
I was wondering if that 2*4 breaks during the video. Haha, Proud to be a Boilermaker.!!
Good Explanation!
Thank you for making this so easy to learn!
Greetings, It was really great way of explaining.
Found it useful
what I found! This video is so great!!! Thank you very much
Thanks for making the video.
thanku and best part is knowing that moi is the stiffness of a bar due to its shape
Perfect explanation!
excellent video on the subject, principles and real-life demo. It would have been interesting to make the same beam with 1/4-inch-thick pine box beam glue up, same size as the pine board you are using and demo that also. I am sure the beam would hold you also. I would have been good to have measured the deflection and know your weight to have further understanding till you have broken the board. The video could of had a free body diagram, to define the 'design specification', review of the formulas, did the demos, talk a little fo tbe design requirements and safety margins would of completed the video for me! But well done, nevertheless.
Very good explanation sir.
Sir can you make a video to explain radius of gyration also. Thank you
great educator
Thank you! Just what I needed
Thank you Sir. Please solve problem on second area moment of inertia for pendulum wrt axis.
stiffness is 5.444 times higher on vertical position, but strength is the same, am i right?
I'm afraid not. The normal stress is My/I. If you substitute I=1/12*b*h^3, it works out that the stress at the top and bottom of the beam goes down as h^2
Great video..thanks
Hello, Professor!
You call I "stiffness". How do you call then EI?
Thank you for the answer and the videos!
Hi Marius, EI is a stiffness expression that includes both material contribution and the contribution from the cross-sectional shape. I is the portion of the stiffness due to geometry - the cross-sectional shape.
@@purdueMET Superior answer!
Amazing sir
Great explanation!!
Thank you sir, I can understand easily by this video
very helpfull thank you very much sir
Sir,I understood everything clearly but I am having a small doubt why moment of Inertia is calculated only for cross sectional area??
I think that
When the load is applied on the beam it acts perpendicular to the surface and try to bend the material along its surface. And the material shows stiffness (resistance to rigidity) towards it, and to calculate how much stiffness the beam or material shows we calculate it's moment of inertia. For the calculation of moment of inertia we need to know the cross-section of the element along a desired axis we want to find.
Remember when we study in class 11, the moment of inertia with its parallel axis theorem. In there the cross-section can be of regular or any irregular shape. But in case if beams we have standard shapes.
I hope that your doubt is cleared.
Furthermore you can calculate the beam stiffness at any point of fibre by changing its axis.
Any more questions..... reply me.!
Keep learning and growing.!
*The knowledge is aggregation of marginal gains*
@@risky_world5692 thanks a lot
Sir, when we say first moment of area = O, what do we mean by that , physically?...like area moment of inertia tell stiffness due to shape.
Moment in general means quantity multiplied by distance to a reference point. First moment of area is area multiplied (or rather integrated) with distance to the centroidal axis. Second moment of area, squares this distance.
A practical reason why we care about first moment of area, is the strength of a member against shear loads. Maximum shear stress is inversely proportional to the first moment of area, and thus the shear strength of a cross section, is based on the first moment of area.
The first moment of area is also part of the algorithm for calculating the centroid.
thank you ❤
finally I understood what is moment of inertia
thank you sir that practical xplaination 🙏
i=1/12bh^3......Where did the 1/12 come from, and why is h^3....?
It comes from the cascading coefficients of 3 and 4 as you take integrals of a polynomial function.
Thanks for the great explanation!
You're most welcome. I'm glad the video was helpful.
from iraq btw. great explanation!
Thanks very much :-)
Thanks you so much sir it is vary help full to me
nice thanks so much sir
You're most welcome :-)
Thanks man, god bless
Great video! thanks!
most lecturers teach this topics on materials in civil engineering class,but they never give us the practical meaning of them.i graduated from civil engineering class in kenya but struggled to understand the practical aspect of things like moment of inertia till i started researching on youtube videos.
Thank you so much. It was so usefull.
Well done. except you need to mention the role of buckling.
Thank you sir.
lovely
Sir, Thank you
Thanks sir
i love his tee
Thanks, though it may somewhat overstate my musical skills...
Eureka! 👍
👌
We are poor, no one has told us such things in the University.
Shroud
Thank you sir
thank you sir
thanks sir