@@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
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 😊
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.....! 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.
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.
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!
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 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*
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
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.
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.
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.
