Here's a description of first and second moments of area along with some sample calculations. First moment of area is used to find centroid location and second moment of area is also called the area moment of inertia.
First moment of area is commonly used to determine the centroid of an area. The second moment of area is a measure of the 'efficiency' of a shape to resist bending caused by loading. A beam tends to change its shape when loaded. The second moment of area is a measure of a shape's resistance to change.
Great explanation. I would only add that the resistance mentioned can also be generalized to any sort of angular "movement" and is therefore also used when describing angular inertia (the resistance of a body to rotation about a particular axis).
Good explanation. To build off of your comment, the first moment of area (often denoted by Q) is the trait of area (not mass) rotating (moment) about a given axis - whether the x-axis, or y-axis - in which case fall into the centroidal x or y axes. This is reflected in the fact that there is a mathematical means to calculating Qx & Qy. If anyone is interested in knowing more about this, Dr. Mohammad Izadi's statics lecture(s) (CPPMechEngTutorials) is an excellent resource for actually gaining a deeper intuition of what Q is.
finally - someone who knows wth they are talking about - the abuse of terminology on this topic is incredible - start here and you will not go wrong - avoid everything else being taught by "experts"
Really good delivery and explanation, its so good to see a teacher that can cut through stupid terms and explain things at the fundamental level. Keep up the good work!
I like your way that uses the double integral to represent the area. This makes a lot of sense after learning the double integral. I wish my professor could have figured out this way of teaching the static moment of an area and the second order moment of an area.
Hi Mark, fellow Engineering Technology professor here. I love your videos and definitely try to channel some of your vibe when explaining things. When it comes to 2nd moment of area, in addition to stiffness, I tell my students it describes how the area is distributed around the centroid...large I, lots of material away from the centroid. First moment of area (aka statical moment) is used in calculating vertical shear in a beam. What I have always struggled is providing a physical feel for first moments, similar to what I can do with 2nd moments. As engineering technology students, I try to avoid getting into the weeds of deriving vertical shear stress and show them where the first moment shows up. Do you have a good physical explanation of what the first moment represents? I love to hear it if you do.
This is a great explanation of what mathematicians mean by the kth moment. Could you make a video on "product moment" (e.g., I_xy) if possible? Thanks!
Hello Professor. Firstly, thank you for your videos which I love. I had a question. As a structural engineer I've been designing floors slabs using only the loading they experience, span ratios and support conditions (BS8110) is it safe to assume this is using statics and why when I design with an FEA software like Robot I get much smaller moments and therefore require less reinforcement? Thanks
It's dangerous to generalize too much when designing structures. Here's the big idea - statics assumes that the stiffness is infinite because that makes the analysis much simpler. Finite element analysis is at the other end of the spectrum of sophistication and estimates stiffness and displacement all across the structure. By using a more accurate mathematical description of the structure, FEA will often give you slightly (we hope) different answers than will statics. Whether there are any general trends in the differences between the two depends on a lot of things, including the geometry. I wouldn't recommend trying to make any general observations before comparing a large number of results, including test data.
FEM results are more accurate for sure, but there should not be that kind of big difference between FEM and simplified method (Code method). Even when using the software, it doesn't mean perfectness, if you tried the same model with the same input data but with another software probably you'll some differences.
@@purdueMET btw I love the way you explain things! Do you mind making videos solving some complex questions related to this topic and the theorems of pappus guldinus?
I had a question I was hoping you could answer: For the rectangle you take y to be the distance from the centroid to the outer surface, but for the traingle you take y to be the distance from the bottom of the triangle. You mentioned that the bending axis for a rectangle would be through its centroid, is this not also the case for a triangle? Very informative video thanks for sharing.
hello sir, Thank you for such great video. I have one question that how rapid change in cross section affect the second moment of area. is there any book or reference for suggestion. Hoping for your positive reply. Thanks in advanced.
Sorry for the delay in replying. Just about any good book on Strength of Materials will have an explanation of Second Moment of Area. One popular text is by Beer and Johnson. Another is by Mott.
I still understand why Y (the distance between centroidal axis of the triangle and X-axis) is second power... What does it mean exactly in the real world ? What does it mean if it's third power ?
Thank you so much. My professor explained this so strangely, complexly, and ambiguously that I didn't get it at all, even though I've already done this in my mathematics classes but with much more complex problems. This really helped!
Hi Mark, greetings from Texas! Thanks again for all the great videos. I tell all my students about them. The history is so fascinating - how did someone figure out the second moment of area had a practical application? Regarding the use of the letter 'I' for (area) moment of interia, James Boyd's "Strength of Materials" book, published in 1911, uses I for the moment of inertia. So, it goes back at least that far!
why are there so many names mass moment of inertia, polar moment of inertia, first moment of area, second moment of area,... Why soo many names??? can someone please separate these into which are the same and which are different? its seriously pissing me off how confusing the names are. im so glad i found this channel awesome content
Can someone please clarify for me these few things First moment of area Second moment of area First moment of Inertia Second moment of Inertia Mass moment of Inertia From my understanding first moment of area = First moment of Inertia And Second moment of area = Second moment of inertia and mass moment of inertia is its own thing ?? is that correct?
Yes you're right. First moment of inertia used to find the centroid of the object. Second moment of inertia is used to measure the amount of resistance of the body shape for bending. mass moment of inertia indicates how much the object resist the rotation.
