Moment of Inertia of composite bodies
Description:
In this engineering mechanics tutorial, we dive deep into the process of calculating the moment of inertia for composite shapes about both the X and Y axes. Understanding this concept is crucial for students and professionals working with complex geometries and structural analysis.
We break down the problem-solving approach into the following key steps:
1) Dividing the composite shape into simpler, known shapes (rectangles, quarter circles, triangles)
2) Determining the centroid location of each shape from the X and Y axes
3) Calculating the area of each individual shape, assigning negative areas for unshaded or subtracted sections
4) Applying the parallel axis theorem to find the moment of inertia of each shape about the X and Y axes
-Calculating the moment of inertia of each shape about its centroidal axis using appropriate formulas
-Determining the distances (DX and DY) from the centroid of each shape to the X and Y axes
-Using the parallel axis theorem: IX = ΣIX̄ + ΣA(DX)² and IY = ΣIȲ + ΣA(DY)²
5) Tabulating the results and summing up the individual moments of inertia and area terms to find the total moment of inertia about the X and Y axes
By following along with this detailed tutorial, you'll gain a solid understanding of how to approach the moment of inertia calculations for composite shapes, breaking down the problem into manageable steps. Perfect for students in engineering mechanics courses and professionals who need to refresh their knowledge of this essential concept.
#EngineeringMechanics #MomentOfInertia #CompositeShapes #ParallelAxisTheorem #StructuralAnalysis #CivilEngineering #MechanicalEngineering
Пікірлер: 23
I couldn't believe when I found video that is so helpful for engineering students in Ethiopia in Amharic... keep up the good job we need mores like u
@Civiltimes2210
6 ай бұрын
Thank you. And I will make more videos
Waw a very clear and conceptual video.
I thought there was some mistake in this computing but your work is amazing to understand
@Civiltimes2210
Жыл бұрын
Where is the mistake? I will fix it.
@simegnewtesfaye4455
Жыл бұрын
dude, see it again there is no mistake
@-Sadiahoque
Жыл бұрын
@@simegnewtesfaye4455 here dx=(60 -12.73). . But it will be dy=60-12.73.. And dx=12.73
@eulzzzz7682
5 ай бұрын
@@-Sadiahoquemeriam says the same thing I'm confused
Thank you so much ❤
thank you teach.
how did you get the -(π/16-4/9π)?
Ur answer is fully wrong
r is 40 mm, no?
@Civiltimes2210
Жыл бұрын
How 40?
D
Semicircle are id πr²/2 not πr²/4
@Civiltimes2210
11 ай бұрын
It is not semicircle
This answer is wrong. You must find first the centroid of the whole composite shape in order to find each 'd' for each area moment of inertia. The value of y bar that I computed for that same problem was 29.941 mm. And the area moment of Inertia about the X axis is 914,673.809 mm^4.
@Civiltimes2210
Ай бұрын
Recheck your answer. It seems that you are wrong.
@TolibasEzekiel
5 күн бұрын
@@Civiltimes2210 After one month, I realized that you are finding the area moment of Inertia 'with respect to the x axis'. You are correct. I was wrong because I thought it was respect with the centroidal axis. Thank you so much for pointing it out. This helped me improve. Mucho Gracias!
@Civiltimes2210
5 күн бұрын
@@TolibasEzekiel Thank you for your interaction, I really appreciate that.
Might most important words, please speak the universal English
Bl poraichee sagol