✅ How to calculate the CENTROID and MOMENT OF INERTIA of the T Beam | Mechanics for Engineering

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To determine the moment of inertia of the cross section of the T-beam, we must first identify the rectangles that compose it.
Now, do we know the location of the centroid of the section?
As it is an asymmetric section, it is necessary to calculate the location of its centroid, which will be important to determine the moment of inertia.
How to calculate centroid?
The geometric center of the section area is given by:
Ycg = (A1.Ycg1 + A2.Ycg2)/(A1 + A2), where:
A1 = area of ​​rectangle 1;
Ycg1 = geometric center of rectangle 1;
A2 = area of ​​rectangle 2;
Ycg2 = geometric center of rectangle 2.
After finding the centroid of the cross section, we must calculate the moment of inertia of each rectangle by the parallel axes theorem, since such a moment occurs in relation to the x' axis of the section.
And how to calculate the moment of inertia of the rectangle about x'?
It is determined by the following formula:
(Ix')ret = b.h³/12 + A.dy², where:
b = base of the rectangle;
h = height of the rectangle;
A = area of ​​the rectangle;
dy = distance between the centroid of the section and the centroid of the rectangle: dy = Ycg - (Ycg)ret
Okay, now it's easy to determine the moment of inertia of the section, as it will be given by the sum of the moments of inertia obtained from the rectangles:
Ix' = Ix1' + Ix2'
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📚 Source: Statics: Mechanics for Engineering 14th Ed. (R.C. Hibbeler)
Browse Video________________________________________
00:00 | Dividing the Cross Section into Rectangles
01:45 | Calculation of the Centroid of the Cross Section
05:05 | The Moment of Inertia Formula
06:35 | Calculation of the Moment of Inertia of each Rectangle
10:30 | Calculation of the Moment of Inertia of the Cross Section
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