second momentt of area of a T shape?

Question

Anyone know the formula to calculate the second moment of area for a T shape??

Actually that doesnt work because the shape isnt symmetrical

Answer 1

JUst draw a line so you end up with two oblongs. Find the area of each and add them together for total area.

Answer 2

Find the center of gravity first of the overall T shape.

The moment of Inertia of the top part of the T is base*height^3/12 and calculate the same for the bottom part.

You know where the center axis of both rectangles is so now you just have to shift the inertias you just calculated.

total inertia = Inertia top + Area top*(distance from center axis of top - distance to center of gravity)^2 + Inertia bottom + Area bottom*(disntance from center axis of bottom - distane to center of gravity)^2

Answer 3

Horizontal bar data : b, e1 => A1=b*e1
Vertical bar date : h, e2=> A2=h*e2

Center of gravity: (equation from the bottom)
A2*h/2+A1*(h+e1/2)=Yg*(A1+A2)
=>Yg=... (you can do it)

Inertia:
Own inertia's 1: (b*(e1)^3)/12
Own inertia's 2:
(e2*(Yg)^3)/12+
(e2*(h-YG)^3)/12
Displacement term for 1:
A1*(h+e1/2-Yg)^2
Displacement term for 2:
Yg*e2*(Yg/2)^2+
(h-Yg)*e2*((h-Yg)/2)^2