This document discusses moment of inertia formulas for common geometric shapes including rectangles, triangles, circles, semicircles, quadrants, and ellipses. Rectangles have an Iz of 1/12bh^3 and Iy of 1/12bh^3. Triangles have an Iz of 1/36bh^3 and Iy of 1/12bh^3. Circles, semicircles, and quadrants all have an Iy=Iz of 1/4πr^4. Ellipses have an Iz of 1/4πba^3.

1. PEF2308/PEF2309 - Fundamentos de Mecânica das Estruturas
30
Momentos de inércia de figuras geométricas comuns
Retângulo
12
3
'
hb
Iz
⋅
=
12
3
'
hb
I y
⋅
=
3
3
hb
Iz
⋅
=
3
3
hb
I y
⋅
=
Triângulo
36
3
'
hb
Iz
⋅
=
12
3
hb
Iz
⋅
=
Círculo
4
4
r
II yz
⋅
==
π
Semicírculo
8
4
r
II yz
⋅
==
π
z'
z
y y’
h
b
G
z’
b
z
h
h/3
G
G
z
r
G
z
y
r
y

2. PEF2308/PEF2309 - Fundamentos de Mecânica das Estruturas
31
Quadrante
16
4
r
II yz
⋅
==
π
Elipse
4
3
ba
Iz
⋅⋅
=
π
4
3
ba
Iz
⋅⋅
=
π
z
r
y
G
G
z
b
y
a