Centroids Of Common Shapes Of Areas And Lines
edit
A
r
e
a
=
b
∗
h
2
{\displaystyle Area={\frac {b*h}{2}}}
Quarter Circular Area
edit
A
r
e
a
=
π
r
2
4
{\displaystyle Area={\frac {\pi \ r^{2}}{4}}}
A
r
e
a
=
π
r
2
2
{\displaystyle Area={\frac {\pi \ r^{2}}{2}}}
A
r
e
a
=
2
a
h
3
{\displaystyle Area={\frac {2ah}{3}}}
A
r
e
a
=
4
a
h
3
{\displaystyle Area={\frac {4ah}{3}}}
A
r
e
a
=
a
h
3
{\displaystyle Area={\frac {ah}{3}}}
A
r
e
a
=
α
r
2
{\displaystyle Area=\alpha \ r^{2}}
Quarter Circular Arc
edit
A
r
e
a
=
π
2
{\displaystyle Area={\frac {\pi \ }{2}}}
A
r
e
a
=
π
r
{\displaystyle Area=\pi \ r}
A
r
e
a
=
2
α
r
{\displaystyle Area=2\alpha \ r}
Area Moments Of Inertia of Common Geometric Shapes
edit
I
x
=
1
3
b
h
3
{\displaystyle I_{x}={\frac {1}{3}}bh^{3}}
I
y
=
1
3
h
b
3
{\displaystyle I_{y}={\frac {1}{3}}hb^{3}}
I
x
′
=
1
12
b
h
3
{\displaystyle I_{x'}={\frac {1}{12}}bh^{3}}
I
y
′
=
1
12
h
b
3
{\displaystyle I_{y'}={\frac {1}{12}}hb^{3}}
Right Triangular Area
edit
I
x
=
1
12
b
h
3
{\displaystyle I_{x}={\frac {1}{12}}bh^{3}}
I
y
=
1
4
h
b
3
{\displaystyle I_{y}={\frac {1}{4}}hb^{3}}
I
x
′
=
1
36
b
h
3
{\displaystyle I_{x'}={\frac {1}{36}}bh^{3}}
I
y
′
=
1
36
h
b
3
{\displaystyle I_{y'}={\frac {1}{36}}hb^{3}}
I
x
=
1
12
b
h
3
{\displaystyle I_{x}={\frac {1}{12}}bh^{3}}
I
x
′
=
1
36
b
h
3
{\displaystyle I_{x'}={\frac {1}{36}}bh^{3}}
J
C
=
π
r
4
2
{\displaystyle J_{C}={\frac {\pi \ r^{4}}{2}}}
I
x
′
=
I
y
′
=
π
r
4
4
{\displaystyle I_{x'}=I_{y'}={\frac {\pi \ r^{4}}{4}}}
This is used for hollow cylinders where there is solid material between the outer and inner radius, but no material between the inner radius and the center, like a pipe's cross-section.
I
=
π
(
r
o
4
−
r
i
4
)
4
{\displaystyle I={\frac {\pi \ (r_{o}^{4}-r_{i}^{4})}{4}}}
r
o
{\displaystyle r_{o}}
r
i
{\displaystyle r_{i}}
I
x
=
I
y
=
1
8
π
r
4
{\displaystyle I_{x}=I_{y}={\frac {1}{8}}\pi \ r^{4}}
I
x
′
=
(
π
8
−
8
9
π
)
r
4
{\displaystyle I_{x'}=({\frac {\pi }{8}}-{\frac {8}{9\pi }})r^{4}}
I
y
′
=
1
8
π
r
4
{\displaystyle I_{y'}={\frac {1}{8}}\pi \ r^{4}}
I
x
=
I
y
=
1
16
π
r
4
{\displaystyle I_{x}=I_{y}={\frac {1}{16}}\pi \ r^{4}}
I
x
′
=
I
y
′
=
(
π
16
−
4
9
π
)
r
4
{\displaystyle I_{x'}=I_{y'}=({\frac {\pi }{16}}-{\frac {4}{9\pi }})r^{4}}
