Statics/Geometric Properties of Lines and Areas

Centroids Of Common Shapes Of Areas And Lines

Triangular Area

$Area = \frac {b*h}{2}$

Quarter Circular Area

$Area = \frac { \pi\ r^2}{4}$

Semicircular Area

$Area = \frac { \pi\ r^2}{2}$

Semiparabolic Area

$Area = \frac {2ah}{3}$

Parabolic Area

$Area = \frac {4ah}{3}$

Parabolic Spandrel

$Area = \frac {ah}{3}$

Circular Sector

$Area = \alpha\ r^2$

Quarter Circular Arc

$Area = \frac { \pi\ }{2}$

Semi Circular Arc

$Area = \pi\ r$

Arc Of Circle

$Area = 2 \alpha\ r$

Moments Of Inertia of Common Geometric Shapes

Rectangle

$I = \frac {b h^3}{12}$

Triangle

$I = \frac {b h^3}{36}$

Circle

$I = \frac { \pi\ r^4}{4}$

Hollow circle

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.

$I = \frac { \pi\ (r_o^4 - r_i^4) } {4}$

r_o is the outer radius r_i is the inner radius

Semicircle

I=(1/8)*pi*(r^4)