Table 101

Properties of Areas

This table provides formula for calculating section Area, Moment of inertia, Polar moment of inertia, Section modulus, Radius of gyration, and Centroidal distance, for various cross section shapes.

Formula for rectangular, triangular, hollow circle and full circle sections is provided.

PROPERTIES OF SECTIONS
Nomenclature: 
A = Area, in^2 
I = Moment of inertia, in^4 
J = Polar moment of inertia, in^4 
Z = Section modulus, in^3 
k = Radius of gyration, in 
y = Centroidal distance, in 

Rectangle relationships:
------------------------
A = b * h 
I = b * h^3 / 12
Z = b * h^2 / 6
k = 0.289 * h
y = h / 2

Triangle relationships:
-----------------------
A = b * h / 2
I = b * h^3 / 36
Z = b * h^2 / 24
k = 0.236 * h
y = h / 3

Circle relationships:
---------------------
A = 3.14159 * d^2 / 4
I = 3.14159 * d^4 / 64
Z = 3.14159 * d^3 / 32
J = 3.14159 * d^4 / 32
k = d / 4
y = d / 2

Hollow circle relationships:
----------------------------
A = 3.14159 / 4 * (d^2 - di^2)
I = 3.14159 / 64 * (d^4 - di^4)
Z = 3.14159 / (32 * d) * (d^4 - di^4)
J = 3.14159 / 32 * (d^4 - di^4)
k = sqrt((d^2 + di^2) / 16)
y = d / 2