Second Moment of Area Calculator

Second Moment of Area

Calculator

Beam Cross Section:

Large Width (B):

Large Height (H):

Small Width (b):

Small Height (h):

Total height of L section (d):

Thickness of Flange in L Section (t):

Outer Diameter (D):

Inner Diameter (d):

I_xx:

Second Moment of Area Equations

Rectangular Cross-Section: $$ I_{xx} = \frac{B H^3}{12} $$
$$ I_{yy} = \frac{HB^3}{12} $$
Rectangle Area

Hollow Rectangular Cross-Section: $$ I_{xx} = \frac{B H^3}{12} - \frac{b h^3}{12} $$
$$ I_{yy} = \frac{H B^3}{12} - \frac{h b^3}{12} $$
Hollow Rectangle Area

I Beam Cross-Section: $$ I_{xx} = \frac{H^3 b}{12} + 2 \left(\frac{h^3 B}{12} + \frac{hB(H+h)^2}{4} \right) $$
$$ I_{yy} = \frac{b^3 H}{12} + 2 \left(\frac{B^3 h}{12} \right) $$
I Beam Area

C Channel Cross-Section: $$ I_{xx} = \frac{H^3 b}{12} + 2 \left( \frac{h^3 B}{12} + \frac{hB(h+H)^2}{4} \right) $$
$$ I_{yy} = \frac{b^3 H}{12} + bH \left( \frac{x_c - b}{2} \right)^2 + \frac{2 B^3 h}{12} + 2 B^3 h \left( \frac{x_c-B}{2} \right)^2 $$ C Beam Area

T Cross-Section: $$ I_{xx} = bH {\left(y_c - \frac{H}{2}\right)}^2 + \frac{b H^3}{12} + hB {\left( H + \frac{h}{2} - y_c\right)}^2 + \frac{h^3 B}{12} $$
$$ I_{yy} = \frac{b^3 H}{12} + \frac{B^3 h}{12} $$
T Beam Area

L Cross-Section: $$ I_{xx} = \frac{1}{3} \left(b d^3 - (b-t) (d-t)^3 \right) - A (d-y_c)^2 $$
$$ I_{yy} = \frac{1}{3} \left(d b^3 - (d-t) (b-t)^3 \right) - A (b-x_c)^2 $$
L Beam Area

Circular Cross-Section: $$ I_{xx} = \frac{\pi D^4}{64} $$
$$ I_{yy} = \frac{\pi D^4}{64} $$
Circular Area

Hollow Circular Cross-Section: $$ I_{xx} = \frac{\pi D^4}{64} - \frac{\pi d^4}{64} $$
$$ I_{yy} = \frac{\pi D^4}{64} - \frac{\pi d^4}{64} $$
Hollow Circular Area