MOMENT OF INERTIA OF RECTANGLE

Moment of inertia of rectangle calculator for area moment of inertia, section modulus, cross section area and radius of gyration calculation of rectangle section.

Steel rectangular bars are covered by ASTM A108 “Standard Specification for Steel Bar, Carbon and Alloy, Cold-Finished”, A36/A36m “Standard Specification for Carbon Structural Steel” and ASTM A276 “Standard Specification for Stainless Steel Bars and Shapes“ standards.

Moment of Inertia of Rectangle Calculator:

Sectional properties of solid rectangle
INPUT PARAMETERS
Parameter Value
Height [H]
Width [B]
Length [L]
Density [p]



RESULTS
Parameter Value
Cross section area [A] ---
Mass [M] ---
Second moment of area [Ixx] ---
Second moment of area [Iyy] ---
Section modulus [Sxx] ---
Section modulus [Syy] ---
Radius of gyration [rx] ---
Radius of gyration [ry] ---
Centroid distance in x direction [xc] ---
Centroid distance in y direction [yc] ---

Note: Use dot "." as decimal separator.

 

Definitions:

Second Moment of Area: The capacity of a cross-section to resist bending.

Radius of Gyration (Area): The distance from an axis at which the area of a body may be assumed to be concentrated and the second moment area of this configuration equal to the second moment area of the actual body about the same axis.

Section Modulus: The moment of inertia of the area of the cross section of a structural member divided by the distance from the center of gravity to the farthest point of the section; a measure of the flexural strength of the beam.

Supplements:

Moment of Inertia Formula Rectangle:

SOLID RECTANGLE FORMULA
Sectional properties of solid rectangle
Parameter Symbol Equation
Cross section area A A = BH
Area moment of inertia Ixx Ixx = BH3/12
Area moment of inertia Iyy Iyy = HB3/12
Section modulus Sxx Sxx = Ixx/yc
Section modulus Syy Syy = Iyy/xc
Centroid xc xc=B/2
Centroid yc yc=H/2
Mass M M = ALρ
Radius of gyration r r = (I/A)^0.5

Reference:

  • Oberg, E. , Jones ,F.D. , Horton H.L. , Ryffel H.H., (2016) . Machinery's Handbook . 30th edition.  Industrial Press Inc., pp 226-235 .
  • Oberg, E. , Jones ,F.D. , Horton H.L. , Ryffel H.H., (2012) . Machinery's Handbook . 29th edition.  Industrial Press Inc., pp 234-256.