SECTIONAL PROPERTIES CALCULATOR - RECTANGULAR HOLLOW STRUCTURAL SECTIONS (TUBES)


Hollow structural sections are metal profiles with square or rectangular tube section. They are also known as rectangular steel tubes. ASTM A500 is the most common steel specification for hollow structural section in North America. This specification is for cold formed welded and seamless carbon steel tubing in round, square and rectangular shapes. ASTM A501 is another standard for hot formed steel tubing. Hollow rectangular sections are used in structural applications such as structural supports and building columns.

The following calculator has been developed to calculate the sectional properties of structural hollow rectangular sections (tubes).



Calculator:

Sectional properties of hollow rectangle
INPUT PARAMETERS
Parameter Symbol Value Unit
Height H
Width B
Internal height h
Internal width b
Length L
Density p



OUTPUT PARAMETERS
Parameter Symbol Value Unit
Cross section area (A) A ---
Mass (M) M ---
Second moment of area (Ixx) Ixx ---
Second moment of area (Iyy) Iyy ---
Section modulus (Sxx) Sxx ---
Section modulus (Syy) Syy ---
Radius of gyration (rx) rx ---
Radius of gyration (ry) ry ---
CoG distance in x direction (xcog) xcog ---
CoG distance in y direction (ycog) ycog ---

Note: Use dot "." as decimal separator.



Definitions:

Radius of Gyration (Area): The capacity of a cross-section to resist bending.

Second Moment of 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:



Link Usage
Hollow Structural Section (HSS) Design for Strength This calculator has been developed to calculate normal stress, shear stress and Von Mises stress on a given cross section of a HSS.
Square Hollow Structural Sections (HSS) Dimensions This page gives sizes, dimensions and section properties of square hollow structural sections (HSS) per Steel Construction Manual.
Rectangular Steel Tube Sizes and Dimensions This page gives sizes, dimensions and section properties of rectangular steel tubes (hollow structural sections - HSS) per Steel Construction Manual.

List of Equations:

HOLLOW RECTANGLE
Sectional properties of hollow rectangle
Step Parameter/Condition Symbol Equation
1 Cross section area A A = BH-bh
2 Area moment of inertia Ixx Ixx = BH3/12 - bh3/12
3 Area moment of inertia Iyy Iyy = HB3/12 - hb3/12
4 Section modulus Sxx Sxx = Ixx/ycog
5 Section modulus Syy Syy = Iyy/xcog
6 Center of gravity xcog xcog=B/2
7 Center of gravity ycog ycog=H/2
8 Mass M M = ALρ
9 Radius of gyration r r = (I/A)^0.5
10 Polar moment of inertia J J = Ixx + Iyy

Reference:

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