Hollow Structural Section (HSS) Design Calculator for Strength has been developed to calculate normal stress, shear stress and Von Mises stress at critical points of a given cross section of hollow structural section.

The transverse loading on a hollow structural section may result normal and shear stresses simultaneously on any transverse cross section of the HSS. The normal stress on a given cross section changes with respect to distance y from the neutral axis and it is largest at the farthest point from the neural axis. The normal stress also depends on the bending moment in the section and the maximum value of normal stress in hollow structural section occurs where the bending moment is largest. Maximum shear stress occurs on the neutral axis of the HSS section where shear force is maximum.

Note: For more information on the subject, please refer to "Shearing Stresses in Thin-Walled Members" and "Design of Beams and Shafts for Strength" chapters of Mechanics of Materials .


Sectional properties of HSS
Parameter Symbol Value Unit
Structural Beam Height 2c
Structural Beam Width w
Beam Wall Thickness t
Shear Force V
Bending Moment M

Note: V and M are the shear force and bending moment in a section as shown in the figure.Visit " Structural Beam Deflection and Stress Calculators". for shear force and bending moment calculations.

Note: Structural beam is assumed to be subjected a vertical shearing force in its vertical plane of symmetry.

Parameter Symbol Value Unit
Cross section area A ---
First moment of area for section A QA ---
First moment of area for Section B QB ---
First moment of area for section D QD ---
Second moment of area Izz ---
Stress Calculation at Section A
Normal stress σx_A ---
Shear stress τxy_A ---
Von Mises stress at A σv_A ---
Stress Calculation at Section B
Normal stress at B σx_B ---
Shear stress at B τxy_B ---
Von Mises stress at B σv_B ---
Stress Calculation at Section D
Normal stress at D σx_D ---
Shear stress at D τxy_D ---
Von Mises stress at D σv_D ---

Note: Use dot "." as decimal separator.

Note: Stresses are positive numbers, and these are stress magnitudes in the beam. It does not distinguish between tension or compression of the structural beam.

Note: Effects of stress concentrations are not included in the calculations.



Normal Stress: Stress acts perpendicular to the surface (cross section).

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

Shear stress: A form of a stress acts parallel to the surface (cross section) which has a cutting nature.

Stress: Average force per unit area which results strain of material.


Link Usage
Structural beam deflection and stress calculators Calculates parameters of the compression member (column) for different end conditions and loading types. Calculators also covers bending moment, shear force, bending stress, deflections and slopes calculations of simply supported and cantilever structural beams for different loading conditions.
Sectional Properties Calculator of Profiles Sectional properties needed for the structural beam stress analysis can be calculated with sectional properties calculator.

List of Equations:

Parameter/Condition Symbol Equation
Cross section area A A = 2cw-(2c-2t)*(w-2t)
Area moment of inertia Izz Izz = (8wc3-8*(w-2t)*(c-t)3)/12
Normal stress σx σx=My/I
Shear stress τxy τxy=(VQ)/(Ib)
First moment of area for section B QB QB=w*t*(c-t/2)
First moment of area for section C QD QD=w*t*(c-t/2)+t*(c-t)2
Thickness b for section B and C b b=2t
Von Mises Stress σv Plane Von Mises Stress

  • Beer.F.P. , Johnston.E.R. (1992). Mechanics of Materials , 2nd edition. McGraw-Hill, Chapter 5.9 and Chapter 7.6