HOLLOW STRUCTURAL SECTION (HSS) DESIGN FOR STRENGTH
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 ThinWalled Members" and "Design
of Beams and Shafts for Strength" chapters of Mechanics of Materials
.
Calculator:
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.
OUTPUT PARAMETERS 
Parameter 
Symbol 
Value 
Unit 
Cross section area 
A 



First moment of area for section A 
Q_{A} 



First moment of area for Section B 
Q_{B} 


First moment of area for section D 
Q_{D} 


Second moment of area 
I_{zz} 



Stress Calculation at Section A 

Normal stress 
σ_{x_A} 


Shear stress 
τ_{xy_A} 


Von Mises stress at A 
σ_{v_A} 


Stress Calculation at Section B 
Normal stress at B 
σ_{x_B} 


Shear stress at B 
τ_{xy_B} 


Von Mises stress at B 
σ_{v_B} 


Stress Calculation at Section D 
Normal stress at D 
σ_{x_D} 


Shear stress at D 
τ_{xy_D} 


Von Mises stress at D 
σ_{v_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.
Definitions:
Normal Stress: Stress acts perpendicular to the surface (cross section).
Second Moment of Area: The
capacity of a crosssection 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.
Supplements:
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(2c2t)*(w2t) 
Area moment of inertia 
I_{zz} 
I_{zz} = (8wc^{3}8*(w2t)*(ct)^{3})/12 
Normal stress 
σ_{x} 
σ_{x}=My/I 
Shear stress 
τ_{xy} 
τ_{xy}=(VQ)/(Ib) 
First moment of area for section B 
Q_{B} 
Q_{B}=w*t*(ct/2) 
First moment of area for section C 
Q_{D} 
Q_{D}=w*t*(ct/2)+t*(ct)^{2} 
Thickness b for section B and C 
b 
b=2t 
Von Mises Stress 
σ_{v} 

Reference:
 Beer.F.P. , Johnston.E.R. (1992). Mechanics of Materials
, 2nd edition. McGrawHill, Chapter 5.9 and Chapter 7.6