RECTANGULAR BEAM DESIGN FOR STRENGTH
The transverse loading on a rectangular beam may result normal and shear
stresses simultaneously on any transverse cross section of the structural
rectangular beam. 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 rectangular beams
occurs where the bending moment is largest. Maximum shear stress occurs on the
neutral axis of the rectangular beam section where shear force is maximum.
The design of rectangular beams is generally driven by the maximum bending moment. In the case of short structural beams, the design may be driven by the maximum shear force.
This calculator has been developed to calculate normal stress, shear stress and Von Mises stress on a given cross section. Calculator also draws graphics of the stress variations with respect to distance from the neutral axis.
Note: For more information on the
subject, please refer to "Design of Beams and Shafts for Strength" chapter of Mechanics of Materials
.
Calculator:
Definitions:
Normal Stress: Stress acts perpendicular to the surface (cross section).
Second Moment of Area: The
capacity of a crosssection to resist bending.
Saint Venant's Principle: Stresses on a surface which are reasonably far from
the loading on body are not notably modified if this load is changed to a static equivalent load. The distribution of stress and strain is altered only near the regions where load is acting.
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:
List of Equations:
Parameter/Condition 
Symbol 
Equation 
Cross section area 
A 
A = 2cb 
Area moment of inertia 
I_{zz} 
I_{zz} = 8bc^{3}/12 
Normal stress at point y 
σ_{x} 
σ_{x}=My/I 
Maximum normal stress 
σ_{max} 
σ_{x}=Mc/I 
Shear stress at point y 
τ_{xy} 
τ_{xy}=(3V/2A)(1(y/c)^{2}) 
Maximum
shear stress 
τ_{max} 
τ_{max}= 3V/2A 
Von Mises Stress 
σ_{v} 

Reference: