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 .


Sectional properties of solid rectangle
Parameter Symbol Value Unit
Structural Beam Height 2c
Structural Beam Width b
Height y y
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 the portion of
 the cross section above point y
Q ---
Second moment of area Izz ---
Normal stress at point y σx ---
Shear stress at point y τxy ---
Von Mises stress at point y σv ---
Maximum normal stress σmax ---
Maximum shear stress τmax ---
Maximum Von Mises stress σv_max ---

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.
Normal Stress Shear Stress
Von Mises Stress  



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

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


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.
Timber Beam Design for Strength Example An example about the calculation of normal and shear stresses on a timber beam.

List of Equations:

Parameter/Condition Symbol Equation
Cross section area A A = 2cb
Area moment of inertia Izz Izz = 8bc3/12
Normal stress at point y σx σx=My/I
Maximum normal stress σmax σx=Mc/I
Shear stress at point y τxy τxy=(3V/2A)(1-(y/c)2)
Maximum shear stress τmax τmax= 3V/2A
Von Mises Stress σv Plane Von Mises Stress