# RECTANGULAR BEAM STRESS STRENGTH DESIGN CALCULATOR

Rectangular Beam Stress Strength Design Calculator to calculate normal stress, shear stress and Von Mises stress on a given solid rectangular cross section. Calculator also draws graphics of the stress variations with respect to distance from the neutral axis.

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.

Note: For more information on the subject, please refer to "Design of Beams and Shafts for Strength" chapter of Mechanics of Materials .

### Rectangular Beam Stress Strength Design Calculator: INPUT PARAMETERS Parameter Value Structural Beam Height [2c] mm cm m inch ft Structural Beam Width [b] Height y Shear Force [V] kN N lbf Bending Moment [M] N*m kN*m lbf*in lbf*ft

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.

 RESULTS Parameter Value Cross section area [A] --- mm^2 cm^2 inch^2 ft^2 First moment of area for the portion of the cross section above point y [Q] --- mm^3 cm^3 inch^3 ft^3 Second moment of area [Izz] --- mm^4 cm^4 inch^4 ft^4 Normal stress at point y [σx] --- MPa psi ksi 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

### Definitions:

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.

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

### List of Equations:

 Parameter 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] σν=( σx2- σxσy+ σy2+3 τxy2)1/2

### Reference:

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