CANTILEVER STRUCTURAL BEAM WITH CONCENTRATED LOAD AT ANY POINT

Following calculator has been developed to find forces, moments, stresses, deflections and slopes in structural beam for a specific case which is concentrated loading of a cantilever structural beam. Concentrated load can be applied at any point of the structural beam.

Note: For more information on shear, moment, slope and deflection calculations for different end constraints, please refer to "Beams; Flexure of Straight Bars" chapter of Roark's Formulas for Stress and Strain.

Calculator:

 INPUT PARAMETERS Parameter Symbol Value Unit Load * P kN N lbf Beam Length L mm m inch ft Distance a a Distance x x Modulus of Elasticity E GPa ksi Distance from neutral axis to extreme fibers c mm m inch ft Second moment of area ** I mm^4 cm^4 inch^4 ft^4

Note ** : For second moment of area calculations of structural beams, visit " Sectional Properties Calculators".

 RESULTS Parameter Symbol Value Unit Reaction Force 1 R1 --- N kN lbf Reaction Force 2 R2 --- Transverse Shear Force @ distance x Vx --- Maximum Transverse  Shear Force Vmax --- Reaction Moment 1 M1 --- N*m kN*m lbf*in lbf*ft Reaction Moment 2 M2 --- Moment @ distance x Mx --- Maximum Moment Mmax --- Slope 1 θ1 --- radian degree arcmin arcsec Slope 2 θ2 --- Slope @ distance x θx --- Maximum Slope θmax --- End Deflection 1 y1 --- mm m inch ft End Deflection 2 y2 --- Deflection @ distance x yx --- Maximum Deflection ymax --- Bending Stress @ distance x σx --- MPa psi ksi Maximum Bending Stress σmax ---

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. This distinction depends on which side of the beam's neutral plane c input corresponds.
 Slope Deflection Moment Shear Force

Definitions:

Distributed load: A load which acts evenly over a structural member or over a surface that supports the load.

Fixed support: Fixed supports can resist vertical and horizontal forces as well as a moment. Since they restrain both rotation and translation, they are also known as rigid supports.

Pin support: A pinned support resist both vertical and horizontal forces but not a moment. They will allow the structural member to rotate, but not to translate in any direction. A pinned connection could allow rotation in only one direction; providing resistance to rotation in any other direction.

Roller support: Roller supports are free to rotate and translate along the surface upon which the roller rests. The resulting reaction force is always a single force that is perpendicular to the surface. Roller supports are commonly located at one end of long bridges to allow the expansion and contraction of the structure due to temperature changes.

Cantilever beam: Cantilever is a beam which is fixed at only one end.

Structural beam: A structural element that withstands loads and moments. General shapes are rectangular sections, I beams, wide flange beams and C channels.

Supplements:

 Link Usage 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 Reaction Force 1 R1 Reaction Force 2 R2 Shear force at distance x V Reaction Moment 1 M1 Reaction Moment 2 M2 Moment at distance x M Bending stress at distance x σ End Deflection 1 y1 End Deflection 2 y2 Deflection at distance x y Slope 1 θ1 Slope 2 θ2 Slope θ