# CANTILEVER STRUCTURAL BEAM DEFLECTION AND STRESS CALCULATOR FOR MULTIPLE LOADS AND MOMENTS

Following calculator has been developed to find forces, moments, stresses, deflections and slopes in a cantilever beam. Multiple point loads, distributed loads and concentrated moments can be defined as input loading for structural beam. This calculator has been developed by using formulas given in the "Cantilever Beam with Concentrated Load at any Point", "Cantilever Beam with Concentrated Intermediate Moment" and "Cantilever Beam with Partially Distributed Load" calculator pages.

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 POINT LOADS Parameter Symbol Magnitude Distance N kN lbf m mm inch ft Load 1 * P1 Load 2 * P2 Load 3 * P3 Load 4 * P4 Load 5 * P5 CONCENTRATED MOMENTS Parameter Symbol Magnitude Distance N*m kN*m lbf*in lbf*ft m mm inch ft Moment 1 * M1 Moment 2 * M2 Moment 3 * M3 Moment 4 * M4 Moment 5 * M5 DISTRIBUTED LOADS Parameter Symbol Magnitude Distance Pa-m N/m Pa-cm Pa-mm lbf/in psi-in psi-ft lbf/ft m mm inch ft wa wb a b Distributed Load 1 * w1 Distributed Load 2 * w2 Distributed Load 3 * w3 Distributed Load 4 * w4 Distributed Load 5 * w5 STRUCTURAL BEAM PROPERTIES Parameter Symbol Value Unit Structural Beam Length L m mm inch ft 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".

CONCENTRATED MOMENTS
RESULTS
Parameter Symbol Value Unit
Reaction Force 1  R1 ---
Reaction Force 2 R2 ---
Transverse Shear Force
@ distance x
Vx ---
Maximum Transverse
Shear Force
Vmax ---
Reaction Moment 1 M1 ---
Reaction Moment 2 M2 ---
Moment @ distance x Mx ---
Maximum Moment Mmax ---
Slope 1  θ1 ---
Slope 2 θ2 ---
Slope
@ distance x
θx ---
Maximum Slope θmax ---
End Deflection 1 y1 ---
End Deflection 2 y2 ---
Deflection @ distance x yx ---
Maximum Deflection ymax ---
Bending Stress @ distance x σx ---
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:

"Cantilever Beam with Concentrated Load at any Point", Cantilever Beam with Partially Distributed Load" and Cantilever Beam with Concentrated Moment at any Point" calculators have been used for the calculation of forces, moments, stresses, deflections and slopes with superposition principal.