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

Cantilever Beam Deflection and Stress Calculator to find forces, moments, stresses, deflections and slopes for a cantilever beam. Multiple point loads, distributed loads and concentrated moments can be defined as an input loading for the beam. Cantilever beam deflection and stress formulas are given on 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 .

### Cantilever Beam Deflection and Stress Calculator:

Note : Use dot "." as decimal separator.

Note * : P is positive in downward direction as shown in the figure and negative in upward direction. M is positive in clockwise direction as shown in the figure. wa and wb are positive in downward direction as shown in the figure and negative in upward direction.

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

CONCENTRATED MOMENTS

 RESULTS Param. Value 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 * : R1 and R2 are vertical end reactions at the left and right, respectively, and are positive upward. Shear forces and deflections are positive in upward direction and negative in downward direction. M1 and M2 are the reaction end moments at the left and right, respectively. All moments are positive when producing compression on the upper portion of the beam cross section. All slopes are positive when up and to the right.

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.