Simply supported beam with bending moment calculator to find forces, moments, stresses, deflections and slopes of a simple beam which is subjected to a
moment. The bending moment can be applied at any point of the beam. Formulas are given below the calculator.
Simply Supported Beam with Bending Moment Calculator:
Note : Use dot "." as decimal separator.
Note * : M is positive in clockwise direction as shown in the figure.
Note ** : For second moment of area calculations of structural beams, visit "
Sectional Properties Calculators".
RESULTS 
Parameter 
Value 
Reaction Force 1 [R_{1}] 



Reaction Force 2 [R_{2}] 


Transverse Shear Force @ distance x [V_{x}] 


Maximum Transverse Shear Force [V_{max}] 


Moment @ distance x [M_{x}] 



Maximum Moment [M_{max}] 


Slope 1 [θ_{1}] 



Slope 2 [θ_{2}] 


Slope @ distance x [θ_{x}] 


Maximum Slope [θ_{max}] 


Deflection @ distance x [y_{x}] 



Maximum Deflection [y_{max}] 


Bending Stress @ distance x [σ_{x}] 



Maximum Bending Stress [σ_{max}] 


Note * : R_{1} and R_{2} 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. 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
Note: In these formulas, equations in brackets "< >" are singularity
functions. >" are singularity
functions.