Simply Supported Beam with Two Distributed Loads.

Simply Supported Beam with Two Distributed Loads Calculator:

Simply Supported Beam with Two Partially Distributed Loads
Parameter Value
Distributed load magnitude at a1 [wa1]
Distributed load magnitude at b1[wb1]
Distributed load magnitude at a2[wa2]
Distributed load magnitude at b2[wb2]
Beam Length [L]
Distance a1
Distance b1
Distance a2
Distance b2
Distance x
Modulus of Elasticity [E]
Distance from neutral axis to extreme fibers [c]
Second moment of area [I] **

Note : Use dot "." as decimal separator.

Note * : wa1, wb1, wa2 and wb2 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".


Parameter Value
Reaction Force 1 [R1] ---
Reaction Force 2 [R2] ---
Transverse Shear Force @ distance x [Vx] ---
Maximum Transverse Shear Force [Vmax] ---
Moment @ distance x [Mx] ---
Maximum Moment [Mmax] ---
Slope 1 [θ1] ---
Slope 2 [θ2] ---
Slope @ distance x [θx] ---
Maximum Slope [θmax] ---
Deflection @ distance x [yx] ---
Maximum Deflection [ymax] ---
Bending Stress @ distance x [σx] ---
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. 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.




Shear Force


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.

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.

Simply supported beam: A beam which is free to rotate at its supports, and also to expand longitudinally at 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.