SIMPLY SUPPORTED STRUCTURAL BEAM WITH PARTIALLY DISTRIBUTED LOAD
Following calculator has been developed to find forces, moments, stresses, deflections and slopes in structural beam for a specific case which is partially distributed loading of a simply supported 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.
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.
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.
Supplements:
List of Equations:
Parameter 
Symbol 
Equation 
Reaction Force 1 
R_{1} 

Reaction Force 2 
R_{2} 

Shear force at distance x 
V 

Moment at distance x

M 

Bending stress at distance x 
σ 

Deflection at distance x 
y 

Shear force at distance x 
V 

Slope 1 
θ_{1} 

Slope 2 
θ_{2} 

Slope 
θ 

Note: In these formulas, equations in brackets "< >" are singularity
functions.
Reference:

Young, W. C., Budynas, R. G.(2002). Roark's Formulas for Stress and Strain
. 7nd Edition, McGrawHill, Chapter 8
, pp 125  267

Oberg.E , Jones.D.J., Holbrook L.H, Ryffel H.H., (2012) . Machinery's Handbook
. 29th edition. Industrial Press Inc.
, pp 236  261
 Beer.F.P. , Johnston.E.R. (1992). Mechanics of Materials
, 2nd edition. McGrawHill, Chapter 45789