# 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.

##### Calculator:

 INPUT PARAMETERS Parameter Symbol Value Unit Distributed load magnitude at a * wa Pa-m N/m Pa-cm Pa-mm lbf/in psi-in psi-ft lbf/ft Distributed load magnitude at L * wL Beam Length L mm m inch ft Distance a a 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".

 RESULTS Parameter Symbol Value Unit Reaction Force 1 R1 --- N kN lbf Reaction Force 2 R2 --- Transverse Shear Force @ distance x Vx --- Maximum Transverse  Shear Force Vmax --- Moment @ distance x Mx --- N*m kN*m lbf*in lbf*ft Maximum Moment Mmax --- Slope 1 θ1 --- radian degree arcmin arcsec Slope 2 θ2 --- Slope @ distance x θx --- Maximum Slope θmax --- Deflection @ distance x yx --- mm m inch ft Maximum Deflection ymax --- Bending Stress @ distance x σx --- MPa psi ksi 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.

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:

 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:

 Parameter Symbol Equation Reaction Force 1 R1 Reaction Force 2 R2 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 θ1 Slope 2 θ2 Slope θ