SIMPLY-SUPPORTED BEAM WITH TWIN CONCENTRATED FORCES

US Customary Units

SI/Metric Units
INPUT   DATA ♥ EXAMPLE Of Input/Output

Title  

Length, L ft

    

Loadpoint distance, a ft
Modulus of elasticity, E   106lb/in2 
Area moment of inertia, I   in4
Force applied, F lb

     Reset

OUTPUT   VARIABLES   &   GRAPHS

Variables   Values   Units
 ♦  Maximum Shear force, Vmax lb Graphs:
 Shear force Vs Distance  
 Bending moment Vs Distance  
 Deflection Vs Distance  
 ♦  Maximum Bending moment, Mmax   ft.lb  
 ♦  Maximum Deflection, Dmax in
 ♦  Distance of point of Dmax ft
 ♦  Deflection at loadpoint in
 ♦  Reaction force, R1 lb
 ♦  Reaction force, R2 lb
 ♦  Slope angle, θ1 °
 ♦  Slope angle, θ2 °
THEORY  &   FORMULAE

Bending Of A Straight Elastic Prismatic Beam

Consider a simply-supported bar, having two concentrated forces acting vertically and located equidistant from each end of the beam. The following equations describe the distribution of shear force, bending moment and deformation:

    

where
     F = applied force at each load pointt
     L = length of beam or distance between supports
     a = location of load point from end of beam
     x = distance from left end of beam
     E = modulus of elasticity of beam material
     I = area moment of inertia of cross-sectional area about axis through centroid
     V = shear force
     M = bending moment
     D = deflection
     R1 = vertical reaction at left support
     R2 = vertical reaction at right support
     θ1 = angle of slope at left support
     θ2 = angle of slope at right support

The deflection at load point is given by D=[(Fa(3La -4a2)/6EI]. The maximum deflection is:
Dmax=[(Fa/24EI)*(3L2-4a2] occuring at x=L/2.

Tips

    ◊ Use link EXAMPLE Of Input/Output  to demo data entry expectations and results; you may edit & use it as starting point

BIBLIOGRAPHY