# Simply-Supported Beam with Concentrated Force at Intermediate Point Simply-Supported Beam with Concentrated Force at Intermediate Point

THEORY  &   FORMULAE : Bending Of A Straight Elastic Prismatic Beam
Consider a simply-supported bar, having a concentrated force acting vertically at any intermediate point (including the mid-point) along its length. The following equations describe the distribution of shear force, bending moment and deformation:  where
F = applied force at any intermediate point
L = length of beam or distance between supports
a = location of load point from left 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 delection at load point is given by:

D=[(Fa2(L-a)2/3EIL]

The maximum deflection eg. for the case where x < a, is:
Dmax=[(F(L-a)/3EIL)*(a(2L-a)/3)3/2] occuring at x=√[a(2L-a)/3]

Simply-Supported Beam with Concentrated Force

at Intermediate Point Free Software Analysis.