Deflection (engineering) - End Load Cantilever Beams

End Load Cantilever Beams

The elastic deflection δ and angle of deflection φ (in radians) in the example image, a (weightless) cantilever beam, with an end load on it, can be calculated (at the free end B) using:

where

F = force acting on the tip of the beam

L = length of the beam (span)

E = modulus of elasticity

I = area moment of inertia

The deflection at any point along the span can be calculated using the above-mentioned methods.

From this formula it follows that the span L and height h are the most determining factors; if the span doubles, the deflection increases 2³ = 8 fold, and if the height doubles, the deflection decreases 2³ = 8 fold.

where (for a beam with rectangular cross section);

b = width (x-dimension),

h = height (y-dimension)