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)
Read more about this topic: Deflection (engineering)
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