# Cantilever Beam - Concentrated Load at Free End

### Cantilever Beam - Concentrated Load at Free End Formula

\(\large{ R = V = P }\)

\(\large{ M_{max} \; }\) (at fixed end) \(\large{ = PL }\)

\(\large{ M_x = Px }\)

\(\large{ \Delta_{max} \; }\) (at free end) \(\large{ = \frac {P L^3} {3 \lambda I} }\)

\(\large{ \Delta_x = \frac {P} {6 \lambda I} \left( 2L^3 - 3L^2x + x^3 \right) }\)

Where:

\(\large{ I }\) = moment of inertia

\(\large{ L }\) = span length of the bending member

\(\large{ M }\) = maximum bending moment

\(\large{ P }\) = total concentrated load

\(\large{ R }\) = reaction load at bearing point

\(\large{ V }\) = shear force

\(\large{ w }\) = load per unit length

\(\large{ W }\) = total load from a uniform distribution

\(\large{ x }\) = horizontal distance from reaction to point on beam

\(\large{ \lambda }\) (Greek symbol lambda) = modulus of elasticity

\(\large{ \Delta }\) = deflection or deformation