# Cantilever Beam - Load Increasing Uniformly to One End

Written by Jerry Ratzlaff on . Posted in Structural

### Cantilever Beam - Load Increasing Uniformly to One End Formula

$$\large{ R = V = W }$$

$$\large{ V_x = W \frac{x^2}{L^2} }$$

$$\large{ M_{max} \; }$$   (at fixed end)   $$\large{ = \frac{W L}{3} }$$

$$\large{ M_x = \frac{ Wx^3 }{3L^2} }$$

$$\large{ \Delta_{max} \; }$$   (at free end)   $$\large{ = \frac{W L^3}{15 \lambda I} }$$

$$\large{ \Delta_x = \frac{Wx^2}{60 \lambda I L^2} \left( x^5 + 5L^4 x + 4L^5 \right) }$$

Where:

$$\large{ I }$$ = moment of inertia

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

$$\large{ M }$$ = maximum bending moment

$$\large{ R }$$ = 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