# Cantilever Beam - Load Increasing Uniformly to One End

Written by Jerry Ratzlaff on . Posted in Structural

## formulas that use Cantilever Beam - Load Increasing Uniformly to One End

 $$\large{ R = V = W }$$ $$\large{ V_x = W\; \frac{x^2}{L^2} }$$ $$\large{ M_{max} \; }$$   (at fixed end)   $$\large{ = \frac{W\; L}{3} }$$ $$\large{ M_x = \frac{ W\;x^3 }{3\;L^2} }$$ $$\large{ \Delta_{max} \; }$$   (at free end)   $$\large{ = \frac{W\; L^3}{15\; \lambda\; I} }$$ $$\large{ \Delta_x = \frac{W\;x^2}{60\; \lambda \;I \;L^2} \; \left( x^5 + 5\;L^4 x + 4\;L^5 \right) }$$

### 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