Cantilever Beam - Load Increasing Uniformly to One End

Written by Jerry Ratzlaff on . Posted in Structural

cb 2ACantilever 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

 

Tags: Equations for Beam Support