Cantilever Beam - Concentrated Load at Free End

Written by Jerry Ratzlaff on . Posted in Structural

Cantilever Beam - Concentrated Load at Free Endcb 5A

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

 

Tags: Equations for Beam Support