Cantilever Beam - Concentrated Load at Free End

Written by Jerry Ratzlaff on . Posted in Structural

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Cantilever Beam - Concentrated Load at Free End formulas

\(\large{ R = V =  P  }\)   
\(\large{ M_{max} \; }\)   (at fixed end)   \(\large{   =  P\;L  }\)   
\(\large{ M_x   =   P\;x   }\)   
\(\large{ \Delta_{max} \; }\)   (at free end)   \(\large{   =  \frac {P\; L^3} {3\; \lambda\; I}  }\)  
\(\large{ \Delta_x   =  \frac {P} {6\; \lambda\; I} \; \left(   2\;L^3 - 3\;L^2\;x + x^3   \right)     }\)  

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