Cantilever Beam - Uniformly Distributed Load and Variable End Moments

Written by Jerry Ratzlaff on . Posted in Structural

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Cantilever Beam - Uniformly Distributed Load and Variable End Moments formulas

\(\large{ R = V =  w\;L  }\)   
\(\large{ V_x =  w\;x    }\)   
\(\large{ M_{max} \; }\)   (at fixed end)   \(\large{   =  \frac{w\; L^2}{3}  }\)   
\(\large{ M_1 \; }\)   (at free end)   \(\large{   =  \frac {w \;L^2} {6}  }\)  
\(\large{ M_x   =   \frac{ w }{6}  \;  \left( L^2 - 3\;x^2 \right)      }\)  
\(\large{ \Delta_{max} \; }\)   (at free end)   \(\large{   =  \frac{w\; L^4}{24\; \lambda\; I}  }\)  
\(\large{ \Delta_x   =  \frac{w \; \left(   L^2\; - \;  \left(  L\; - \;x  \right)^2    \right)^2       }{24 \;\lambda\; I}      }\)  

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