Cantilever Beam - Uniformly Distributed Load

Written by Jerry Ratzlaff on . Posted in Structural

cb 1Aformulas that use Cantilever Beam - Uniformly Distributed Load

\(\large{ R = V =  w\;L  }\)   
\(\large{ V_x =  w\;x    }\)   
\(\large{ M_{max} \; }\)   (at fixed end)   \(\large{   =  \frac {w\; L^2} {2}  }\)   
\(\large{ M_x   =   \frac  { w\;x^2 } {2}   }\)  
\(\large{ \Delta_{max} \; }\)   (at free end)   \(\large{   =  \frac {w\; L^4} {8 \;\lambda\; I}  }\)  
\(\large{ \Delta_x   =  \frac {w} {24\; \lambda\; I} \; \left(   x^4 - 4\;L^3\;x + 3\;L^4   \right)     }\)  

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