Cantilever Beam - Concentrated Load at Any Point

Written by Jerry Ratzlaff on . Posted in Structural

cb 4Aformulas that use Cantilever Beam - Concentrated Load at Any Point

\(\large{ R = V =  P  }\)   
\(\large{ M_{max} \; }\)   (at fixed end)   \(\large{   =  P\;b  }\)   
\(\large{ M_x  \; }\) when  \(\large{ \left( x > a \right)   =   P \; \left( x - a \right)       }\)   
\(\large{ \Delta_{max} \; }\)   (at free end)   \(\large{   =  \frac {P\; b^2} {6\; \lambda\; I} \; \left( 3\;L - b \right)       }\)  
\(\large{ \Delta_a \; }\)   (at point of load)   \(\large{   =  \frac {P\; b^3} {3 \;\lambda\; I}    }\)  
\(\large{ \Delta_x \; }\) when  \(\large{ \left( x < a \right) =  \frac {P\; b^2 } {6\; \lambda\; I} \; \left( 3\;L - 3\;x - b  \right)       }\)  
\(\large{ \Delta_x \; }\) when  \(\large{ \left( x > a \right) =  \frac {P\; \left( L\; - \;x \right)^2    } {6 \;\lambda\; I} \; \left( 3\;b - L + x \right)       }\)  

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