Cantilever Beam - Concentrated Load at Any Point

Written by Jerry Ratzlaff on . Posted in Structural

cb 4ACantilever Beam - Concentrated Load at Any Point Formula

\(\large{ R = V =  P  }\)     

\(\large{ M_{max} \; }\)   (at fixed end)   \(\large{   =  Pb  }\)

\(\large{ M_x  \; }\) when  \(\large{ \left( x > a \right)   =   P  \left( x - a \right)       }\)

\(\large{ \Delta_{max} \; }\)   (at free end)   \(\large{   =  \frac {P b^2} {6 \lambda I}  \left( 3L - b \right)       }\)

\(\large{ \Delta_a \; }\)   (at point of load)   \(\large{   =  \frac {P b^3} {3 \lambda I}    }\)

\(\large{ \Delta_x \; }\) when  \(\large{ \left( x < a \right) =  \frac {P b^2 } {6 \lambda I}  \left( 3L - 3x - b  \right)       }\)

\(\large{ \Delta_x \; }\) when  \(\large{ \left( x > a \right) =  \frac {P \left( L - x \right)^2    } {6 \lambda I}  \left( 3b - L + x \right)       }\)

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