Cantilever Beam - Uniformly Distributed Load and Variable End Moments

Written by Jerry Ratzlaff on . Posted in Structural

Cantilever Beam - Uniformly Distributed Load and Variable End Momentscb 3A

Uniformly Distributed Load and Variable End Moments Formula

\(\large{ R = V =  wL  }\)

\(\large{ V_x =  wx    }\)       

\(\large{ M_{max} \; }\)   (at fixed end)   \(\large{   =  \frac{w L^2}{3}  }\)

\(\large{ M_1 \; }\)   (at free end)   \(\large{   =  \frac {w L^2} {6}  }\)

\(\large{ M_x   =   \frac{ w }{6}    \left( L^2 - 3x^2 \right)      }\)

\(\large{ \Delta_{max} \; }\)   (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