Beam Fixed at One End - Uniformly Distributed Load

Written by Jerry Ratzlaff on . Posted in Structural

Beam Fixed at One End - Uniformly Distributed Loadfeoe 1A

Uniformly Distributed Load Formula

\(\large{ R_1 = V_1 =  \frac {3 w L} {8}  }\)

\(\large{ R_2 = V_2 =  \frac {5 w L} {8}  }\)

\(\large{ V_x =  R_1 - wx    }\)       

\(\large{ M_{max}   =  \frac {w L^2} {8}  }\)

\(\large{ M_1 }\)   at  \(\large{ \left( x = \frac {3L}{8}  \right)  =   \frac  { 9wL^2 } {128}   }\)

\(\large{ M_x   =  R_1 x - \frac {w x^2} {2}  }\)

\(\large{ \Delta_{max}   =  }\)  at   \(\large{   \left(  x  =  \frac {L} {16}   \left( 1 + \sqrt {33}  \right)  \right)   }\)  or  \(\large{  \left( x = 0.4215L  \right)  =  \frac {w L^4} {185 \lambda I}    }\)

\(\large{ \Delta_x =  \frac {w x} {48 \lambda I}       \left(   L^3 - 3Lx^2 + 2x^3    \right)     }\)

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