Beam Fixed at Both Ends - Uniformly Distributed Load

Written by Jerry Ratzlaff on . Posted in Structural

Beam Fixed at Both Ends - Uniformly Distributed Loadfebe 1A

Uniformly Distributed Load Formula

\(\large{ R = V =  \frac {w L} {2}  }\)

\(\large{ V_x =  w    \left(   \frac {L} {2} - x \right)     }\)     

\(\large{ M_{max}  }\) (at ends)  =  \(\large{  \frac {w L^2} {12}  }\)

\(\large{ M_1  }\) (at center)  =  \(\large{  \frac {w L^2} {24}  }\)

\(\large{ M_x  = \frac {w}{12}    \left( 6Lx - L^2 - 6x^2  \right)   }\)

\(\large{ M_{max}  }\) (at center)  \(\large{  =   \frac {w L^4} {384 \lambda I}     }\)

\(\large{ \Delta_x   =   \frac {w x^2} {24 \lambda I}   \left( L - x  \right) ^2        }\)

\(\large{ x  }\) (points of contraflexure)  \(\large{  =   \left(  0.2113   \right)  L    }\)

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