Beam Fixed at Both Ends - Uniformly Distributed Load

Written by Jerry Ratzlaff on . Posted in Structural

febe 1Aformulas that use beam fixed at both ends - Uniformly Distributed Load

\(\large{ R = V =  \frac {w\; L} {2}  }\)   
\(\large{ V_x =  w  \;  \left(   \frac {L} {2} - x \right)     }\)   
\(\large{ M_{max}  }\) (at ends)  =  \(\large{  \frac {w\; L^2} {12}  }\)   
\(\large{ M_1  }\) (at center)  =  \(\large{  \frac {w\; L^2} {24}  }\)  
\(\large{ M_x  = \frac {w}{12}  \;  \left( 6\;L\;x - L^2 - 6\;x^2  \right)   }\)  
\(\large{ M_{max}  }\) (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)  \(\large{  =  0.2113 \; L    }\)  

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