Beam Fixed at Both Ends - Concentrated Load at Center

Written by Jerry Ratzlaff on . Posted in Structural

febe 2ABeam Fixed at Both Ends - Concentrated Load at Center Formula

\(\large{ R = V =  \frac {P} {2}  }\)  

\(\large{ M_{max}  }\) (at center and ends)  =  \(\large{  \frac {P L} {8}  }\)

\(\large{ M_x \; }\) when  \(\large{  \left( x <  \frac {L}{2}  \right)   = \frac {P} {8}  \left( 4x - L  \right)    }\)

\(\large{ \Delta_{max}   }\) (at center)  =  \(\large{   = \frac {PL^3}{192 \lambda I}   }\)

\(\large{ \Delta_{max} \; }\) when  \(\large{ \left( x <   \frac {L}{2}  \right)   = \frac {Px^2} {48 \lambda I}  \left( 3L - 4x  \right)    }\)

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