Beam Fixed at One End - Concentrated Load at Center

Written by Jerry Ratzlaff on . Posted in Structural

feoe 2ABeam Fixed at One End - Concentrated Load at Center Formula

\(\large{ R_1 = V_1 = \frac {5P} {16}  }\)

\(\large{ R_2 = V_2 = \frac {11P} {16}  }\)

\(\large{ M_{max}  }\)  (at fixed end)  \(\large{ =  \frac {3PL} {16}  }\)

\(\large{ M_1  }\)  (at point of load)  \(\large{ =  \frac {5PL} {32}  }\)

\(\large{ M_x   \; }\)  when \(\large{    \left(  x < \frac {L}{2}    \right)   =   \frac  { 5Px} {16}    }\)

\(\large{ M_x   \; }\)  when \(\large{    \left(  x > \frac {L}{2}    \right)   =  P \left(  \frac { L} {2}  - \frac { 11x} {16}  \right)  }\)

\(\large{ \Delta_{max}   \; }\)  at  \(\large{  \left( x = L \sqrt { \frac {1}{5} } = .4472L   \right)   =  \frac {PL^3} {48 \lambda I \sqrt {5}  }  =  .009317  \frac { PL^3} { \lambda I}    }\)

\(\large{ \Delta_x \; }\)  (at point of load)  \(\large{ =  \frac { 7PL^3} {768 \lambda I}  }\)

\(\large{ \Delta_x   \; }\)  when \(\large{    \left(  x < \frac {L}{2}    \right)   =   \frac  { Px} {96 \lambda I}  \left( 3L^2 - 5x^2  \right)    }\)

\(\large{ \Delta_x   \; }\)  when \(\large{    \left(  x > \frac {L}{2}    \right)   =  \frac  { P} {96 \lambda I}  \left( x - L  \right)^2  \left( 11x - 2L  \right)   }\)

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