Simple Beam - Concentrated Load at Center

Written by Jerry Ratzlaff on . Posted in Structural

sb 7DSimple Beam - Concentrated Load at Center Formula

(Eq. 1)  \(\large{ R = V = \frac {P} {2}  }\)

(Eq. 2)  \(\large{ M_{max}  }\)  (at point of load)  \(\large{ =  \frac {PL} {4}  }\)

(Eq. 3)  \(\large{ M_x   \; }\)  when \(\large{    \left(  x < \frac {L}{2}    \right)   =   \frac  { Px} {2}    }\)

(Eq. 4)  \(\large{ \Delta_{max} }\)  (at point of load)  \(\large{ =  \frac { PL^3} {48 \lambda I}  }\)

(Eq. 5)  \(\large{ \Delta_x   \; }\)  when \(\large{  \left(  x < \frac {L}{2}    \right)    =  \frac {Px} {48 \lambda I}    \left(  3L^2 - 4x^2  \right)     }\)

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

\(\large{ V }\) = maximum shear force

\(\large{ x }\) = 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