Simple Beam - Two Point Loads Equally Spaced

Written by Jerry Ratzlaff on . Posted in Structural

sb 9DSimple Beam - Two Point Loads Equally Spaced Formula

\(\large{ R = V   = P   }\)

\(\large{ M_{max} \; }\)  (between loads)  \(\large{ =  P\;a   }\)

\(\large{ M_x \; }\)  when \(\large{ \left(  x < a \right)  =   P\;x   }\)

\(\large{ \Delta_{max} \; }\)  (at center)  \(\large{ =  \frac{ P\;x }{24\; \lambda\; I} \;l \left( 3\;L^2  - 4\;a^2  \right)     }\)

\(\large{ \Delta_x \; }\)  when \(\large{ \left(  x < a \right)  =  \frac{ P\;x  }{6\; \lambda \;I} \; \left( 3\;L\;a  - 3\;a^2 - x^2  \right)     }\)

\(\large{ \Delta_x  \; }\)  when  \(\large{ \left(  x > a \right)  \; }\)  and  \(\large{ <  \left(  L - a  \right) =  \frac{  P\;a  }{6\; \lambda\; I}   \;   \left(  3\;L\;a  - 3\;x^2 - a^2  \right)     }\)

Where:

\(\large{ \Delta }\) = deflection or deformation

\(\large{ x }\) = horizontal distance from reaction to point on beam

\(\large{ a }\) = length to point load

\(\large{ M }\) = maximum bending moment

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

\(\large{ \lambda  }\)   (Greek symbol lambda) = modulus of elasticity

\(\large{ I }\) = moment of inertia

\(\large{ R }\) = reaction load at bearing point

\(\large{ L }\) = span length of the bending member

\(\large{ P }\) = total concentrated load

 

Tags: Equations for Beam Support