Simple Beam - Two Unequal Point Loads Unequally Spaced

Written by Jerry Ratzlaff on . Posted in Structural

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Simple Beam - Two Unequal Point Loads Unequally Spaced formulas

\(\large{ R_1 = V_1  =  \frac {P_1 \; \left(  L \;- \;a  \right)  \;+\; P_2\; b     }  { L }   }\)   
\(\large{ R_2 = V_2  =  \frac {P_1 \;a \;+\; P_2 \; \left(  L\; - \;b  \right)   }  { L }    }\)   
\(\large{ V_x   \; }\)  when  \(\large{ \left(  x > a \right)  \; }\)  and  \(\large{ < \; \left(  L - b  \right) =   R_1 - P_1  }\)   
\(\large{ M_1 }\)  max. when  \(\large{ \left(  R_1 < P_1  \right)  =  R_1\; a     }\)  
\(\large{ M_2 }\)  max. when  \(\large{ \left(  R_2 < P_2  \right)  =  R_2\; b     }\)  
\(\large{ M_x }\)  max. when  \(\large{ \left(  x < a  \right)  =  R_1\; x     }\)  
\(\large{ M_x \; }\)  when  \(\large{ \left(  x > a \right)  \; }\)  and  \(\large{ <  \;\left(  L - b  \right) =  R_1\; x  - P_1\; \left(  x - a  \right)   }\)  

Where:

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

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

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

\(\large{ M }\) = 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

 

Tags: Equations for Beam Support