Simple Beam - Two Unequal Point Loads Unequally Spaced

Written by Jerry Ratzlaff on . Posted in Structural

Simple Beam - Two Unequal Point Loads Unequally Spacedsb 11C

Two Unequal Point Loads Unequally Spaced Formula

\(\large{ R_1 = V_1  =  \frac {P_1  \left(  L - a  \right)  + P_2 b     }  { L }   }\)

\(\large{ R_2 = V_2  =  \frac {P_1 a + P_2  \left(  L - b  \right)   }  { L }    }\)

\(\large{ V_x   \; }\)  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

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

\(\large{ R }\) = 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