# Simple Beam - Two Unequal Point Loads Unequally Spaced

Written by Jerry Ratzlaff on . Posted in Structural

## 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