# Simple Beam - Two Unequal Point Loads Unequally Spaced

Written by Jerry Ratzlaff on . Posted in Structural

### Simple Beam - Two Unequal Point Loads Unequally Spaced Formula

(Eq. 1)  $$\large{ R_1 = V_1 = \frac {P_1 \left( L - a \right) + P_2 b } { L } }$$

(Eq. 2)  $$\large{ R_2 = V_2 = \frac {P_1 a + P_2 \left( L - b \right) } { L } }$$

(Eq. 3)  $$\large{ V_x \; }$$  when  $$\large{ \left( x > a \right) \; }$$  and  $$\large{ < \left( L - b \right) = R_1 - P_1 }$$

(Eq. 4)  $$\large{ M_1 }$$  max. when  $$\large{ \left( R_1 < P_1 \right) = R_1 a }$$

(Eq. 5)  $$\large{ M_2 }$$  max. when  $$\large{ \left( R_2 < P_2 \right) = R_2 b }$$

(Eq. 6)  $$\large{ M_x }$$  max. when  $$\large{ \left( x < a \right) = R_1 x }$$

(Eq. 7)  $$\large{ M_x \; }$$  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