# Simple Beam - Two Equal Point Loads Unequally Spaced

Written by Jerry Ratzlaff on . Posted in Structural

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

$$\large{ R_1 = V_1 }$$  max. when  $$\large{ \left( a < b \right) = \frac {P} {L} \; \left( L - a + b \right) }$$

$$\large{ R_2 = V_2 }$$  max. when  $$\large{ \left( a < b \right) = \frac {P} {L} \; \left( L - b + a \right) }$$

$$\large{ V_x \; }$$  when  $$\large{ \left( x > a \right) \; }$$  and  $$\large{ < \left( L - b \right) = \frac {P}{L} \; \left( b - a \right) }$$

$$\large{ M_1 }$$  max. when  $$\large{ \left( a > b \right) = R_1 \;a }$$

$$\large{ M_2 }$$  max. when  $$\large{ \left( a < b \right) = R_2 \;b }$$

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

$$\large{ M_x \; }$$  when  $$\large{ \left( x > a \right) \; }$$  and  $$\large{ < \left( L - b \right) = R_1 \;x - P\; \left( x - a \right) }$$

Where:

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

$$\large{ a, b }$$ = 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