# Overhanging Beam - Uniformly Distributed Load Overhanging Both Supports

Written by Jerry Ratzlaff on . Posted in Structural Engineering

## Overhanging Beam - Uniformly Distributed Load Overhang Both Supports formulas

 $$\large{ R_1 = \frac{w\; L \; \left( L\; -\; 2\;c \right) }{2\;b} }$$ $$\large{ R_2 = \frac{w\; L \; \left( L \;-\; 2\;a \right) }{2\;b} }$$ $$\large{ V_1 = w\;a }$$ $$\large{ V_2 = R_1 - V_1 }$$ $$\large{ V_3 = R_2 - V_4 }$$ $$\large{ V_4 = w\;c }$$ $$\large{ V_{x_1} = V_1 - w \; \left( a - x_1 \right) }$$ $$\large{ V_x \;\left( x < b \right) = R_1 - w \; \left( a + x \right) }$$ $$\large{ M_1 = \frac{w\; a^2}{2} }$$ $$\large{ M_2 = \frac{w \;c^2}{2} }$$ $$\large{ M_3 = R_1 \; \left( \frac{R_1}{2\;w} - a \right) }$$ $$\large{ M_x = R_1 \; x \; \frac{ w \; \left( a \;+\; x \right)^2}{2} }$$

### 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