# Overhanging Beam - Uniformly Distributed Load Over Supported Span

Written by Jerry Ratzlaff on . Posted in Structural

## Overhanging Beam - Uniformly Distributed Load Over Supported Span formulas

 $$\large{ R = V = \frac{w\; L }{2} }$$ $$\large{ V_x = w \; \left( \frac{L}{2} - x \right) }$$ $$\large{ M_{max} \; }$$  (at center)   $$\large{ = \frac{w\; L^2 }{8} }$$ $$\large{ M_x = \frac{w\; x }{2} \; \left( L - x \right) }$$ $$\large{ \Delta_{max} \; }$$  (at center)   $$\large{ = \frac{5\;w\; L^4 }{348\; \lambda \; I} }$$ $$\large{ \Delta_x = \frac{w\; x }{24\; \lambda\; I} \; \left( L^3 - 2\;L\;x^2 + x^3 \right) }$$ $$\large{ \Delta_{x_1} = \frac{ -\; w \; L^3 \;x_1 }{24\; \lambda\; I} }$$

### 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