Overhanging Beam - Uniformly Distributed Load Over Supported Span

Written by Jerry Ratzlaff on . Posted in Structural Overhanging Beam - Uniformly Distributed Load Over Supported Span Formula

$$\large{ R = V = \frac{w L }{2} }$$

$$\large{ V_x = w \left( \frac{L}{2} - x \right) }$$

$$\large{ M_{max} \; }$$  (at center)   $$\large{ = \frac{w L^2 }{8} }$$

$$\large{ M_x = \frac{w x }{2} \left( L - x \right) }$$

$$\large{ \Delta_{max} \; }$$  (at center)   $$\large{ = \frac{5w L^4 }{348 \lambda I} }$$

$$\large{ \Delta_x = \frac{w x }{24 \lambda I} \left( L^3 - 2Lx^2 + x^3 \right) }$$

$$\large{ \Delta_{x_1} = \frac{ - w L^3 x_1 }{24 \lambda I} }$$

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