Overhanging Beam - Uniformly Distributed Load Over Supported Span

Written by Jerry Ratzlaff on . Posted in Structural

Overhanging Beam - Uniformly Distributed Load Over Supported Spanob 3

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

Tags: Equations for Beam Support