Overhanging Beam - Uniformly Distributed Load Over Supported Span

Written by Jerry Ratzlaff on . Posted in Structural

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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

 

Tags: Equations for Beam Support