Overhanging Beam - Uniformly Distributed Load Overhanging Both Supports

Written by Jerry Ratzlaff on . Posted in Structural

Overhanging Beam - Uniformly Distributed Load Overhanging Both Supportsob 4A

Uniformly Distributed Load Overhang Both Supports Formula

\(\large{ R_1 =  \frac{w L  \left( L - 2c  \right)   }{2b}      }\)

\(\large{ R_2 =  \frac{w L  \left( L - 2a  \right)   }{2b}      }\)

\(\large{ V_1  =   wa   }\)

\(\large{ V_2  =   R_1 - V_1   }\)

\(\large{ V_3  =   R_2 - V_4   }\)

\(\large{ V_4  =   wc   }\)

\(\large{ V_{x_1}  =   V_1 - w  \left( a - x_1  \right)   }\)

\(\large{ V_x \left( x < b  \right)   =   R_1 - w  \left( a + x  \right)   }\)

\(\large{ M_1 =  \frac{w a^2}{2}    }\)

\(\large{ M_2 =  \frac{w c^2}{2}    }\)

\(\large{ M_3 =  R_1  \left(  \frac{R_1}{2w} - a  \right)   }\)

\(\large{ M_x =  R_1  x   \frac{ w  \left(  a + x  \right)^2}{2}     }\)

 

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

 

Tags: Equations for Beam Support