Simple Beam - Uniform Load Partially Distributed at Any Point

Written by Jerry Ratzlaff on . Posted in Structural

sb 5DSimple Beam - Uniform Load Partially Distributed at Any Point Formula

\(\large{ R_1 = V_1 }\)  max. when  \(\large{ \left( a < c \right)  = \frac{w \;b}{2\;L} \; \left( 2\;c + b  \right)     }\)

\(\large{ R_2 = V_2  }\)  max. when  \(\large{ \left(  a > c \right) = \frac {w \;b} {2\;L} \; \left( 2\;a + b  \right)  }\)

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

\(\large{ M_{max} \; }\)  at \(\large{ \left(  x = a + \frac {R_1}{w}  \right)  =  R_1 \; \left(  a  +  \frac{ R_1 } { 2\;w }   \right)   }\)

\(\large{ M_x  }\)  when  \(\large{ \left(  x < a \right)  =  R_1  \;x   }\)

\(\large{ M_x }\)  when  \(\large{  \left[  a < x < \; \left(  a + b \right)   \right]  =  R_1 \;x  - \frac{w}{2} \; \left(  x - a  \right)^2   }\)

\(\large{ M_x  }\)  when  \(\large{  \left[  x > \left(  a + b \right)   \right]  =  R_2 \;  \left(  L - x  \right)   }\)

Where:

\(\large{ x }\) = horizontal distance from reaction to point on beam

\(\large{ w }\) = load per unit length

\(\large{ V }\) = maximum shear force

\(\large{ M }\) = maximum bending moment

\(\large{ R }\) = reaction load at bearing point

\(\large{ L }\) = span length of the bending member

\(\large{ a, b, c }\) = width and seperation of UDL

 

Tags: Equations for Beam Support