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

(Eq. 1)  \(\large{ R_1 = V_1 }\)  max. when  \(\large{ \left(  a < c  \right)  = \frac {w b} {2L}    \left(  2c + b  \right)     }\)

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

(Eq. 3)  \(\large{ V_x    }\)  when  \(\large{ \left[  a < x  <  \left(  a + b \right)   \right]  =     R_1 -  w   \left(  x - a  \right)     }\)      

(Eq. 4)  \(\large{ M_{max} \; }\)  at \(\large{ \left(  x = a + \frac {R_1}{w}  \right)  =  R_1  \left(  a  +  \frac { R_1 } { 2w }   \right)   }\)

(Eq. 5)  \(\large{ M_x  }\)  when  \(\large{ \left(  x < a \right)  =     R_1  x   }\)

(Eq. 6)  \(\large{ M_x }\)  when  \(\large{  \left[  a < x < \left(  a + b \right)   \right]  =     R_1 x  - \frac {w}{2}  \left(  x - a  \right)^2   }\)

(Eq. 7)  \(\large{ M_x  }\)  when  \(\large{  \left[  x > \left(  a + b \right)   \right]  =     R_2   \left(  L - x  \right)   }\)

Where:

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

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

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

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

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

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

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

 

Tags: Equations for Beam Support