Simple Beam - Uniform Load Partially Distributed at Any Point

Written by Jerry Ratzlaff on . Posted in Structural

Simple 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