# 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

(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