# Beam Fixed at One End - Uniformly Distributed Load

Written by Jerry Ratzlaff on . Posted in Structural

### Beam Fixed at One End - Uniformly Distributed Load Formula

$$\large{ R_1 = V_1 = \frac {3 w L} {8} }$$

$$\large{ R_2 = V_2 = \frac {5 w L} {8} }$$

$$\large{ V_x = R_1 - wx }$$

$$\large{ M_{max} = \frac {w L^2} {8} }$$

$$\large{ M_1 }$$   at  $$\large{ \left( x = \frac {3L}{8} \right) = \frac { 9wL^2 } {128} }$$

$$\large{ M_x = R_1 x - \frac {w x^2} {2} }$$

$$\large{ \Delta_{max} = }$$  at   $$\large{ \left[ x = \frac {L} {16} \left( 1 + \sqrt {33} \right) \right] }$$  or  $$\large{ \left( x = 0.4215L \right) = \frac {w L^4} {185 \lambda I} }$$

$$\large{ \Delta_x = \frac {w x} {48 \lambda I} \left( L^3 - 3Lx^2 + 2x^3 \right) }$$

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