# Simple Beam - Uniformly Distributed Load

Written by Jerry Ratzlaff on . Posted in Structural

### Simple Beam - Uniformly Distributed Load Formula

(Eq. 1)  $$\large{ R = V_{max} = \frac {w L} {2} }$$

(Eq. 2)  $$\large{ V_x = w \left( \frac {L} {2} - x \right) }$$

(Eq. 3)  $$\large{ M_{max} }$$  (at center)  $$\large{ = \frac {w L^2} {8} }$$

(Eq. 4)  $$\large{ M_x = \frac {w x} {2} \left( L - x \right) }$$

(Eq. 5)  $$\large{ \Delta_{max} }$$  (at center)  $$\large{ = \frac {5 w L^4} {384 \lambda I} }$$

(Eq. 6)  $$\large{ \Delta_x = \frac {w x} {24 \lambda I} \left( L^3 - 2Lx^2 + x^3 \right) }$$

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

$$\large{ V }$$ = maximum shear force

$$\large{ w }$$ = load per unit length

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

$$\large{ \lambda }$$   (Greek symbol lambda) = modulus of elasticity

$$\large{ \Delta }$$ = deflection or deformation