Simple Beam - Uniformly Distributed Load

Written by Jerry Ratzlaff on . Posted in Structural

sb 1EASimple Beam - Uniformly Distributed Load Formula

\(\large{ R = V_{max} = \frac{w \; L}{2}  }\)

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

\(\large{ M_{max}  }\)  (at center)  \(\large{ =  \frac{w \; L^2}{8}  }\)

\(\large{ M_x =   \frac{w \; x}{2} \;  \left(   L  - x    \right)     }\)

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

\(\large{ \Delta_x =  \frac{w\; x}{24\; \lambda \;I}   \;  \left(   L^3 - 2\;L\;x^2 + x^3    \right)     }\)

Where:

\(\large{ \Delta }\) = deflection or deformation

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

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

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

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

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

\(\large{ I }\) = moment of inertia

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

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

 

Tags: Equations for Beam Support