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)  \(\large{ =  \frac {5 w L^4} {384 \lambda I}  }\)

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

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

 

Tags: Equations for Beam Support