Simple Beam - Load Increasing Uniformly to Center

Written by Jerry Ratzlaff on . Posted in Structural

Simple Beam - Load Increasing Uniformly to Centersb 3D

Load Increasing Uniformly to Center Formula

\(\large{ R = V = \frac {W } {2}  }\)

\(\large{ V_x   \; }\)  when \(\large{ \left(  x < \frac {L}{2} \right)  =  \frac  {W} {2L^2}   \left(  L^2 - 4x^2    \right)     }\)        

\(\large{ M_{max}  }\)  (at center)  \(\large{ =  \frac {W L} {6}  }\)

\(\large{ M_x   \; }\)  when \(\large{ \left(  x < \frac {L}{2}  \right)   =  Wx   \left(  \frac {1}{2} - \frac {2x^2}{3L^2}   \right)     }\)

\(\large{ \Delta_{max} }\)  (at center)  \(\large{ =  \frac {W L^3} {60 \lambda I }  }\)

\(\large{ \Delta_x =  \frac {W x} {480 \lambda I L^2}       \left(   5L^2 - 4x^2   \right)^2     }\)

 

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

 

Tags: Equations for Beam Support