Simple Beam - Load Increasing Uniformly to One End

Written by Jerry Ratzlaff on . Posted in Structural

sb 2DSimple Beam - Load Increasing Uniformly to One End Formula

\(\large{ R_1 = V_1 = \frac {W } {3}  }\)

\(\large{ R_2 = V_2 = \frac {2W } {3}  }\)

\(\large{ V_x =    \frac {W} {3}   -    \frac {Wx^2} {L^2} }\)        

\(\large{ M_{max} \; }\)  at \(\large{ \left(  x = \frac {L}{ \sqrt {3} } =  0.5774L  \right)  =  \frac { 2WL } { 9 \sqrt{3} } =0.1283 WL   }\)

\(\large{ M_x =   \frac  {W x} {3L^2}   \left(   L^2  - x^2    \right)     }\)

\(\large{ \Delta_{max} \; }\)  at \(\large{ \left(  x =  L \sqrt {1 -   \frac{8}{15} } = 0.5193L   \right)  =  0.01304  \frac { W L^3} { \lambda I}  }\)

\(\large{ \Delta_x =  \frac {W x} { 180 \lambda I L^2  }   \left(   3x^4 - 10L^2x^2 + 7L^4    \right)     }\)

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

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

\(\large{ W }\) = total load or wL/2

\(\large{ x }\) = 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