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

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

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

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

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

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

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

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

Where:

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

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

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

\(\large{ M }\) = 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

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

 

Tags: Equations for Beam Support