Simple Beam - Load Increasing Uniformly to Center

Written by Jerry Ratzlaff on . Posted in Structural

sb 3DSimple Beam - Load Increasing Uniformly to Center Formula

\(\large{ R = V_{max} = \frac{W}{2}  }\)

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

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

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

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

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

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