Cantilever Beam - Load at Free End Deflection Vertically with No Rotation

Written by Jerry Ratzlaff on . Posted in Structural

Cantilever Beam - Load at Free End Deflection Vertically with No Rotationcb 6A

Load at Free End Deflection Vertically with No Rotation Formula

\(\large{ R = V =  P  }\)      

\(\large{ M_{max} \; }\)   (at both end)   \(\large{   =  \frac{P L}{2}  }\)

\(\large{ M_x   =  P  \left(     \frac{ L }{2} - x  \right)       }\)

\(\large{ \Delta_{max} \; }\)   (at free end)   \(\large{   =  \frac{P L^3}{12 \lambda I}  }\)

\(\large{ \Delta_x   =  \frac{P  \left( L -x \right)^2      }{12 \lambda I}  \left( L + 2x   \right)     }\)

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

\(\large{ V }\) = 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