Simple Beam - Concentrated Load at Center

Written by Jerry Ratzlaff on 23 April 2018. Posted in Structural

\(\large{ R = V = \frac{P}{2} }\)

\(\large{ M_{max} }\) (at point of load) \(\large{ = \frac{P\;L}{4} }\)

\(\large{ M_x \; }\) when \(\large{ \left( x < \frac{L}{2} \right) = \frac{ P\;x}{2} }\)

\(\large{ \Delta_{max} }\) (at point of load) \(\large{ = \frac{ P\;L^3}{48\; \lambda\; I} }\)

\(\large{ \Delta_x \; }\) when \(\large{ \left( x < \frac{L}{2} \right) = \frac{P\;x}{48 \;\lambda\; I} \; \left( 3\;L^2 - 4\;x^2 \right) }\)

Where:

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

\(\large{ x }\) = 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

\(\large{ P }\) = total concentrated load