Simple Beam - Concentrated Load at Center

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Simple Beam - Concentrated Load at Center formulas

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