Simple Beam - Concentrated Load at Center

Written by Jerry Ratzlaff on . Posted in Structural

Simple Beam - Concentrated Load at Center Formula

$$\large{ R = V = \frac{P}{2} }$$

$$\large{ M_{max} }$$  (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