# Simple Beam - Two Point Loads Equally Spaced

Written by Jerry Ratzlaff on . Posted in Structural

### Simple Beam - Two Point Loads Equally Spaced Formula

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

$$\large{ M_{max} \; }$$  (between loads)  $$\large{ = P\;a }$$

$$\large{ M_x \; }$$  when $$\large{ \left( x < a \right) = P\;x }$$

$$\large{ \Delta_{max} \; }$$  (at center)  $$\large{ = \frac{ P\;x }{24\; \lambda\; I} \;l \left( 3\;L^2 - 4\;a^2 \right) }$$

$$\large{ \Delta_x \; }$$  when $$\large{ \left( x < a \right) = \frac{ P\;x }{6\; \lambda \;I} \; \left( 3\;L\;a - 3\;a^2 - x^2 \right) }$$

$$\large{ \Delta_x \; }$$  when  $$\large{ \left( x > a \right) \; }$$  and  $$\large{ < \left( L - a \right) = \frac{ P\;a }{6\; \lambda\; I} \; \left( 3\;L\;a - 3\;x^2 - a^2 \right) }$$

Where:

$$\large{ \Delta }$$ = deflection or deformation

$$\large{ x }$$ = horizontal distance from reaction to point on beam

$$\large{ a }$$ = length to point load

$$\large{ M }$$ = 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