# Simple Beam - Two Point Loads Equally Spaced

Written by Jerry Ratzlaff on . Posted in Structural

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

(Eq. 1)  $$\large{ R = V = P }$$

(Eq. 2)  $$\large{ M_{max} \; }$$  (between loads)  $$\large{ = Pa }$$

(Eq. 3)  $$\large{ M_x \; }$$  when $$\large{ \left( x < a \right) = Px }$$

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

(Eq. 5)  $$\large{ \Delta_x \; }$$  when $$\large{ \left( x < a \right) = \frac{ Px }{6 \lambda I} \left( 3La - 3a^2 - x^2 \right) }$$

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

Where:

$$\large{ I }$$ = moment of inertia

$$\large{ L }$$ = span length of the bending member

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

$$\large{ M }$$ = maximum bending moment

$$\large{ P }$$ = total concentrated load

$$\large{ R }$$ = reaction load at bearing point

$$\large{ V }$$ = maximum shear force

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

$$\large{ \lambda }$$   (Greek symbol lambda) = modulus of elasticity

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