# Simple Beam - Concentrated Load at Center

Written by Jerry Ratzlaff on . Posted in Structural

### Simple Beam - Concentrated Load at Center Formula

(Eq. 1)  $$\large{ R = V = \frac {P} {2} }$$

(Eq. 2)  $$\large{ M_{max} }$$  (at point of load)  $$\large{ = \frac {PL} {4} }$$

(Eq. 3)  $$\large{ M_x \; }$$  when $$\large{ \left( x < \frac {L}{2} \right) = \frac { Px} {2} }$$

(Eq. 4)  $$\large{ \Delta_{max} }$$  (at point of load)  $$\large{ = \frac { PL^3} {48 \lambda I} }$$

(Eq. 5)  $$\large{ \Delta_x \; }$$  when $$\large{ \left( x < \frac {L}{2} \right) = \frac {Px} {48 \lambda I} \left( 3L^2 - 4x^2 \right) }$$

Where:

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

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

$$\large{ M }$$ = 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