# Beam Fixed at Both Ends - Concentrated Load at Center

Written by Jerry Ratzlaff on . Posted in Structural

## Beam Fixed at Both Ends - Concentrated Load at Center ### Concentrated Load at Center Formula

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

$$\large{ M_{max} }$$ (at center and ends)  =  $$\large{ \frac {P L} {8} }$$

$$\large{ M_x \; }$$ when  $$\large{ \left( x < \frac {L}{2} \right) = \frac {P} {8} \left( 4x - L \right) }$$

$$\large{ \Delta_{max} }$$ (at center)  =  $$\large{ = \frac {PL^3}{192 \lambda I} }$$

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

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

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

$$\large{ w }$$ = load per unit length

$$\large{ W }$$ = total load from a uniform distribution

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

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

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