# Three Span Continuous Beam - Equal Spans, Uniform Load on Two Spans at Each End

Written by Jerry Ratzlaff on . Posted in Structural

### Three Span Continuous Beam - Equal Spans, Uniform Load on Two Spans at Each End Formula

$$\large{ R_1 = V_1 = R_4 = V_4 = 0.450wL }$$

$$\large{ R_2 = V_2 = R_3 = V_3 = 0.550wL }$$

$$\large{ M_1 = M_3 \; }$$ at  $$\large{ \left( x = 0.450L \right) \; }$$ from $$\large{ \left( R_1 \right) \; }$$ or  $$\large{ \left( R_2 \right) \; = 0.1013wL^2 }$$

$$\large{ M_2 \; }$$ (at mid span)  $$\large{ \; = -0.050wL }$$

$$\large{ \Delta_{max} \; }$$ at  $$\large{ \left( 0.479L \right) \; }$$ from  $$\large{ \left( R_1 \right) \; }$$ or  $$\large{ \left( R_4 \right) \; = \frac{0.0099wL^4}{\lambda I} }$$

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