# Two Span Continuous Beam - Unequal Spans, Uniformly Distributed Load

Written by Jerry Ratzlaff on . Posted in Structural

### Two Span Continuous Beam - Unequal Spans, Uniformly Distributed Load Formula

$$\large{ R_1 = V_1 = \frac{M_1}{a} + \frac{wa}{2} }$$

$$\large{ R_2 = wa + wb - R_1 - R_3 }$$

$$\large{ R_3 = V_4 = \frac{M_1}{b} + \frac{wa}{2} }$$

$$\large{ V_2 = wa - R_1 }$$

$$\large{ V_3 = wb - R_3 }$$

$$\large{ M_1 = \frac{wb^3 + wa^3}{8 \left( a+ b \right) } }$$

$$\large{ M_{x_1} \; \left( x_1 = \frac{R_1}{w} \right) = R_1 x_1 \frac{wx_{1}{^2} }{2} }$$

$$\large{ M_{x_2} \; \left( x_2 = \frac{R_2}{w} \right) = R_3 x_2 \frac{wx_{2}{^2} }{2} }$$

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