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

Written by Jerry Ratzlaff on . Posted in Structural

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

 $$\large{ R_1 = V_1 = \frac{M_1}{a} + \frac{w\;a}{2} }$$ $$\large{ R_2 = w\;a + w\;b - R_1 - R_3 }$$ $$\large{ R_3 = V_4 = \frac{M_1}{b} + \frac{w\;a}{2} }$$ $$\large{ V_2 = w\;a - R_1 }$$ $$\large{ V_3 = w\;b - R_3 }$$ $$\large{ M_1 = \frac{w\;b^3 \;+\; w\;a^3}{8 \; \left( a\;+ \;b \right) } }$$ $$\large{ M_{x_1} \; \left( x_1 = \frac{R_1}{w} \right) = R_1\; x_1 \; \frac{w\;x_{1}{^2} }{2} }$$ $$\large{ M_{x_2} \; \left( x_2 = \frac{R_2}{w} \right) = R_3 \;x_2 \; \frac{w\;x_{2}{^2} }{2} }$$

### 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