# Two Span Continuous Beam - Equal Spans, Two Equal Concentrated Loads Symmetrically Placed

Written by Jerry Ratzlaff on . Posted in Structural

### Two Span Continuous Beam - Equal Spans, Two Equal Concentrated Loads Symmetrically Placed Formula

$$\large{ R_1 = V_1 = R_3 = V_3 = \frac{5P}{16} }$$

$$\large{ R_2 = 2V_2 = \frac{11P}{8} }$$

$$\large{ V_2 = P - R_1 = \frac{11P}{16} }$$

$$\large{ V_{max} = V_2 }$$

$$\large{ M_1 = \frac{3PL}{16} }$$

$$\large{ M_2 = \frac{5PL}{32} }$$

$$\large{ M_x \; \left( x < \frac{L}{2} \right) = R_1 x }$$

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