# Two Span Continuous Beam - Equal Spans, Uniform Load on One Span

Written by Jerry Ratzlaff on . Posted in Structural

### Two Span Continuous Beam - Equal Spans, Uniform Load on One Span Formula

$$\large{ R_1 = V_1 = \frac{7wL}{16} }$$

$$\large{ R_2 = v_2 + V_3 = \frac{5wL}{8} }$$

$$\large{ R_3 = V_3 = \frac{wL}{16} }$$

$$\large{ V_2 = \frac{9wL}{16} }$$

$$\large{ M_{max} \; }$$ at  $$\large{ \left( x = \frac{7L}{16} \right) = \frac{49wL^2}{512} }$$

$$\large{ M_1 \; }$$ at support  $$\large{ \left( R_2 \right) = \frac{wL^2}{16} }$$

$$\large{ M_x \; \left( x < L \right) = \frac{wx}{16} \left( 7L - 8x \right) }$$

$$\large{ \Delta_{max} \; \left( 0.472L \right) }$$  from  $$\large{ \left( R_1 \right) = 0.0092 \frac{wL^4}{ \lambda I} }$$

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