# Two Span Continuous Beam - Equal Spans, Concentrated Load at Any Point

Written by Jerry Ratzlaff on . Posted in Structural Engineering

## Two Span Continuous Beam - Equal Spans, Concentrated Load at Any Point formulas

 $$\large{ R_1 = V_1 = \frac{P\;b}{4\;L^3} \; \left[ 4\;L^2 - a \; \left( L + a \right) \right] }$$ $$\large{ R_2 = \frac{P\;a}{2\;L^3} \left[ 2\;L^2 + b \; \left( L + a \right) \right] }$$ $$\large{ R_3 = V_3 = \frac{P\;a\;b}{4\;L^3} \; \left( L + a \right) }$$ $$\large{ V_2 = \frac{P\;a}{4\;L^3} \; \left[ 4\;L^2 + b \; \left( L + a \right) \right] }$$ $$\large{ M_1 \; }$$ at support   $$\large{ \left( R_2 \right) = \frac{P\;a\;b}{4\;L^2} \; \left( L + a \right) }$$ $$\large{ M_{max} = \frac{P\;a\;b}{4\;L^3} \; \left[ 4\;L^2 - a \; \left( L + a \right) \right] }$$

### 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