Two Span Continuous Beam - Unequal Spans, Concentrated Load on Each Span Symmetrically Placed

Written by Jerry Ratzlaff on . Posted in Structural

cb3s 7ATwo Span Continuous Beam - Unequal Spans, Concentrated Load on Each Span Symmetrically Placed Formula

\(\large{ R_1 = V_1   =  \frac{M_2}{a}  +  \frac{P_1}{2}   }\)

\(\large{ R_2   =  P_1 + P_2 - R_1 - R_3   }\)

\(\large{ R_3 = V_4   =  \frac{M_2}{b}  +  \frac{P_2}{2}   }\)

\(\large{ M_1   =  R_1 a   }\)

\(\large{ M_2   =  \frac{3}{16}    \left(  \frac{P_1 a^2 + P_2 b^2}{a + b}  \right)  }\)

\(\large{ M_3   =  R_3 b   }\)

 

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

 

Tags: Equations for Beam Support