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

Written by Jerry Ratzlaff on . Posted in Structural

cb3s 6Aformulas that use Two Span Continuous Beam - Equal Spans, Concentrated Load at Any Point

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

 

Tags: Equations for Beam Support