Two Span Continuous Beam - Equal Spans, Uniformly Distributed Load

Written by Jerry Ratzlaff on . Posted in Structural

cb3s 1Aformulas that use Two Span Continuous Beam - Equal Spans, Uniformly Distributed Load

\(\large{ R_1 = V_1 = R_3 = V_3    = \frac{3\;L}{8}    }\)   
\(\large{ R_2    = \frac{10\;w\;L}{8}    }\)   
\(\large{ V_2 = V_{max}   = \frac{5\;w\;L}{8}    }\)   
\(\large{ M_1   = \frac{w\;L^2}{8}    }\)  
\(\large{ M_2 \; }\) at  \(\large{  \left(  \frac{3\;L}{8} \right)    = \frac{9\;w\;L^2}{128}    }\)  
\(\large{ \Delta_{max} \;\; \left( 0.4215 \;L \right)  }\)  from  \(\large{  \left( R_1,  R_3 \right)  =  \frac{w\;L^4}{185\; \lambda\; I}    }\)  

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

 

Tags: Equations for Beam Support