Three Span Continuous Beam - Equal Spans, Uniform Load on Two Spans to One Side

Written by Jerry Ratzlaff on . Posted in Structural

cb4s 2Aformulas that use Three Span Continuous Beam - Equal Spans, Uniform Load on Two Spans to One Side

\(\large{ R_1 = V_1  = 0.383\;w\;L    }\)   
\(\large{ R_2   = 1.200\;w\;L    }\)   
\(\large{ R_3   = 0.450\;w\;L    }\)   
\(\large{ R_4   = -\;0.033\;w\;L    }\)  
\(\large{ V_{2_1}    = 0.58\;3w\;L    }\)  
\(\large{ V_{2_2}   = 0.617\;w\;L    }\)  
\(\large{ V_{3_1} = V_4   = 0.033\;w\;L    }\)  
\(\large{ V_{3_2}  = 0.417\;w\;L    }\)  
\(\large{ M_1  \; }\) at  \(\large{  \left( x = 0.383\;L \right)  \; }\) from  \(\large{ \left( R_1 \right)  \;  = 0.0735\;w\;L^2    }\)  
\(\large{ M_2  \; }\) at  \(\large{  \left( x = 0.538\;L \right)  \; }\) from  \(\large{ \left( R_2 \right)  \;  = 0.0534\;w\;L^2    }\)  
\(\large{ M_3  \; }\)  at  \(\large{  \left( R_3 \right)   = 0.0333\;w\;L^2    }\)  
\(\large{ \Delta_{max}  \; }\) at  \(\large{  \left(  0.430\;L \right)  \; }\) from  \(\large{ \left( R_1 \right)  \;   =  \frac{0.0059\;w\;L^4}{\lambda\; I}    }\)  

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

 

Tags: Equations for Beam Support