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

Written by Jerry Ratzlaff on . Posted in Structural

Three Span Continuous Beam - Equal Spans, Uniform Load on Two Spans to One Sidecb4s 2A

Equal Spans, Uniform Load on Two Spans to One Side Formula

\(\large{ R_1 = V_1  = 0.383wL    }\)

\(\large{ R_2   = 1.200wL    }\)

\(\large{ R_3   = 0.450wL    }\)

\(\large{ R_4   = -0.033wL    }\)

\(\large{ V_{2_1}    = 0.583wL    }\)

\(\large{ V_{2_2}   = 0.617wL    }\)

\(\large{ V_{3_1} = V_4   = 0.033wL    }\)

\(\large{ V_{3_2}  = 0.417wL    }\)

\(\large{ M_1  \; }\) at  \(\large{  \left( x = 0.383L \right)  \; }\) from  \(\large{ \left( R_1 \right)  \;  = 0.0735wL^2    }\)

\(\large{ M_2  \; }\) at  \(\large{  \left( x = 0.538L \right)  \; }\) from  \(\large{ \left( R_2 \right)  \;  = 0.0534wL^2    }\)

\(\large{ M_3  \; }\)  at  \(\large{  \left( R_3 \right)   = 0.0333wL^2    }\)

\(\large{ \Delta_{max}  \; }\) at  \(\large{  \left(  0.430L \right)  \; }\) from  \(\large{ \left( R_1 \right)  \;   =  \frac{0.0059wL^4}{\lambda I}    }\)

 

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