Three Span Continuous Beam - Equal Spans, Uniform Load on Two Spans at Each End

Written by Jerry Ratzlaff on . Posted in Structural

cb4s 3AThree Span Continuous Beam - Equal Spans, Uniform Load on Two Spans at Each End Formula

\(\large{ R_1 = V_1 = R_4 = V_4  = 0.450wL    }\)

\(\large{ R_2 = V_2 = R_3 = V_3  = 0.550wL    }\)

\(\large{ M_1 = M_3  \; }\) at  \(\large{  \left( x = 0.450L \right)  \; }\) from \(\large{ \left( R_1 \right)  \; }\) or  \(\large{ \left( R_2 \right)  \;  = 0.1013wL^2   }\)

\(\large{ M_2  \; }\) (at mid span)  \(\large{  \;  = -0.050wL    }\)

\(\large{ \Delta_{max}  \; }\) at  \(\large{  \left(  0.479L \right)  \; }\) from  \(\large{ \left( R_1 \right)  \; }\) or  \(\large{ \left( R_4 \right)  \;   =  \frac{0.0099wL^4}{\lambda I}    }\)

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