Three Span Continuous Beam - Equal Spans, Uniformly Distributed Load

Written by Jerry Ratzlaff on . Posted in Structural

Three Span Continuous Beam - Equal Spans, Uniformly Distributed Loadcb4s 1A

Equal Spans, Uniformly Distributed Load Formula

\(\large{ R_1 = V_1 = R_4 = V_4    = 0.400wL    }\)

\(\large{ R_2 = R_3   = 1.100wL    }\)

\(\large{ V_{2_1} =  V_{3_2}    = 0.500wL    }\)

\(\large{ V_{2_2} =  V_{3_1}    = 0.600wL    }\)

\(\large{ M_1 =  M_5 \; }\) at  \(\large{  \left( 0.400L \right)  \; }\) from  \(\large{ \left( R_1 \right)  \; }\)  or   \(\large{  \left( R_4 \right)    = 0.080wL^2    }\)

\(\large{ M_2 =  M_4 \; }\) at   \(\large{ \left( R_2 \right)  \; }\)  or   \(\large{  \left( R_3 \right)    = 0.100wL^2    }\)

\(\large{ M_3  \; }\)  (at mid center Span)  \(\large{  = 0.025wL^2    }\)

\(\large{ \Delta_{max}  \; }\) at  \(\large{  \left(  0.446L \right)  \; }\) from  \(\large{ \left( R_1 \right)  \; }\)  or   \(\large{  \left( R_4 \right)    =  \frac{0.0069wL^4}{\lambda I}    }\)

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