Two Span Continuous Beam - Equal Spans, Uniformly Distributed Load

Written by Jerry Ratzlaff on . Posted in Structural

cb3s 1ATwo Span Continuous Beam - Equal Spans, Uniformly Distributed Load Formula

\(\large{ R_1 = V_1 = R_3 = V_3    = \frac{3wL}{8}    }\)

\(\large{ R_2    = \frac{10wL}{8}    }\)

\(\large{ V_2 = V_{max}   = \frac{5wL}{8}    }\)

\(\large{ M_1   = \frac{wL^2}{8}    }\)

\(\large{ M_2 \; }\) at  \(\large{  \left(  \frac{3L}{8} \right)    = \frac{9wL^2}{128}    }\)

\(\large{ \Delta_{max} \;\; \left( 0.4215L \right)  }\)  from  \(\large{  \left( R_1,  R_3 \right)  =  \frac{wL^4}{185 \lambda I}    }\)

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