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

Written by Jerry Ratzlaff on . Posted in Structural

cb3s 2ATwo Span Continuous Beam - Equal Spans, Uniform Load on One Span Formula

\(\large{ R_1 = V_1   = \frac{7wL}{16}    }\)

\(\large{ R_2 = v_2 + V_3   = \frac{5wL}{8}    }\)

\(\large{ R_3 = V_3   = \frac{wL}{16}    }\)

\(\large{ V_2   = \frac{9wL}{16}    }\)

\(\large{ M_{max} \; }\) at  \(\large{  \left( x = \frac{7L}{16} \right)    = \frac{49wL^2}{512}    }\)

\(\large{ M_1 \; }\) at support  \(\large{  \left( R_2 \right)    = \frac{wL^2}{16}    }\)

\(\large{ M_x \;  \left( x < L \right)    = \frac{wx}{16}  \left( 7L - 8x \right)  }\)

\(\large{ \Delta_{max} \; \left( 0.472L \right)  }\)  from  \(\large{  \left( R_1 \right)  = 0.0092  \frac{wL^4}{ \lambda I}    }\)

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