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

Written by Jerry Ratzlaff on . Posted in Structural

cb3s 2Aformulas that use Two Span Continuous Beam - Equal Spans, Uniform Load on One Span

\(\large{ R_1 = V_1   = \frac{7\;w\;L}{16}    }\)   
\(\large{ R_2 = v_2 + V_3   = \frac{5\;w\;L}{8}    }\)   
\(\large{ R_3 = V_3   = \frac{w\;L}{16}    }\)   
\(\large{ V_2   = \frac{9\;w\;L}{16}    }\)  
\(\large{ M_{max} \; }\) at  \(\large{  \left( x = \frac{7\;L}{16} \right)    = \frac{49\;w\;L^2}{512}    }\)  
\(\large{ M_1 \; }\) at support  \(\large{  \left( R_2 \right)    = \frac{w\;L^2}{16}    }\)  
\(\large{ M_x \;  \left( x < L \right)    = \frac{w\;x}{16} \; \left( 7\;L - 8\;x \right)  }\)  
\(\large{ \Delta_{max} \; \left( 0.472 \; L \right)  }\)  from  \(\large{  \left( R_1 \right)  = 0.0092 \; \frac{w\;L^4}{ \lambda\; I}    }\)  

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