Two Span Continuous Beam - Equal Spans, Concentrated Load at Center of One Span

Written by Jerry Ratzlaff on . Posted in Structural

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Two Span Continuous Beam - Equal Spans, Concentrated Load at Center of One Span formulas

\(\large{ R_1 = V_1   = \frac{13\;P}{32}    }\)   
\(\large{ R_2 = V_2 + V_3   = \frac{11\;P}{16}    }\)   
\(\large{ R_3 = V_3   = \frac{3\;P}{32}    }\)   
\(\large{ V_2   = \frac{19\;P}{32}    }\)  
\(\large{ M_{max}  \; }\) (at point of load)   \(\large{  = \frac{13\;P\;L}{64}    }\)  
\(\large{ M_{max}  \; }\)  at support   \(\large{  \left( R_2 \right)  = \frac{3\;P\;L}{32}    }\)  
\(\large{ \Delta_{max}  \;   \left( 0.408\;L \right)    }\)  from  \(\large{  \left( R_1 \right)  = 0.015 \; \frac{P\;L^3}{\lambda \; I}    }\)  

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