Two Span Continuous Beam - Equal Spans, Two Equal Concentrated Loads Symmetrically Placed

Written by Jerry Ratzlaff on . Posted in Structural

cb3s 5Aformulas that use Two Span Continuous Beam - Equal Spans, Two Equal Concentrated Loads Symmetrically Placed

\(\large{ R_1 = V_1 = R_3 = V_3   = \frac{5\;P}{16}    }\)  
\(\large{ R_2 = 2V_2  = \frac{11\;P}{8}    }\)   
\(\large{ V_2 = P - R_1   = \frac{11\;P}{16}    }\)   
\(\large{ V_{max}   = V_2   }\)  
\(\large{ M_1  = \frac{3\;P\;L}{16}    }\)  
\(\large{ M_2  = \frac{5\;P\;L}{32}    }\)  
\(\large{ M_x  \;   \left( x < \frac{L}{2}  \right)   =  R_1\; x    }\)  

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