Two Span Continuous Beam - Unequal Spans, Uniformly Distributed Load

Written by Jerry Ratzlaff on . Posted in Structural

cb3s 3Aformulas that use Two Span Continuous Beam - Unequal Spans, Uniformly Distributed Load

\(\large{ R_1 = V_1   = \frac{M_1}{a} + \frac{w\;a}{2}   }\)   
\(\large{ R_2   =  w\;a + w\;b - R_1 - R_3    }\)   
\(\large{ R_3 = V_4   = \frac{M_1}{b} + \frac{w\;a}{2}   }\)   
\(\large{ V_2   =  w\;a - R_1  }\)  
\(\large{ V_3   =  w\;b - R_3  }\)  
\(\large{ M_1  = \frac{w\;b^3 \;+\; w\;a^3}{8 \; \left( a\;+ \;b \right) }   }\)  
\(\large{ M_{x_1} \;  \left( x_1 = \frac{R_1}{w} \right)   =  R_1\; x_1 \; \frac{w\;x_{1}{^2} }{2}    }\)  
\(\large{ M_{x_2} \;  \left( x_2 = \frac{R_2}{w} \right)   =  R_3 \;x_2 \; \frac{w\;x_{2}{^2} }{2}    }\)  

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