Three Span Continuous Beam - Equal Spans, Uniform Load on Two Spans at Each End

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• Tags: Beam Support

diagram Symbols

• Bending moment diagram (BMD)  -  Used to determine the bending moment at a given point of a structural element.  The diagram can help determine the type, size, and material of a member in a structure so that a given set of loads can be supported without structural failure.
• Free body diagram (FBD)  -  Used to visualize the applied forces, moments, and resulting reactions on a structure in a given condition.
• Shear force diagram (SFD)  -  Used to determine the shear force at a given point of a structural element.  The diagram can help determine the type, size, and material of a member in a structure so that a given set of loads can be supported without structural failure.
• Uniformly distributed load (UDL)  -  A load that is distributed evenly across the entire length of the support area.

 

 

three Span Continuous Beam - Equal Spans, Uniform Load on Two Spans at Each End formulas
\( R_1 \;=\; V_1 \;=\; R_4 \;=\; V_4  \;=\; 0.450\;w\;L    \)  \( R_2 \;=\; V_2 \;=\; R_3 \;=\; V_3  \;=\; 0.550\;w\;L    \)  \( M_1 \;=\; M_3 \; (at\; x = 0.450\;L  \;  from \; R_1 \; or \; R_2 ) \; \;=\; 0.1013\;w\;L^2   \)  \( M_2 \; (at\;mid \;span ) \;=\; -\;(0.050\;w\;L)    \) \( \Delta_{max} \; ( at\; 0.479\;L \; from \; R_1  \;  or \; R_4 ) \;=\; (0.0099\;w\;L^4) \;/\; (\lambda \;I)    \)
Symbol	English	Metric
\( FB \) = free body	\(lbf\)	\(N\)
\( SF \) = shear force	\(lbf\;/\;in^2\)	\(Pa\)
\( BM \) = bending moment	\(lbf\;/\;sec\)	\(kg-m\;/\;s\)
\( UDL \) = uniformly distributed load	\(lbf\)	\(N\)
\( \Delta \) = deflection or deformation	\(in\)	\(mm\)
\( w \) = load per unit length	\(lbf\;/\;in\)	\(N\;/\;m\)
\( M \) = maximum bending moment	\(lbf-ft\)	\(N-m\)
\( V \) = maximum shear force	\(lbf\)	\(N\)
\( \lambda  \)   (Greek symbol lambda) = modulus of elasticity	\(lbf\;/\;in^2\)	\(Pa\)
\( I \) = second moment of area (moment of inertia)	\(in^4\)	\(mm^4\)
\( R \) = reaction load at bearing point	\(lbf\)	\(N\)
\( L \) = span length under consideration	\(in\)	\(mm\)