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

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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 to One Side formulas
\( R_1 \;=\; V_1  \;=\; 0.383\;w\;L    \)  \( R_2   \;=\; 1.200\;w\;L    \)  \( R_3   \;=\; 0.450\;w\;L    \)  \( R_4   \;=\;   -\;(0.033\;w\;L)    \) \( V_{2_1}    \;=\; 0.583\;w\;L    \) \( V_{2_2}   \;=\; 0.617\;w\;L    \) \( V_{3_1} \;=\; V_4   \;=\; 0.033\;w\;L    \) \( V_{3_2}  \;=\; 0.417\;w\;L    \) \( M_1  \; ( at\; x = 0.383\;L  \; from\; R_1 )   \;=\; 0.0735\;w\;L^2    \) \( M_2  \;  ( at\; x = 0.538\;L  \; from \; R_2 )   \;=\; 0.0534\;w\;L^2    \) \( M_3  \; (at\; R_3 )   \;=\; - \;(0.0333\;w\;L^2)    \) \( \Delta_{max}  \; (at\;  0.430\;L  \;  from \; R_1 )   \;=\; (0.0059\;w\;L^4) \;/\; (\lambda\; I)    \)
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	\(in\)	\(mm\)