Two Span Continuous Beam - Equal Spans, Concentrated Load at Any Point

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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.

 

 

 

 

Two Span Continuous Beam - Equal Spans, Two Equal Concentrated Loads Symmetrically Placed  formulas
\( R_1 \;=\; V_1  \;=\; (P\;b\;/\;4\;L^3) \; [\; 4\;L^2 - a \; ( L + a ) \;]  \)  \( R_2   \;=\; (P\;a\;/\;2\;L^3) \; [\; 2\;L^2 + b \; ( L + a ) \;]  \)  \( R_3 \;=\; V_3   \;=\;  [\; -\; (P\;a\;b\;/\;4\;L^3 )\;] \; ( L + a )    \)  \( V_2   \;=\; (P\;a\;/\;4\;L^3) \; [\; 4\;L^2 + b \; ( L + a ) \;]  \) \( M_1  \; \left(at\; support\; R_2  \right)  \;=\; (P\;a\;b\;/\;4\;L^2)  \; ( L + a )   \) \( M_{max}   \;=\; (P\;a\;b\;/\;4\;L^3)  \; [\; 4\;L^2 - a \; ( L + a ) \;]  \)
Symbol	English	Metric
\( a, b \) = horizontal distance to point load	\(in\)	\(mm\)
\( M \) = maximum bending moment	\(lbf-in\)	\(N-mm\)
\( V \) = maximum shear force	\(lbf\)	\(N\)
\( R \) = reaction load at bearing point	\(lbf\)	\(N\)
\( L \) = span length under consideration	\(in\)	\(mm\)
\( P \) = total consideration load	\(lbf\)	\(N\)