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

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

 

diagrams

• 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.