Two Span Continuous Beam - Unequal Spans, Concentrated Load on Each Span Symmetrically Placed

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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 - Unequal Spans, Concentrated Load on Each Span Symmetrically Placed formulas
\( R_1 \;=\; V_1   \;=\;  (M_2\;/\;a)  +  (P_1\;/\;2)   \)  \( R_2   \;=\; P_1 + P_2 - R_1 - R_3   \)  \( R_3 \;=\; V_4   \;=\; (M_2\;/\;b)  +  (P_2\;/\;2)   \)  \( M_1   \;=\; R_1 \; (a\;/\;2)   \) \( M_2   \;=\; [\; -\; (3\;/\;16)\;]  \;  ( P_1\; a^2 \;+ \;P_2 \; b^2\;/\;a \;+\; b )  \) \( M_3   \;=\; R_3\; (b\;/\;2)   \)
Symbol	English	Metric
\( M \) = maximum bending moment	\(lbf-in\)	\(N-mm\)
\( V \) = maximum shear force	\(lbf\)	\(N\)
\( R \) = reaction load at bearing point	\(lbf\)	\(N\)
\( a, b \) = span length under consideration	\(in\)	\(mm\)
\( P \) = total consideration load	\(lbf\)	\(N\)