Two Span Continuous Beam - Unequal Spans, Uniformly Distributed Load

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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.

 

 

 

 

Span Continuous Beam - Unequal Spans, Uniformly Distributed Load formulas
\( R_1 \;=\; V_1   \;=\; (M_1\;/\;a) + (w\;a\;/\;2)   \)  \( R_2   \;=\; w\;a + w\;b - R_1 - R_3    \)  \( R_3 \;=\; V_4   \;=\; (M_1\;/\;b) + (w\;a\;/\;2)   \)  \(V_2   \;=\; w\;a - R_1  \) \( V_3   \;=\; w\;b - R_3  \) \( M_1  \;=\; (w\;b^3 + w\;a^3) \;/\;[\;8 \; ( a+b ) \;]   \) \( M_1  \;=\; (w\;b^3 + w\;a^3)  \;/\; [\;8 \; ( a+ b) \;]   \) \( M_{x_2} \; ( x_2 = \frac{R_3}{w} )   \;=\; R_3 \;x_2  - (w\;x_2^2 \;/\; 2)   \)
Symbol	English	Metric
\( \Delta \) = deflection or deformation	\(in\)	\(mm\)
\( x \) = horizontal distance from reaction to point on beam	\(in\)	\(mm\)
\( w \) = load per unit length	\(lbf\;/\;in\)	\(N\;/\;m\)
\( M \) = 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	\(in\)	\(mm\)