Two Span Continuous Beam - Equal Spans, Two Equal Concentrated Loads Symmetrically Placed

• See Article Link  -  Beam Design Formulas
• Tags: Beam Support

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
\( R_1 \;=\; V_1 \;=\; R_3 \;=\; V_3   \;=\; 5\;P\;/\;16 \) \( R_2 \;=\; 2V_2  \;=\; 11\;P\;/\;8 \)  \( V_2 \;=\; P - R_1   \;=\; 11\;P\;/\;16 \)  \( V_{max}   \;=\; V_2  \) \( M_1  \;=\; - \;(3\;P\;L\;/\;16) \) \( M_2  \;=\; 5\;P\;L\;/\;32 \) \( M_x  \; ( x < \frac{L}{2} )  \;=\; R_1\; x  \)
Symbol	English	Metric
\( x \) = horizontal distance from reaction to point on beam	\(in\)	\(mm\)
\( M \) = 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	\(lbf\)	\(N\)