Two Span Continuous Beam - Equal Spans, Concentrated Load at Center of One Span

• 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, Concentrated Load at Center of One Span formulas
\( R_1 \;=\; V_1 \;=\; 13\;P\;/\;32   \)  \( R_2 \;=\; V_2 + V_3  \;=\; 11\;P\;/\;16   \)  \( R_3 \;=\; V_3  \;=\; 3\;P\;/\;32   \) \( V_2  \;=\; 19\;P\;/\;32   \) \( M_{max} \; (at \;point \;of \;load )  \;=\; 13\;P\;L\;/\;64   \) \( M_{max}  \; (at \;support \; R_2 )  \;=\; 3\;P\;L\;/\;32  \) \( \Delta_{max}  \; ( 0.408\;L \; from \;R_1)  \;=\; 0.015 \; (P\;L^3\;/\; \lambda \; I ) \)
Symbol	English	Metric
\( \Delta \) = deflection or deformation	\(in\)	\(mm\)
\( M \) = maximum bending moment	\(lbf-in\)	\(N-mm\)
\( V \) = maximum shear force	\(lbf\)	\(N\)
\( \lambda  \)   (Greek symbol lambda) = modulus of elasticity	\(lbf\;/\;in^2\)	\(Pa\)
\( I \) = second moment of area (moment of inertia)	\(in^4\)	\(mm^4\)
\( R \) = reaction load at bearing point	\(lbf\)	\(N\)
\( L \) = span length under consideration	\(in\)	\(mm\)
\( P \) = total concentrated load	\(lbf\)	\(N\)