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

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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 - 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 \(lbf\) \(N\)

 

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Tags: Beam Support