Two Span Continuous Beam - Equal Spans, Uniform Load on 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 are

 

 

 

 

Two Span Continuous Beam - Equal Spans, Uniform Load on One Span formulas

\( R_1 \;=\; V_1  \;=\; 7\;w\;L\;/\;16   \) 

\( R_2 \;=\; V_2 + V_3   \;=\; 5\;w\;L\;/\;8   \) 

\( R_3 \;=\; V_3   \;=\; w\;L\;/\;16   \) 

\( V_2   \;=\; 9\;w\;L\;/\;16   \)

\( M_{max} \; (at\; x = \frac{7\;L}{16} )  \;=\; 49\;w\;L^2\;/\;512    \)

\( M_1 \; \left(at \;support\; R_2 \right)  \;=\; w\;L^2\;/\;16   \)

\( M_x \;  \left( x < L \right)  \;=\; (w\;x\;/\;16) \; ( 7\;L - 8\;x )  \)

\( \Delta_{max} \; ( 0.472 \; L \; from\;R_1 )  \;=\; 0.0092 \; (w\;L^4\;/\; \lambda\; I ) \)

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 \(lbf\) \(N\)
\( \lambda  \)   (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 \(in\) \(mm\)

 

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Tags: Beam Support