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

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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.

 

Four Span Continuous Beam - Equal Spans, Uniform Load on Two Spans formula

\( R_1 \;=\; V_1   \;=\; 0.446\;w\;L    \) 

\( R_2  \;=\; 0.572\;w\;L    \) 

\( R_3  \;=\; 0.464\;w\;L    \) 

\( R_4  \;=\; 0.572\;w\;L    \)

\( R_5  \;=\; - \;0.054\;w\;L    \)

\( V_{2_1}   \;=\; 0.0554\;w\;L    \)

\( V_{2_2} \;=\; V_{3_1}  \;=\; 0.018\;w\;L    \)

\( V_{3_2}   \;=\; 0.482\;w\;L    \)

\( V_{4_1}   \;=\; 0.518\;w\;L    \)

\( V_{4_2} \;=\; V_5  \;=\; 0.054\;w\;L    \)

\( M_1  \;   \left( 0.446\;L  \;  from  \; R_1 \right) \;=\; 0.0996\;w\;L^2   \)

\( M_2  \;  \left(at\; R_2 \right)   \;=\; -\; (0.0536\;w\;L^2 )   \)

\( M_3  \; \left(at\; R_3 \right)    \;=\; - \; (0.0357\;w\;L^2 )   \)

\( M_4  \;   \left( 0.518\;L  \; from \; R_4 \right) \;=\; 0.805\;w\;L^2   \)

\( M_5  \; \left(at\; R_4 \right)  \;   \;=\; -\; (0.0536\;w\;L^2)    \)

\( \Delta_{max}  \;  \left(at\;  0.477\;L  \;  from \; R_1 \right)    \;=\; (0.0097\;w\;L^4) \;/\; (\lambda\; I)    \)

Symbol English Metric
\( \Delta \) = deflection or deformation \(in\) \(mm\)
\( w \) = 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 \(lbf\;/\;in^2\) \(Pa\)
\( R \) = reaction load at bearing point \(lbf\) \(N\)
\( I \) = second moment of area (moment of inertia) \(in^4\) \(mm^4\)
\( L \) = span length under consideration \(in\) \(mm\)

 

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Tags: Beam Support