Four Span Continuous Beam - Equal Spans, Uniform Load on Three 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 Three Spans formulas

\( R_1 \;=\; V_1   \;=\; 0.380\;w\;L    \) 

\( R_2  \;=\; 1.223\;w\;L    \) 

\( R_3  \;=\; 0.357\;w\;L    \) 

\( R_4  \;=\; 0.598\;w\;L    \)

\( R_5 \;=\; V_5   \;=\; 0.442\;w\;L    \)

\( V_{2_1}   \;=\; 0.620\;w\;L    \)

\( V_{2_2}   \;=\; 0.603\;w\;L    \)

\(V_{3_1}   \;=\; 0.397\;w\;L    \)

\( V_{3_2} \;=\; V_{4_1}    \;=\; 0.040\;w\;L    \)

\( V_{4_2}  \;=\; 0.558\;w\;L    \)

\( M_1  \; ( 0.380\;L  \; from \; R_1 ) \;=\; 0.072\;w\;L^2   \)

\( M_2  \; (at\; R_2 )   \;=\; -\; (0.1205\;w\;L^2)    \)

\(vM_3  \;  ( 0.603\;L  \;  from \;  R_2 ) \;=\; 0.611\;w\;L^2   \)

\( M_4  \; (at\; R_3 )   \;=\; - \; (0.0179\;w\;L^2)    \)

\( M_5  \; (at\; R_4 )    \;=\; - \; (0.058\;w\;L^2)    \)

\( M_6  \;   ( 0.442\;L  \; from \;  R_5 ) \;=\; 0.0977\;w\;L^2   \)

\( \Delta_{max}  \; ( at\; 0.475\;L  \; from \; R_5 )   \;=\; (0.0094\;w\;L^4) \;/\; (\lambda\; I)   \)

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