Four Span Continuous Beam - Equal Spans, Uniformly Distributed Load

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Four Span Continuous Beam - Equal Spans, Uniformly Distributed Load formulas

\(\large{ R_1 = V_1 = R_5 = V_5    \;\;=\;\; 0.393\;w\;L    }\) 

\(\large{ R_2 = R_4   \;\;=\;\; 1.143\;w\;L    }\) 

\(\large{ R_3  \;\;=\;\; 0.928\;w\;L    }\) 

\(\large{ V_{2_1} =  V_{4_2}    \;\;=\;\; 0.607\;w\;L    }\)

\(\large{ V_{2_2} =  V_{4_1}    \;\;=\;\; 0.536\;w\;L    }\)

\(\large{ V_{3_1} =  V_{3_2}    \;\;=\;\; 0.464\;w\;L    }\)

\(\large{ M_1  \;  \left(at\; 0.393\;L \; from \;  R_1 \right) = M_7 \; \left(at\; 0.393\;L  \; from \; R_5 \right)   \;\;=\;\; 0.0772\;w\;L^2    }\)

\(\large{ M_2 \; \left(at\; R_2 \right)   \;\;=\;\; -\; 0.1071\;w\;L^2    }\)

\(\large{ M_3  \;  \left(at\; 0.536\;L \; from \;  R_2 \right) = M_5 \; \left(at\; 0.536\;L  \; from \; R_4 \right)   \;\;=\;\; 0.0364\;w\;L^2    }\)

\(\large{ M_4 \;  \left(at\; R_3 \right)   \;\;=\;\; -\; 0.0714\;w\;L^2    }\)

\(\large{ \Delta_{max}  \;  \left(at\;  0.440\;L  \; from \; R_1  \;  and \; R_5 \right)    \;\;=\;\;  \frac{0.0065\;w\;L^4}{\lambda\; I}    }\)

Symbol English Metric
\(\large{ \Delta }\) = deflection or deformation \(\large{in}\) \(\large{mm}\)
\(\large{ w }\) = load per unit length \(\large{\frac{lbf}{in}}\) \(\large{\frac{N}{m}}\)
\(\large{ M }\) = maximum bending moment \(\large{lbf-in}\) \(\large{N-mm}\)
\(\large{ V }\) = maximum shear force \(\large{lbf}\) \(\large{N}\)
\(\large{ \lambda  }\)   (Greek symbol lambda) = modulus of elasticity \(\large{\frac{lbf}{in^2}}\) \(\large{Pa}\)
\(\large{ R }\) = reaction load at bearing point \(\large{lbf}\) \(\large{N}\)
\(\large{ I }\) = second moment of area (moment of inertia) \(\large{in^4}\) \(\large{mm^4}\)
\(\large{ L }\) = span length under consideration \(\large{in}\) \(\large{mm}\)

 

diagrams

  • 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.

 

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Tags: Beam Support