Three Member Frame - Pin/Roller Center Point Load

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Three Member Frame - Pin/Roller Center Point Load formulas

\(\large{ R_A = R_E  =  \frac{ P }{ 2 }   }\)   
\(\large{ H_A =  0   }\)   
\(\large{ M_{max} \;(at \; C)  =  \frac{ PL }{ 4 }   }\)   
\(\large{ \Delta_{Ex}  =  \frac{P\;h\;L^2}{8\; \lambda \;I}  }\)  

Where:

 Units English Metric
\(\large{ \Delta }\) = deflection or deformation \(\large{in}\) \(\large{mm}\)
\(\large{ h }\) = height of frame \(\large{in}\) \(\large{mm}\)
\(\large{ H }\) = horizontal reaction load at bearing point \(\large{lbf}\) \(\large{N}\)
\(\large{ M }\) = maximum bending moment \(\large{lbf-in}\) \(\large{N-mm}\)
\(\large{ A, B, C, D, E }\) = point of intrest on frame - -
\(\large{ L }\) = span length under consideration \(\large{in}\) \(\large{mm}\)
\(\large{ P }\) = total concentrated load \(\large{lbf}\) \(\large{N}\)
\(\large{ R }\) = vertical reaction load at bearing point \(\large{lbf}\) \(\large{N}\)

 

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: Frame Support