Two Member Frame - Fixed/Pin Side Point Load

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Two Member Frame - Fixed/Pin Side Point Load formulas

\(\large{ e  \;\;=\;\; \frac{h}{L}  }\)   
\(\large{ \beta \;\;=\;\; \frac{I_h}{I_v}  }\)   
\(\large{ R_A = R_D \;\;=\;\;  \frac{3\;P\;y \; \left( h\;-\;y^2 \right) }{h\;L^2} \; \left( \frac{ \beta }{ 3\;\beta\;e \;+\; 4} \right) }\)   
\(\large{ H_A  \;\;=\;\;  \frac{P\;y}{h}  \; \left[ 1+ \; \frac{h\;-\;y}{h^2} \; \left( \frac{  3\;a\;\beta\;e \;+\; 2\; \left( h\;+\;y \right) }{ 3\;\beta\;e \;+\; 4} \right) \right] }\)  
\(\large{ H_D  \;\;=\;\;  P - H_A }\)  
\(\large{ M_A \;\;=\;\;  \frac{P\;x \; \left( h\;-\;y \right) }{h^2} \; \left( \frac{  3\;a\;\beta\;e \;+\; 2\; \left( h\;+\;y \right) }{ 3\;\beta\;e \;+\; 4} \right) }\)  
\(\large{ M_B \;\;=\;\;  H_A \; \left( h\;-\;y \right) - M_A  }\)  
\(\large{ M_C \;\;=\;\;  \frac{3\;P\;y \; \left( h\;-\;y \right)^2 }{h\;L} \; \left( \frac{ \beta }{ 3\;\beta\;e \;+\; 4} \right) }\)  

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 \(\large{lbf}\) \(\large{N}\)
\(\large{ I_h }\) = horizontal member second moment of area (moment of inertia) \(\large{in^4}\) \(\large{mm^4}\)
\(\large{ I_v }\) = vertical member second moment of area (moment of inertia) \(\large{in^4}\) \(\large{mm^4}\)
\(\large{ M }\) = maximum bending moment \(\large{lbf-in}\) \(\large{N-mm}\)
\(\large{ A, B, C, D }\) = point of intrest on frame - -
\(\large{ L }\) = span length under consideration \(\large{in}\) \(\large{mm}\)
\(\large{ P }\) = total concentrated load \(\large{lbf}\) \(\large{N}\)
\(\large{ y }\) = vertical distance from reaction to point on beam \(\large{in}\) \(\large{mm}\)
\(\large{ R }\) = 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