Three Member Frame - Pin/Pin Side Point Load

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Three Member Frame - Pin/Pin Side Point Load formulas

\(\large{ e  = \frac{h}{L}  }\)   
\(\large{ \beta = \frac{I_h}{I_v}  }\)   
\(\large{ R_A  = R_E = \frac{ P \; \left(h\;-\;y\right) }{L}  }\)   
\(\large{ H_A =  \frac{P}{2\;h} \; \left( h+y-\; \left( h-y\right) \;  \frac{y\; \beta \; \left( 2\;h\;-\;y\right) }{h\;\left(2\;h\; \beta\;+\; 3\;L\right) }   \right) }\)  
\(\large{ H_E =  \frac{P\; \left( h\;-\;y \right) }{2\;h}  \; \left( 1+\; \frac{ y\; \beta \; \left( 2\;h\;-\;y\right) }{h\;\left( 2\;h\; \beta\;+\; 3\;L\right) } \right) }\)  
\(\large{ M_B =  \frac{P\;\left( h\;-\;y \right) }{2\;h} \;    \left( h+y- \; \left( h-y \right) \;     \frac{x\; \beta \; \left( 2\;h\;-\;y \right) }{h\; \left( 2\;h\; \beta\;+\; 3\;L \right) }   \right) }\)  
\(\large{ M_C =  \frac{P\; \left( h\;-\;y \right) }{2}  \; \left( 1-\; \frac{ y\; \beta \; \left( 2\;h\;-\;y\right) }{h\;\left( 2\;h\; \beta\;+\; 3\;L\right) } \right) }\)  
\(\large{ M_D =  \frac{P\; \left( h\;-\;y \right) }{2}  \; \left( 1+\; \frac{ y\; \beta \; \left( 2\;h\;-\;y\right) }{h\;\left( 2\;h\; \beta\;+\; 3\;L\right) } \right) }\)  

Where:

 Units English Metric
\(\large{ h }\) = 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 \(\large{lbf-in}\) \(\large{N-mm}\)
\(\large{ A, B, C, D, E }\) = point of intrest on frame - -
\(\large{ L }\) = span length under consideration \(\large{in}\) \(\large{mm}\)
\(\large{ P }\) = total concentrated load \(\large{lbf}\) \(\large{N}\)
\(\large{ y }\) = vertical distance from reaction point \(\large{in}\) \(\large{mm}\)
\(\large{ R }\) = 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