Two Member Frame - Pin/Pin Top Point Load

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Two Member Frame - Pin/Pin Top Point Load Formula

Needed Values

\(\large{ e  = \frac{h}{L}  }\)
\(\large{ \beta = \frac{I_h}{I_v}  }\)

Support Reaction

\(\large{ R_A  =  \frac{ P\;x \; \left( L^2 \; \left(2\; \beta\;e \;+\; 3 \right) \;-\; x^2 \right)  }{ 2\;L^2 \left( \beta\;e \;+\; 1 \right) }   }\)
\(\large{ R_D  =  P - R_A   }\)
\(\large{ H_A  = H_D = \frac{ P\;x \; \left( L^2 \;-\; x^2 \right)  }{ 2\;h\;L^2 \; \left( \beta\;e \;+\; 1 \right) }   }\)

Bending Moment

\(\large{ M_B  = \frac{ P\;x \; \left( L^2 \;-\; x^2 \right)  }{ 2\;L^2 \; \left( \beta\;e \;+\; 1 \right) }   }\)
\(\large{ M_D  = \frac{  x \; \left( P \; \left( L \;-\; x \right) \;-\; M_C \right)  }{ L }   }\)

Where:

 Units English Metric
\(\large{ h }\) = height of frame \(\large{in}\) \(\large{mm}\)
\(\large{ x }\) =  horizontal distance from reaction point \(\large{in}\)  \(\large{mm}\) 
\(\large{ H }\) = 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 - -
\(\large{ R }\) = vertical reaction load at bearing point  \(\large{lbf}\) \(\large{N}\) 
\(\large{ L }\) = span length of the bending member \(\large{in}\) \(\large{mm}\)
\(\large{ P }\) = total concentrated load \(\large{lbf}\) \(\large{N}\)

 

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