Two Member Frame - Pin/Pin Top Point Load

Written by Jerry Ratzlaff on . Posted in Structural

2fpbe 1Two Member Frame - Pin/Pin Top Point Load Formula

\(\large{ e  = \frac{h}{L}  }\)

\(\large{ \beta = \frac{I_h}{I_v}  }\)

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

\(\large{ R_D  =  P - R_A   }\)

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

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

\(\large{ M_D  = \frac{  x \; \left( P \; \left( L \;-\; x \right) \;-\; M_C \right)  }{ L }   }\)

Where:

\(\large{ h }\) = height of frame

\(\large{ x }\) =  horizontal distance from reaction point

\(\large{ H }\) =  horizontal reaction load at bearing point

\(\large{ M }\) = maximum bending moment

\(\large{ A, B, C, D }\) = points of intersection on frame

\(\large{ R }\) = reaction load at bearing point

\(\large{ L }\) = span length of the bending member

\(\large{ P }\) = total concentrated load

 

Tags: Equations for Frame Support