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Two Member Frame - Pin/Pin Top Point Load

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Two Member Frame - Pin/Pin Top Point Load formulas

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

Where:

 Units English SI
\(\large{ FB }\) = free body - -
\(\large{ BM }\) = bending moment - -
\(\large{ h }\) = 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 \(\large{lbf-ft}\) \(\large{N-m}\)
\(\large{ A, B, C, D }\) = point of intrest on frame - -
\(\large{ L }\) = span length under consideration \(\large{in}\) \(\large{mm}\)
\(\large{ P }\) = total consideration load \(\large{lbf}\) \(\large{N}\)
\(\large{ R }\) = vertical reaction load at bearing point \(\large{lbf}\) \(\large{N}\)