Two Member Frame - Pin/Pin Top Point Load

Written by Jerry Ratzlaff on 03 September 2019. Posted in Structural

\(\large{ e = \frac{h}{L} }\)

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

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

\(\large{ R_D = P - R_A }\)

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

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

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

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