Two Member Frame - Pin/Pin Top Point Load

Written by Jerry Ratzlaff on . Posted in Structural

Two 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