# Three Member Frame - Pin/Pin Top Point Load

Written by Jerry Ratzlaff on . Posted in Structural

## formulas that use Three Member Frame - Pin/Pin Top Point Load

 $$\large{ e = \frac{h}{L} }$$ $$\large{ \beta = \frac{I_h}{I_v} }$$ $$\large{ R_A = P\; \frac{L\;-\;x}{L} }$$ $$\large{ R_E = P\; \frac{x}{L} }$$ $$\large{ H_A = H_E = \frac{3\;P\;x}{2\;h\;L} \; \left( \frac{L\;-\;x}{2\; \beta\;e \;+\; 3} \right) }$$ $$\large{ M_B = M_D = \frac{3\;P\;x}{2\;L} \; \left( \frac{L\;-\;x}{2\; \beta\;e \;+\; 3} \right) }$$ $$\large{ M_C = \frac{P\;x \; \left( L\;-\;x \right) }{2\;L} \; \left( \frac{4\; \beta\;e \;+\; 3}{2\; \beta\;e \;+\; 3} \right) }$$

### 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

$$\large{ A, B, C, D, E }$$ = points of intersection on frame

$$\large{ R }$$ = reaction load at bearing point

$$\large{ I }$$ = second moment of area (moment of inertia)

$$\large{ I_h }$$ = horizontal second moment of area (moment of inertia)

$$\large{ I_v }$$ = vertical second moment of area (moment of inertia)

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

$$\large{ P }$$ = total concentrated load