# Three Member Frame - Pin/Pin Side Point Load

Written by Jerry Ratzlaff on . Posted in Structural

### Three Member Frame - Pin/Pin Side Point Load Formula

$$\large{ e = \frac{h}{L} }$$

$$\large{ \beta = \frac{I_h}{I_v} }$$

$$\large{ R_A = R_E = \frac{ P \; \left(h\;-\;y\right) }{L} }$$

$$\large{ H_A = \frac{P}{2\;h} \; \left( h+y-\; \left( h-y\right) \; \frac{y\; \beta \; \left( 2\;h\;-\;y\right) }{h\;\left(2\;h\; \beta\;+\; 3\;L\right) } \right) }$$

$$\large{ H_E = \frac{P\; \left( h\;-\;y \right) }{2\;h} \; \left( 1+\; \frac{ y\; \beta \; \left( 2\;h\;-\;y\right) }{h\;\left( 2\;h\; \beta\;+\; 3\;L\right) } \right) }$$

$$\large{ M_B = \frac{P\;\left( h\;-\;y \right) }{2\;h} \; \left( h+y- \; \left( h-y \right) \; \frac{x\; \beta \; \left( 2\;h\;-\;y \right) }{h\; \left( 2\;h\; \beta\;+\; 3\;L \right) } \right) }$$

$$\large{ M_C = \frac{P\; \left( h\;-\;y \right) }{2} \; \left( 1-\; \frac{ y\; \beta \; \left( 2\;h\;-\;y\right) }{h\;\left( 2\;h\; \beta\;+\; 3\;L\right) } \right) }$$

$$\large{ M_D = \frac{P\; \left( h\;-\;y \right) }{2} \; \left( 1+\; \frac{ y\; \beta \; \left( 2\;h\;-\;y\right) }{h\;\left( 2\;h\; \beta\;+\; 3\;L\right) } \right) }$$

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

$$\large{ y }$$ = vertical distance from reaction point