# Three Member Frame - Fixed/Fixed Center Point Load

Written by Jerry Ratzlaff on . Posted in Structural

## Three Member Frame - Fixed/Fixed Center Point Load formulas

 $$\large{ e = \frac{h}{L} }$$ $$\large{ \beta = \frac{I_h}{I_v} }$$ $$\large{ R_A = R_E = \frac{ P }{ 2 } }$$ $$\large{ H_A = H_E = \frac{3\;P\;L}{8\;h\; \left( \beta\;e\;+\;2 \right) } }$$ $$\large{ M_A = M_E = \frac{P\;L}{8\; \left( \beta\;e\;+\;2 \right) } }$$ $$\large{ M_B = M_D = \frac{P\;L}{4\; \left( \beta\;e\;+\;2 \right) } }$$ $$\large{ M_C = \frac{P\;L}{4} \; \left( \frac{ \beta\;e\;+\;1 }{ \beta\;e\;+\;2 } \right) }$$

### Where:

$$\large{ h }$$ = height of frame

$$\large{ H }$$ =  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