# Two Member Frame - Fixed/Pin Side Point Load

Written by Jerry Ratzlaff on . Posted in Structural

## Two Member Frame - Fixed/Pin Side Point Load formulas

 $$\large{ e = \frac{h}{L} }$$ $$\large{ \beta = \frac{I_h}{I_v} }$$ $$\large{ R_A = R_D = \frac{3\;P\;y \; \left( h\;-\;y^2 \right) }{h\;L^2} \; \left( \frac{ \beta }{ 3\;\beta\;e \;+\; 4} \right) }$$ $$\large{ H_A = \frac{P\;y}{h} \; \left[ 1+ \; \frac{h\;-\;y}{h^2} \; \left( \frac{ 3\;x\;\beta\;e \;+\; 2\; \left( h\;+\;y \right) }{ 3\;\beta\;e \;+\; 4} \right) \right] }$$ $$\large{ H_D = P - H_A }$$ $$\large{ M_A = \frac{P\;x \; \left( h\;-\;y \right) }{h^2} \; \left( \frac{ 3\;x\;\beta\;e \;+\; 2\; \left( h\;+\;y \right) }{ 3\;\beta\;e \;+\; 4} \right) }$$ $$\large{ M_B = H_A \; \left( h\;-\;y \right) - M_A }$$ $$\large{ M_C = \frac{3\;P\;y \; \left( h\;-\;y \right)^2 }{h\;L} \; \left( \frac{ \beta }{ 3\;\beta\;e \;+\; 4} \right) }$$

### 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

$$\large{ A, B, C, D }$$ = 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 to reaction point