# Two Member Frame - Pin/Pin Top Point Load

on . Posted in Structural Engineering

## Two Member Frame - Pin/Pin Top Point Load formulas

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

### Where:

 Units English SI $$\large{ FB }$$ = free body - - $$\large{ BM }$$ = bending moment - - $$\large{ h }$$ = height of frame $$\large{in}$$ $$\large{mm}$$ $$\large{ x }$$ = horizontal distance from reaction point $$\large{in}$$ $$\large{mm}$$ $$\large{ H }$$ = horizontal reaction load at bearing point $$\large{lbf}$$ $$\large{N}$$ $$\large{ I_h }$$ = horizontal member second moment of area (moment of inertia) $$\large{in^4}$$ $$\large{mm^4}$$ $$\large{ I_v }$$ = vertical member second moment of area (moment of inertia) $$\large{in^4}$$ $$\large{mm^4}$$ $$\large{ M }$$ = maximum bending moment $$\large{lbf-ft}$$ $$\large{N-m}$$ $$\large{ A, B, C, D }$$ = point of intrest on frame - - $$\large{ L }$$ = span length under consideration $$\large{in}$$ $$\large{mm}$$ $$\large{ P }$$ = total consideration load $$\large{lbf}$$ $$\large{N}$$ $$\large{ R }$$ = vertical reaction load at bearing point $$\large{lbf}$$ $$\large{N}$$

Tags: Frame Support