Two Member Frame - Pin/Pin Top Point Load
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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