Two Member Frame - Fixed/Fixed Top Point Load
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two Member Frame - Fixed/Fixed Top Point Load formulas
| \(\large{ e \;\;=\;\; \frac{h}{L} }\) |
| \(\large{ \beta \;\;=\;\; \frac{I_h}{I_v} }\) |
| \(\large{ R_A \;\;=\;\; \frac{P\;x^2}{2\;L^3 \; \left( \beta \; e \;+\; 1 \right) } \; \left[ \beta \; e \; \left( 3 \; L - x \right) + 2 \;\left( 3 \; L - 2 \; x \right) \right] }\) |
| \(\large{ R_D \;\;=\;\; P - R_A }\) |
| \(\large{ H_A = H_D \;\;=\;\; \frac{3\;P\;x^2}{2\;h\;L^2} \; \left( \frac{L\;-\;x}{ \beta\;e \;+\; 1} \right) }\) |
| \(\large{ M_A \;\;=\;\; \frac{P\;x^2}{2\;L^2} \; \left( \frac{L\;-\;x}{ \beta\;e \;+\; 1} \right) }\) |
| \(\large{ M_B \;\;=\;\; \frac{P\;x^2}{L^2} \; \left( \frac{L\;-\;x}{ \beta\;e \;+\; 1} \right) }\) |
| \(\large{ M_C \;\;=\;\; R_B\;x - M_B }\) |
| \(\large{ M_D \;\;=\;\; \frac{P\;x \;\left( L \;-\; x \right) }{ 2\;L^2 } \; \left( \frac{ \beta\;e\;\left( 2\;L \;-\; x \right) \;+\;2\;\left( L \;-\; x \right) }{\beta \;e\;+\;1} \right) }\) |
Where:
| Units | English | Metric |
| \(\large{ h }\) = 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 | \(\large{lbf-in}\) | \(\large{N-mm}\) |
| \(\large{ A, B, C, D, E }\) = point of intrest on frame | - | - |
| \(\large{ L }\) = span length under consideration | \(\large{in}\) | \(\large{mm}\) |
| \(\large{ P }\) = total concentrated load | \(\large{lbf}\) | \(\large{N}\) |
| \(\large{ R }\) = vertical reaction load at bearing point | \(\large{lbf}\) | \(\large{N}\) |
diagrams
- Bending moment diagram (BMD) - Used to determine the bending moment at a given point of a structural element. The diagram can help determine the type, size, and material of a member in a structure so that a given set of loads can be supported without structural failure.
- Free body diagram (FBD) - Used to visualize the applied forces, moments, and resulting reactions on a structure in a given condition.
- Shear force diagram (SFD) - Used to determine the shear force at a given point of a structural element. The diagram can help determine the type, size, and material of a member in a structure so that a given set of loads can be supported without structural failure.
- Uniformly distributed load (UDL) - A load that is distributed evenly across the entire length of the support area.
Tags: Frame Support