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Two Member Frame - Pin/Pin Top Point Load Formula
Needed Values |
| \(\large{ e = \frac{h}{L} }\) |
| \(\large{ \beta = \frac{I_h}{I_v} }\) |
Support Reaction |
| \(\large{ R_A = \frac{ P\;x \; \left( L^2 \; \left(2\; \beta\;e \;+\; 3 \right) \;-\; x^2 \right) }{ 2\;L^2 \left( \beta\;e \;+\; 1 \right) } }\) |
| \(\large{ R_D = P - R_A }\) |
| \(\large{ H_A = H_D = \frac{ P\;x \; \left( L^2 \;-\; x^2 \right) }{ 2\;h\;L^2 \; \left( \beta\;e \;+\; 1 \right) } }\) |
Bending Moment |
| \(\large{ M_B = \frac{ P\;x \; \left( L^2 \;-\; x^2 \right) }{ 2\;L^2 \; \left( \beta\;e \;+\; 1 \right) } }\) |
| \(\large{ M_D = \frac{ x \; \left( P \; \left( L \;-\; x \right) \;-\; M_C \right) }{ L } }\) |
Where:
| Units | English | 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 | \(\large{lbf-in}\) | \(\large{N-mm}\) |
| \(\large{ A, B, C, D }\) = point of intrest on frame | - | - |
| \(\large{ R }\) = vertical reaction load at bearing point | \(\large{lbf}\) | \(\large{N}\) |
| \(\large{ L }\) = span length of the bending member | \(\large{in}\) | \(\large{mm}\) |
| \(\large{ P }\) = total concentrated load | \(\large{lbf}\) | \(\large{N}\) |
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.
