Three Member Frame - Pin/Pin Side Point Load
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Three Member Frame - Pin/Pin Side Point Load formulas
| \(\large{ e = \frac{h}{L} }\) | |
| \(\large{ \beta = \frac{I_h}{I_v} }\) | |
| \(\large{ R_A = R_E = \frac{ P \; \left(h\;-\;y\right) }{L} }\) | |
| \(\large{ H_A = \frac{P}{2\;h} \; \left( h+y-\; \left( h-y\right) \; \frac{y\; \beta \; \left( 2\;h\;-\;y\right) }{h\;\left(2\;h\; \beta\;+\; 3\;L\right) } \right) }\) | |
| \(\large{ H_E = \frac{P\; \left( h\;-\;y \right) }{2\;h} \; \left( 1+\; \frac{ y\; \beta \; \left( 2\;h\;-\;y\right) }{h\;\left( 2\;h\; \beta\;+\; 3\;L\right) } \right) }\) | |
| \(\large{ M_B = \frac{P\;\left( h\;-\;y \right) }{2\;h} \; \left( h+y- \; \left( h-y \right) \; \frac{x\; \beta \; \left( 2\;h\;-\;y \right) }{h\; \left( 2\;h\; \beta\;+\; 3\;L \right) } \right) }\) | |
| \(\large{ M_C = \frac{P\; \left( h\;-\;y \right) }{2} \; \left( 1-\; \frac{ y\; \beta \; \left( 2\;h\;-\;y\right) }{h\;\left( 2\;h\; \beta\;+\; 3\;L\right) } \right) }\) | |
| \(\large{ M_D = \frac{P\; \left( h\;-\;y \right) }{2} \; \left( 1+\; \frac{ y\; \beta \; \left( 2\;h\;-\;y\right) }{h\;\left( 2\;h\; \beta\;+\; 3\;L\right) } \right) }\) |
Where:
| Units | English | Metric |
| \(\large{ h }\) = height of frame | \(\large{in}\) | \(\large{mm}\) |
| \(\large{ H }\) = 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 | \(\large{lbf}\) | \(\large{N}\) |
| \(\large{ y }\) = vertical distance from reaction point | \(\large{in}\) | \(\large{mm}\) |
| \(\large{ R }\) = 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