- See Article - Frame Design Formulas
Diagram Symbols
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.
two Member Frame - Fixed/Free Free End Horizontal Point Load formulas |
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\( R_A \;=\; 0 \) \( H_A \;=\; P \) \( M_{max} \left(at \;point\; A\right) \;=\; P \cdot h \) \( \Delta_{Cx} \;=\; \dfrac{ P \cdot h^3 }{ 3 \cdot \lambda \cdot I } \) \( \Delta_{Cy} \;=\; \dfrac{ P \cdot h^2 \cdot L }{ 2 \cdot \lambda \cdot I } \) |
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| Symbol | English | Metric |
| \( R \) = vertical reaction load at bearing point | \(lbf\) | \(N\) |
| \( H \) = horizontal reaction load at bearing point | \(lbf\) | \(N\) |
| \( M \) = maximum bending moment | \(lbf-in\) | \(N-mm\) |
| \( h \) = height of frame | \(in\) | \(mm\) |
| \( L \) = span length under consideration | \(in\) | \(mm\) |
| \( I_h \) = horizontal member second moment of area (moment of inertia) | \(in^4\) | \(mm^4\) |
| \( I_v \) = vertical member second moment of area (moment of inertia) | \(in^4\) | \(mm^4\) |
| \( P \) = total concentrated load | \(lbf\) | \(N\) |
| \( x \) = horizontal distance from reaction point | \(in\) | \(mm\) |
| \( A, B, C, D, E \) = point of intrest on frame | \(dimensionless\) | \(dimensionless\) |
Where:
| Units | English | Metric |
| \(\large{ \Delta }\) = deflection or deformation | \(\large{in}\) | \(\large{mm}\) |
| \(\large{ h }\) = 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 | \(\large{lbf-in}\) | \(\large{N-mm}\) |
| \(\large{ \lambda }\) (Greek symbol lambda) = modulus of elasticity | \(\large{\frac{lbf}{in^2}}\) | \(\large{Pa}\) |
| \(\large{ A, B, C }\) = 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 | \(\large{lbf}\) | \(\large{N}\) |
