Beam Design Formulas
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Simple Supported Beam
Beam Fixed at One End
Beam Fixed at Both Ends
Cantilever Beam
Overhanging Beam
Two Span Continuous Beam
Three Span Continuous Beam
Four Span Continuous Beam
Nomenclature, Symbols, and Units for Beam Supports
Symbol | Greek Symbol | Definition | English | Metric | SI | Value |
\(\Delta\) | Delta | deflection or deformation | \(in\) | \(mm\) | \(mm\) | - |
\(a, b\) | - | distance to point load | \(in\) | \(mm\) | \(mm\) | - |
\(w\) | - | highest load per unit length | \(\large{\frac{lbf}{in}}\) | \(\large{\frac{N}{m}}\) | \(N-m^{-1}\) | |
\(x\) | - | horizontal distance from reaction to point on beam | \(in\) | \(mm\) | \(mm\) | - |
\(w\) | - | load per unit length | \(\large{\frac{lbf}{in}}\) | \(\large{\frac{N}{m}}\) | \(N-m^{-1}\) | - |
\(M\) | - | maximum bending moment | \(lbf-in\) | \(N-mm\) | \(N-mm\) | - |
\(V\) | - | maximum shear force | \(lbf\) | \(N\) | \(kg-m-s^{-2}\) | |
\(\lambda\) | lambda | modulus of elasticity | \(\large{\frac{lbf}{in^2}}\) | \(MPA\) | \(N-mm^{-2}\) | - |
\(R\) | - | reaction load at bearing point | \(lbf\) | \(N\) | \(kg-m-s^{-2}\) | - |
\(I\) | - | second moment of area (moment of inertia) | \(in^4\) | \(mm^4\) | \(mm^4\) | - |
\(L\) | - | span length of the bending member | \(in\) | \(mm\) | \(mm\) | - |
\(P\) | - | total concentrated load | \(lbf\) | \(N\) | \(kg-m-s^{-2}\) | - |
\(W\) | - | total load \(\left( \frac{w\;L}{2} \right)\) | \(lbf\) | \(N\) | \(kg-m-s^{-2}\) | - |
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: Pipe Sizing Equations Beam Support Equations Pipe Support Equations Surveying Equations