# Beam Design Formulas

Structural beam design refers to the process of determining the appropriate size and shape of beams that will be used in construction to support and distribute loads within a building or structure. Beams are horizontal or inclined structural members that carry vertical loads. The design of structural beams involves several important considerations to ensure the safety, stability, and efficiency of a structure.

- See Article Links - Beam Design Formulas, Frame Design Formulas, Plate Design Formulas, Geometric Properties of Structural Shapes, Welding Stress and Strain Connections, and Welding Symbols
- Tags: Beam Support Pipe Support

### Beam Design Formulas Index

- Key Points about Design of Structural Beams
- Diagram Symbols
- 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

### Key Points about Design of Structural Beams

**Load Calculation**- The first step is to calculate the various loads that the beams will need to support, including dead loads (permanent loads) and live loads (temporary loads). Additionally, factors such as wind, snow, earthquakes, and other environmental loads must also be considered.**Material Selection**- Beams can be constructed from various materials, such as steel, concrete, timber, or composite materials. The choice of material depends on factors like the type of structure, load requirements, cost considerations, and desired aesthetics.**Bending and Shear Stress Analysis**- Beams primarily experience bending stresses due to the applied loads, which cause the beam to bend or deflect. Shear stresses also play a role, especially near supports. Engineers analyze these stresses to ensure that the beam can safely withstand the loads without failure.**Beam Sizing**- Based on the load calculations and stress analysis, engineers determine the appropriate size and shape (cross-sectional dimensions) of the beam. This includes selecting the appropriate width, depth, and other dimensions to distribute the loads effectively and avoid excessive deflection or failure.**Code Compliance**- Designing beams involves adhering to building codes and standards set by relevant authorities. These codes dictate the minimum safety requirements and design practices that must be followed to ensure structural integrity.**Connection Design**- Beams are often connected to other structural members, such as columns, beams, and foundations. The design of these connections is crucial to ensure load transfer and overall stability of the structure.**Deflection Control**- Excessive deflection can lead to discomfort for occupants and potential damage to finishes. Engineers design beams to limit deflection within acceptable limits.**Economic Considerations**- Beam design also takes into account economic factors. This includes optimizing beam sizes and material choices to achieve a balance between structural performance and cost effectiveness.**Construction Considerations**- The practicality of constructing the designed beams is an important aspect. Engineers need to ensure that the beams can be fabricated, transported, and installed effectively.**Safety Factors**- Engineers apply safety factors to the calculated loads and stresses to provide an additional margin of safety, accounting for uncertainties in material properties, construction practices, and loading conditions.

### 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.

### Simple Supported Beam

### Beam Fixed at One End

### Beam Fixed at Both Ends

### Cantilever Beam

### Overhanging Beam

### Two 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 | \(lbf\;/\;in\) | \(N\;/\;m\) | \(N-m^{-1}\) | |

\(x\) | - | horizontal distance from reaction to point on beam | \(in\) | \(mm\) | \(mm\) | - |

\(w\) | - | load per unit length | \(lbf\;/\;in\) | \(N\;/\;m\) | \(N-m^{-1}\) | - |

\(M\) | - | maximum bending moment | \(lbf-in\) | \(N-mm\) | \(N-mm\) | - |

\(V\) | - | maximum shear force | \(lbf\) | \(N\) | \(kg-m-s^{-2}\) | |

\(\lambda\) | lambda | modulus of elasticity | \(lbf\;/\;in^2\) | \(MPA\) | \(N-mm^{-2}\) | - |

\(R\) | - | 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 \(\left( \frac{w\;L}{2} \right)\) | \(lbf\) | \(N\) | \(kg-m-s^{-2}\) | - |

Tags: Beam Support Pipe Support