Beam calculation measures the stress and deflection of a structural beam under load. Factors include beam characteristics, loading, and supports. Material choice, cross-sectional shape, and force per unit length are also considered. Boundary conditions depend on beam support type. The Euler-Bernoulli beam equation describes the relationship between deflection and static load. Load tables and beam calculators are used for practical applications. Structural engineering ensures safety and aesthetic quality in construction, while radius calculations are used in aeronautics and mechanical engineering.
Beam calculation is the measurement of the stress and deflection of a structural beam when a given load is applied to it. Many factors contribute to a beam’s ability to resist bending, such as beam characteristics, loading and supports. Calculating the load displacement of a single beam using the Euler-Bernoulli beam equation is straightforward, but beam software is used in most practical applications. Radius calculations are used to ensure safety and avoid overbuilding in a variety of disciplines such as construction and aeronautics.
It is necessary to calculate the load capacity of the beam in order to build structures with the lightest and cheapest materials, while meeting safety requirements and maintaining the aesthetic quality of the structure. The entire discipline of structural engineering is devoted to this analysis and design, ensuring that roofs do not collapse under the weight of snow, that underground parking garages are safe when traffic is elevated, and that high-rise buildings built along fault lines meet seismic safety requirements. Radius calculation also finds its applications in mechanical engineering, when testing the load resistance of individual parts of a machine, such as the load an airplane wing can withstand before developing potentially dangerous stresses. Finally, architects must consider beam deformation when constructing and renovating post-and-beam homes and when considering the visual impact of sagging floors, roofs, and balconies.
One of the most important factors in calculating the bearing capacity of a beam is the choice of materials. Typically, beams are made from wood, steel, reinforced concrete, or aluminum. Each material has a different tendency to deform elastically, called the modulus of elasticity, which refers to the material’s ability to spring back into place. At its yield point, the material will deform plastically, retaining the deformation after the applied force is removed.
The cross-sectional shape of the beam is the second characteristic that is considered in the calculation of the beam. Beams can be rectangular, round, or hollow, as well as have many types of flanking, such as I-beams, Z-beams, or T-beams. Each shape has a different moment of inertia, otherwise known as the second moment of area, which predicts the stiffness of a beam.
Force per unit length is another parameter used in beam calculation and depends on the type of load. Fixed loads are simply the weight of the structure, and imposed or live loads are forces that the structure will be exposed to on an intermittent basis, such as snow, traffic or wind. Most loads are static, but special attention should be paid to dynamic loads, earthquakes, waves and hurricanes, which repeatedly apply force over an extended duration. A load might be distributed, usually evenly or asymmetrically, such as a snowfall or a mound of earth. It could also be concentrated in one spot, centrally, or at various intervals.
The boundary conditions for the beam calculation depend on the type of beam support. A beam might simply be supported at both ends, like a floor joist between two load-bearing walls. It could be cantilevered or supported on one end, such as a balcony or airplane wing. The boundary conditions apply to all points along the length of the beam.
The relationship between the deflection of a beam and a static load is described by the Euler-Bernoulli beam equation. Another equation, the Euler-Lagrange beam equation, describes this relationship for a dynamic load, but due to the complexity of its application, static approximations are generally used. It is possible to derive the deflection, bending moments and shear force of a beam given an applied load. In a practical context, load tables are used to summarize this information and list common materials that meet safety requirements for a known load. For more complex applications, beam calculators are readily available on company websites and as add-ons to computer aided design (CAD) software.
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