Beam (structure)

A beam is a structural element that is capable of withstanding load primarily by resisting against bending. The bending force induced into the material of the beam as a result of the external loads, own weight, span and external reactions to these loads is called a bending moment. Beams are characterized by their profile (shape of cross-section), their length, and their material.

Beams are traditionally descriptions of building or civil engineering structural elements, but smaller structures such as truck or automobile frames, machine frames, and other mechanical or structural systems contain beam structures that are designed and analyzed in a similar fashion.

Overview

Historically beams were squared timbers but are also metal, stone, or combinations of wood and metal such as a flitch beam. Beams generally carry vertical gravitational forces but can also be used to carry horizontal loads (e.g., loads due to an earthquake or wind or in tension to resist rafter thrust as a tie beam or (usually) compression as a collar beam). The loads carried by a beam are transferred to columns, walls, or girders, which then transfer the force to adjacent structural compression members. In light frame construction joists may rest on beams.

Beam

Beam may refer to:

BEAM

Beam (nautical)

The beam of a ship is its width at the widest point as measured at the ship's nominal waterline. The beam is a bearing projected at right-angles from the fore and aft line, outwards from the widest part of ship. Beam may also be used to define the maximum width of a ship's hull, or maximum width plus superstructure overhangs.

Generally speaking, the wider the beam of a ship (or boat), the more initial stability it has, at expense of reserve stability in the event of a capsize, where more energy is required to right the vessel from its inverted position.

Typical values

Typical length-to-beam ratios for small sailboats are from 2:1 (dinghies to trailerable sailboats around 20 ft or 6 m) to 5:1 (racing sailboats over 30 ft or 10 m).

Large ships have widely varying beam ratios, some as large as 20:1.

Rowing shells designed for flatwater racing may have length to beam ratios as high as 30:1, while a coracle has a ratio of almost 1:1 – it is nearly circular.

Formula

The beam of many monohull vessels can be calculated using the following formula:

Balance beam

The balance beam is an artistic gymnastics apparatus, as well as the event performed using the apparatus. Both the apparatus and the event are sometimes simply referred to as "beam". The English abbreviation for the event in gymnastics scoring is BB. The beam is a small, thin beam which is typically raised from the floor on a leg or stand at both ends. The balance beam is only performed by female gymnasts. Beams are usually made of leather like material.

Balance beams used in international gymnastics competitions must conform to the guidelines and specifications set forth by the International Gymnastics Federation Apparatus Norms brochure. Several companies manufacture and sell beams, including AAI (USA), Jannsen and Fritsen (Europe) and Acromat (Australia). Most gymnastics schools purchase and use balance beams that meet the FIG's standards, but some may also use beams with carpeted surfaces for practice situations. While learning new skills, gymnasts often work on low beams that have the same dimensions and surface of regulation apparatus, but are set a very short distance from the ground. They may also work on practice beams, mini beams, road beams, or even lines on a mat.

Structure

Structure is an arrangement and organization of interrelated elements in a material object or system, or the object or system so organized. Material structures include man-made objects such as buildings and machines and natural objects such as biological organisms, minerals and chemicals. Abstract structures include data structures in computer science and musical form. Types of structure include a hierarchy (a cascade of one-to-many relationships), a network featuring many-to-many links, or a lattice featuring connections between components that are neighbors in space.

Load-bearing

Buildings, aircraft, skeletons, anthills, beaver dams and salt domes are all examples of load-bearing structures. The results of construction are divided into buildings and non-building structures, and make up the infrastructure of a human society. Built structures are broadly divided by their varying design approaches and standards, into categories including building structures, architectural structures, civil engineering structures and mechanical structures.

Structure (mathematical logic)

In universal algebra and in model theory, a structure consists of a set along with a collection of finitary operations, and relations that are defined on it.

Universal algebra studies structures that generalize the algebraic structures such as groups, rings, fields and vector spaces. The term universal algebra is used for structures with no relation symbols.

Model theory has a different scope that encompasses more arbitrary theories, including foundational structures such as models of set theory. From the model-theoretic point of view, structures are the objects used to define the semantics of first-order logic. For a given theory in model theory, a structure is called a model, if it satisfies the defining axioms of that theory, although it is sometimes disambiguated as a semantic model when one discusses the notion in the more general setting of mathematical models. Logicians sometimes refer to structures as interpretations.

In database theory, structures with no functions are studied as models for relational databases, in the form of relational models.

Structure (category theory)

In mathematics, progress often consists of recognising the same structure in different contexts - so that one method exploiting it has multiple applications. In fact this is a normal way of proceeding; in the absence of recognisable structure (which might be hidden) problems tend to fall into the combinatorics classification of matters requiring special arguments.

In category theory structure is discussed implicitly - as opposed to the explicit discussion typical with the many algebraic structures. Starting with a given class of algebraic structure, such as groups, one can build the category in which the objects are groups and the morphisms are group homomorphisms: that is, of structures on one type, and mappings respecting that structure. Starting with a category C given abstractly, the challenge is to infer what structure it is on the objects that the morphisms 'preserve'.

The term structure was much used in connection with the Bourbaki group's approach. There is even a definition. Structure must definitely include topological space as well as the standard abstract algebra notions. Structure in this sense is probably commensurate with the idea of concrete category that can be presented in a definite way - the topological case means that infinitary operations will be needed. Presentation of a category (analogously to presentation of a group) can in fact be approached in a number of ways, the category structure not being (quite) an algebraic structure in its own right.