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A statically determinate beam, bending (sagging) under an evenly distributed load.

A beam is a horizontal structural element that is capable of withstanding load primarily by resisting 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 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[link]

Beams generally carry vertical gravitational forces but can also be used to carry horizontal loads (i.e., loads due to an earthquake or wind). 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 the joists rest on the beam.

Types of beams[link]

Beams are characterized by their profile (the shape of their cross-section), their length, and their material. In contemporary construction, beams are typically made of steel, reinforced concrete, or wood. One of the most common types of steel beam is the I-beam or wide-flange beam (also known as a "universal beam" or, for stouter sections, a "universal column"). This is commonly used in steel-frame buildings and bridges.^[1] Other common beam profiles are the C-channel, the hollow structural section beam, the pipe, and the angle.

Beams are also described by how they are supported. Supports restrict lateral and/or rotational movements so as to satisfy stability conditions as well as to limit the deformations to a certain allowance. A simple beam is supported by a pin support at one end and a roller support at the other end. A beam with a laterally and rotationally fixed support at one end with no support at the other end is called a cantilever beam. A beam simply supported at two points and having one end or both ends extended beyond the supports is called an overhanging beam.

Structural characteristics[link]

Moment of inertia[link]

The moment of inertia of an object about a given axis describes how difficult it is to change its angular motion about that axis. Therefore, it encompasses not just how much mass the object has overall, but how far each bit of mass is from the axis. The farther out the object's mass is, the more rotational inertia the object has, and the more force is required to change its rotation rate.

Diagram of stiffness of a simple square beam (A) and universal beam (B). The universal beam flange sections are three times further apart than the solid beam's upper and lower halves. The second moment of inertia of the universal beam is nine times that of the square beam of equal cross section (universal beam web ignored for simplification)

Stress in beams[link]

Internally, beams experience compressive, tensile and shear stresses as a result of the loads applied to them. Typically, under gravity loads, the original length of the beam is slightly reduced to enclose a smaller radius arc at the top of the beam, resulting in compression, while the same original beam length at the bottom of the beam is slightly stretched to enclose a larger radius arc, and so is under tension. The same original length of the middle of the beam, generally halfway between the top and bottom, is the same as the radial arc of bending, and so it is under neither compression nor tension, and defines the neutral axis (dotted line in the beam figure). Above the supports, the beam is exposed to shear stress. There are some reinforced concrete beams in which the concrete is entirely in compression with tensile forces taken by steel tendons. These beams are known as prestressed concrete beams, and are fabricated to produce a compression more than the expected tension under loading conditions. High strength steel tendons are stretched while the beam is cast over them. Then, when the concrete has cured, the tendons are slowly released and the beam is immediately under eccentric axial loads. This eccentric loading creates an internal moment, and, in turn, increases the moment carrying capacity of the beam. They are commonly used on highway bridges.

The primary tool for structural analysis of beams is the Euler–Bernoulli beam equation. Other mathematical methods for determining the deflection of beams include "method of virtual work" and the "slope deflection method". Engineers are interested in determining deflections because the beam may be in direct contact with a brittle material such as glass. Beam deflections are also minimized for aesthetic reasons. A visibly sagging beam, even if structurally safe, is unsightly and to be avoided. A stiffer beam (high modulus of elasticity and high second moment of area) produces less deflection.

Mathematical methods for determining the beam forces (internal forces of the beam and the forces that are imposed on the beam support) include the "moment distribution method", the force or flexibility method and the direct stiffness method.

General shapes[link]

Most beams in reinforced concrete buildings have rectangular cross sections, but the most efficient^{[citation needed]} cross section for a simply supported beam is an I or H section. Because of the parallel axis theorem and the fact that most of the material is away from the neutral axis, the second moment of area of the beam increases, which in turn increases the stiffness.

An I-beam is only the most efficient shape in one direction of bending: up and down looking at the profile as an I. If the beam is bent side to side, it functions as an H where it is less efficient. The most efficient shape for both directions in 2D is a box (a square shell) however the most efficient shape for bending in any direction is a cylindrical shell or tube. But, for unidirectional bending, the I or wide flange beam is superior.^{[citation needed]}

Efficiency means that for the same cross sectional area (volume of beam per length) subjected to the same loading conditions, the beam deflects less.

Other shapes, like L (angles), C (channels) or tubes, are also used in construction when there are special requirements.

References[link]

See also[link]

• Beam engine
• Building code
• Cantilever
• Classical mechanics
• Deflection (engineering)
• Elasticity (physics) and Plasticity (physics)
• Euler–Bernoulli beam equation
• Flexural modulus
• Finite element method in structural mechanics
• Free body diagram
• Influence line
• Materials science and Strength of materials
• Moment (physics)
• Poisson's ratio
• Post and lintel
• Shear strength
• Statics and Statically indeterminate
• Stress (physics) and Strain (materials science)
• Tensile strength, tensile stress and Hooke's law
• Thin-shell structure
• Truss
• Yield (engineering)

Further reading[link]

• Popov, Egor P. (1968). Introduction to mechanics of solids. Prentice-Hall. ISBN 978-0-13-726159-8. 

External links[link]

Wikimedia Commons has media related to: Beams

• David Childs Ltd Consulting Civil Engineers: Tutorials
  • Steel Beam Design
  • Prestressed Concrete Beam Design Tutorial
• American Wood Council: Free Download Library Wood Construction Data
  • Wood Structural Design Data (pdf file)
  • online Span Calculator
• Introduction to Structural Design, U. Virginia Dept. Architecture
  • Glossary
  • Course Sampler Lectures, Projects, Tests
  • Beams and Bending review points (follow using next buttons)
  • Structural Behavior and Design Approaches lectures (follow using next buttons)
• U. Maryland, J.A. Clark School of Engineering: HAMLET engineering simulations and models
  • BeamAnalysis
• U. Wisconsin–Stout, Strength of Materials online lectures, problems, tests/solutions, links, software
  • Beams I - Shear Forces and Bending Moments
  • Beams II - Bending Stress
• Beam calculations in MS Excel from ExcelCalcs.com
• Beam Calculation Software for Windows from beams.com

Look up beam in Wiktionary, the free dictionary.

Beam may refer to:

• Beam (structure), a construction element
• Beam (nautical), the most extreme width (or breadth) of a nautical vessel, or a point alongside the ship at the mid-point of its length
• A narrow, propagating stream of particles or energy:
  • Bessel beam
  • Gaussian beam
  • Light beam
    • Laser beam
  • Particle beam
    • Charged particle beam
      • Cathode ray, or "electron beam"
    • Molecular beam
• Beam Inc., a NYSE-listed spirits company that produces Jim Beam, a popular brand of Bourbon whiskey, and a variety of other brands
• Beam (music), a connection line in musical notation
• Balance beam, a piece of gymnastics equipment
• BEAM robotics, an automatically moving machine based on analog electronics
• Beam search, a search algorithm
• Beam Software, a computer game developer
• BEAM.TV, a global distribution network
• Blaster Beam, a musical instrument
• BEAM, an aggressive chemotherapy regimen involving the use of BCNU (Carmustine), Etoposide, Ara-C (Cytarabine), and Melphalan
• BEAM, brain electrical activity mapping
• BEAM, the virtual machine at the core of the Erlang programming language
• Beam, operate the Transporter in the fictional Star Trek series

See also[link]

• Beam theory, a means of calculating the load-carrying and deflection characteristics of beams
• Battle of the Beams, radio countermeasures used against navigational system used by the Luftwaffe during WWII
• The Beam (disambiguation)

This disambiguation page lists articles associated with the same title. If an internal link led you here, you may wish to change the link to point directly to the intended article.

Structure is a fundamental, tangible or intangible notion referring to the recognition, observation, nature, and permanence of patterns and relationships of entities. This notion may itself be an object, such as a built structure, or an attribute, such as the structure of society. From a child's verbal description of a snowflake, to the detailed scientific analysis of the properties of magnetic fields, the concept of structure is now often an essential foundation of nearly every mode of inquiry and discovery in science, philosophy, and art.^[1] In early 20th-century and earlier thought, form^{[disambiguation needed ]} often plays a role comparable to that of structure in contemporary thought. The neo-Kantianism of Ernst Cassirer (cf. his Philosophy of Symbolic Forms, completed in 1929 and published in English translation in the 1950s) is sometimes regarded as a precursor of the later shift to structuralism and poststructuralism.^[2]

The description of structure implicitly offers an account of what a system is made of: a configuration of items, a collection of inter-related components or services. A structure may be 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.

Types of structure[link]

Physical structure[link]

In engineering and architecture, a structure is a body or assemblage of bodies in space to form a system capable of supporting loads. Physical structures include man-made and natural arrangements. Buildings, aircraft, soap films, skeletons, anthills, beaver dams and salt domes are all examples of physical structures. The effects of loads on physical structures are determined through structural analysis. Structural engineering refers to engineering of physical structures.

Built structures are a subset of physical structures resulting from construction. These are divided into buildings and nonbuilding structures, and make up the infrastructure of a human society. Built structures are composed of structural elements such as columns, beams and trusses. 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.

Biological structure[link]

In biology, structures exist at all levels of organization, ranging hierarchically from the atomic and molecular to the cellular, tissue, organ, organismic, population and ecosystem level. Usually, a higher-level structure is composed of multiple copies of a lower-level structure.

Chemical structure[link]

Chemistry is the science treating matter at the atomic to macromolecular scale, the reactions, transformations and aggregations of matter, as well as accompanying energy and entropy changes during these processes. The chemical structure refers to both molecular geometry and to electronic structure. The structural formula of a chemical compound is a graphical representation of the molecular structure showing how the atoms are arranged. A protein structure is the three dimensional coordinates of the atoms within (macro) molecules made of protein.

Musical composition[link]

Music is an art form consisting of sound and silence expressed through time. The term musical form, a type of structure, refers to two related concepts:

• the type of composition (for example, a musical work can have the form of a symphony, a concerto, or other generic type)
• the structure of a particular piece (for example, a piece can be written in binary form, sonata form, as a fugue, etc.)

Social structure[link]

A social structure is a pattern of relations. They are social organizations of individuals in various life situations. Structures are applicable to people in how a society is as a system organized by a characteristic pattern of relationships. This is known as the social organization of the group. Sociologists have studied the changing structure of these groups. Structure and agency are two confronted theories about human behaviour. The debate surrounding the influence of structure and agency on human thought is one of the central issues in sociology. In this context "agency" refers to the capacity of individual humans to act independently and to make their own free choices. "Structure" here refers to those factors such as social class, religion, gender, ethnicity, customs etc. which seem to limit or influence the opportunities that individuals have.

Data structure[link]

In computer science, a data structure is a way of storing data in a computer so that it can be used efficiently. Often a carefully chosen data structure will allow the most efficient algorithm to be used. The choice of the data structure often begins from the choice of an abstract data type. A well-designed data structure allows a variety of critical operations to be performed, using as few resources, both execution time and memory space, as possible. Data structures are implemented in a programming language as data types and the references (e.g. relationships, links and pointers) and operations that are possible with them. For structure tables and structure functions, see data structure.

See also[link]

• Crystal structure
• Data structure
• Mathematical structure
• Building
• Nonbuilding structure
• Structural analysis
• Structural engineering
• Structural geology
• Protein structure
• Biomolecular structure
  • Primary structure
  • Secondary structure
  • Tertiary structure
  • Quaternary structure

References[link]