A beam is a

structural element In structural engineering, structural elements are used in structural analysis to split a complex structure into simple elements (each bearing a structural load). Within a structure, an element cannot be broken down (decomposed) into parts of dif ...

that primarily resists loads applied laterally across the beam's axis (an element designed to carry a load pushing parallel to its axis would be a strut or column). Its mode of deflection is primarily by

bending In applied mechanics, bending (also known as flexure) characterizes the behavior of a slender structural element subjected to an external Structural load, load applied perpendicularly to a longitudinal axis of the element. The structural eleme ...

, as loads produce reaction forces at the beam's support points and internal bending moments, shear, stresses, strains, and deflections. Beams are characterized by their manner of support, profile (shape of cross-section), equilibrium conditions, length, and material. Beams are traditionally descriptions of building or

civil engineering Civil engineering is a regulation and licensure in engineering, professional engineering discipline that deals with the design, construction, and maintenance of the physical and naturally built environment, including public works such as roads ...

structural elements, where the beams are horizontal and carry vertical loads. However, any structure may contain beams, such as automobile frames, aircraft components, machine frames, and other mechanical or structural systems. Any

, in any orientation, that primarily resists loads applied laterally across the element's axis is a beam.

Overview

Historically a beam is a squared timber, but may also be made of metal, stone, or a combination of wood and metal such as a flitch beam. Beams primarily carry vertical gravitational

force In physics, a force is an influence that can cause an Physical object, object to change its velocity unless counterbalanced by other forces. In mechanics, force makes ideas like 'pushing' or 'pulling' mathematically precise. Because the Magnitu ...

s, but they are also used to carry horizontal loads such as those due to

earthquake An earthquakealso called a quake, tremor, or tembloris the shaking of the Earth's surface resulting from a sudden release of energy in the lithosphere that creates seismic waves. Earthquakes can range in intensity, from those so weak they ...

or wind, or in tension to resist rafter thrust ( tie beam) or compression ( collar beam). The loads carried by a beam are transferred to

column A column or pillar in architecture and structural engineering is a structural element that transmits, through compression, the weight of the structure above to other structural elements below. In other words, a column is a compression member ...

wall A wall is a structure and a surface that defines an area; carries a load; provides security, shelter, or soundproofing; or serves a decorative purpose. There are various types of walls, including border barriers between countries, brick wal ...

s, or

girder A girder () is a Beam (structure), beam used in construction. It is the main horizontal support of a structure which supports smaller beams. Girders often have an I-beam cross section composed of two load-bearing ''flanges'' separated by a sta ...

s, then to adjacent structural compression members, and eventually to the ground. In light frame construction,

joist A joist is a horizontal structural member used in Framing (construction), framing to span an open space, often between Beam (structure), beams that subsequently transfer loads to vertical members. When incorporated into a floor framing system, joi ...

s may rest on beams.

Classification based on supports

In engineering, beams are of several types: # Simply supported – a beam supported on the ends which are free to rotate and have no moment resistance. # Fixed or encastré (encastrated) – a beam supported on both ends and restrained from rotation. # Overhanging – a simple beam extending beyond its support on one end. # Double overhanging – a simple beam with both ends extending beyond its supports on both ends. # Continuous – a beam extending over more than two supports. # Cantilever – a projecting beam fixed only at one end. # Trussed – a beam strengthened by adding a cable or rod to form a

truss A truss is an assembly of ''members'' such as Beam (structure), beams, connected by ''nodes'', that creates a rigid structure. In engineering, a truss is a structure that "consists of two-force members only, where the members are organized so ...

. # Beam on spring supports # Beam on elastic foundation

Second moment of area (area moment of inertia)

In the beam equation, the variable ''I'' represents the ''second moment of area'' or ''moment of inertia'': it is the sum, along the axis, of ''dA''·''r''², where ''r'' is the distance from the neutral axis and ''dA'' is a small patch of area. It measures not only the total area of the beam section, but the square of each patch's distance from the axis. A larger value of ''I'' indicates a stiffer beam, more resistant to bending.

Stress

Loads on a beam induce internal compressive, tensile and

shear stress Shear stress (often denoted by , Greek alphabet, Greek: tau) is the component of stress (physics), stress coplanar with a material cross section. It arises from the shear force, the component of force vector parallel to the material cross secti ...

es (assuming no torsion or axial loading). Typically, under gravity loads, the beam bends into a slightly circular arc, with its original length compressed at the top to form an arc of smaller radius, while correspondingly stretched at the bottom to enclose an arc of larger radius in tension. This is known as ''sagging''; while a configuration with the top in tension, for example over a support, is known as ''hogging''. The axis of the beam retaining its original length, generally halfway between the top and bottom, 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 Reinforced concrete, also called ferroconcrete or ferro-concrete, is a composite material in which concrete's relatively low tensile strength and ductility are compensated for by the inclusion of reinforcement having higher tensile strength or ...

beams in which the concrete is entirely in compression with tensile forces taken by steel tendons. These beams are known as

prestressed concrete Prestressed concrete is a form of concrete used in construction. It is substantially prestressed (Compression (physics), compressed) during production, in a manner that strengthens it against tensile forces which will exist when in service. Post-t ...

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. Prestressed beams are commonly used on highway bridges. Parallam support beam

The primary tool for

structural analysis Structural analysis is a branch of solid mechanics which uses simplified models for solids like bars, beams and shells for engineering decision making. Its main objective is to determine the effect of loads on physical structures and their c ...

of beams is the Euler–Bernoulli beam equation. This equation accurately describes the elastic behaviour of slender beams where the cross sectional dimensions are small compared to the length of the beam. For beams that are not slender a different theory needs to be adopted to account for the deformation due to shear forces and, in dynamic cases, the rotary inertia. The beam formulation adopted here is that of Timoshenko and comparative examples can be found in NAFEMS Benchmark Challenge Number 7. Other mathematical methods for determining the deflection of beams include "method of

virtual work In mechanics, virtual work arises in the application of the '' principle of least action'' to the study of forces and movement of a mechanical system. The work of a force acting on a particle as it moves along a displacement is different fo ...

" and the "slope deflection method". Engineers are interested in determining deflections because the beam may be in direct contact with a

brittle A material is brittle if, when subjected to stress, it fractures with little elastic deformation and without significant plastic deformation. Brittle materials absorb relatively little energy prior to fracture, even those of high strength. ...

material such as

glass Glass is an amorphous (non-crystalline solid, non-crystalline) solid. Because it is often transparency and translucency, transparent and chemically inert, glass has found widespread practical, technological, and decorative use in window pane ...

. 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/or one of higher second moment of area) creates 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 In structural engineering, the flexibility method, also called the method of consistent deformations, is the traditional method for computing member forces and displacements in structural systems. Its modern version formulated in terms of the mem ...

and the direct stiffness method.

General shapes

Most beams in

buildings have rectangular cross sections, but a more efficient cross section for a beam is an - or H-shaped section which is typically seen in steel construction. 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. Ahmaskoski_road_bridge

An -beam is only the most efficient shape in one direction of bending: up and down looking at the profile as an ''. 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); the most efficient shape for bending in any direction, however, is a cylindrical shell or tube. For unidirectional bending, the -beam or wide flange beam is superior. 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-beam (angles), C (channels), T-beam and double-T or tubes, are also used in construction when there are special requirements.

Walers and struts

This system provides horizontal bracing for small trenches, ensuring the secure installation of utilities. It's specifically designed to work in conjunction with steel trench sheets.

Thin walled

A thin walled beam is a very useful type of beam (structure). The cross section of ''thin walled beams'' is made up from thin panels connected among themselves to create closed or open cross sections of a beam (structure). Typical closed sections include round, square, and rectangular tubes. Open sections include I-beams, T-beams, L-beams, and so on. Thin walled beams exist because their bending stiffness per unit cross sectional area is much higher than that for solid cross sections such a rod or bar. In this way, stiff beams can be achieved with minimum weight. Thin walled beams are particularly useful when the material is a composite laminate. Pioneer work on composite laminate thin walled beams was done by Librescu. The torsional stiffness of a beam is greatly influenced by its cross sectional shape. For open sections, such as I sections, warping deflections occur which, if restrained, greatly increase the torsional stiffness.

References

External links

American Wood Council
Wood Construction Data
Introduction to Structural Design
, U. Virginia Dept. Architecture *

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