Beam (structure)
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A beam is a structural element that carries load primarily in bending (flexure). Beams generally carry vertical gravitational forces but can also be used to carry horizontal loads (i.e. loads due to a gust of wind or an earthquake). The loads carried by a beam are transferred to columns, walls or girders, which in turn transfer the force to adjacent structural members.
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. Other common beam profiles are the C-channel, the hollow structural section beam, the pipe, and the angle.
Internally, beams experience compressive, tensile and shear stresses as a result of the loads applied to them. Under gravity loads, the top of the beam is under compression while the bottom of the beam is under tension, leaving the middle of the beam relatively stress-free in the middle of the span, with shear stress above the supports. However, there are some reinforced concrete beams that are entirely in compression. These beams are known as prestressed concrete beams. High strength steel tendons are stretched while the beam is cast over them. Then, when the concrete has begun to cure, the tendons are 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 minimised for aesthetic reasons. A visibly sagging beam, though 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 matrix stiffness method.
[edit] General Shapes
Mostly the beams have rectangular cross sections in reinforced concrete buildings, but the most efficient cross-section is an I-shaped beam. The fact that most of the material is placed away from the neutral axis (axis of symmetry in case of I beams) increases the second moment of area of the beam 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 and 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 beam rules.
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.
[edit] References
- Introduction to mechanics of solids, Egor P. Popov, Prentice-Hall, 1968
