Beam deflection is the behavior of solid and homogeneous structural elements that resist bending. The Euler-Bernoulli equation relates deflection to applied forces, cross-sectional characteristics, and material properties. I-beams are designed with material concentrated towards the lower and upper regions of the cross section for high bending strength.
In civil engineering, beam deflection refers to the behavior of certain structural elements in a physical design. An element can be considered a beam if it is solid and homogeneous and its length is many times its height or width. The primary function of the beam is to resist bending; this contrasts with structural elements which primarily resist tensile, compressive or shear stresses. The structural properties of a beam in bending are determined by its dimensions, materials, and cross-sectional shape.
A simple example of beam bending is a bridge with a car on it. Bridges often have concrete roads over them, but the concrete is generally only strong in compression. A long bridge, however, will tend to give way in the middle where there is no ground to support it. This settlement will be in the form of a circular arc and occurs due to the way internal stresses are distributed in bending of the beam. To resist this bending, a stronger metal beam is usually placed under a road surface.
The most important equation in beam bending is the Euler-Bernoulli beam equation. This equation relates the deflection of the beam to the applied forces, cross-sectional characteristics, and material properties of the beam. The amount of deflection in beam bending can be reduced by reducing the net applied forces, reshaping the beam cross section, and using a stronger material.
In a horizontal beam to which downward forces are applied, the top of the beam will actually go into compression while the bottom will go into tension. In fact, the lower the material is, the more tension it will experience. It turns out that, for a given amount of total material, reinforcing the lower and upper cross-sectional regions is the best way to strengthen the beam. Therefore, engineers design beams with material concentrated towards the lower and upper regions of the cross section.
This is the principle behind the design of I-beams, or beams with cross sections resembling the letter “I”. It is expensive to produce and transport beams with a lot of mass, so it is important to minimize the amount of material used. In the cross section of an I-beam, there is only enough material at intermediate heights to hold the beam together as one solid piece. The rest of the material is concentrated at the bottom and top of the cross section, giving the beam high bending strength. The bending resistance of a beam is called its stiffness.
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