Bending: Difference between revisions
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[[Image: Beam in Bending.png|frame|right|'''Figure 1.''' A side view of a simply supported beam (top) bending under a distributed lateral load (bottom).]][[Image: Internal Forces and Stresses from Bending.png|frame|right|'''Figure 2.''' The internal forces and the cross-sectional stress distribution of a beam in bending.]]In [[engineering mechanics]], '''bending''' (also known as '''flexure''') characterizes the behavior of a structural member subjected to a lateral [[load]]; a structural element subjected to bending is known as a [[beam]]. A [[closet]] rod sagging under the weight of clothes on [[coat hanger]]s is an example of a beam experiencing bending. |
[[Image: Beam in Bending.png|frame|right|'''Figure 1.''' A side view of a simply supported beam (top) bending under a distributed lateral load (bottom).]][[Image: Internal Forces and Stresses from Bending.png|frame|right|'''Figure 2.''' The internal forces and the cross-sectional stress distribution of a beam in bending.]]In [[engineering mechanics]], '''bending''' (also known as '''flexure''') characterizes the behavior of a structural member subjected to a lateral [[load]]; a structural element subjected to bending is known as a [[beam]]. A [[closet]] rod sagging under the weight of clothes on [[coat hanger]]s is an example of a beam experiencing bending. |
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Bending produces reactive [[force]]s inside a beam as the beam attempts to accommodate the flexural load: in the case of the beam in Figure 1, the material at the top of the beam is being compressed while the material at the bottom is being stretched. There are three notable internal forces caused by lateral loads (shown in Figure 2): [[shear]] parallel to |
Bending produces reactive [[force]]s inside a beam as the beam attempts to accommodate the flexural load: in the case of the beam in Figure 1, the material at the top of the beam is being compressed while the material at the bottom is being stretched. There are three notable internal forces caused by lateral loads (shown in Figure 2): [[shear]] parallel to the lateral loading, [[compression]] along the top of the beam, and [[tension]] along the bottom of the beam. These last two forces form a [[couple]] or [[moment]] as they are equal in magnitude and opposite in direction. This '''bending moment''' produces the sagging deformation characteristic of members experiencing bending. |
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The compressive and tensile forces shown in Figure 2 induce [[stress]]es on the beam. The maximum compressive stress is found at the uppermost edge of the beam while the maximum tensile stress is located at the lower edge of the beam. Since the stresses between these two opposing maxima vary [[linear]]ly, there therefore exists a point on the linear path between them where there is no bending stress. The [[Locus_(mathematics)|locus]] of these points is the neutral axis. Because of this area with no stress and the adjacent areas with low stress, using uniform cross section beams in bending is not a particularly efficient means of supporting a load as it does not use the full capacity of the beam until it is on the brink of collapse. Wide-flange beams (I-Beams) and [[truss]] [[girder]]s effectively address this inefficiency as they minimize the amount of material in this under-stressed region. |
The compressive and tensile forces shown in Figure 2 induce [[stress]]es on the beam. The maximum compressive stress is found at the uppermost edge of the beam while the maximum tensile stress is located at the lower edge of the beam. Since the stresses between these two opposing maxima vary [[linear]]ly, there therefore exists a point on the linear path between them where there is no bending stress. The [[Locus_(mathematics)|locus]] of these points is the neutral axis. Because of this area with no stress and the adjacent areas with low stress, using uniform cross section beams in bending is not a particularly efficient means of supporting a load as it does not use the full capacity of the beam until it is on the brink of collapse. Wide-flange beams (I-Beams) and [[truss]] [[girder]]s effectively address this inefficiency as they minimize the amount of material in this under-stressed region. |
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Revision as of 10:32, 6 February 2005
In engineering mechanics, bending (also known as flexure) characterizes the behavior of a structural member subjected to a lateral load; a structural element subjected to bending is known as a beam. A closet rod sagging under the weight of clothes on coat hangers is an example of a beam experiencing bending.
Bending produces reactive forces inside a beam as the beam attempts to accommodate the flexural load: in the case of the beam in Figure 1, the material at the top of the beam is being compressed while the material at the bottom is being stretched. There are three notable internal forces caused by lateral loads (shown in Figure 2): shear parallel to the lateral loading, compression along the top of the beam, and tension along the bottom of the beam. These last two forces form a couple or moment as they are equal in magnitude and opposite in direction. This bending moment produces the sagging deformation characteristic of members experiencing bending.
The compressive and tensile forces shown in Figure 2 induce stresses on the beam. The maximum compressive stress is found at the uppermost edge of the beam while the maximum tensile stress is located at the lower edge of the beam. Since the stresses between these two opposing maxima vary linearly, there therefore exists a point on the linear path between them where there is no bending stress. The locus of these points is the neutral axis. Because of this area with no stress and the adjacent areas with low stress, using uniform cross section beams in bending is not a particularly efficient means of supporting a load as it does not use the full capacity of the beam until it is on the brink of collapse. Wide-flange beams (I-Beams) and truss girders effectively address this inefficiency as they minimize the amount of material in this under-stressed region.