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4: Bending

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    This modules in this section will develop relations between stresses, deflections, and applied loads for beams and flat plates subjected to bending loads. This will be done using the direct method employed in Module 7 for circular shafts in torsion. However, bending problems have a higher order of dimensionality than twisted shafts, and it will be convenient to use the more general formulations developed in Modules 8 - 11. In particular, pseudovector-matrix notation will allow easy extension of beam concepts to flat plates.

    • 4.1: Shear and Bending Moment Diagrams
    • 4.2: Stresses in Beams
    • 4.3: Beam Displacements
      We want to be able to predict the deflection of beams in bending, because many applications have limitations on the amount of deflection that can be tolerated. Another common need for deflection analysis arises from materials testing, in which the transverse deflection induced by a bending load is measured. If we know the relation expected between the load and the deflection, we can "back out" the material properties (specifically the modulus) from the measurement.
    • 4.4: Laminated Composite Plates

    Thumbnail: Element of a bent beam: the fibers form concentric arcs, the top fibers are compressed and bottom fibers stretched. (Cc BY-SA 3.0; Cdang via Wikipedia)

    This page titled 4: Bending is shared under a CC BY-NC-SA 4.0 license and was authored, remixed, and/or curated by David Roylance (MIT OpenCourseWare) via source content that was edited to the style and standards of the LibreTexts platform; a detailed edit history is available upon request.