These last two forces form a couple or moment as they are equal in magnitude and opposite in direction.
Direct compressive stress in the upper region of the beam, and direct tensile stress in the lower region of the beam. Shear stress parallel to the lateral loading plus complementary shear stress on planes perpendicular to the load direction. There are two forms of internal stresses caused by lateral loads: In a horizontal beam supported at the ends and loaded downwards in the middle, the material at the over-side of the beam is compressed while the material at the underside is stretched. In the quasi-static case, the amount of bending deflection and the stresses that develop are assumed not to change over time. 1.2 Extensions of Euler-Bernoulli beam bending theoryĪ beam deforms and stresses develop inside it when a transverse load is applied on it. Therefore, to make the usage of the term more precise, engineers refer to a specific object such as the bending of rods, the bending of beams, the bending of plates, the bending of shells and so on. In the absence of a qualifier, the term bending is ambiguous because bending can occur locally in all objects. A large diameter, but thin-walled, short tube supported at its ends and loaded laterally is an example of a shell experiencing bending. On the other hand, a shell is a structure of any geometric form where the length and the width are of the same order of magnitude but the thickness of the structure (known as the 'wall') is considerably smaller. For example, a closet rod sagging under the weight of clothes on clothes hangers is an example of a beam experiencing bending. When the length is considerably longer than the width and the thickness, the element is called a beam. The structural element is assumed to be such that at least one of its dimensions is a small fraction, typically 1/10 or less, of the other two. PMID 15212931.In applied mechanics, bending (also known as flexure) characterizes the behavior of a slender structural element subjected to an external load applied perpendicularly to a longitudinal axis of the element. "Anisotropic strain-dependent material properties of bovine articular cartilage in the transitional range from tension to compression". 
The science and engineering of materials. ^ D790-03: Standard Test Methods for Flexural Properties of Unreinforced and Reinforced Plastics and Electrical Insulating Materials, West Conshohocken, PA: ASTM International, 2003.Wardle (1979), "Test methods for fiber tensile strength, composite flexural modulus, and properties of fabric-reinforced laminates", Composite Materials: Testing and Design (Fifth Conference), ASTM International: 228–228–35, doi: 10.1520/STP36912S, ISBN 978-0-8031-4495-8 Moreover, composite materials like fiber-reinforced polymers or biological tissues are inhomogeneous combinations of two or more materials, each with different material properties, therefore their tensile, compressive, and flexural moduli usually are not equivalent. However, in anisotropic materials, for example wood, these values may not be equivalent.
For a 3-point test of a rectangular beam behaving as an isotropic linear material, where w and h are the width and height of the beam, I is the second moment of area of the beam's cross-section, L is the distance between the two outer supports, and d is the deflection due to the load F applied at the middle of the beam, the flexural modulus: E f l e x = L 3 F 4 w h 3 d ( Elastic modulus)įor very small strains in isotropic materials like glass, metal or polymer, flexural or bending modulus of elasticity is equivalent to the tensile modulus ( Young's modulus) or compressive modulus of elasticity.
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